Alliance UniversityCF 406CF MCQ for exam

Executive Post Graduate Diploma in Management Subject: Corporate Finance Sample Question paper (Reference only) Level 1: Objective Type (2 marks each) 1. If you invest Rs.25,000 today at a compound interest of 9 perc ...

Executive Post Graduate Diploma in Management Subject: Corporate Finance Sample Question paper (Reference only) Level 1: Objective Type (2 marks each) 1. If you invest Rs.25,000 today at a compound interest of 9 percent, what will be the future value after 15 years ? a) Rs. 91,620 b) Rs. 91,062 c) Rs. 91,260 d) Rs.91,200 e) None Hint (FVIF=3.6425) 2. What is the payback period on cash flow (non-discounted) of the following project? Project C0 C1 C2 C3 C4 A -5,000 1,000 1,000 3,000 5,000 a) 2 years b) 2.5 years c) 3 years d) 3.5 years e) None of the above 3. ‘X’ Ltd. Company issues Rs.50,000 8% debentures at a premium of 10%. The tax rate applicable to the company is 60%. What is the cost of debt? a) 4.21% b)2.91% c) 4% d)3.5% e) None4. What is the NPV (approximate) if cost of capital is 10 percent on cash flow of the following project? Project C0 C1 C2 C3 C4 A -10,000 3,000 3,000 3,000 3,000 a) Rs. - 493.40 b) Rs. 493.40 c) Rs. 9507.60 d) Rs.-9507.60 e) None 5. What is the risk premium of a security, if the market return is 15%, Beta 0.8 and risk-free rate of return is 9%. a) 7.2% b) 4.8% c) 6.0% d) 8.4% e) None (Hint Beta*(Rm-Rrf) 6. If you 20,000, what will be the future value after 15 years ? a) Rs.75,930 b) Rs.75,960 c) Rs.75,396 d) Rs.75,460 e) None (Hint 20000*1.0925˄15 7. What is the NPV if cost of capital is 10 percent on cash flow of the following project? Project C0 C1 C2 C3 C4 A -5,000 1,000 1,000 3,000 5,000 a) Rs.2,340 b) Rs.2,404 c) Rs.2,450 d) Rs.2,400 e) None8. Compute the cost of equity using CAPM where risk-free rate of return is 11%, Beta co-efficient of the firm is 1.25 and assuming a market return of 15 percent next year. a) 16% b) 15% c) 16.5% d) 16.3% e) None Ke=RRF+Ba(Rm-Rrf)=11+1.25(15-11)=11+5=16 9. Find out the weighted average cost of capital from the following data: Securities Book value After tax cost Equity 5,00,000 13% Retained earnings 2,00,000 8% Preference capital 2,00,000 14% Debentures 4,00,000 5% -------------- 13,00,000 ======== a) 8.0% b) 7.5% c) 8.11 (500000*.13+200000*.08+20000*0.14+40000*.05)/1300000=9.92% (check answer) d) 8.2% e) None of the above 10. From the following information; Interest Rs. 5,000 Sales Rs.50,000 Variable cost Rs.25,000 Fixed cost Rs.15,000 Find out, (a) Operating Leverage & Financial Leverage a) 3.0 & 2.0b) 2.5 & 2.0 (O.L.=cont/ebit=sales-v.c/ sales-v.c.-f.c)=25000/10000=2.5) (DOFL=ebit/ebt=10000/5000=2.0) c) d) 3.5 & 2.5 e) 3.0 & 2.5 f) none of the above 11. If you invest Rs.30,000 today at a compound interest of 9.50 percent, what will be the future value after 10 years ? a) Rs.74,934 b) Rs.74,347 c) Rs.74,734 d) Rs.74,897 d) None 12. What is the NPV if cost of capital is 12 percent on cash flow of the following project? Project C0 C1 C2 C3 C4 A -100,000 20,000 35,000 43,000 36,000 a) Rs.567 b) Rs.657 c) Rs.-756 d) Rs.-765 e) None of the above 13. Compute the cost of equity using CAPM where risk-free rate of return is 9%, Beta co-efficient of the firm is 1.1 and assuming a market return of 15 percent next year. a) 16.6% b) 15.6% c) 16.5% d) 15.8% e) None of the above Ke=9+1.1(15-9)=9+6.6=15.6 14. Find out the weighted average cost of capital from the following data: Securities Book value After tax cost Equity 10,00,000 12% Retained earnings 4,00,000 11% Preference capital 4,00,000 12% Debentures 8,00,000 7%26,00,000 a) 10.3% (Hint: 1000000*0.12+40000*0.11+400000*0.12+800000*0.07=268000) Divide by 2600000 and it would be 10.3% b) 12.0% c) 11.15 d) 9.26% e) None of the above 15. Equity shares of Phonex Ltd. are quoted in the market at Rs.17.00. The dividend expected a year hence is Rs.1.50. The expected rate of dividend growth is 8%. The cost of equity capital to the company is; a. 11.08% b. 13.88% c. 15.46% d. 16.82% e. None of the above (Hint: Ke= D1/P0+g = 1.5/17+.08=0.1682 or 16.82%) 16. If the cost of equity is 18%, and the cost of debt is 15% what would be the cost of capital, at a tax rate of 35% and a debt-equity ratio of 2:1? a. 13.50% b. 13.25% c. 12.48% d. 16.0% e. None of the above (Hint WCOC= 1/3 *0.18+2/3 *0.15(1-0.35)=0.06+0.065=.125 or 12.5% 17. If the interest rate on long-term debt is 18% p.a. and the tax rate of the company is 35%, the cost of debt is a. 10.70% b. 11.70% c. 12.85% d. 12.70% e. None of the above (Hint : Kd= YTM(1-Tax Rate)=0.18(1-.35)=0.18*0.65=0.117 or 11.70% 18. Ravi & Co. issues 10% irredeemable preference shares. The face value of each share is Rs.100 and net amount realized share is Rs.96. The cost of the preference capital is a. 9.6% b. 10%c. 10.42% d. 14.32% e. None (Hint Cost of preference Share= Preference Dividend/ Market Value of Preference share= 10/96=.10416 or 10.42% 19. The future value of a regular annuity of Rs.1000 earning a rate of interest of 12% p.a. for 5 years is equal to a. Rs.6,250 b. Rs.6,353 c. Rs.6,425 d. Rs.6,538 e. None Hint (Use Table 2: Multiplying factor = 6.3528 Therefore Ans=6.3528*1000=6353 20. How much is a Rupee worth today, if you can expect to receive it a year from now, with no risk of default? a. Less than Rs.1 b. Rs. 1 c. More than Rs.1 d. Zero None (UGC-NET/SET: Commerce (Paper II & III) JRF and Assistant Professor Exam) 21. The present value of Rs.10,00,000 receivable after 60 years, at a discount rate of 10% is a. Rs.3,284 b. Rs.6,898 c. Rs.18,649 d. Rs.39,440 e. Rs.48,376 (Use Table 1 FD FVIF=PxCVF Therefore P=FVIF/ CVF=1000000/304.4816=3284 22. How much should a company invest at the beginning of each year at 14% so that it can redeem debentures of Rs.10 lakh at the end of year 10? a. Rs. 48,195 b. Rs.45,363 c. Rs.51,714 d. Rs. 65,236 e. Rs.71,535 (Hint : Case of Future value of annuity due FVAD=P*(FVIFA)14%,10Yr * (1+i) 1000000=P*19.3373*1.14 Therefore P=1000000/(19.3373*1.14)=45362.74 Ans23. Alpha company paid a dividend of Rs.4.50. The current market price of an equity share is Rs.90. Dividend are expected to grow at the rate of 7%, the cost of equity capital is a. 11.5% b. 12.35% c. 14.25% d. 16% e. 18.5% Hint Ke=D1/P0 + g = {D0(1+g)/ P0} + g = {4.5(1+0.07) / 90} +0.07 = 12.35% 24. Consider the following data: Source Market Value (Rs.) Cost (%) Equity 10,00,000 18 Debt 5,00,000 13 If the tax rate is 35%, the weighted-average cost of funds taking market value as weights is a. 13.00% b. 13.82% c. 14.00% d 14.82% e. 14.62% 25. If the cost of equity is 20%, and the cost of debt is 13% what would be the cost of capital, at a tax rate of 30% and a debt-equity ratio of 1:3? a. 18.50% b. 15.25% c. 17.28% d. 20.0% e. None of the above 26. What is the risk premium of a security, if the market return is 18%, Beta 1.25 and risk-free rate of return is 10.5%. a) 9.38% b) 10.50% c) 19.87% d) 12.76% e) None of the above Hint : Risk Premium = Beta(Market rate-risk free rate)=1.25*(18-10.5)=1.25*7.5=9.3827. If the interest rate on long-term debt is 19% p.a. and the tax rate of the company is 33%, the cost of debt is a. 14.72% b. 12.73% c. 6.27% d. 13.33% e. None of the above 28. What is the payback period on cash flow (non-discounted) of the following project? Project C0 C1 C2 C3 C4 A -50,000 10,000 25,000 35,000 15,000 a. 2 years a. 2.5 years b. 3 years c. 3.5 years e. None 29. A company has retained earnings of Rs.72 lakh and equity capital of Rs.38 lakh. If the equity investors expect a rate of return of 17% and the cost of issuing fresh equity is 6%, the cost of the external equity is a. 16.4% b. 17.4% c. 17.7% d. 18.10% e. 19.1% (cost of external equity=Dividend expected/ Market price of share= 17/ (1-.06)=18.08% 30. The future value of a regular annuity of Rs.6000 earning a rate of interest of 9% p.a. for years is equal to a. Rs.75,048 b. Rs.78,480 c. Rs.74,480 d. Rs.78,840 e. None of the above (Qustion is wrong – no time duration given)31. The primary objective of corporate management is; a) Maximization of EBIT b) Maximization of EPS c) Maximization of market share price d) Maximization of wealth of share holders e) All of them 32. Which of the following statements is/are true for the given values of interest and time? a. Present Value Interest Factor is the reciprocal of Future Value Interest Factor. b. Future Value Interest Factor Annuity is the reciprocal of Present Value Interest Factor Annuity. c. Capital recovery factor is a product of Future Value Interest Factor and reciprocal of Future Value Annuity Factor. d. Both (a) and (c) above. e. None of the above 33. Which of the following statements is/are not true? a. The more frequent the compounding, the higher the future value, other things being equal. b. For a given amount, greater the discount rate, lesser is the present value. c. Converting an annuity to an annuity due decreases the present value. d. Converting an annuity to an annuity due increases the present value. e. None of the above Hint : FVADn=P(FVIFA i,n)(1+i) hence P=FVADn/FVIFA*(1+i) 34. Money has a time value because a. the individuals prefer future consumption to present consumption b. a rupee today is worth more than a rupee tomorrow in terms of purchasing power c. a rupee today can be productively deployed to generate real returns tomorrowd. both (b) and (c) e. All of them 35. Cash flows occurring in different periods should not be compared unless a. interest rates are expected to be stable b. the flows occur no more than one year from each other c. high rates of interest can be earned on the flows d. the flows have been discounted to a common date e. All of them 36. Sinking fund factor is the reciprocal of a. future value interest factor b. present value interest factor c. future value interest factor of annuity d. present value interest factor of annuity e. None of them 37. You have determined the profitability of a planned project by finding the present value of all the cash flows from that project. Which of the following would cause the project to look more appealing in terms of the present value of those cash flows? a. The discount rate decreases. b. The cash flows are extended over a longer period of time, but the total amount of the cash flows remains the same. c. The discount rate increases. d. Answers b and c above. e. None of them38. Which of the following statements is most correct? a. A 5-year $100 annuity due will have a higher present value than a 5- year $100 ordinary annuity. b. A 15-year mortgage will have larger monthly payments than a 30-year mortgage of the same amount and same interest rate. c. If an investment pays 10 percent interest compounded annually, its effective rate will also be 10 percent. d. All of the statements above are correct. e. None of the above 39. Which of the following statements is most correct? a. An investment which compounds interest semiannually, and has a nominal rate of 10 percent, will have an effective rate less than 10 percent. b. The present value of a three-year $100 annuity due is less than the present value of a threeyear $100 ordinary annuity. c. The proportion of the payment of a fully amortized loan which goes toward interest declines over time. d. None of the answers above is correct. e. All of them 40. Which of the following bank accounts has the highest effective annual return? a. An account which pays 10 percent nominal interest with monthly com-pounding. b. An account which pays 10 percent nominal interest with daily com-pounding. c. An account which pays 10 percent nominal interest with annual com-pounding. d. An account which pays 9 percent nominal interest with daily com-pounding. e. None of the above 1. Corporate Finance 1. If you invest Rs.25,000/- today at a compound interest of 9%, what will be the future value after 15 years?  (a) Rs.91,062/-  (b) Rs.91,260/-  (c) Rs.91,620/-  (d) Rs.91,200/-  (e) None of the above If choice a is selected set score to 2.2. Finance function involves:-  (a) Safe custody of funds only  (b) Expenditure of funds only  (c) Procurement of finance only  (d) Procurement and effective utilization of funds  (e) None of the above If choice d is selected set score to 2. 3. The primary objective of corporate management is:-  (a) Maximization of wealth of shareholders  (b) Maximization of EBIT  (c) Maximization of market share price  (d) Maximization of EPS  (e) All of the above If choice e is selected set score to 2. 4. What is the payback period on cash flow (non discounted) of the following project?  (a) 2.5 years  (b) 3 years  (c) 3.5 years  (d) 2 years  (e) None of the above If choice b is selected set score to 2. 5. The goal of wealth maximization takes into consideration:-  (a) Risk related to uncertainty of returns  (b) Timing of expected returns  (c) Amount of returns expected  (d) All of the above  (e) None of the above If choice e is selected set score to 2. 6. Time value of money facilitates comparison of cash flows occurring at different time periods by:-  (a) a) Compounding all cash flows to a common point of time  (b) b) Discounting all cash flows to a common point of time  (c) c) Using either (a) or (b)  (d) d) Neither (a) nor (b)  (e) e) None of the above If choice c is selected set score to 2.7. 'X' Ltd. Company issues Rs.50,000/-, 8% debentures at a premium of 10%. The tax rate applicable to the company is 60%. What is the cost of debt?  (a) 3.5%  (b) 4.21%  (c) 2.91%  (d) 4%  (e) None of the above If choice c is selected set score to 2. 8. What is the NPV (approximate), if cost of capital is 10% on cash flow of the following project?  (a) Rs.493.40/-  (b) Rs.-9507.60/-  (c) Rs.9507.60/-  (d) Rs.-493.40/-  (e) None of the above If choice d is selected set score to 2. 9. Money has a time value because:-  (a) a) The individuals prefer future consumption to present consumption  (b) b) A rupee today is worth more than a rupee tomorrow in terms of purchasing power  (c) c) A rupee today can be productively deployed to generate real returns tomorrow  (d) Both (b) and (c)  (e) All of the above If choice d is selected set score to 2. 10. Cash flows occurring in different periods should not be compared unless:-  (a) The flows occur no more than one year from each other  (b) The flows have been discounted to a common date  (c) High rates of interest can be earned on the flows  (d) Interest rates are expected to be stable  (e) All of the above If choice b is selected set score to 2. 11. What is the risk premium of a security, if the market return is 15%, Beta 0.8 and risk-free rate of return is 9%.  (a) 6.0%  (b) 4.8%  (c) 8.4%  (d) 7.2%  (e) None of the above If choice b is selected set score to 2.12. Relationship between annual effective rate of interest and annual nominal rate of interest is, if frequency of compounding is more than 1:-  (a) Effective Rate ‹ Nominal rate  (b) Effective rate › Nominal rate  (c) Effective Rate = Nominal rate  (d) All of the above  (e) None of the above If choice b is selected set score to 2. 13. If you invest Rs.20,000/- today at a compound interest of 9.25%, what will be the future value after 15 years?  (a) Rs.75,396/-  (b) Rs.75,960/-  (c) Rs.75,930/-  (d) Rs.75,460/-  (e) None of the above If choice a is selected set score to 2. 14. What is the NPV if cost of capital is 10% on cash flow of the following project?  (a) Rs.2,340/-  (b) Rs.2,400/-  (c) Rs.2,450/-  (d) Rs.2,404/-  (e) None of the above If choice d is selected set score to 2. 15. A student takes a loan of Rs.50,000/- from SBI. The rate of interest being charged by SBI is 10 percent per annum. What would be the amount of equal annual installment if he wishes to pay it back in five installments at the end of every year ( PVIF 10%, 5 Years is 0.621 and PVIFA is 3.791 )?  (a) Approx. Rs.15,620/-  (b) Approx. Rs.15,450/-  (c) Approx. Rs.13,190/-  (d) Approx. Rs.11,000/-  (e) None of the above If choice c is selected set score to 2.16. You have determined the profitability of a planned project by finding the present value of all the cash flows from that project. Which of the following would cause the project to look more appealing in terms of the present value of those cash flows?  (a) The discount rate decreases  (b) The cash flows are extended over a longer period of time, but total amount of the cash flows remains the same  (c) The discount rate increases  (d) All of the above  (e) None of the above If choice a is selected set score to 2. 17. Which of the following statements is correct?  (a) An investment which compounds interest semiannually, and has a nominal rate of 10 p ercent, will have an effective rate less than 10 percent  (b) The present value of a 3-year $100 annuity due is less than the present value of a 3- year $100 ordinary annuity  (c) The proportion of the payment of a fully amortized loan which goes toward interest dec lines over time  (d) All of the above  (e) None of the above If choice c is selected set score to 2. 18. A company wants to retire a loan Rs.5,00,000/-, 10 years from today. What amount should it invest each year for 10 years if the funds can earn 8 percent per annum. The first investment will be made at the beginning of this year ( FVIF 10%, 10 Years is 2.594 and FVIFA is 15.937.  (a) Approx. Rs.31,950/-  (b) Approx. Rs.40,000/-  (c) Approx. Rs.34,000/-  (d) Approx. Rs.28,000/-  (e) None of the above If choice e is selected set score to 2. 19. Find out the weighted average cost of capital from the following data:-  (a) 8.0%  (b) 8.11%  (c) 8.2%  (d) 7.5%  (e) None of the above If choice b is selected set score to 2.20. A company has 10 percent perpetual debt of Rs.1,00,000/-. The tax rate is 35 percent. Determine the cost of debt if the company issued at discount of 10 percent.  (a) 5.0 percent  (b) 5.91 percent  (c) 7.22 percent  (d) 6.5 percent  (e) None of the above If choice c is selected set score to 2. 21. Which of the following bank accounts has the highest effective annual return?  (a) An account which pays 9 percent nominal interest with daily compounding  (b) An account which pays 10 percent nominal interest with daily compounding  (c) An account which pays 10 percent nominal interest with annual compounding  (d) An account which pays 10 percent nominal interest with monthly compounding  (e) None of the above If choice b is selected set score to 2. 22. What is the NPV (approximate), if cost of capital is 10% on cash flow of the following project?  (a) Approx. Rs.-5,500/-  (b) Approx. Rs.5,500/-  (c) Approx. Rs. 4,600/-  (d) Approx. Rs.4,600/-  (e) None of the above If choice c is selected set score to 2. 23. If you invest Rs.30,000/- today at a compound interest of 9.50%, what will be the future value after 10 years?  (a) Rs.74,734/-  (b) Rs.74,897/-  (c) Rs.74,347/-  (d) Rs.74,934/-  (e) None of the above If choice c is selected set score to 2. 24. You are interested in investing your money in a bank account. Which of the following banks provides you with the highest effective rate of interest?  (a) Bank 1; 8 percent with monthly compounding  (b) Bank 2; 8 percent with annual compounding  (c) Bank 4; 8 percent with daily (365-day) compounding  (d) Bank 3; 8 percent with quarterly compounding  (e) None of the above If choice c is selected set score to 2.25. What is the NPV if cost of capital is 12% on cash flow of the following project?  (a) Rs.657/-  (b) Rs.-765/-  (c) Rs.567/-  (d) Rs.-756/-  (e) None of the above If choice d is selected set score to 2. 26. Which of the following is not considered a capital component for the purpose of calculating the weighted average cost of capital as it applies to capital budgeting?  (a) Accounts payable  (b) Long term debt  (c) Common stock  (d) Preferred stock  (e) None of the above If choice a is selected set score to 2. 27. A company has determined that its optimal capital structure consists of 40 percent debt and 60 percent equity. Given the following information, calculate the firm's weighted average cost of capital, where rd = 6%, Tax rate = 40%, Share Price = $25, Growth = 0%, Dividend = $2.00.  (a) 7.2%  (b) 7%  (c) 6.2%  (d) 6%  (e) 8% If choice c is selected set score to 2. 28. Find out the weighted average cost of capital from the following data:-  (a) 9.26%  (b) 12.0%  (c) 11.15%  (d) 10.3%  (e) None of the above If choice d is selected set score to 2.29. Which of the following is not considered a capital component?  (a) Long term debt  (b) Common stock  (c) Permanent short term debt  (d) All of the above are considered capital components  (e) None of the above If choice d is selected set score to 2. 30. The common stock of Anthony Steel has a beta of 1.20. The risk-free rate is 5 percent and the market risk premium (rM - rRF) is 6 percent. What is the companys cost of common stock, rs?  (a) 7%  (b) 12.4%  (c) 7.2%  (d) 12.2%  (e) 11% If choice d is selected set score to 2. 31. Equity shares of Phonex Ltd. are quoted in the market at Rs.17.00/-. The dividend expected a year hence is Rs.1.50/-. The expected rate of dividend growth is 8%. The cost of equity capital to the company is:-  (a) 13.88%  (b) 16.82%  (c) 15.46%  (d) 11.08%  (e) None of the above If choice b is selected set score to 2. 32. Which of the following statements is correct?  (a) a) If a company's tax rate increases but the yield to maturity of its non callable bonds r emains the same, the company's marginal cost of debt capital used to calculate its weighted average cost of capital will fall  (b) b) All else equal, an increase in a company's stock price will increase the marginal cos t of common stock,re.  (c) c) All else equal, an increase in interest rates will decrease the marginal cost of comm on stock, re.  (d) d) Both (a) and (b)  (e) e) None of the above If choice a is selected set score to 2. 33. A stock split will cause a change in the total rupee amounts shown in which of the following balance sheet accounts?  (a) Cash  (b) Common stock  (c) Paid-in capital  (d) Retained earnings  (e) None of the above If choice e is selected set score to 2.34. Which of the following statements is correct?  (a) a) The WACC is a measure of the before-tax cost of capital  (b) b) Typically the after-tax cost of debt financing exceeds the after-tax cost of equity fina ncing  (c) c) The WACC measures the marginal after-tax cost of capital  (d) d) Both (a) and (b)  (e) e) None of the above If choice c is selected set score to 2. 35. Which of the following actions will enable a company to raise additional equity capital (that is, which of the following will raise the total book value of equity)?  (a) a) The establishment of a new-stock dividend reinvestment plan  (b) b) A stock split  (c) c) The establishment of an open-market purchase dividend reinvestment plan  (d) d) A stock repurchase  (e) e) Both (a) and (d) If choice a is selected set score to 2. 36. A company has a capital structure which consists of 50 percent debt and 50 percent equity. Which of the following statements is correct?  (a) The WACC represents the cost of capital based on historical averages. In that sense, i t does not represent the marginal cost of capital  (b) The cost of equity financing is greater than or equal to the cost of debt financing  (c) The WACC exceeds the cost of equity financing  (d) The WACC is calculated on a before-tax basis  (e) None of the above If choice b is selected set score to 2. 37. Which of the following statements is correct?  (a) a) The weighted average cost of capital for a given capital budget level is a weighted a verage of the marginal cost of each relevant capital component which makes up the firm's tar get capital structure  (b) b) The weighted average cost of capital is calculated on a before-tax basis  (c) c) An increase in the risk-free rate is likely to increase the marginal costs of both debt and equity financing  (d) d) Both (a) and (c)  (e) e) All of the above If choice d is selected set score to 2. 38. Which of the following is not an advantage of using book value weights for computing the cost of capital?  (a) The calculation of the weights is very simple  (b) Book value weights are likely to fluctuate less over a period as these are not affected b y the fluctuations in market prices  (c) Book value weights are consistent with the concept of cost of capital  (d) Book value weights are the only usable basis when market values are not obtainable o r reliable  (e) None of the above If choice d is selected set score to 2.39. Which of the following are examples of a primary market transaction?  (a) a) A company issues new common stock  (b) b) A company issues new bonds  (c) c) An investor asks his broker to purchase 1,000 shares of Microsoft common stock  (d) d) All of the above  (e) e) Both (a) and (b) If choice e is selected set score to 2. 40. If the expected rate of return on a stock exceeds the required rate:-  (a) The company is probably not trying to maximize price per share  (b) The stock is a good buy  (c) The stock should be sold  (d) Dividends are not being declared  (e) The stock is experiencing supernormal growth If choice b is selected set score to 2. 41. Which of the following is/are true about NPV?  (a) a) It considers all the cash flows  (b) b) It gives more weightage to distant flows than to near-term flows  (c) c) It considers time value of money  (d) Both (a) and (c)  (e) None of the above If choice d is selected set score to 2. 42. Cash flows occurring from a project in different period are comparable unless:-if:  (a) Interest rates are expected to be stable  (b) The flows have been discounted to a single date  (c) The flows occur periodically every year  (d) Interest can be earned on the cash flows  (e) None of the above If choice b is selected set score to 2. 43. Consider the following data: If the tax rate is 35%, the weighted average cost of funds taking market value as weights is:-  (a) 14.00%  (b) 15.82%  (c) 14.96%  (d) 15.00%  (e) 16.62% If choice c is selected set score to 2.44. The _________ is the time period that elapses from the point when the firm sells a finished good on account to the point when the receivable is collected..  (a) cash conversion cycle  (b) average payment period  (c ) average collection period  (d) average age of inventory  (e) None of the above If choice c is selected set score to 2. 45. Conflicts in ranking of projects on the basis of NPV and IRR arise due to:-  (a) a) Disparity in the timing of cash inflows  (b) b) Disparity in the size of cash inflows  (c) c) Disparity in the life of cash flows  (d) Both (a) and (b)  (e) None of the above If choice d is selected set score to 2. 46. _________ projects do not compete with each other; the acceptance of one _________ the others from consideration.  (a) Independent; does not eliminate  (b) Capital; eliminates  (c) Replacement; does not eliminate  (d) Mutually exclusive; eliminates  (e) None of the above If choice a is selected set score to 2. 47. The rationale for not including sunk costs in capital budgeting decisions is that they:-  (a) Revert at the end of the investment  (b) Represent nominal, not real, outflows  (c) Are usually small in magnitude  (d) Are historical costs  (e) None of the above If choice d is selected set score to 2. 48. Which of the following events is likely to encourage a company to raise its target debt ratio?  (a) a) An increase in the corporate tax rate  (b) b) An increase in the personal tax rate  (c) c) An increase in the company's operating leverage  (d) Both (a) and (c)  (e) All of the above If choice a is selected set score to 2.49. Which of the following would increase the likelihood that a company would increase its debt ratio in its capital structure?  (a) a) An increase in costs incurred when filing for bankruptcy  (b) b) An increase in the corporate tax rate  (c) c) A decrease in the firm's business risk  (d) Both (b) and (c)  (e) None of the above If choice b is selected set score to 2. 50. The aggressive financing strategy results in the firm financing its short-term needs with _________ funds and its long-term needs with _________ funds.  (a) long-term; short-term  (b) short-term; long-term  (c) Permanent; seasonal  (d) seasonal; permanent  (e) None of the above If choice b is selected set score to 2. 51. Which of the following statements is correct?  (a) a) A firm can use retained earnings without paying a flotation cost. Therefore, while the cost of retained earnings is not zero, the cost of retained earnings is generally lower than the after-tax cost of debt financing  (b) b) The capital structure that minimizes the firm's cost of capital is also the capital struct ure that maximizes the firm's stock price  (c) c) The capital structure that minimizes the firm's cost of capital is also the capital struct ure that maximizes the firm's earnings per share  (d) d) If a firm finds that the cost of debt financing is currently less than the cost of equity fi nancing, an increase in its debt ratio will always reduce its cost of capital  (e) Both (a) and (b) If choice b is selected set score to 2. 52. Which of the following statements is correct?  (a) a) Since debt financing raises the firm's financial risk, raising a company's debt ratio wi ll always increase the company's WACC  (b) b) Since debt financing is cheaper than equity financing, raising a company's debt ratio will always reduce the company's WACC  (c) c) Increasing a company's debt ratio will typically reduce the marginal cost of both debt and equity financing; however, it still may raise the company's WACC  (d) Both (a) and (c)  (e) None of the above If choice e is selected set score to 2. 53. According to NI approach:-  (a) a) The total market value of a firm and the cost of capital are dependent on the capital structure  (b) b) The total market value of a firm and the cost of capital are independent of capital str ucture  (c) c) The capital structure has no relevance  (d) Both (a) and (c)  (e) None of the above If choice a is selected set score to 2.54. Under Net Income Approach (NIA), change in the capital structure of a company:-  (a) Does not cause any change either in the overall cost of capital or in the total value of a firm  (b) No changes in overall cost of capital  (c) Causes corresponding change in the overall cost of capital as well as the total value of a firm  (d) Causes corresponding change in the overall cost of capital only  (e) None of the above If choice c is selected set score to 2. 55. In Net Operating Income (NOI) approach, market value of a firm:-  (a) Is sometimes affected by capital structure changes  (b) Is affected by capital structure changes  (c) Is affected proportionately  (d) Is not at all affected by capital structure changes  (e) None of the above If choice d is selected set score to 2. 56. Financial structure includes:-  (a) Long term as well as short term sources of funds  (b) Equity share capital of the company  (c) Long term sources of funds  (d) Medium term source of funds  (e) None of the above If choice a is selected set score to 2. 57. The term capital structure:-  (a) Is not part of financial structure  (b) Is part of financial structure  (c) Is part of appropriation account  (d) Is part of profit & loss account  (e) None of the above If choice b is selected set score to 2. 58. Which of the following statement(s) is true?  (a) Risk that can be eliminated by diversification is called specific risk  (b) Risk that cannot be avoided, regardless of how much you diversity is known as market risk  (c) The variability of earnings before interest and taxes is referred to as business risk  (d) All of the above  (e) None of the above If choice d is selected set score to 2. 59. Which of the following is not a feature of debt finance?  (a) a) Dilution of control  (b) b) Low cost  (c) c) Financial risk  (d) Both (b) and (c)  (e) None of the above If choice a is selected set score to 2.60. Which of the following factors has an effect on business risk?  (a) Demand for products manufactured by the firm  (b) Volatility in prices of the products manufactured by the firm  (c) Variability in input prices  (d) All of the above  (e) None of the above If choice d is selected set score to 2. 61. The Modigliani-Miller argument is that:-  (a) a) The value of the levered firm will be more than that of unlevered firm  (b) b) The value of the unlevered firm will be more than the levered firm  (c) c) Levered firms cannot enjoy a premium over unlevered firms as the investors will abo lish the difference through personal leverage  (d) Either (a) or (b) may be true depending on other circumstances  (e) None of the above If choice c is selected set score to 2. 62. Business risk refers to:-  (a) a) Variability of sales  (b) b) Variability of the market value of the firm  (c) c) Variability of cost of raw materials  (d) Both (a) and (c)  (e) None of the above If choice d is selected set score to 2. 63. Which of the following is true?  (a) Operating leverage measures the sensitivity of EBT to changes in the quantity produce d and sold  (b) Operating leverage measures the sensitivity of EBIT to changes in quantity produced a nd sold  (c) Operating leverage measures the sensitivity of PAT to changes in quantity produced a nd sold  (d) Operating leverage measures the sensitivity of PBDT to changes in quantity produced and sold  (e) None of the above If choice b is selected set score to 2. 64. Total or Combined leverage measures the relationship between:-  (a) PAT and sales  (b) Sales and EPS  (c) EBIT and sales  (d) EPS and EBIT  (e) None of the above If choice b is selected set score to 2. 65. Which of the following is/are correct?  (a) a) Value of the firm and cost of capital are directly related  (b) b) Value of the firm and cost of capital are inversely related  (c) c) The claim of preference shareholders is prior to that of equity shareholders  (d) Both (b) and (c)  (e) None of the above If choice d is selected set score to 2.66. The ultimate objective of any company is:-  (a) Wealth maximization  (b) Sale maximization  (c) Profit maximization  (d) Improving its reputation  (e) None of the above If choice a is selected set score to 2. 67. Which of the following best describes a firm's cost of capital?  (a) a) It is the weighted arithmetic average of the cost of various sources of long term fina nce used by it  (b) b) The rate of return the firm must earn on its investments in order to satisfy the expect ations of investors who provide long term funds to it  (c) c) It is the weighted arithmetic average of the cost of various sources of long term finan ce and short term finance used by it  (d) Both (a) and (b)  (e) None of the above If choice d is selected set score to 2. 68. Which of the following statements is true?  (a) Retained earnings is the only principal source of finance for growing firms  (b) Retained earnings represent the profits ploughed back into the business  (c) Retained earnings represent the extent to which the firm has invested in liquid assets o ut of its profits  (d) Retained earnings are given lesser importance when a firm follows a residual dividend policy  (e) None of the above If choice b is selected set score to 2. 69. Which of the following long term sources of finance puts maximum restraint on managerial freedom?  (a) Retained earnings  (b) Preference capital  (c) Equity capital  (d) Term loans  (e) None of the above If choice d is selected set score to 2. 70. The cost of debt remains more or less constant up to a certain degree of leverage but rises thereafter at an increasing rate. This proposition is based on:-  (a) Net income approach on capital structure  (b) Miller-Modigliani approach  (c) Net operating income approach on capital structure  (d) Traditional position/Traditional approach on capital structure  (e) None of the above If choice d is selected set score to 2.71. Which of the following is true regarding sound capital market structure of a company?  (a) The capital structure should be determined within the debt capacity of the company an d this capacity should not be exceeded  (b) Use of debt should be avoided as it adds to financial risk of the company  (c) Minimum use of leverage at minimum cost  (d) The risk of loss of control of the company due to capital structure is a major concern in a closely held company  (e) The capital structure should not change over a period of time If choice a is selected set score to 2. 72. Which of the following concepts explains the relationship between shareholders and Managers?  (a) Valuation  (b) Value based management  (c) Agency consideration  (d) Shareholder wealth maximization  (e) Miller-Modigliani If choice c is selected set score to 2. 73. A significant assumption of the net operating income is that:-  (a) Debt and equity levels do not change  (b) Dividend increase at a constant rate  (c) It remains constant regardless of changes in leverage  (d) Interest expense and taxes are included in the calculation  (e) It decreases up to a certain point of time, and then increases at an increasing rate, wit h increasing levels of leverage If choice c is selected set score to 2. 74. Which of he following best describes the situation in which a firm is having problem meeting its financial obligations?  (a) Business risk  (b) Legal bankruptcy  (c) Technical bankruptcy  (d) Financial risk  (e) Financial distress If choice e is selected set score to 2. 75. Which of the following risks is revealed by capital structure ?  (a) a) Liquidity risk  (b) b) Financial risk  (c) c) Market risk  (d) d) Firm's total risk  (e) Both (b) and (d) If choice a is selected set score to 2. 76. Trade creditors of a company are mostly interested in the company's:-  (a) Activity ratios  (b) Liquidity ratio  (c) Profitability ratios  (d) Valuation ratios  (e) Leverage ratios If choice b is selected set score to 2.77. A decrease in a firm's willingness to pay dividends is likely to result from an increase in its:-  (a) Profitable investment opportunities  (b) Stock price  (c) Access to capital markets  (d) Earnings stability  (e) None of the above If choice a is selected set score to 2. 78. A stock split will cause a change in the total dollar amounts shown in which of the following balance sheet accounts?  (a) Cash  (b) Common stock  (c) Paid in capital  (d) All of the above  (e) None of the above If choice e is selected set score to 2. 79. Which of the following statements is correct?  (a) a) If a company puts in place a 2-for-1 stock split, its stock price should roughly double  (b) b) Share repurchases are taxed less favorably than dividends; this explains why comp anies typically pay dividends and avoid share repurchases  (c) c) On average, a company's stock price tends to rise when it announces that it is initiati ng a share repurchase program  (d) Both (a) and (b) If choice c is selected set score to 2. 80. Longer the manufacturing period  (a) Greater is the requirement of working capital  (b) There is no change in the operating cycle  (c) Shorter is the requirements of working capital  (d) Lesser is the requirement of working capital  (e) None of the above If choice a is selected set score to 2. 81. Which of the following factors influence the pay out ratio of a firm?  (a) a) Funds requirement  (b) b) Liquidity position of the firm  (c) c) Access to external sources of financing  (d) All of the above  (e) Both (a) and (b) If choice d is selected set score to 2. 82. Which of the following sources cannot be used for payment of dividend?  (a) a) Current profits after providing for depreciation  (b) b) Profits for any previous financial year to years  (c) c) Capital  (d) Both (b) and (c)  (e) Either (b) or (c) If choice c is selected set score to 2.83. Net working capital denotes:-  (a) Total liabilities  (b) Excess of fixed assets over current assets  (c) Excess of current liabilities over current assets  (d) Excess of current assets over current liabilities  (e) None of the above If choice d is selected set score to 2. 84. Other things held constant, which of the following will cause an increase in working capital?  (a) Merchandize is sold at a profit, but the sale is on credit  (b) A cash dividend is declared and paid  (c) Cash is used to buy marketable securities  (d) Long term bonds are retired with the proceeds of a preferred stock issue  (e) None of the above If choice a is selected set score to 2. 85. Which of the following statements is correct?  (a) Trade credit is provided to a business only when purchases are made  (b) Commercial paper is a form of short term financing that is primarily used by large, fina ncially stable companies  (c) Short term debt, while often cheaper than long term debt, exposes a firm to the potenti al problems associated with rolling over loans  (d) All of the above  (e) None of the above If choice d is selected set score to 2. 86. Which of the following is not a current asset?  (a) a) Prepaid expenses  (b) b) Short term loans and advances  (c) c) Marketable securities  (d) Both (a) and (b)  (e) None of the above If choice b is selected set score to 2. 87. Which of the following is the least liquid among current assets?  (a) Inventories  (b) Prepaid expenses  (c) Cash  (d) Short term securities  (e) Debtors If choice a is selected set score to 2. 88. The current ratio is obtained by:-  (a) Dividing quick assets by total liabilities  (b) Dividing quick assets by long term liabilities  (c) Dividing current assets by current liabilities  (d) Dividing current assets by total liabilities  (e) Dividing quick assets by current liabilities If choice c is selected set score to 2.89. Which of the following best describes working capital gap?  (a) Quick assets less current liabilities other than bank  (b) Current assets less short term bank borrowings  (c) Current assets less current liabilities other than bank borrowings  (d) Quick assets less current liabilities  (e) Current assets less current liabilities If choice c is selected set score to 2. 90. Financial risk involves:-  (a) a) Fluctuations in exchange rates  (b) b) Different interest and inflation rates  (c) c) Balance of payments position  (d) All of the above  (e) Both (a) and (b) If choice d is selected set score to 2. 91. Which of the following features of preference shares is/are similar to those of equity shares?  (a) a) Redeemability  (b) b) No obligation to pay dividend  (c) c) Voting rights  (d) d) Charge over assets  (e) e) Both (b) and (c) If choice b is selected set score to 2. 92. Euro-Convertible Bonds (ECBs) issued by Indian Companies refer to bonds issued in foreign currency in:-  (a) India and any country in Europe  (b) European countries only  (c) Europe and North America  (d) India or any country outside India  (e) Any country other than India If choice e is selected set score to 2. 93. Which of the following is a/are feature(s) of equity capital?  (a) a) The payment of dividend is compulsory, irrespective of the company's financial perf ormance  (b) b) The dividend, if not paid during a year, becomes payable in the next year  (c) c) Dividend becomes payable only if recommended by the BoD and passed by the co mpany in the AGM  (d) d) Both (a) and (b)  (e) e) None of the above If choice c is selected set score to 2. 94. The major advantages of privately placing the securities are:-  (a) Faster access to funds  (b) Fewer procedural formalities  (c) Lower issue cost  (d) Easy access for any company  (e) All of the above If choice e is selected set score to 2.95. Which of the following is not a source of long term finance?  (a) Equity capital  (b) Term loan  (c) Debenture capital  (d) Commercial paper  (e) Preference capital If choice d is selected set score to 2. 96. Which of the following statements is true?  (a) Equity shareholders enjoy the rewards of ownership and bear the risks of the ownershi p (b) Post-tax cost of debentures is always less than the post-tax cost of the term loans  (c) The par value and issue price of an equity share are always capital  (d) All outstanding issues of shares are traded in the primary markets  (e) None of the above If choice a is selected set score to 2. 97. The costliest of long term source of finance is:-  (a) Preference share capital  (b) Equity share capital  (c) Debentures  (d) Retained earnings  (e) Capital raised through private placement If choice b is selected set score to 2. 98. Which of the following statements is/are true? With the commencement of the Companies Act, 1956, the issue of preference shares with voting rights has been restricted only to the following cases:-  (a) There are arrears in dividends for two or more years incase of cumulative preference s hares  (b) Preference dividend is due for a period of two or more consecutive preceding years  (c) In the preceding six years including the immediately preceding financial year, if the co mpany has not paid the preference dividend for a period of three or more years  (d) All of the above  (e) None of the above If choice d is selected set score to 2. 99. A cumulative preference share is one:-  (a) In which all the unpaid dividends are carried forward and payable  (b) Which allows the issuing company the right to call the preference shares wholly or part ly at a certain price  (c) Which can be redeemed  (d) Which can be converted into equity shares  (e) None of the above If choice a is selected set score to 2.100. Which of the following is/are true about equity capital as a source of finance?  (a) a) Using equity capital to finance working capital may lead to a situation of 'technical in solvency'  (b) b) Assessing the cost of equity capital is a difficult and complex task  (c) c) Equity capital provides tax benefits to the issuing company  (d) d) Cost of retained earnings is lesser than the cost of debt capital  (e) e) Both (b) and (d) If choice b is selected set score to 2. 101. Rights issue is the method of raising funds:-  (a) a) In which secur ities are simultaneously issued to the existing shareholders and the public  (b) b) Generally issued to the existing shareholders at a price lower than the current mark et price  (c) c) Generally entailing lower costs of issue  (d) d) Generally made to high net worth individuals  (e) e) Both (b) and (c) If choice e is selected set score to 2. 102. Which of the following, from the firm's point of view, can be considered as the advantage(s) of using equity capital as a source of long term funds?  (a) a) It does not involve any fixed obligation for payment of dividends  (b) b) Equity dividends are payable from post-tax earnings. They are not tax deductible ex penses  (c) c) It enhances the creditworthiness of the company  (d) d) Both (a) and (c)  (e) e) None of the above If choice d is selected set score to 2. 103. Which of the following characteristics is/are true, with reference to preference capital?  (a) a) Preference dividend is payable only out of distributable profits  (b) b) Preference dividend is tax deductible  (c) c) The claim of preference shareholders is prior to the claim of equity shareholders  (d) d) Both (a) and (c)  (e) e) All of the above If choice d is selected set score to 2. 104. What is/are the factor(s) which make(s) debentures attractive to investors?  (a) a) They enjoy a high order of priority in the event of liquidation  (b) b) Stable rate of return  (c) c) Protected by the provisions of Debenture Trust Deed  (d) d) All of the above  (e) e) Both (a) and (b) If choice d is selected set score to 2.105. The major advantage(s) of entering into a Buy Out Deal (BOD) is/are:-  (a) An advantage accruing to the investor is that the issue price usually reflects the compa ny's intrinsic value  (b) Companies, both existing and new, which do not satisfy conditions laid down by the S EBI for premium issues, may issue at a premium through the BOD method  (c) There is less issue cost  (d) The procedural complexities are reduced considerably and the funds reach the firm up front  (e) All of the above If choice e is selected set score to 2. 1. The present value interest factor of an (ordinary) annuity (PVIFA) is the reciprocal of the future value interest factor of an (ordinary) annuity (FVIFA). Your Answer: True Correct Answer: False The reciprocal of the FVIF is the PVIF -- (1 + i)n = FVIF; 1/(1 + i)n = PVIF; but this technique does not work with the annuity factors. 2. If you would like to double your money in 6 years, the approximate annual return you need is 12 percent (Rule of 72). Your Answer: True 3. A savings account at Bank A pays 6.2 percent interest, compounded annually. Bank B's savings account pays 6 percent compounded semiannually. Bank B is paying less total interest each year. Your Answer: False Correct Answer: True Bank B is paying the equivalent of 3% twice a year. The effective annual rate (EAR) is [ (1+.03)2 -1 ] or 6.09%. This is less than Bank A at 6.2% annually. 4. All other things being equal, I'd rather have $10,000 in 10 years than to receive $10,000 today. Your Answer: False5. The rate of interest is used to express the time value of money. Your Answer: True 1. Finding the present value is simply the reverse of compounding. Ans True 2. The present value interest factor (PVIF) is the reciprocal of the future value interest factor (FVIF). Ans True 3. If the discount rate decreases, the present value of a given future amount decreases. Ans False 4. The present value interest factor for a dollar on hand today is 0. Ans False ( hint The PVIF at n = 0 is equal to one) 5. If you would like to double your money in 8 years, the approximate compound annual return you need is 9 percent (Rule of 72). Ans True 6. A saving account at Bank A pays 6 percent interest, compounded annually. Bank B's savings account pays 6 percent compounded semiannually. Bank B is paying twice as much interest. Ans False (hint : Bank B is paying the equivalent of 3% twice a year. The effective annual interest rate is (1+.03) ² - 1 or 6.09%. This is more than Bank A is paying, but certainly not double.) 7. All other things being equal, I'd rather have $1,000 today than to receive $1,000 in 10 years. Ans True 8. For a given nominal interest rate, the more numerous the compounding periods, the less the effective annual interest rate. Ans : False (As compounding periods increase, the effective annual interest rate becomes LARGER.) 9. If money has a time value, then the future value will always be more than the original amount invested.Ans : True 10. All other things remaining the same, an annuity received at the beginning of each period has more present value than does one received at the end of each period. Ans : True 1. Question: Find present value of Rupees 80,000 to be received after five years when required rate of return is 10% Solution: PV = Cash flow/(1+r)t = 80,000/(1+0.10)5 = 80,000/1.61051 = Rupees 49,674 2. Find the present value of a series of cash flows occurred in different years when the required rate of return is 10% PERIOD FUTURE CASH FLOWS 1 RUPEES 80,000 2 RUPEES 70,000 3 RUPEES 50,000 4 RUPEES 30,000 As we know, PV = Future cash flow/(1+r)t S PV = {80,000/(1+0.10)1} + {70,000/(1+0.10)2} + {50,000/(1+0.10)3} + {30,000/(1+0.10)4} = (80,000/1.10) + (70,000/1.21) + (50,000/1.331) + (30,000/1.4641) = 72727 + 57851 + 37566 +20490 = Rupees 1,88,634 1. Interest paid (earned) on only the original principal borrowed (lent) is often referred to as? (a) Compound interest (b) Future value (c) Present value (d) Simple interest 2. Treasury bills are? (a) Issued on a premium basis and pay a fixed annual interest rate (b) Issued on a discount basis and mature at par (c) Issued on a premium basis and mature at par (d) Issued on a discount basis and pay a fixed annual interest rate 3. Nominal Interest Rate is also known as? (a) Annual percentage rate (b) Effective interest Rate (c) Periodic interest rate (d) Coupon rate4. The concept of compound interest refers to? (a) The process of gradually retiring a debt through periodic payments of principal and interest (b) The process of servicing a debt with regular interest payments, followed lump sum payment of principal and interest at the end of the loan term (c) The process of converting future lump sums and annuities into present values at a stated interest rate (d) The process of earning interest on an original amount, plus interest on interest previously earned Correct! 5. The value of money to be received in the future is _______the value of the same amount of money in hand today? (a) Higher than (b) Lower than (c) The same as (d) None of the above 6. The Time value of money must be considered in total outlay decision because? (a) Cash inflows and out flows occur at different point (b) Inflation greatly reduce the outflows (c) A dollar received in future is more value able than a dollar today (d) Cash flows are not known with certainty 7. Interest paid (earned) on both the original principal borrowed (lent) and previous interest allowed (earned) is often referred to as __________? (a) Compound interest (b) Double interest (c) Simple interest (d) Present value 8. Money has time value because? (a) Individuals prefer future consumption to present consumption (b) Money today is worth more than money tomorrow in terms of purchasing power(c) There is a possibility of earning risk free return on money invested today (d) B and C above Correct! 9. The real rate of interest reflects compensation for? (a) Present value (b) Future value (c) Time value of money (d) None of above 10. Interest has 3 types? (a) Fixed rate, current rate, market rate (b) Market rate, combination rate, fixed rate (c) Fixed rate, floating rate, current rate (d) Fixed rate, floating rate, combination rate MCQs 11-20 11. The basic rule of the time value of money is? (a) Investments will always be worth more tomorrow than they are today (b) Its always wiser to save a dollar for tomorrow than to spend it today (c) A dollar in hand today is worth more than a dollar promised at some time in the future (d) All of the above express an aspect of the basic rule of time value of money Wrong! 12. A decrease in the supply for loanable funds, holding demand constant, will cause interest rates to? (a) Increase (b) Decrease (c) Stay the same(d) Not enough information to tell Wrong! 13. The value of money results from? (a) Its backing (b) Rates set by the State Bank (c) Its purchasing power (d) None of the above Correct! 14. The basic price that equates the demand for and supply of loanable funds in the financial markets is the _______? (a) Interest rate (b) yield curve (c) Term structure (d) Cash price Correct! 15. If the interest rate is greater than 0%, then a dollar today is worth? (a) Less than a dollar tomorrow (b) The same as a dollar tomorrow (c) More than a dollar tomorrow (d) There is not sufficient information to tell Correct! 16. In an inflationary period, interest rates have a tendency to? (a) Fall (b) Rise (c) Stay the same (d) Act erratically Correct!17. Which of the following is not a determinant of market interest rates? (a) The inflation premium (b) The maturity risk premium (c) The volatility risk premium (d) The real rate of interest Wrong! 18. An unexpected increase in inflation should? (a) Increase the demand for loanable funds (b) Decrease the interest rate on loans (c) Increase the interest rate on loans (d) None of the above Correct! 19. If the interest rate is less than 0%, then a dollar today is worth? (a) More than a dollar tomorrow (b) The same as a dollar tomorrow (c) Less than a dollar tomorrow (d) There is not sufficient information to tell Correct! 20. The risk-free interest rate is composed of? (a) An inflation premium and a default risk premium (b) A default risk premium and a maturity risk premium (c) A real rate of interest and a liquidity premium (d) A real rate of interest and an inflation premium Correct!Level 2: Descriptive Type (10 marks each) 1.“Working capital must be adequate, but at the same time not excessive”. Comment. 2.‘From an account keeper to strategic decision maker – the role of finance manager has undergone a see change during recent times’. Explain. 3. ‘Wealth maximization is an operationally feasible criterion for evaluation of financial decisions’. Comment. 4. Which working capital approach or finance policy do you recommend for profitability-solvency tangle for the company? Comment. 5.“The credit policy of a company is criticized because the bad-debt period has also increased considerably and the collection period has also increased”. Discuss under what conditions this criticism may not be justified. 6. What do you understand by a Capital Structure? What basic principles will you advocate in the matter of deciding on a proper pattern of capital structure for a company? Explain with one illustration. 7. What are the various long-term sources are available to the Indian businessman for raising funds to the business. 8. “Venture capital can provide a tremendous boost to the entrepreneurial activities in the developing countries”. Comment. 9. Compare and contrast the features of equity shares, preference shares and debentures and suggest which is better instrument to finance a new company. 10. What is the difference between primary market and secondary market? Top 4 Sources of Finance (With Formula and Calculations) This article throws light upon the top four sources of finance. The sources are: 1. Cost of Debt 2. Cost of Preference Capital 3. Cost of Equity Share Capital 4. Cost of Retained Earnings. Finance: Source # 1. Cost of Debt: i. Cost Perpetual/Irredeemable Debt:The cost of debt is the rate of interest payable on debt. For example, a company issues Rs. 1,00,000 10% debentures at par; the before-tax cost of this debt issue will also be 10% By way of a formula, beforetax cost of debt may be calculated as: ADVERTISEMENTS: (i) Kdb = I/P where, K db = Before tax cost of debt I = Interest and P = Principal In case the debt is raised at premium or discount, we should consider P as the amount of net proceeds received from the issue and not the face value of securities. The formula may be changed to: (ii) Kdb = I/NP (where, NP= Net Proceeds) Further, when debt is used as a source of finance, the firm saves a considerable amount in payment of tax as interest is allowed as a deductible expense in computation of tax. Hence, the effective cost of debt is reduced. The After-tax cost of debt may be calculated with the help of following formula: (iii) Kda= Kdb(1-t) = I/NP (1-t) where, K da = After-tax cost of debt t = Rate of tax. Illustration 1: (a) X Ltd. issues Rs. 50,000 8% debentures at par. The tax rate applicable to the company is 50%. Compute the cost of debt capital. (b) Y Ltd. issues Rs. 50,000 8% debentures at a premium of 10%. The tax rate applicable to the company is 60%. Compute cost of debt capital.(c) A Ltd. issues Rs. 50,000 8% debentures at a discount of 5%. The tax rate is 50%, Compute the cost of debt capital. (d) B Ltd. issues Rs. 1,00,000 9% debentures at a premium of 10%. The costs of floatation are 2%. The tax rate applicable is 60%. Compute cost of debt-capital. Solution: ii. Cost of Redeemable Debt: Usually, the debt is issued to be redeemed after a certain period during the life time of a firm. Such a debt is known as redeemable debt. The cost of redeemable debt capital may be computed by using yield to maturity, also called internal rate of return or trial and error method. The approximate cost of redeemable debt can also be computed by using the simple shortcut method. (a) Yield to Maturity or Trial and Error Method: (i) Before tax cost of redeemable debt:where, V0 = Current value or the issue price of debt/debenture Vn = Redeemable value of debt I, I2 …In = Amount of annual interest in period 1, 2 ………………… , and so on n = Number of years to redemption kd = Yield to maturity or internal rate of return or cost of debt/debenture The value of kd (yield to maturity) can be found by trial and error method using present value tables. (ii) After tax cost of redeemable debt: kda = kdb(1-t) Where, kdb = After tax cost of debt kdb = Before tax cost of debt t = Tax Rate Illustration 2: A five year Rs. 100 debenture of a firm can be sold for a net price of Rs. 95.90. The coupon rate of interest is 14 per cent per annum, and the debenture will be redeemed at 5 per cent premium on maturity. The firm’s tax rate is 35 per cent. Compute the yield to maturity and the after tax cost of debenture. The present value factors at 15% and 17% per p.a. are as given below: Solution:(b) Shortcut Method to Compute Cost of Redeemable Debt: In order to avoid the complex calculations of hit and trial method, we can compute the approximate cost of redeemable debt by using the following simple formula: (i) Before-tax cost of redeemable debt, where, I = Annual Interest n = Number of years in which debt is to be redeemed RV = Redeemable value of debt NP = Net proceeds of debentures (ii) After-tax cost of redeemable debtWhere, I = Annual interest t = Tax rate n = Number of years in which debt is to be redeemed RV = Redeemable value of debt NP = Net proceeds of debentures Illustration 3: A company issues Rs. 10,00,000 10% redeemable debentures at a discount of 5%. The costs of floatation amount to Rs. 30,000. The debentures are redeemable after 5 years. Calculate before-tax and after-tax cost of debt assuming a tax rate of 50%. Solution: Illustration 4: A 5-year Rs. 100 debenture of a firm can be sold for a net price of Rs. 96.50. The coupon rate of interest is 14 per cent per annum, and the debenture will be redeemed at 5 per cent premium on maturity. The firm’s tax rate is 40 per cent. Compute the after-tax cost of debenture. Solution:Illustration 5: Assuming that a firm pays tax at 50% rate, compute the after tax cost of debt capital in the following cases: (i) A perpetual bond sold at par, coupon rate of interest being 7%; (ii) A 10 year, 8% Rs. 1.000 per bond sold at Rs. 950 less 4% underwriting commission. Solution: iii. Cost of Debt Redeemable in Installments:Financial institutions generally require principal to be amortised in installments. A company may also issue a bond or debenture to be redeemed periodically. In such a case, principal amount is repaid each period instead of a lump sum at maturity and hence cash outflows each period include interest and principal. The amount of interest goes on decreasing each period as it is calculated on the outstanding amount of debt. The before-tax cost of such a debt can be calculated as below: Illustration 6: A company is proposing to issue a 5-year debenture of Rs. 1000 at 14 per cent rate of interest per annum. The debenture amount will be amortised equally over its life. If the present value of the debenture for an investor is Rs. 1046.59, calculate the minimum required rate of return or the cost of debt. Solution: iv. Cost of Existing Debt:If a firm wants to compute the current cost of its existing debt, the current market yield of the debt should be taken into consideration. Suppose a firm has 10% debentures of Rs. 100 each outstanding on January 1, 2006 to be redeemed on December 31, 2012 and the new debentures could be issued at a net realisable price of Rs. 90 in the beginning of 2008, the current cost of existing debt may be computed as: v. Cost of Zero Coupon Bonds: Sometimes companies issue bonds or debentures at a discount from their eventual maturity value and having zero interest rate. No interest is payable on such debentures before their redemption and at the time of redemption the maturity value of the bond is to be paid to the investors. The cost of such debt can be calculated by finding the present values of cash flows as below: (i) Prepare the cash flow table using an arbitrary assumed discount rate to discount the cash flows to the present value. (ii) Find out the net present value by deducting the present value of the outflows from the present value of the inflows. (iii) If the net present value is positive, apply higher rate of discount. (iv) If the higher discount rate still gives a positive net present value, increase the discount rate further until the NPV becomes negative.(v) If the NPV is negative at this higher rate, the cost of debt must be between these two rates. The following illustration explains the procedure of determining the cost of zero coupon bonds. Illustration 7: X Ltd. has issued redeemable zero coupon bonds of Rs. 100 each at a discount rate of Rs. 60 repayable at the end of fourth year. Calculate the cost of debt. Solution: vi. Floating or Variable Rate Debt: The interest on floating rate debt changes depending upon the market rate of interest payable on gilt edged securities or the prime lending rate of the bank. For example, suppose a company raises debt from external sources on the terms of prime lending rate of the bank plus four per cent. If the prime lending rate of the bank is 8% p.a., the company will have to pay interest at the rate of 12% p.a. Further, if the prime lending rate falls to 6% p.a., the company shall pay interest at only 10% p.a. Illustration 8: ABC Ltd. raised a debt of? 50 lakhs on the terms that interest shall be payable at prime lending rate of bank plus three percent. The prime lending rate of the bank is7 per cent. Calculate the cost of debt assuming that the corporate rate of tax is 35%. Solution: vii. Real or Inflation Adjusted Cost of Debt: In the days of inflation, the real cost of debt is much less than the nominal cost as the fixed amount is payable irrespective of the fall in the value of money because of price level changes. The real cost of debt can be calculated as below: Real Cost of Debt = 1 + Nominal Cost of Debt/1 + Inflation Rate Illustration 9: Excel Ltd. has issued 5000 10% Debentures of Rs. 100 each. The rate of inflation is 6%. Calculate the real cost of debt. Solution: Finance: Source # 2. Cost of Preference Capital: A fixed rate of divided is payable on preference shares. Though dividend is payable at the discretion of the Board of directors and there is no legal binding to pay dividend, yet it does not mean that preference capital is cost free. The cost of preference capital is a function of dividend expected by its investors, i.e., its stated dividend. In case dividends are not paid to preference shareholders, it will affect the fund raising capacity of the firm. Hence, dividends are usually paid regularly onpreference shares except when there are no profits to pay dividends. The cost of preference capital which is perpetual can be calculated as: KP = D/P where KP = Cost of Preference Capital D = Annual Preference Dividend P = Preference Share Capital (Proceeds.) Further, if preference shares are issued at Premium or Discount or when costs of floatation are incurred to issue preference shares, the nominal or par value of preference share capital has to be adjusted to find out the net proceeds from the issue of preference shares. In such a case, the cost of preference capital can be computed with the following formula: KP = D/NP It may be noted that as dividends are not allowed to be deducted in computation of tax, no adjustment is required for taxes. Sometimes Redeemable Preference Shares are issued which can be redeemed or cancelled on maturity date. The cost of redeemable preference share capital can be calculated as: where, Kpr = Cost of Redeemable Preference Shares D = Annual Preference Dividend MV = Maturity Value of Preference Shares NP = Net Proceeds of Preference Shares. Illustration 10:A company issues 10,000 10% Preference Shares of Rs. 100 each. Cost of issue is Rs. 2 per share. Calculate cost of preference capital if these shares are issued (a) at par, (b) at a premium of 10%, and (c) at a discount of 5%. Solution: Illustration 11: A company issues 10,000 10% Preference Shares of Rs. 100 each redeemable after 10 years at a premium of 5%. The cost of issue is Rs. 2 per share. Calculate the cost of preference capital. Solution: Illustration 12: A company issues 1,000 7% Preference Shares of Rs. 100 each at a premium of 10% redeemable after 5 years at par. Compute the cost of preference capital. Solution:Finance: Source # 3. Cost of Equity Share Capital: The cost of equity is the ‘maximum rate of return that the company must earn on equity financed portion of its investments in order to leave unchanged the market price of its stock.’ The cost of equity capital is a function of the expected return by its investors. The cost of equity is not the out-of-pocket cost of using equity capital as the equity shareholders are not paid dividend at a fixed rate every year. Moreover, payment of dividend is not a legal binding. It may or may not be paid. But it does not mean that equity share capital is a cost free capital. Shareholders invest money in equity shares on the expectation of getting dividend and the company must earn this minimum rate so that the market price of the shares remains unchanged. Whenever a company wants to raise additional funds by the issue of new equity shares, the expectations of the shareholders have to evaluate. The cost of equity share capital can be computed in the following ways: (a) Dividend Yield Method or Dividend/Price Ratio Method: According to this method, the cost of equity capital is the ‘discount rate that equates the present value of expected future dividends per share with the net proceeds (or current market price) of a share’. Symbolically:Ke = D/NP or D/MP where, Ke = Cost of Equity Capital D = Expected dividend per share NP = Net proceeds per share and MP = Market Price per share. The basic assumptions underlying this method are that the investors give prime importance to dividends and risk in the firm remains unchanged. The dividend price ratio method does not seem to consider the growth in dividend: (i) It does not consider future earnings or retained earnings, and (ii) It does not take into account the capital gains. This method of computing cost of equity capital is suitable only when the company has stable earnings and stable dividend policy over a period of time. Illustration 13: A company issues 1000 equity shares of Rs. 100 each at a premium of 10%. The company has been paying 20% dividend to equity shareholders for the past five years and expects to maintain the same in the future also. Compute the cost of equity capital. Will it make any difference if the market price of equity share is Rs. 160? Solution: (b) Dividend Yield Plus Growth in Dividend Method:When the dividends of the firm are expected to grow at a constant rate and the dividend-pay-out ratio is constant this method may be used to compute the cost of equity capital. According to this method the cost of equity capital is based on the dividends and the growth rate. Further, in case cost of existing equity share capital is to be calculated, the NP should be changed with MP (market price per share) in the above equation. Ke = D1/MP + G Illustration 14: (a) A company plans to issue 1000 new shares of Rs. 100 each at par. The floatation costs are expected to be 5% of the share price. The company pays a dividend of Rs. 10 per share initially and the growth in dividends is expected to be 5%. Compute the cost of new issue of equity shares. (b) If the current market price of an equity share is Rs. 150, calculate the cost of existing equity share capital. Solution: Illustration 15: The shares of a company are selling at Rs. 40 per share and it had paid a dividend of Rs. 4 per share last year. The investor’s market expects a growth rate of 5 per cent per year.(a) Compute the company’s equity cost of capital; (b) If the anticipated growth rate is 7 per cent per annum, calculate the indicated market price per share. Solution: Alternatively: Ke = D1/MP + g Or, MP = D1/Ke – g = 4.28/0.155 – 0.07 = Rs. 50.35 (c) Earning Yield Method/Earning Price Ratio: According to this method, the cost of equity capital is the discount rate that equates the present values of expected future earnings per share with the net proceeds (or, current market price) of a share. Symbolically: Ke = Earnings per share/Net Proceeds = EPS/NP where, the cost of existing capital is to be calculated: Ke = Earnings per share/Market Price per share = EPS/MPThis method of computing cost of equity capital may be employed in the following cases: (i) When the earnings per share are expected to remain constant. (ii) When the dividend pay-out- ratio is 100 per cent or when the retention ratio is zero, i.e., all the available profits are distributed as dividends. (iii) When a firm is expected to earn an amount on new equity shares capital, which is equal to the current rate of earnings. (iv) The market price of the share is influenced only by earnings per share. Illustration 16: A firm is considering an expenditure of Rs. 60 lakhs for expanding its operations. The relevant information is as follows: Compute the cost of existing equity share capital and of new equity capital assuming that new shares will be issued at a price of Rs. 52 per share and the costs of new issue will be Rs. 2 per share. Solution: (d) Realised Yield Method:One of the serious limitations of using dividend yield method or earnings yield method is the problem of estimating the expectations of the investors regarding future dividends and earnings. It is not possible to estimate future dividends and earnings correctly; both of these depend upon so many uncertain factors. To remove this drawback, realised yield method, which takes into account the actual average rate of return realised in the past, may be applied to compute the cost of equity share capital. To calculate the average rate of return realised, dividend received in the past along with the gain realised at the time of sale of shares should be considered. The cost of equity capital is said to be the realised rate of return by the shareholders. This method of computing cost of equity share capital is based upon the following assumptions: (a) The firm will remain in the same risk class over the period; (b) The shareholders’ expectations are based upon the past realised yield; (c) The investors get the same rate of return as the realised yield even if they invest elsewhere; (d) The market price of shares does not change significantly. Finance: Source # 4. Cost of Retained Earnings: It is sometimes argued that retained earnings do not involve any cost because a firm is not required to pay dividends on retained earnings. However, the shareholders expect a return on retained profits. Retained earnings accrue to a firm only because of some sacrifice made by the shareholders in not receiving the dividends out of the available profits.The cost of retained earnings may be considered as the rate of return which the existing shareholders can obtain by investing the after-tax dividends in alternative opportunity of equal qualities. It is, thus, the opportunity cost of dividends foregone by the shareholders. Cost of retained earnings can be computed with the help of following formula: Kr = D1/NP + G or D1/MP + G where, Kr = Cost of retained earnings D = Expected dividend at the end of the year NP = Net proceeds of share issue G = Rate of growth. MP = Market price per share Further, it is important to note that shareholders, usually, cannot obtain the entire amount of retained profits by way of dividends even if there is 100 per cent payout ratio. It is so because the shareholders are required to pay tax on their dividend income. So, some adjustment has to be made for tax. However, tax adjustment in determining the cost of retained earnings is a difficult problem because all shareholders do not fall under the same tax bracket. Moreover, if the shareholders wish to invest their aftertax dividend income in alternative securities, they may have to incur some costs of purchasing the securities, such as brokerage. Hence, the effective rate of return realised by the shareholders from the new investment will be somewhat lesser than their present return from the firm. To make adjustment in the cost of retained earnings for tax and costs of purchasing new securities, the following formula may be adopted:Illustration 17: A firm’s Ke (return available to shareholders) is 15%, the average tax rate of shareholders is 40% and it is expected that 2% is brokerage cost that shareholders will have to pay while investing their dividends in alternative securities. What is the cost of retained earnings? Solution: Supernormal Growth: It dividends of a firm are expected to grow at a supernormal growth rate during the periods when it is experiencing very high demand for its products and then, the dividends grow at a normal rate when the demand reaches the normal level, the constant growth equation [P0 (or MP) = D0 (1+g)/Ke– g] can be suitably modified to calculate the cost of equity. In case, the dividends of a firm are expected to grow at a supernormal growth rate, gs, for n years and then grow at a normal growth rate, gn, till infinity; the cost of equity share can be calculated as: Illustration 18: The equity share of a company is currently selling at Rs. 305.08 and it is currently paying a dividend of Rs. 4.24 per share. The dividend is expected to grow at a 18 percent annual rate for five years and then at 12 per cent forever. Calculate the cost of equity capital. Solution:UNIT V Cost of Capital 5.1 Introduction The cost of capital is an important financial concept. It links the company's long- term decisions with the wealth of the shareholders as determined in the market place. Whenever, a business organization raises funds, it has to keep in mind its cost. Hence computation of cost of capital is very important and finance managers must have a closelook on it. In this unit, we shall discuss the concept, classification, and importance of cost of capital the process of computing cost of capital of individual components, weighted cost of capital, importance of cost of capital and a few misconceptions. 5.2 Meaning and Importance The term cost of capital refers to the minimum rate of return which a firm must earn on its investments so that the market value of the company's equity shares does not fall.5.2.1 Meaning of Cost of Capital Hampton, John defines the term as "the rate of retur n the firm requires from investment in order to increase the value of the firm in the market place". The following are the basic characteristics of cost of capital : i) Cost of capital is a rate of return, It is not a cost as such. ii) This return, however, is calculated on the basis of actual cost of different components of capital. iii) A firm's cost of capital represents minimum rate of return that will result in atleast maintaining (If not increasing) the value of its equity shares. iv) It is related to long term capital funds. v) Cost of capital consists of three components : a) Return at Zero Risk Level. (r0) b) Premium for Business Risk (b) c) Premium for Financial Risk (f) vi) The cost of capital may be put in the form of the following equation : K = ro + b + f Where K = Cost of Capital ro = Return at Zero Risk Level b = Premium for Business Risk f = Premium for Financial RiskA firm's cost of capital has mainly three risks : • Return at Zero Risk Level : This refers to the expected rate of return when a project involves no risk whether business or financial. • Premium for Business Risk : Business risk is possibility where in the firm will not be able to operate successfully in the market. Greater the business risk, the higher will be the cost of capital. • Premium for Financ ial Risk : It refers to the risk on account of pattern of capital structure. In other words, a firm having a higher debt content in its capital structure is more risky as compared to a firm which has a comparatively low debt content. 5.2.2 Importance The determination of the firm's cost of capital is important from the point of view of the following : i) It is the basis of appraising new capital expenditure proposals. This gives the acceptance / rejection criterion for capital expenditure projects. ii) The financ e manager must raise capital from different sources in a way that it optimizes the risk and cost factors. The source of funds which have less cost involve high risk. Cost of capital helps the managers in determining the optimal capital structure. iii) It is the basis for evaluating the financial performance of top management. iv) It helps in formulating appropriate dividend policy.v) It also helps the organization in developing an appropriate working capital policy. 5.3 Classification of Cost of Capital There is no fixed base of classification of cost of capital. It varies according to need, process and purpose. It may be classified as follows : • Explicit Cost and Implicit Cost : Explicit cost is the discount rate that equates the present value of the funds received by the firm net of underwriting costs, with the present value of expected cash outflows. Thus, it is `the rate of return of the cash flows of financing opportunity’. On the other hand, the implicit cost is the rate of return associated with the best investment opportunity for the firm and its shareholders that will be foregone if the project presently under consideration by the firm were accepted . In the other words, explicit cost relate to raising of funds and implicit costs relate to usage of funds. • Average Cost and Marginal Cost : The average cost is the weighted average of the costs of each components of funds. After ascertaining costs of each source of capital, appropriate weights are assigned to each component of capital. Marginal cost of capital is the weighted average cost of new funds raised by the firms. • Future Cost and Historical Cost : In financial decision making, the relevant costs are future costs. Future cost i.e expected cost of funds to finance the projects is ascertained with the help of historical costs.• Specific Cost and Combined Cost : The costs of individual components of capital are specific costs of capital. The combined cost of capital is the average cost of capital as it is inclusive of cost of capital from all sources. In capital budgeting decisions, combined cost of capital is used for accepting / rejecting the proposals. 5.4 Computing Cost of Capital of Individual components There are four basic sources of long term funds for a business firm : (i) Long-term Debt and Debentures (ii) Preferences share capital, (iii) Equity share capital, (iv) Retained Earnings. Through all of these sources may not be tapped by the firm for funding its activities, each firm will have some of these sources in its capital structure.5.4.1 Cost of Long Term Debt Debt may be issued at par, or at premium or at of discount. It may be perpetual or redeemable. The technique of computation of cost in each case has been explained in the following paragraphs. (a) The formula for computing the Cost of Long Term debt at par is Kd = (1 – T) R where Kd = Cost pf long term debt T = Marginal Tax Rate R = Debenture Interest Rate For example, if a company has issued 10% debentures and the tax rate is 50%, the cost of debt will be (1 - .5) 10 = 5%(b) In case the debentures are issued at premium or discount, the cost of debt should be calculated on the basis of net proceeds realised. The formula will be as follows :where IK d = ------ (1 – T) NP Kd = Cost of debt after tax I = Annual Interest Payment NP = Net Proceeds of Loans T = Tax Rate Illustration No. 1 : A company issue 10% irredeemable debentures of Rs. 10,000. The company is in 50% tax bracket. Calculate cost of debt capital at par, at 10% discount and at 10% premium Solution : Rs. 1,000 Cost of debt at par = ----------------- * (1 - .50) Rs. 10,000 = 5% Rs. 1,000 Cost of debt issued at = ----------------- * (1 - .50) 10% discount Rs. 9,000 = 5.55% Rs. 1,000 Cost of debt issued at = ----------------- * (1 - .50) 10% premium Rs. 11,000 = 4.55%(c) For computing cost of redeemble debts, the period of redemption is considered. The cost of long term debt is the investor’s yield to maturity adjusted by the firm’s tax rate plus distribution cost. The question of yield to maturity arises only when the loan is taken either at discount or at premium. The formula for cost of debt will bewhere Disc ount Prem ium I + ------ ------ --- (In case of Prem ium, ------ ------ --- will be subtr acted )mp mp ------ ------ ------ ---- * 100 (1 – T) p + np-----------2mp = maturity period p = nominal or par value np = net proceeds i.e. (Par value – Discount + Premium) Illustration No. 2 : A firm issued 100 10% debentures, each of Rs. 100 at 5% discount. The debentures are to be redeemed at the end of 10th year. The tax rate is 50%. Calculate cost of debt capital. Solution : 500 1,000 + -------- 10 1,050 Cost of Debt Capital = ---------------------- * ------------ * .50 10,000 + 9,500 9,750 ---------------------- 2 = 5.385% Or 10 (1-.50) + (100-95)/10 .………..………………. (As discussed in class) (100 + 95)/2 Activity 2 1. A firm in tends to issue 10,000 10% debentures each of Rs. 10. What is the cost of capital if the firm desires to sell at 5% premium. The tax rate is 50%. 2. A firm issued 10,000, 10% debentures of Rs,. 10 each at a premium of .5% with a maturity period of 20 years. The tax rate is 50%. Find the cost of capital. 3. A company raised loan of Rs. 25,000 by 10% debentures at 10% discount for a periodof ten years, underwriting costs are 3% and tax rate is 50% 5.4.2 Cost of Preference Capital The preference share represents a special type of ownership interest in the firm. Preference shareholders must receive their stated dividends prior to the distribution of any earnings to the equity shareholders. In this respect preference shares are very much like bonds or debentures with fixed interest payment. The cost of preference shares can be estimated by dividing the preference dividend per share by the current price per share, as the dividend can be considered a continuous level payment.Dividend Cost of Preference Capital = --------------------------------- Market Price – Issue Cost For example, A company is planning to issue 9% preference shares expected to sell at Rs. 85 per share. The costs of issuing and selling the shares are expected to be Rs. 3 per share. The first step in finding out the cost of the preference capital is to determine the rupee amount of preference dividends, which are stated as 9% of the share of Rs. 85 per share. Thus 9% of Rs. 85 is Rs. 7.65. After deducting the floatation costs, the net proceeds are Rs. 82 per share. Thus the cost of preference capital : Dividend per share = --------------------------------- Net proceeds after selling Rs. 7.65 = ----------- = 9.33 % Rs. 82 Cost of Reedemable Preference Share as discussed in class 5.4.3 Cost of Equity Capital “Cost of equity capital is the cost of the estimated stream of net capital outlays desired from equity sources” E.W. Walker. James C. Van Horne defines the cost of equity capital can be thought of as therate of discount that equates the present value of all expected future dividends per share, as perceived by investors. The cost of equity capital is the most difficult to measure. A few problems in this regard are as follows : i) The cost of equity is not the out of pocket cost of using equity capital.ii) The cost of equity is based upon the stream of future dividends as expected by shareholders (very difficult to estimate). iii) The relationship between market price with earnings is known. Dividends also affect the market value (which one is to be considered). The following are the approaches to computation of cost of equity capital : (a) E / P Ratio Method : Cost of equity capital is measured by earning price ratio. Symbolically Eo (current earnings per share) ----- * 100 Po (current market price per share) (b) E / P Ratio + Growth Rate Method : This method considers growth in earnings. A period of 3 years is usually being taken into account for growth. The formula will be asfollows : Eo (1 + b) 3 ------------- PoWhere (1 + b) 3 = Growth factor where b is the growth rate as a percentage and estimated for a period of three years. For example, A firm has Rs. 5 EPS and 10% growth rate of earnings over a period of 3 years. The current market price of equity share is Rs. 50 Rs. 5 (1+.10) 3 ------------------ * 100 Rs. 50 Rs. 5 (1.331) 6.655 ------------------ * 100 = --------------- * 100 Rs. 50 50 = 13.31% (c) D / P Ratio Method : Cost of equity capital is measured by dividends price ratio. Symbolically Do (Dividend per share) ----- * 100 Po (Market price per share)If a firm is playing a dividend of 20% on a share with a par value of Rs. 10 as a level perpetual dividend, and its market price is Rs. 20, then D P = -------- Ke 2 20 = -------- Ke 2 Ke = -------- = 10% 20 (d) D / P + Growth Rate Method : The method is comparatively more realistic as i) it considers future growth in dividends, ii) it considers the capital appreciation. Thuswhere, D1 Ke = ------- + g PoPo = the current price of the equity share D1 = the per share dividend expected at the end of year 1. G = the constant annual rate growth in dividends and earnings. The equation indicate that the cost of equity share can be found by dividing the dividend expected at the end of the year 1 by the current price of the share and adding the expected growth rate. (f) Security’s Beta Method : An investor is concerned with the risk of his entire portfolio, and that the relevant risk of a particular security is the effect that the security has on the entire portfolio. By “diversified portfolio” we mean that each investor’s portfolio is representative if the market as a whole and that the portfolio Beta is 1.0. A security’s Beta indicate how closely the security’s returns move with from a diversified portfolio. A beta of 1.0 for a given security means that, if the total value of securities in the market moves up by 10 percent, the stock’s price will also move up, on the average by 10 percent. If security has a beta of 2.0, its price will, on the whole, rises or falls by 20 percent when the market rises or falls by 10 percent. A share with –0.5 percent beta will rises by 10 percent, when the market falls by 20 percent. A beta of any portfolio of securities is the weighted average of the betas of the securities, where the weights are the proportions of investments in each security. Adding a high beta (beta greater than 1.0) security to a diversified portfolio increase the portfolio’s risk, and adding a low beta (beta less than zero) security to a diversified security reduces the portfolio’s risk. How is beta determined ? The beta co-efficient for a security (or asset) can be found by examining security’s historical returns rela tive to the return of the market. As it is, notfeasible to take all securities, a sample of securities is used. The Capital Asset Pricing Model (CAPM) uses these beta co-efficients to estimate the required rate of return on the securities. The CAPM, specifies that the required rate on the share depends upon its beta. The relationship is : Ke = riskless rate + risk premium x betawhere, Ke = expected rate of return. The current rate on government securities can be used as a riskless rate. The difference between the long-run average rate of returns between shares and government securities may represent the risk premium. During 1926-1981, this was estimated in USA to be 6 percent. Beta co-efficient are provided by the published date or can be independently estimated. The beta for Pan Am’s stock was estimated by Value Line to be 0.95 in 1984. Longterm government bond rates were about 12 percent in November 1984. Thus the required rate of return on Pan Am’s stock in November 1984 was – Required Rate = 12% + 6% * 0.95 = 17.7 % The use of beta to measure the cost of equity capital is definitely a better approach. The major reason is that the method incorporates risk analysis, which other methods do not. However, its application remains limited perhaps because it is tedious to calculate Beta value. Activity 3 1. A firm has Rs. 3 EPS and 10% growth rate of earnings over a period of 3 years. The current market price of equity share is Rs. 100. Compute the cost of equity capital. 2. The current dividend paid by the company is Rs. 5 per share, the market price of the equity share is Rs. 100 and the growth rate of dividend is expected to remain constant at 10%. Find out the cost of capital.5.4.4 Cost of Retained Earnings Some authors do not consider it necessary to calculate separately cost of retained earnings. They say that the cost of retained earnings is included in the cost of equity share capital. They say that the existing share price is used to determine cost of equity capital and this price includes the impact of dividends and retained earnings. There are authorities who also suggest that cost of retained earnings is to be determined separately. Two alternative approaches are there : i) One is to regard cost of equity capital as the cost of retained earnings. ii) The concept of external yields as suggested by Ezra Soloman. It assures investment of retained earnings in another firm. Symbolically Cost of Retained Earnings = D1 ( -------- + G ) ( 1 – TR ) (1-B) Powhere = Ke ( 1 – TR) ( 1 – B )Ke = Cost of equity capital based on dividends growth method TR = Shareholder’s Tax Rate B = Percentage Brokerage Cost For example, A firm’s cost of equity capital is 12% and tax rate of majority of shareholders is 30%. Brokerage is 3% = 12% ( 1 – 30% ) ( 1 – 3% ) = 12 * .70 * .97 = 8.15% 5.5 Weighted Cost of Capital Weighted cost of capital is also called as composite cost of capital, overall cost of capital, weighted marginal cost of capital, combined cost of debt and equity etc. It comprises the costs of various components of financing. These components are weighted according to their relative proportions in the total capital. 5.5.1 Choice of Weights The weights to be employed can be book value, market values, historic or target. Book value weights are based on the accounting values to assess the proportion of each type of capital in the firm’s structure. Market value weights measure the proportion of each type of financing at its market value. Market value weights are preferred because they approximate the curre nt value of various instruments of finance employed by the company.Historic weights can be book or market weights based on actual data. Activity 4 1. How is the cost of retained earnings computed ?5.5.2 Calculating The Weighted Cost of Capital : A Few Examples In this subsections, two problems are solved : Illustration No. 8 : A firm has the following capital structure and after tax costs for the different sources of funds used : Source of Funds Amount Rs. Proportion % After tax cost % Debt 40,00,000 20 4.50 Preference Shares 20,00,000 10 9.00 Equity Shares 60,00,000 30 11.00 Retained Earnings 80,00,000 40 10.00 2,00,00,000 100 Calculate cost of weighted capital by using book value method. Solution : Method of Financing Proportion % Cost % Weighted cost Debt 20 4.50 0.90 Preference Shares 10 9.00 0.90 Equity Shares 30 11.00 3.30 Retained Earnings 40 10.00 4.00 9.10%Terms in this set (69) The company cost of capital: A. measures what investors want from the company. B. depends on current profits and cash flows. C. is measured using security book values. D. depends on historical profits and cash flows. A. measures what investors want from the company. Capital structure decisions refer to the: A. dividend yield of the firm's stock. B. blend of equity and debt used by the firm. C. capital gains available on the firm's stock. D. maturity date for the firm's securities. B. blend of equity and debt used by the firm. What appears to be the targeted debt ratio of a firm that issues $15 million in bonds and $35 million in equity to finance its new capital projects? A. 15.00% B. 30.00% C. 35.00% D. 70.00% B. 30.00% Target debt ratio = ($Debt) / ($ Debt + Equty) = 15 / (15+35) = 30% Debt, 70% Equity The company cost of capital for a firm with a 65/35 debt/equity split, 8% cost of debt, 15% cost of equity, and a 35% tax rate would be: A. 7.02%. B. 9.12%. C. 10.45%. D. 13.80%. C. 10.45%. Company cost of capital = Return on Debt x (MV Debt/ Total MV) + Return on Equity x (MV Equity/ Total MV) = (.658%) + (.35 15%) = 10.45% The weighted-average cost of capital, after tax, for a firm with a 65/35 debt/equity split, 8% cost of debt, 15% cost of equity, and a 35% tax rate would be: A. 7.02%. B. 8.63%. C. 10.80%. D. 13.80%. B. 8.63%.WACC = [(D/V) (1-Tax rate) return on debt] + [ (E/V ) * Return on Equity] = (.65 (1-.35) .08) + (.35 * .15) 0.0338 + 0.0525= 0.0863= 8.63% Why is debt financing said to include a tax shield for the company? A. Taxes are reduced by the amount of the debt. B. Taxes are reduced by the amount of the interest. C. Taxable income is reduced by the amount of the debt. D. Taxable income is reduced by the amount of the interest. D. Taxable income is reduced by the amount of the interest. What is the pretax cost of debt for a firm in the 35% tax bracket that has a 10% after-tax cost of debt? A. 5.85% B. 12.15% C. 15.38% D. 25.71% C. 15.38% After-tax cost of debt = pretax cost * (1 -tax rate) 10% = X * (1-.35) .10 = .65x x = 15.38% How much is added to a firm's weighted-average cost of capital for 45% debt financing with a required rate of return of 10% and a tax rate of 35%? A. 1.29% B. 2.93% C. 3.50% D. 4.50% B. 2.93% Component cost of debt = Component % (1-tax rate) Return = .45 (1-.35) .10 = 0.0293 = 2.93% What is the WACC for a firm with 50% debt and 50% equity that pays 12% on its debt, 20% on its equity, and has a 40% tax rate? A. 9.6% B. 12.0% C. 13.6% D. 16.0% C. 13.6% WACC = (.50 12% (1-.40)) + (.50 * 20%) = 3.6% + 10% = 13.6%Company X has 2 million shares of common stock outstanding at a book value of $2.00 per share. The stock trades for $3.00 per share. It also has $2 million in face value of debt that trades at 90% of par. What is its ratio of debt to value for WACC purposes? A. 13.9% B. 23.1% C. 31.0% D. 76.9% B. 23.1% Debt MV= 2*.90 = 1.8 Equity MV = 2 * 3 = 6 Total value = 1.8 + 6 = 7.8 Debt/Value = 1.8 / 7.8 = 0.231 = 23.1% What is the after-tax cost of preferred stock that sells for $10.00 per share and offers a $1.20 dividend when the tax rate is 35%? A. 4.20% B. 7.80% C. 8.33% D. 12.00% D. 12.00% R[preferred] = Div / Purch $ = $1.20 / $10.00 = .12 = 12% What is the WACC for a firm using 55% equity with a required return of 15%, 35% debt with a required return of 8%, 10% preferred stock with a required return of 10%, and a tax rate of 35%? A. 10.72% B. 11.07% C. 11.70% D. 12.05% B. 11.07% WACC = [(.35 8% (1-.35)] + (.5515%) + (.10.10) = 1.82% + 8.25% + 1.00% = 11.07% Should a project be accepted if it offers an annual after-tax cash flow of $1,250,000 indefinitely, costs $10 million, is riskier than the firm's average projects, and the firm uses a 12.5% WACC? A. Yes, since NPV is positive. B. Yes, since a zero NPV indicates marginal acceptability. C. No, since NPV is zero. D. No, since NPV is negative. D. No, since NPV is negative. NPV = CF0 = -10 million CF1 = 1.25 million/12.5% NPV = -10+10 = 0 The 12.5% rate does not reflect the project's greater risk, so NPV is negative.How much will a firm need in cash flow before tax and interest to satisfy debtholders and equityholders if the tax rate is 40%, there is $10 million in common stock requiring a 12% return, and $6 million in bonds requiring an 8% return? A. $1,392,000 B. $1,488,000 C. $2,480,000 D. $2,800,000 C. $2,480,000 After tax CF = 10 million shares x 12% RR = 1.2 million + tax on shares = 40/60 * 1.2 = 800,000 pretax cash flow = 2,000,000 +6 million bonds x 8% interest = 480,000 cash flow before tax and interest = 2,480,000 Reconcile: 2,480,000 -480,000 interest pmts -800,000 taxes = 1,200,000 required How much will a firm need in cash flow before tax and interest to satisfy debtholders and equityholders if the tax rate is 35%, there is $13 million in common stock requiring a 10% return, and $6 million in bonds requiring a 6% return? A. $1,392,000 B. $1,488,000 C. $2,360,000 D. $2,480,000 C. $2,360,000 After tax CF = 13 million shares x 10% = 1.3 million + tax on shares = .35/.65* 1.3 = 700,000 pretax cash flow =2,000,000 +6 million bonds x 6% interest = 360,000 cash flow before tax and interest = 2,360,000 Reconcile: 2,360,000 -360,000 interest pmts -700,000 taxes = 1,300,000 Which of the following statements is incorrect concerning the equity component of the WACC? A. The value of retained earnings is not included. B. Market values should be used in the calculations. C. Preferred equity has a separate component. D. There is a tax shield such as with debt. D. There is a tax shield such as with debt. What will be the effect of using book value of debt in WACC decisions if interest rates have decreased substantially since a firm's long-term bonds were issued? A. The debt-to-value ratio will be overstated. B. The debt-to-value ratio will be understated. C. There will be no effect on WACC decisions.D. It cannot be determined without knowing interest rates. B. The debt-to-value ratio will be understated. MV Equity = 5 million MV Debt = 2 million Value of firm = 7 million D/V = 5/7 = 0.286. if MV Debt = 2.5 million, then MV of firm = 7.5 million then DV = 2.5/7.5 = 0.333 Which component is more likely to be biased if book values are used in the calculation of WACC rather than market values? A. Debt. B. Preferred stock. C. Common stock. D. All categories should be equally biased. C. Common stock. What would you estimate to be the required rate of return for equity investors if a stock sells for $40.00 and will pay a $4.40 dividend that is expected to grow at a constant rate of 5%? A. 7.6% B. 12.0% C. 12.6% D. 16.0% D. 16.0% Requity = (Div1 / P0) +g = (4.4/40) +5% = 11% + 5% = 16% What is the expected growth rate in dividends for a firm in which shareholders require an 18% rate of return and the dividend yield is 10%? A. 1.8% B. 5.2% C. 8.0% D. 28.0% C. 8.0% Requity = (Div1 / P0) +g 18% = 10% + g g = 8% What dividend is paid on preferred stock if investors require a 9% rate of return and the stock has a market value of $54.00 per share and a book value of $50.00 per share? A. $2.92 B. $4.50 C. $4.68 D. $4.86 D. $4.86 RPreferred = Div /Price 9% = Div / $54Div = $4.86 If a firm earns the WACC as an average return on its average-risk assets, then: A. equityholders will be satisfied, but bondholders will not. B. bondholders will be satisfied, but equityholders will not. C. all investors will earn their minimum required rate of return. D. the firm is investing in only positive NPV projects. C. all investors will earn their minimum required rate of return. As debt is added to the capital structure, the: A. WACC will continually decline. B. WACC will continually increase. C. cost of debt can be expected to rise. D. WACC will be unaffected. C. cost of debt can be expected to rise. An implicit cost of increasing the proportion of debt in a firm's capital structure is that: A. the firm's asset beta will increase. B. shareholders will demand a higher rate of return. C. the tax shield will not apply to the added debt. D. the equity-to-value ratio will decrease. B. shareholders will demand a higher rate of return. A firm is considering a project that will generate perpetual cash flows of $50,000 per year beginning next year. The project has the same risk as the firm's overall operations. If the firm's WACC is 12.0%, and its debt-toequity ratio is 1.33, what is the most it could pay for the project and still earn its required rate of return? A. $313,283 B. $375,094 C. $416,667 D. $554,167 C. $416,667 PV perpetuity = CF / RR = 50,000 / .12 = $416,667 With respect to the WACC: A. it is the proper discount rate for everything the company does. B. it is used to value all new projects. C. this benchmark discount rate is adjusted for the riskiness of the project. D. no adjustments need to be made when using it as the discount rate. C. this benchmark discount rate is adjusted for the riskiness of the project. Debt financing is made up of explicit and implicit costs that refer to: A. a higher required ROE and the interest rate bondholders demand, respectively. B. the interest rate bondholders demand and a higher required ROE, respectively. C. the costs of equity and debt, respectively. D. the costs of issuing bonds and the interest rate bondholders demand, respectively. B. the interest rate bondholders demand and a higher required ROE, respectively. Calculate a firm's WACC given that the total value of the firm is $2,000,000, $600,000 of which is debt, the cost of debt and equity is 10% and 15%, respectively, and the firm pays no taxes. A. 9.0% B. 11.5% C. 13.5% D. 14.4% C. 13.5%WACC = .10($600,000/$2,000,000) + .15($1,400,000/$2,000,000) = .10(.3) + .15(.7) = 13.5% A company's CFO wants to maintain a target debt-to-equity ratio of 1/4. If the WACC is 18.6%, and the pretax cost of debt is 9.4%, what is the cost of common equity assuming a tax rate of 34%? A. 19.90% B. 20.90% C. 21.70% D. 22.73% C. 21.70% DV = (1+4) / 5 = 1/5 EV = 4/5 WACC = (DV Rate(d) (1-tax)) + (EV * Rate(e)) 18.6% = (.20 0.094 (1-.34)) +(.80 * Re) 18.6% = 1.24+.80re .80Re = 17.36 Re = 21.70% For a company that pays no corporate taxes, its WACC will be equal to: A. the expected return on it assets. B. the expected return on its debt. C. the total value of its assets. D. the expected return on its equity. A. the expected return on it assets. Which of the following statements is correct for a firm that is 55% debt-financed and the value of equity equals $58 million? A. The firm is valued at approximately $105 million. B. The firm is valued at approximately $129 million. C. The debt is valued at approximately $32 million. D. The debt is valued at approximately $68 million. B. The firm is valued at approximately $129 million. 58 million / .45= value of firm = approx 129 million If a firm has twice as much equity as debt in its capital structure, then the firm has: A. 75.0% debt. B. 66.7% equity. C. 40.0% debt. D. 33.3% equity. B. 66.7% equity. x = % debt, 2x = % equity 3x = 100% = value of firm x = 100/3 = 33.3% = % debt 2x = 33.3*2 = 66.7% = % equity If a firm has three times as much equity as debt in its capital structure, then the firm has: A. 25.0% debt. B. 66.7% equity.C. 40.0% debt. D. 33.3% equity. A. 25.0% debt. x = % debt, 3x = % equity 4x = 100% = value of firm x = 100/4 = 25% = % debt 3x= 25%*2 = 75% = % equity If a company's cost of capital is less than the required return on equity, then the firm: A. is financed with more than 50% debt. B. is perceived to be safe. C. has debt in its capital structure. D. cannot be using any debt. C. has debt in its capital structure. The company cost of capital is the return that is expected on a portfolio of the company's: A. existing securities. B. equity securities. C. debt securities. D. proposed securities. A. existing securities. In general, equity is considered a _____ investment than debt, because payments on debt are _____. A. safer; lower B. safer; less certain C. riskier; guaranteed by the company D. riskier; guaranteed by the federal government C. riskier; guaranteed by the company What is the company cost of capital for a firm financed with 30% debt if the debt requires a 10% return and equity requires a 16% return? A. 11.8% B. 13.3% C. 14.2% D. 14.8% C. 14.2% Rassets = (.310%) + (.716%) = 0.03+0.112 = 14.2% Which of the following changes would tend to increase the company cost of capital for a traditional firm? A. Decrease the proportion of equity financing. B. Increase the market value of the debt. C. Decrease the proportion of debt financing. D. Decrease the market value of the equity. C. Decrease the proportion of debt financing. Using market values rather than book values for cost of capital computations ensures that the firm: A. does not ignore the value of retained earnings. B. gets the full value of the debt tax shield. C. uses expected rates of return. D. will not invest in positive NPV projects. C. uses expected rates of return.How would a company's cost of capital calculated from book values be affected if the company's bonds were selling for more than face value? A. The cost of capital would increase. B. The cost of capital would decrease. C. The cost of capital would not be affected. D. The effect depends on the bonds' coupon rate. B. The cost of capital would decrease. Why is it important to include the tax effect into cost of capital computations for firms with debt financing? A. Firms pay taxes on the outstanding principal amount of the debt. B. Taxable income is reduced by the amount of the interest expense. C. Comparisons with equity financing would otherwise not be possible. D. Taxes are paid on interest but not on dividends. B. Taxable income is reduced by the amount of the interest expense. If the debt is trading at face value, what coupon rate is being paid on debt for a firm with an after-tax cost of debt of 7.5% and a tax rate of 40%? A. 10.5% B. 12.0% C. 12.5% D. 18.75% C. 12.5% 7.50% = before-tax cost * (1 - tax rate) 7.50% = before-tax cost * .60 12.50% = before-tax cost What proportion of a firm is equity financed if the WACC is 14%, the after-tax cost of debt is 7.0%, the tax rate is 35%, and the required return on equity is 18%? A. 54.00% B. 63.64% C. 70.26% D. 77.78% B. 63.64% 14% = (1 - x)(7%) + (x)18% 14% = 7% - (x)7% + (x)18% 7% = (x)11% 63.64% = x What proportion of a firm is equity financed if the WACC is 14%, the before-tax cost of debt is 10.77%, the tax rate is 35%, and the required return on equity is 18%? A. 54.00% B. 63.64% C. 70.26% D. 77.78% B. 63.64% 10.77% * (1 - 35%) = 7% 14% = (1 - x)(7%) + (x)18% 14% = 7% - (x)7% + (x)18% 7% = (x)11% 63.64% = x What is the WACC for a firm with equal amounts of debt and equity financing, a 16% before-tax company cost of capital, a 35% tax rate, and a 10% coupon rate on its debt that is selling at par value?A. 10.40% B. 14.25% C. 15.13% D. 16.00% B. 14.25% Adjustment for tax shield on debt = D/V interest rate paid tax rate = .50 .10 .35 = 1.75% WACC = company cost of capital - adjustment for tax shield on debt WACC = 16% - 1.75% = 14.25% What is the WACC for a firm with equal amounts of debt and equity financing, a 17% before-tax company cost of capital, a 35% tax rate, and a 10% coupon rate on its debt that is selling at par value? A. 10.40% B. 14.25% C. 15.25% D. 16.00% C. 15.25% Adjustment for tax shield on debt = D/V interest rate paid tax rate = .50 .10 .35 = 1.75% WACC = company cost of capital - adjustment for tax shield on debt WACC = 17% - 1.75% = 15.25% A proposed project has a positive NPV when evaluated at the company cost of capital. If the firm employs debt in its capital structure, will the project remain acceptable after evaluation with the WACC? A. Yes, using the WACC will increase the NPV. B. No, using the WACC will decrease the NPV. C. The project may now become unacceptable. D. There will be no change in the project's NPV. A. Yes, using the WACC will increase the NPV. What is the after-tax cost of preferred stock that pays a 12% dividend and sells at par if the firm's tax rate is 35%? A. 7.8% B. 8.5% C. 12.0% D. 16.2% C. 12.0% There is no adjustment for taxes on preferred stock. Therefore, after-tax cost = before-tax cost.What is the WACC for a firm with 40% debt, 20% preferred stock, and 40% equity if the respective costs for these components are 6% after tax, 12% after tax, and 18% before tax? The firm's tax rate is 35%. A. 9.48% B. 11.16% C. 12.00% D. 15.60% C. 12.00% WACC = (.4 .06) + (.2 .12) + (.4 *.18) = .024 + .024 + .072 = 12.0% What is the WACC for a firm with 40% debt, 20% preferred stock, and 40% equity if the respective costs for these components are 9.23% before tax, 12% after tax, and 18% before tax? The firm's tax rate is 35%. A. 9.48% B. 11.16% C. 12.00% D. 15.60% C. 12.00% WACC = [.4 (1 - 35%) .0923] + (.2 .12) + (.4 .18) = .024 + .024 + .072 = 12.0% A project will generate $1 million net cash flow annually in perpetuity. If the project costs $7 million, what is the lowest WACC shown below that will make the NPV negative? A. 10% B. 12% C. 14% D. 16% D. 16% $1 million/.16 = $6.25 million < $7 million Therefore, NPV < $0 At 14%, the NPV is still positive by $142,857. Which of the following changes offer the greatest chance of changing a project's NPV from negative to positive? A. Substituting preferred stock for debt B. Selling the debt at less than par value C. Reducing project risk D. Decreasing the marginal tax rate C. Reducing project risk What decision should be made on a project of above-average risk if the project's IRR exceeds the WACC? A. Accept the project; NPV is positive. B. Reject the project; NPV is negative. C. Decide after discounting at the IRR. D. Decide after discounting at an appropriate rate. D. Decide after discounting at an appropriate rate. If equity investors require a 20% rate of return, what is the maximum acceptable amount of equity financing for a project with $2 million annual cash flows before tax and interest, $3 million in debt with a 10% coupon, and a 35% tax rate? A. $5.53 millionB. $5.87 million C. $8.5 million D. $9.03 million A. $5.53 million Cash flows before tax & interest = 2.0 million - interest payment = 0.3 million pretax cash flow = 1.7 million taxes = 1.7 * .35 = .595 million after tax cash flow = 1.105 million max equity financing = 1.105 / .20 = $5.525 million For purposes of computing the WACC, if the book value of equity exceeds the market value of equity, then: A. the book value of equity should be used. B. the book value of equity less retained earnings should be used. C. the market value of equity should be used. D. the market value of equity less retained earnings should be used. C. the market value of equity should be used. How much cash flow BEFORE tax and interest is necessary to support a project that requires $4 million annually for equity investors and $2 million annually in interest payments if the firm's tax rate is 35%? A. $7.40 million B. $8.10 million C. $8.15 million D. $8.85 million C. $8.15 million Cash flows before tax & interest = 8.15 million - interest payment = 2.0 million pretax cash flow = 6.15 million taxes = 6.15 * .35 = 2.15 million after tax cash flow = 4.00 million What percentage of value should be allocated to equity in WACC computations for a firm with $50 million in debt selling at 85% of par, $50 million in book value of equity, and $65 million in market value of equity? A. 50.0% B. 54.1% C. 56.5% D. 60.5% D. 60.5% 50+65 / (50*.85) +65 = 60.5% According to CAPM estimates, what is the cost of equity for a firm with beta of 1.5 when the risk-free interest rate is 6% and the expected return on the market portfolio is 15%? A. 19.5% B. 21.0% C. 22.5% D. 24.0% A. 19.5% Expected return on stock = 6% + 1.5(15% -6%) = 6 + 13.5 = 19.5%What return on equity do investors seem to expect for a firm with a $55 share price, an expected dividend of $5.50, a beta of .9, and a constant growth rate of 5.5%? A. 9.00% B. 10.00% C. 13.95% D. 15.50% D. 15.50% Requity = (Div/P0) +g = 5.50/55 +5.5% = 10.0% +5.5% = 15.5% Changing the capital structure by adding debt will not: A. increase the return that shareholders require. B. increase default risk. C. decrease debtholder risk. D. increase the cost of debt. C. decrease debtholder risk. XYZ Company issues common stock that is expected to pay a dividend over the next year of $4 at a price of $25 per share. If its expected growth rate is 5%, what is XYZ's cost of common equity? A. 9.0% B. 11.0% C. 16.0% D. 21.0% D. 21.0% Requity = 4/25 + 0.05 = 21.00% Plasti-tech Inc. is financed 60% with equity and 40% with debt. Currently, its debt has a before-tax interest rate of 12%. Plasti-tech's common stock trades at $15.00 per share and its most recent dividend was $1.00. Future dividends are expected to grow by 4%. If the tax rate is 34%, what is Plasti-tech's WACC? A. 7.39% B. 9.57% C. 9.73% D. 11.20% C. 9.73% re = (1(1 + 0.04))/$15) + 0.04 = 10.93% WACC = 0.4[0.12(1 -0.34)] + 0.6(0.1093) = .0317 + .0656 = 9.73% The capital structure for the CR Corporation includes: bonds $5,500 and common stock $11,000. If CR has an after-tax cost of debt of 6%, and a 16% cost of common stock, what is its WACC? A. 9.33% B. 12.67% C. 13.33% D. 14.67% B. 12.67% WACC = [($5,500/$16,500) (0.06)] + [($11,000/$16,500) (0.16)]= .02 + .10667 = 12.67% What is the yield to maturity on Dotte Inc.'s bonds if its after-tax cost of debt is 10% and its tax rate is 35%? A. 6.50% B. 13.50% C. 15.38% D. 16.42% C. 15.38% 0.10 = Rdebt(1 - 0.35) Rdebt= 15.38% Which of the following is not a cost to the firm of increasing debt financing? A. Investors will demand a higher interest rate on debt. B. The risk to common stockholders will increase. C. Stockholders will demand a higher return. D. The cost of common equity will decrease. D. The cost of common equity will decrease. Find the required rate of return for equity investors of a firm with a beta of 1.3 when the risk free rate is 5%, the market risk premium is 5%, and the return on the market is 10%. A. 11.5% B. 13.0% C. 16.5% D. 18.0% A. 11.5% CAPM: Required Rate = 0.05 + 1.30(0.10 -0.05) = 11.5% The present value of a business in the United States will be calculated using all of the following except: A. Weighted-average cost of capital B. Free cash flow for multiple periods C. Some estimated horizon value D. All of these D. All of these Suppose an analyst estimates that free cash flow will be $2.43 million in year 5. What is the present value of this free cash flow if the company cost of capital is 12%, the WACC is 10%, and the equity cost of capital is 15%? A. 1.21 million B. 1.38 million C. 1.51 million D. 2.43 million C. 1.51 million Free cash flow can include: A. dividends. B. coupon payments to bondholders. C. retained earnings. D. all of these. D. all of these.Chapter 17 Does Debt Policy Matter? Answer Key Multiple Choice Questions 1. When a firm has no debt, then such a firm is known as: I) an unlevered firm II) a levered firm III) an all-equity firm A. I only B. II only C. III only D. I and III only Type: Easy 2. Capital structure of the firm can be defined as: I) the firm's debt-equity ratio II) the firm's mix of different securities used to finance assets III) the market imperfection that the firm's manager can exploit A. I only B. II only C. III only D. I, II, and III Type: Easy 3. The total market value (V) of the securities of a firm with both debt (D) and equity (E) is: A. V = D - E B. V = E - D C. V = D * E D. V = D + E Type: Easy 17-20Chapter 17 - Does Debt Policy Matter? 4. If a firm is financed with both debt and equity, the firm's equity is known as: A. unlevered equity B. levered equity C. preferred equity D. none of the above Type: Easy 5. Under what conditions would a policy of maximizing the value of the firm not the same as a policy of maximizing shareholders' wealth? A. If the issue of debt increases the probability of bankruptcy B. If the firm issues debt for the first time C. If the beta of equity is positive D. If an issue of debt affects the market value of existing debt Type: Difficult 6. A policy of maximizing the value of the firm is the same as a policy of maximizing the shareholders' wealth rests on two important assumptions. They are: I) the firm can ignore dividend policy II) the debt equity ratio of the firm does not change III) an issue of new debt does not affect the market value of existing debt A. I only B. II only C. III only D. I and III only Type: Difficult 7. Modigliani and Miller's Proposition I states that: A. The market value of any firm is independent of its capital structure B. The market value of a firm's debt is independent of its capital structure C. The market value of a firm's common stock is independent of its capital structure D. None of the above Type: Difficult 17-21Chapter 17 - Does Debt Policy Matter? 8. An investor can create the effect of leverage on his/her account by: I) buying equity of an unlevered firm II) by investing in risk-free debt like T-bills III) by borrowing on his/her own account A. I only B. II only C. III only D. I and III only Type: Medium 9. If firm U is unlevered and firm L is levered, then which of the following is true: I) VU = EU II) VL = EL + DL III) VL = EU + DL A. I only B. I and II only C. I, II, and III D. III only Type: Medium 10. If an investor buys "a" proportion of an unlevered firm's (firm U) equity then his/her payoff is: A. (a) * (profits) B. (a) * (interest) C. (a) * (profits - interest) D. none of the above Type: Easy 17-22Chapter 17 - Does Debt Policy Matter? 11. If an investor buys "a" proportion of an both debt and equity of a levered firm (firm L) then his/her payoff is: A. (a) * (profits) B. (a) * (interest) C. (a) * (profits - interest) D. none of the above Type: Medium 12. If an investor buys "a" proportion of the equity of a levered firm (firm L) then his/her payoff is: A. (a) * (profits) B. (a) * (interest) C. (a) * (profits - interest) D. none of the above Type: Medium 13. The law of conservation of value implies that: A. The value of a firm's common stock is unchanged when debt is added to its capital structure B. The value of any asset is preserved regardless of the nature of the claims against it C. The value of a firm's debt is unchanged when common stock is added to its capital structure D. None of the above Type: Difficult 17-23Chapter 17 - Does Debt Policy Matter? 14. An investor can undo the effect of leverage on his/her own account by: I) investing in the equity of a levered firm II) by borrowing on his/her own account III) by investing in risk-free debt like T-bills A. I only B. II only C. III only D. I and III above Type: Medium 15. If an individual wanted to borrow with limited liability he/she should: A. Invest in the equity of an unlevered firm B. Borrow on his/her own account C. Invest in the equity of a levered firm D. Invest in a risk-free asset like T-bills Type: Difficult 16. "Value additivity" works for: I) combining assets II) splitting up of assets III) mix of debt securities issued by the firm A. I only B. II only C. I and II only D. I, II, and III Type: Difficult 17-24Chapter 17 - Does Debt Policy Matter? 17. The law of conservation of value implies that: I) the mix of senior and subordinated debt does not affect the value of the firm II) the mix of convertible and non-convertible debt does not affect the value of the firm III) the mix of common stock and preferred stock does not affect the value of the firm A. I only B. II only C. III only D. I, II, and III Type: Medium 18. The law of conservation of value implies that: I) the mix of common stock and preferred stock does not affect the value of the firm II) the mix of long-term and short-term debt does not affect the value of the firm III) the mix of secured and unsecured debt does not affect the value of the firm A. I only B. II only C. III only D. I, II, and III Type: Medium 19. Capital structure is irrelevant if: A. the capital markets are perfect B. each investor holds a fully diversified portfolio C. each investor holds the same proportion of debt and equity of the firm D. all of the above Type: Difficult 17-25Chapter 17 - Does Debt Policy Matter? 20. For a levered firm, A. As earnings before interest and taxes (EBIT) increases, the earnings per share (EPS) increases by the same percent B. As EBIT increases, the EPS increases by a larger percent C. As EBIT increases, the EPS decreases D. None of the above Type: Medium 21. For an all equity firm, A. As earnings before interest and taxes (EBIT) increases, the earnings per share (EPS) increases by the same percent B. As EBIT increases, the EPS increases by a larger percent C. As EBIT increases, the EPS decreases D. None of the above Type: Medium 22. An EPS-Operating Income graph shows the trade-off between financing plans and: I) Greater risk associated with debt financing, which is evidenced by the greater slope II) Their break-even point III) The minimum earnings needed to pay the debt financing for a given level of debt A. I only B. II only C. III only D. I, II, and III only Type: Medium 23. According to EPS-operating income graph, debt financing is preferred if the expected operating income is: A. less than the break-even income B. greater then the break-even income C. equal to the break-even income Type: Medium 17-26Chapter 17 - Does Debt Policy Matter? 24. When comparing levered vs. unlevered capital structures, leverage works to increase EPS for high levels of operating income because: A. Interest payments on the debt vary with EBIT levels B. Interest payments on the debt stay fixed leaving less income to be distributed over fewer shares C. Interest payments on the debt stay fixed, leaving less income to be distributed over more shares D. Interest payments on the debt stay fixed, leaving more income to be distributed over less number of shares Type: Medium 25. In an EPS-Operating Income graphical relationship, the slope of the debt line is steeper than the equity line. The debt line has a negative value for intercept because: A. The break-even point is higher with debt B. A fixed interest charge must be paid even at low earnings C. The amount of interest per share has only a positive effect on the intercept D. The higher the interest rate the greater the slope Type: Difficult 26. The effect of financial leverage on the performance of the firm depends on: A. The rate of return on equity B. The firm's level of operating income C. The current market value of the debt D. The rate of dividend growth Type: Medium 17-27Chapter 17 - Does Debt Policy Matter? 27. Health and Wealth Company is financed entirely by common stock that is priced to offer a 15% expected return. If the company repurchases 25% of the common stock and substitutes an equal value of debt yielding 6%, what is the expected return on the common stock after refinancing? (Ignore taxes.) A. 18% B. 21% C. 15% D. None of the above rE = rA + (D/E)(rA - rD) = 15 + (0.25/0.75)(15 - 6) = 18% Type: Difficult 28. Learn and Earn Company is financed entirely by Common stock that is priced to offer a 20% expected return. If the company repurchases 50% of the stock and substitutes an equal value of debt yielding 8%, what is the expected return on the common stock after refinancing? A. 32% B. 28% C. 20% D. None of the above RE = 0.2 + (0.5/0.5)[0.20 - 0.08] = 0.32 = 32% Type: Difficult17-28Chapter 17 - Does Debt Policy Matter? 29. Wealth and Health Company is financed entirely by common stock that is priced to offer a 15% expected return. The common stock price is $40/share. The earnings per share (EPS) is expected to be $6. If the company repurchases 25% of the common stock and substitutes an equal value of debt yielding 6%, what is the expected value of earnings per share after refinancing? (Ignore taxes.) A. $6.00 B. $7.52 C. $7.20 D. None of the above I = (10)(0.06) = 0.60; new EPS = (6 - 0.60)/0.75 = $7.20/share Type: Difficult 30. Learn and Earn Company is financed entirely by common stock that is priced to offer a 20% expected rate of return. The stock price is $60 and the earnings per share are $12. If the company repurchases 50% of the stock and substitutes an equal value of debt yielding 8%, what is the expected earnings per share value after refinancing? A. $12.00 B. $19.20 C. $24.00 D. None of the above I = 30 (0.08) = $2.40; EPS = [12 - 2.4]/0.5 = $19.20 Type: Difficult 31. MM Proposition II states that: A. The expected return on equity is positively related to leverage B. The required return on equity is a linear function of the firm's debt to equity ratio C. The risk to equity increases with leverage D. All of the above E. None of the above Type: Medium 17-29Chapter 17 - Does Debt Policy Matter? 32. Learn and Earn Company is financed entirely by common stock that is priced to offer a 20% expected rate of return. The stock price is $60 and the earnings per share are $12. The company wishes to repurchase 50% of the stock and substitutes an equal value of debt yielding 8%. Suppose that before refinancing, an investor owned 100 shares of Learn and Earn common stock. What should he do if he wishes to ensure that risk and expected return on his investment are unaffected by refinancing? A. Borrow $3,000 and buy 50 more shares B. Continue to hold 100 shares C. Sell 50 shares and purchase $3,000 debt (bonds) D. None of the above Type: Difficult 33. A firm has zero debt in its capital structure. Its overall cost of capital is 10%. The firm is considering a new capital structure with 60% debt. The interest rate on the debt would be 8%. Assuming there are no taxes its cost of equity capital with the new capital structure would be: A. 8% B. 16% C. 13% D. 10% E. None of the above rE = 10 + (60/40)(10 - 8) = 10 + 3 = 13 Type: Medium 34. The cost of capital for a firm, rWACC, in a tax-free environment is: A. Equal to the expected EBIT divided by market value of the unlevered firm B. Equal to rA, the rate of return for that business risk class C. Equal to the overall rate of return required on the levered firm D. All of the above Type: Medium 17-30Chapter 17 - Does Debt Policy Matter? 35. A firm has a debt-to-equity ratio of 1.0. If it had no debt, its cost of equity would be 12%. Its cost of debt is 9%. What is its cost of equity if there are no taxes? A. 21% B. 18% C. 15% D. 16% rE = 12 + 1.0(12 - 9) = 15% Type: Medium 36. A firm has a debt-to-equity ratio of 0.50. Its cost of debt is 10%. Its overall cost of capital is 14%. What is its cost of equity if there are no taxes? A. 13% B. 16% C. 15% D. 18% 14 = [1/3](10) + (2/3)(X); 42 = 10 + 2X; X = 16% Type: Medium 37. If a firm is unlevered and has a cost of equity capital 9%, what would the cost of equity be if the firms became levered at a debt-equity ratio of 2? The expected cost of debt is 7%. (Assume no taxes.) A. 15.0% B. 16.0% C. 14.5% D. 13% rE = 9 + 2(9 - 7) = 13% Type: Medium 17-31Chapter 17 - Does Debt Policy Matter? 38. A firm has a debt-to-equity ratio of 1. Its (levered) cost of equity is 16%, and its cost of debt is 8%. If there were no taxes, what would be its cost of equity if the debt-to-equity ratio were zero? A. 8% B. 10% C. 12% D. 14% 16 = rA + 1(rA - 8); 16 = 2rA - 8; 24 = 2rA; rA = 12% Type: Medium 39. For a levered firm, beta of equity (bE) is equal to: A. bE = bA B. bE = bA + (D/E) * [bA - bD] C. bE = bA + (D/(D + E)) * [bA - bD] D. None of the above Type: Difficult 40. For a levered firm, return on equity (rE) is equal to: A. rE = rA B. rE = rA + (D/E) * [rA - rB] C. rE = rA + (D/(D + E)) * [rA - rB] D. None of the above Type: Difficult 17-32Chapter 17 - Does Debt Policy Matter? 41. The beta of an all equity firm is 1.2. If the firm changes its capital structure to 50% debt and 50% equity using 8% debt financing, what will be the beta of the levered firm? The beta of debt is 0.2. (Assume no taxes.) A. 1.2 B. 2.2 C. 2.4 D. None of the above βE = 1.2 + (0.5/0.5)(1.2 - 0.2) = 2.2 Type: Medium 42. The equity beta of a levered firm is 1.2. The beta of debt is 0.2. The firm's market value debt to equity ratio is 0.5. What is the asset beta if the tax rate is zero? A. 1.2 B. 0.73 C. 0.2 D. None of the above 1.2 = βA + (0.5)(βA - 0.2); βA = 0. 73 Type: Medium 43. The asset beta of a levered firm is 1.1. The beta of debt is 0.3. If the debt equity ratio is 0.5, what is the equity beta? (Assume no taxes.) A. 1.5 B. 1.1 C. 0.3 D. None of the above bE = 1.1 + 0.5(1.1 - 0.3) = 1.5 Type: Medium 17-33Chapter 17 - Does Debt Policy Matter? 44. Generally, which of the following is true? A. rD > rA > rE B. rE > rD > rA C. rE > rA > rD D. None of the above is true Type: Medium 45. Generally, which of the following is true? (b = beta) A. bD < bA < bE B. bE < bA < bD C. bA < bE < bD D. None of the above is true Type: Medium 46. Generally, which of the following is true? A. rE < rD < rA B. rD < rA < rE C. rE < rA < rD D. None of the above is true Type: Medium 47. Which of the following is true? A. bD > bA > bE B. bE > bA > bD C. bA > bE > bD D. None of the above is true Type: Medium17-34Chapter 17 - Does Debt Policy Matter? 48. The M&M Company is financed by $4 million (market value) in debt and $6 million (market value) in equity. The cost of debt is 5% and the cost of equity is 10%. Calculate the weighted average cost of capital. (Assume no taxes.) A. 10% B. 15% C. 8% D. None of the above Weighted average cost of capital (WACC) = (4/10)(5) + (6/10)(10) = 2 + 6 = 8% Type: Medium 49. The M & M Company is financed by $10 million in debt (market value) and $40 million in equity (market value). The cost of debt is 10% and the cost of equity is 20%. Calculate the weighted average cost of capital assuming no taxes. A. 18% B. 20% C. 10% D. None of the above WACC = (1/5)(10) + (4/5)(20) = 2 + 16 = 18% Type: Medium 50. If beta of debt is zero, then the relationship between equity beta and asset beta is given by: A. equity beta = 1 + [(Beta of assets)/(debt-equity ratio)] B. equity beta = (1 - Debt-equity ratio)(beta of assets) C. equity beta = (1 + Debt-equity ratio)(beta of assets) D. None of the above Type: Medium 17-35Chapter 17 - Does Debt Policy Matter? 51. Minimizing the weighted average cost of capital (WACC) is the same as: A. Maximizing the market value of the firm B. Maximizing the book value of the firm C. Maximizing the profits of the firm D. Maximizing the liquidating value of the firm Type: Medium 52. The after-tax weighted average cost of capital (WACC) is given by: (Corporate tax rate = TC ) A. WACC = (rD)(D/V) + (rE)(E/V) B. WACC = (rD)(D/V) +[(rE )(E/V)/(1 - TC)] C. WACC = [(rD)(D/V) + (rE)(E/V)]/(1 - TC) D. WACC = (rD)(1 - TC)(D/V) + (rE)(E/V) Type: Medium 53. Given the following data for U&P Company: Debt (D) = $100 million; Equity (E) = $300 Million; rD = 6%; rE = 12% and TC = 30%. Calculate the after-tax weighted average cost of capital (WACC): A. 10.5% B. 15% C. 10.05% D. 9.45% After-tax WACC = (1/4)(1 - 0.3)(6) + (3/4)(12) = 10.05% Type: Difficult 17-36Chapter 17 - Does Debt Policy Matter? 54. According to the graph of WACC for Union Pacific, the following is (are) true: I) cost of equity is an increasing function of the debt-equity ratio. II) cost of debt is an increasing function of the debt-equity ratio. III) weighted average cost of capital (WACC) is a decreasing function of the debt-equity ratio. A. I only B. I and II only C. III only D. I, II and III Type: Medium 55. A firm's return on assets is estimated to be 12% and the cost of the firm's debt is 7%. Given a .7 debt to equity ratio, what is the levered cost of equity? A. 7% B. 12% C. 13.6% D. 15.5% Re = .12 + (.12 - .07) × .7 = .155 Type: Medium 56. A firm's equity beta is 1.2 and its debt is risk free. Given a .7 debt to equity ratio, what is the firm's asset beta? A. .7 B. 1.0 C. 1.2 D. 0 Ba = 1.2 × (1/1.7) + 0 × (.7/1.7) = .70 Type: Medium True / False Questions 17-37Chapter 17 - Does Debt Policy Matter? 57. The firm's mix of long-term securities used to finance its assets is called the firm's capital structure. TRUE Type: Medium 58. Value additivity does not hold good when assets are split up. FALSE Type: Difficult 59. The "law of conservation of value" is not applicable to the mix of debt securities. FALSE Type: Medium 60. Modigliani and Miller Proposition I states that the market value of any firm is independent of its capital structure. TRUE Type: Medium 61. According to Modigliani and Miller Proposition II, the rate of return required by the debt holders increases as the firm's debt-equity ratio increases. FALSE Type: Difficult17-38Chapter 17 - Does Debt Policy Matter? 62. Modigliani and Miller Proposition II states that the rate of return required by the shareholders increases, steadily, as the firm's debt-equity ratio increases. TRUE Type: Medium 63. According to Proposition II, the cost of equity increases as more debt is issued, but the weighted average cost of capital remains unchanged. TRUE Type: Medium 64. Financial leverage increases the expected return and risk of the shareholder. TRUE Type: Medium 65. Investors require higher returns on levered equity than on equivalent unlevered equity. TRUE Type: Medium 66. Expected return on assets depends on several factors including the firm's capital structure. FALSE Type: Medium 67. The beta of the firm is equal to the weighted average of the betas on its debt and equity under the assumption of no taxes. TRUEType: Medium 17-39Chapter 17 - Does Debt Policy Matter? 68. Since the expected rate of return on debt is less than the expected rate of return on equity, the weighted average cost of capital declines as more debt is issued. FALSE Type: Medium 69. MM's proposition is violated when the firm, by imaginative design of its capital structure, can offer some financial service that meets the need of such a clientele. TRUE Type: Medium 70. The firm's asset beta is usually higher than the firm's equity beta. FALSE Type: Medium 71. The firm's debt beta is usually approximately 1.0. FALSE Type: Medium Short Answer Questions 72. Explain the concept of arbitrage. In well functioning markets two investments that offer the same payoff must have the same price. Otherwise, investors can buy an asset in one market and simultaneously sell an identical asset in another market at a higher price and make a profit at no cost or risk. Type: Difficult17-40Chapter 17 - Does Debt Policy Matter? 73. State the law of conservation of value. The law of conservation of value states that the value of an asset is preserved regardless of the nature of claims against it. Type: Medium 74. Explain the concept of "value additivity." If we have two streams of cash flow, A and B, the present value of A + B is equal to the present value of A plus the present value of B. The same idea holds good when assets are split up also. Type: Medium 75. Briefly discuss some of the applications of the law of conservation of value. The law of conservation of value can be applied to the choice of various securities issued by a firm. For example, we could apply the law of conservation of value to the choice between issuing preferred stock, common stock, or some combination of the two. The law implies that the choice is irrelevant assuming perfect capital markets and that the choice does not affect the firm's investment, borrowing, and operating policies. The law also applies to the mix of debt securities issued by the firm. The choices of long-term versus short-term, secured versus unsecured, senior versus subordinated, and convertible and nonconvertible debt all should not have any effect on the overall value of the firm. Type: Difficult 17-41Chapter 17 - Does Debt Policy Matter? 76. Briefly explain how EPS-Operating Income analysis helps determine the capital structure of a firm? The plot of EPS - operating income at a specified amount of debt will provide the break-even income. If the firm's income is above the break-even point debt financing is preferred and below that equity financing is preferred. In this method expected level of operating income will determine whether debt financing should be used or equity financing be used. Type: Medium 77. State and explain MM's Proposition II. The expected rate of return on the common stock of a levered firm increases in proportion to the debt-equity ratio, stated in market values. rE = rA + (D/E) * (rA - rD). As the debt-equity ratio increases the cost of equity increases; the cost of debt and the weighted average cost of capital remain constant. This also implies that the beta of the firm's equity also increases in the same manner. Type: Medium 78. Briefly explain how changes in debt-equity ratio impacts on the beta of the firm's equity? There is a linear relationship between the equity beta of a firm and its debt-equity ratio. It is obtained by combining Modigliani-Miller proposition II with the capital asset pricing model (CAPM). The relationship is given by: bE = bA + (D/E)(bA - bD). Many times bD (beta of debt) is zero. Then the relationship is written as: bE = [1 + (D/E)](bA). Type: Difficult 17-42Chapter 17 - Does Debt Policy Matter? 79. Briefly describe the traditional position on capital structure. The traditional view of the debt policy states that moderate amounts of debt increase the expected return on equity, but when the firm borrows too much the expected return on equity declines. The weighted average cost of capital declines initially at low levels of debt and later increases at higher levels of debt. Hence, there is an optimal capital structure for a firm. Type: Medium 80. Under what circumstances would MM's proposition is violated? Briefly discuss. MM's proposition I is violated when the firm, by imaginative design of its capital structure, is able to offer some financial service that meets the needs of a particular clientele. Either the service must be new and unique or the firm must find a way to provide some existing service more cheaply than other firms or financial intermediaries is able to provide. Therefore, smart financial managers look for an unsatisfied clientele, investors who need a particular type of financial instrument but because of market imperfections are unable to get it or get it cheaply. Type: Difficult 81. Discuss a successful example of corporations trying to add value through innovative financing. Citicorp was the first to issue floating rate notes whose interest payments changed with changes in short term interest rates. The success of the issue suggests that Citicorp was able to add value through financing, by meeting an unmet need of the investors. Type: Medium17-43Chapter 17 - Does Debt Policy Matter? 82. State the generalized version of Modigliani-Miller proposition I. Modigliani-Miller proposition I states that changes in capital structure does not affect the value of a firm. MM's proposition I is an extremely general result. Any change in the capital structure of the firm can be duplicated or "undone" by the investors at no cost. The investors need not pay extra for borrowing indirectly (by holding shares in a levered firm) when they can borrow just as easily and cheaply on their own account. It applies equally to trade-offs of any choice of financial instruments. For example, the choice between longterm debt and short-term debt would also not affect the value of the firm. Generally, the choice between issuing preferred stock, common stock, or some combination of the two should not have any effect on the overall value of the firm. It also applies to the mix of debt securities issued by the firm. The choices of longterm versus short-term, secured versus unsecured, senior versus subordinated, and convertible and nonconvertible debt all should not have any effect on the overall value of the firm. Type: Medium 83. Explain why the cost of equity and the cost of debt are concave upward at high levels of debt. As firm's take on higher levels of debt, the risk of default increases. Default risk requires a risk premium for investors. Since the risk of both debt and equity not getting paid increases, the premium also increases. Thus, both issues require an ever increasing risk premium. Question Paper Treasury & Forex Management (MB3H1F) : October 2008 Section A : Basic Concepts (30 Marks) • This section consists of questions with serial number 1 - 30. • Answer all questions. • Each question carries one mark. • Maximum time for answering Section A is 30 Minutes. 1. Which of the following statements is true? (a) Effective rate of interest is always lower than the nominal interest rate (b) The effective rate of interest increases with increase in the frequency of compounding (c) The nominal interest rate increases with increase in the frequency of compounding (d) The effective and nominal interest rates are equal if the frequency of compounding is less than four (e) The frequency of compounding does not affect the effective and nominal interest rates. 2. Rs.1,40,000 was borrowed at an interest rate of 12% per annum. The amount has to be repaid with interest in ten equated annual installments. Each installment is payable at the end of every year. What will be the amount of each installment? (a) Rs.27,225 (b) Rs.26,273 (c) Rs.24,778 (d) Rs.23,469 (e) Rs.22,758.3. A bond with a par value of Rs.3,000 bears coupon rate of 12% and has maturity period of 8 years. If the required rate of return on the bond is 14%, the value of the bond is (a) Rs.2,684.24 (b) Rs.2,721.80 (c) Rs.2,861.45 (d) Rs.2,904.20 (e) Rs.2,986.36. 4. Micro Ltd., is considering investing in a plant requiring outflow of Rs.250 lakh. The plant has an economic life of 5 years. The financial analyst of the company has projected the following cash flows for the project: (Rs. Lakh) Year Cash flow 0 250.00 1 57.50 2 69.50 3 82.10 4 90.20 5 123.68 If the cost of capital for the company is 16%, the discounted pay-back period is approximately (a) 2.58 years (b) 3.36 years (c) 4.25 years (d) 4.79 years (e) 5.00 years. 5. Consider the following data of M/s. Hertz Ltd.: Profit after tax Rs.16.98 lakhs Interest on loan Rs. 9.6 lakhs Non cash charges Rs. 7.5 lakhs Repayment of term loan Rs. 8.4 lakhs Debt-service coverage ratio of the company is (a) 1.72 (b) 1.83 (c) 1.89 (d) 1.98 (e) 2.00. 6. Which of the following ratios measure the long-term solvency of a firm? (a) Liquidity ratios (b) Profitability ratios (c) Earnings ratios (d) Leverage ratios (e) Efficiency ratios. 7. Which of the following reasons of capital expenditure decisions occupy a very important place in corporate finance? I. Once the decision is taken, it has far-reaching consequences which extends over a considerably long period, and influences the risk complexion of the firm. II. These decisions involve huge amount of money. III. These decisions are irreversible in nature. IV. These decisions are difficult to make when the company is faced with various potentially viable investment opportunities.(a) Both (I) and (IV) above (b) Both (II) and (III) above (c) (I), (II) and (IV) above (d) (II), (III) and (IV) above (e) All (I), (II), (III) and (IV) above. 8. The current ratio and quick ratio of Kendra Industries Ltd., are 1.2 and 0.8 respectively. The net working capital of the firm is Rs.6,00,000 with an inventory of (a) Rs. 7.50 lakh (b) Rs. 9.00 lakh (c) Rs.11.25 lakh (d) Rs.12.00 lakh (e) Rs.14.00 lakh. 9. Consider the following rates quoted in forex market: Rs./$: 45.80/82 £/Euro : 0.6940/42 $/£ : 1.7790/92 The synthetic quotes of Rs./Euro are (a) 56.55/56.59 (b) 56.56/56.60 (c) 56.57/56.61 (d) 56.54/56.58 (e) 56.53/56.57. 10. The system under which the exchange rates are determined by the demand and supply position of the currencies in the foreign exchange market is known as (a) Target zone arrangement system (b) Crawling peg system (c) Fixed exchange rate system (d) Floating exchange rate system (e) Currency board system. 11. Which of the following is not a function of EXIM Bank? (a) Lending (b) Guaranteeing (c) Exporting (d) Promotional services (e) Advisory services. 12. Consider the following information about Tide Ltd.: Particulars Rs. Annual consumption of raw material 20,000 Annual cost of production 25,000 Annual cost of sales 1,00,000 Average stock of raw materials 7,500 Average work-in-process 2,000 Assuming 360 days in a year, the average conversion period of the company is (a) 7.2 days (b) 16.0 days (c) 28.8 days(d) 32.4 days (e) 34.2 days. 13. Which of the following statements are true regarding Certificate of Deposits (CDs)? I. CDs can only be subscribed by corporations. II. CDs are issued at a discount to face value. III. CDs are freely transferable by endorsement and delivery. IV. CDs are associated with high amount of default risk. (a) Both (I) and (II) above (b) Both (II) and (III) above (c) Both (III) and (IV) above (d) (II), (III) and (IV) above (e) All (I), (II), (III) and (IV) above. 14. The face value of the equity share of Red Star Ltd., is Rs.100 and the current market price of the share is Rs.80. The company is expected to declare a dividend of 20% during the current year. If the dividends are expected to grow at the rate of 10% p.a., the expected rate of return on the share is (a) 8.0% (b) 12.5% (c) 17.5% (d) 32.0% (e) 37.5%. 15. The following information have been collected about Paradise Ltd.: Total sales Rs.14,00,000 Contribution ratio 25 % Fixed expenses Rs. 1,50,000 12.5% Debentures Rs. 4,00,000 15% Preference shares Rs. 2,00,000 Corporate tax rate 40 % The Degree of Financial Leverage (DFL) for Paradise Ltd., is (a) 1.33 (b) 1.50 (c) 1.67 (d) 2.00 (e) 2.33. 16. A quote expressed in terms of number of units of domestic currency per unit of foreign currency is known as (a) Direct quote (b) Indirect quote (c) American quote (d) European quote (e) Merchant quote. 17. According to the Walter model on dividend policy, if the return on investment of a firm is greater than the cost of equity capital, the value of the firm will be maximized, if the firm (a) Maintains a zero payout ratio (b) Pays out its entire earnings as dividends (c) Retains half of its earnings (d) Pays out more than half of its earnings as dividends(e) Pays out less than half of its earnings as dividends. 18. Capital Indexed Bond is an instrument designed by RBI to minimize which of the following risks? (a) Currency risk (b) Political risk (c) Inflation risk (d) Reinvestment risk (e) Default risk. 19. Fund management, forex management and risk management are the responsibilities of (a) Tax Manager (b) Controller (c) Treasurer (d) Accountant (e) Finance Manager. 20. Stepin Bakers formulates its credit policy on the basis of average days’ sales outstanding (DSO) at the end of every quarter. The monthly sales and outstanding receivables for the year 2008 are as follows: (Rs. Lakh) Month Sales Receivables Month Sales Receivables January 480 1,000 July 500 800 February 540 860 August 550 850 March 550 750 September 600 850 April 400 700 October 500 650 May 450 750 November 600 950 June 450 700 December 600 800 The average collection period in second quarter is (a) 35 days (b) 38 days (c) 44 days (d) 49 days (e) 51 days. 21. Which of the following statements is false? (a) Storage lag represents a cost to the firm (b) The time gap between the sale of goods and collection of cash is known as sales lag (c) Shelf stock refers to items that are stored by the firm and sold with little or no modification to customers (d) Inventories provide a buffer between purchasing, producing and marketing goods (e) Maintaining inventories increases total ordering costs. 22. The average collection period of Delta Ltd., is higher than the credit period extended by it, this indicates that firm I. Has Satisfactory liquidity position. II. Has a Liquidity crunch. III. Has High liquidity. IV. Has to make an effective collection effort. (a) Only (I) above (b) Only (II) above (c) Only (III) above (d) Both (I) and (IV) above(e) Both (II) and (IV) above. 23. Which of the following is not a direct form of finance provided by banks? (a) Cash credit (b) Overdraft (c) Packing credit (d) Letter of credit (e) Discounting of bills. 24. Which of the following statements is/are true? I. Liberalizing credit standards will increase investment in accounts receivables by pushing up sales. II. Shortening the credit period will increase bad debts as customers will not be able to pay within the shorter period. III. A rigorous collection program will bring down sales and increase the percentage of bad debts. IV. A cash discount will increase average collection period and increase bad debts. (a) Only (I) above (b) Only (II) above (c) Only (III) above (d) Only (IV) above (e) Both (III) and (IV) above. 25. A company has retained earnings of Rs.70 lakh and equity capital of Rs.35 lakh. If the equity investors expect a rate of return of 18% and the cost of issuing fresh equity is 7%, the cost of the external equity is (a) 16.42% (b) 17.41% (c) 17.70% (d) 18.16% (e) 19.35%. Gordon Discount Model Hint cost of external equity= D1/net proceeds=18/ (1-.07)=18/0.93=19.35 26. Which of the following is/are reasons for Purchasing Power Parity (PPP) not holding good? I. Constraints on movements of commodities. II. Price index construction. III. Effect of the statistical method employed. (a) Only (I) above (b) Only (III) above (c) Both (I) and (III) above (d) Both (II) and (III) above (e) All (I), (II) and (III) above. 27. Which of the following theories assumes that an identical product or service can be sold in different markets with the same price, provided there are no restrictions on the sales and no transportation costs are involved? (a) The law of one price (b) The Fisher effect (c) Market parity theory (d) Purchasing power parity (e) Efficient Market Theory. 28. Which of the following is true under a currency board system?(a) The interest rates are automatically set by the market mechanism (b) When there is a higher demand for the anchor currency, the reserves with the currency board gets enhanced (c) Lending to either the government or the domestic banks by the currency board is allowed (d) The board can act as the lender of the last resort (e) Exchange rates are unstable. 29. Current account deficit for a country implies that I. Gross domestic investment is greater than gross domestic savings. II. Gross domestic savings are greater than gross domestic investment. III. There is a decline in foreign exchange reserves. (a) Only (I) above (b) Only (II) above (c) Only (III) above (d) Both (I) and (III) above (e) Both (II) and (III) above. 30. Consider the following information relating to Delux Ltd.: Preference dividend Rs. 30,000 Corporate tax rate 40% Interest Rs. 65,000 Fixed expenses Rs.6,00,000 Selling price per unit Rs. 900 Variable cost per unit Rs. 400 The level of output at which the DTL will be undefined is (a) 1,480 units (b) 1,430 units (c) 1,390 units (d) 1,366 units (e) 1,354 units. END OF SECTION A Section B : Problems/Caselet (50 Marks) • This section consists of questions with serial number 1 – 5. • Answer all questions. • Marks are indicated against each question. • Detailed workings/explanations should form part of your answer. • Do not spend more than 110 - 120 minutes on Section B. 1. JayPee Ltd., a construction company is considering 4 projects – P1, P2, P3 and P4 with the following characteristics: (Rs. in Crores) Projects Initial investment (Year 0) Annual net cash flows (Year 1 to 5) P1 (25) 9.5 P2 (6.5) 2.5 P3 (8) 3.5 P4 (9) 4.0 The funds available for investment are limited to Rs.25 crores and the cost of funds to the firm is 12%. You are required to:a. Rank the projects in terms of the NPV and BCR criteria. ( 8 marks) b. Recommend which project(s) should be selected, given the limited availability of funds. ( 2 marks) 2. a. Dataone, in its issue of Flexibonds, offered Growing Interest Bond. The interest will be paid to the investors every year at the rates given below: Year Interest (p.a.) 1 10.50% 2 11.00% 3 12.50% 4 15.25% 5 18.00% You are required to calculate the Yield to Maturity (YTM) of bond assuming that Mr. Brijesh deposited Rs.5,000 on purchasing the bond and holds it till maturity. ( 6 marks) b. Mr. Kiran is planning to invest in the equity stocks of Betavision Ltd. The current share price of Betavision Ltd., is Rs.150 and the company has declared a dividend of Rs.10 per share for the current year. Mr. Kiran is of the opinion that the dividend per share will remain at the same level for the next two years, after which it will grow at the rate of 25% per annum in the third and fourth years. From the fifth year onwards dividends are expected to grow at a normal rate of 12% per annum. If the required rate of return of Mr. Kiran is 14% per annum, you are required to calculate the intrinsic value of the share and suggest Mr. Kiran in purchasing of equity shares of Betavision Ltd. ( 6 marks) 3. Lead Industries, Mumbai imported tanning machines from Holland under an irrevocable letter of credit. The LC negotiating bank forwarded all the shipping documents by courier and obtained reimbursement on 28/08/2008. The bank in Mumbai received the documents on 01/09/ 2008. The bill amount payable was Euro 50,000. The importer had sufficient funds to settle the import bill on 01/09 /2008, but deferred the settlement to the last date i.e. on 11/09/ 2008 by anticipating that the rupee would appreciate. Bank quotes the exchange rate by loading an exchange margin of 0.10%. Commission at the rate of 0.15% was recovered on the bill amount. Interest is recovered at 12%. The spot exchange rates as on 01/09/ 2008 and 11/09/ 2008 are given below: 01/09/ 2008 11/09/ 2008 MumbaiRs. / $ 45.90 / 92 45.96 / 98 London $ / £ 1.8969 / 71 1.8993 / 95 Euro / £ 1.4879 / 81 1.4897 / 99 Note: As per FEDAI rules, sight import bills received under LC are to be retired by the importer on or before 10 days after the date of receipt of the documents by the bank. You are required to calculate: a. The effective exchange rate on 01/09/ 2008. ( 4 marks) b. Gain or Loss to the importer for settling the amount on 11/09/ 2008. ( 3 marks) c. Actual rupee outflow to the importer on the date of settlement. ( 3 marks) Caselet Read the caselet carefully and answer the following questions: 4. Exchange rate is the value of one currency in terms of another and there are many ways in which exchange rate can be determined. Explain the difference between floating exchange rate and fixed exchange rate mechanisms in determining foreign exchange rates in foreign exchange transactions. ( 9 marks) 5. State and explain the advantages of the flexible exchange rate system. ( 9 marks) The world has witnessed many changes and developments – in technology, politics, culture, as well as economics – over the years, and the IMF has adapted itself accordingly. At the time of IMF’s establishment, its policy advice focused mainly on helping members to shape sound macroeconomic and financial policies, within the disciplines of the Breton Woods system of fixed exchange rates. The breakdown of that system in the early 1970s, and the resultant Second Amendment of the IMF’s Articles of Agreement, led to a reorientation of the IMF’s functions. In particular, the revision of Article IV, and the introduction of thesurveillance process, explicitly recognized the close relationship between domestic economic policies and international stability. To this day, this forms the basis for systematic and comprehensive review of economic conditions and policies in each member country. Similarly, the wave of de-colonization that swept the world from the 1950s onwards placed new and complex responsibilities on the Fund. The IMF quickly found that countries looked to it for advice and assistance beyond the traditional macroeconomic areas of fiscal policy, monetary policy, and exchange rate systems. In addition to these subjects, IMF advice and assistance were also sought on establishing the institutions of monetary and fiscal policy, and on supply-side structural policies to help promote sustained growth. In the last fifteen years, following the end of the Cold War, new challenges were created in this regard by the transition of former centrally-planned economies to market-based systems. Through its work in these areas, it also became increasingly clear that structural and institutional issues were important for stability and growth in other member countries too, including the major industrial economies. The area of IMF financing has also seen great transformation. For example, although IMF lending continues to be targeted at short-term balance of payments needs, its financing instruments have, for nearly two decades, included concessional lending for low-income countries. In response to the rapid development of international capital markets as a major source of financing for countries, special IMF financing policies have also been put in place to assist countries facing capital account driven crises. Related to these capital market developments, the Fund also began to play an unanticipated role in facilitating the resolution of sovereign debt problems. This function became critically important following the emergence of the debt crisis in 1982, and it remains so today. All of these changes – ranging from de-colonization and transition, to the rapid development of private international capital flows and new instruments, to the emergence of capital-account driven crises – posed new challenges for the IMF. In many cases, these developments touched upon issues which lay at the frontiers of economic knowledge and research. Addressing them has led to a significant transformation of the Fund, including a broadening of the skills private financial sectors, and more involvement in institutional development in member countries. In the process, the IMF has also become a more open and transparent institution. END OF CASELET END OF SECTION B Section C : Applied Theory (20 Marks) • This section consists of questions with serial number 6 - 7. • Answer all questions. • Marks are indicated against each question. • Do not spend more than 25 -30 minutes on Section C. 6. For running business smoothly, a firm always maintains large number of inventory items. However, it is extremely difficult to monitor information to control each item. In this context, explain the ABC system of inventory management that enables a firm for better control of stock position. Also discuss its advantages and disadvantages. ( 10 marks) 7. Despite all the obvious benefits of international trade, governments have an inclination to put-up trade barriers in order to discourage imports. Discuss the various types of trade barriers that a government can resort to. ( 10 marks) END OF SECTION C END OF QUESTION PAPER Suggested Answers Treasury & Forex Management (MB3H1F) : October 2008 Section A : Basic ConceptsAnswer Reason 1. B The interest rate usually specified on an annual basis in a loan agreement or security is known as the nominal rate of interest. If compounding is done more than once a year, the actual rate of interest paid (or received) is called effective interest rate. Effective interest rate would be higher than the nominal interest rate. The effective rate of interest increases with increase in the frequency of compounding. For example, the effective rate of interest under quarterly compounding will be more than the effective rate of interest under semi-annual compounding. < TOP > 2. C The amount of each installment will be = 24777.88 = 24,778(approx) < TOP > 3. B V = I( + = 360 ( ) + 3000 ( ) = 360 (4.6389) + 3000 (0.3506) = 1670.004 + 1051.80 = 2721.804. < TOP > 4. D Year Cash flow PVIF@16% Present value 0 250.00 1.000 250.00 1 57.50 0.862 49.57 2 69.50 0.743 51.64 3 82.10 0.641 52.63 4 90.20 0.552 49.79 5 123.68 0.476 58.87 < TOP > 5. C Debt service coverage ratio = = = 1.89 < TOP > 6. D Leverage ratios measure the long-term solvency of a firm. Hence (d) is the answer. < TOP > 7. E Capital expenditure decisions occupy a very important place in corporate finance for the following reasons: • Once the decision is taken, it has far-reaching consequences which extend over a considerably long period, and influences the risk complexion of the firm. • These decisions involve huge amounts of money. • These decisions are irreversible once taken. • These decisions are among the most difficult to make when the company is faced with various potentially viable investment opportunities. < TOP > 8. D Given CA/CL = 1.2 and (CA – Inventory)/CL = 0.8 Net working capital = CA – CL = Rs.6,00,000 1.2 CL – CL = 6,00,000 CL = Rs.30,00,000 CA = 1.2 x 30,00,000 = Rs.36,00,000 Now, (36,00,000 – Inventory)/30,00,000 = 0.8 36,00,000 – Inventory = 0.8 x 30,00,000 = 24,00,000 Inventory = Rs.12,00,000.< TOP > 9. A (Rs./Euro)bid = (Rs./$)bid ´ ($/£)bid ´ (£/Euro)bid = 45.80 ´ 1.7790 ´ 0.6940 = 56.55 (Rs./Euro)ask = (Rs./$)ask ´ ($/£)ask ´ (£/Euro)ask= 45.82 ´ 1.7792 ´ 0.6942 = 56.59 Rs./Euro= 56.55/59. < TOP > 10. D The exchange rates under floating exchange rate system are determined by the demand and supply position for the currencies in the foreign exchange market. a) When a group of countries form together and agree to maintain the exchange rates between the currencies within a certain band around fixed central exchange rates, then it is called a target zone arrangement. b) A crawling peg system is a hybrid of fixed and flexible exchange rate system. Under this system, while the value of a currency is fixed in terms of a reference currency, this peg itself keeps changing in accordance with the underlying economic fundamentals. c) Under fixed exchange rate system, the value of a currency in terms of another is fixed and it is determined by Governments or Central banks of the respective countries. e) Under a currency board system, a country fixes the rate of its domestic currency in terms of a foreign currency and its exchange rate in terms of other currencies depends on the < TOP > 11. C Barring export all are functions of EXIM Bank. < TOP > 12. C Average conversion period = Average daily cost of production = = Rs.69.44 \ Average conversion period = = 28.8 days. < TOP > 13. B CDs are available for subscription for individuals, corporations, companies, trusts, Funds, Association, etc., Statement (I) is false. CDs are issued at a discount to face value. Statement (II) is true. CDs are freely transferable by endorsement and delivery. Statement (III) is true. CDs are considered as virtually risk less instruments as the default risk is almost nil, and investors are sure of receiving the invested amount with interest. Statement (IV) is false. Hence (b) is the correct answer. < TOP > 14. E We know, P0 = Where, P0 = Current market price ke = Expected rate of return g = Growth rate in dividends D1 = Dividend at the end of one year. The above equation can be rewritten as: ke = Putting the values for the variables we get: ke = = = 0.375 i.e., 37.5% Hence (e) is the correct answer. < TOP > 15. D Amount of contribution = Rs.14,00,000 ´ 25 percent = Rs.3,50,000. EBIT = Rs.3,50,000 – Rs.1,50,000 = Rs.2,00,000 Interest on debentures = Rs.4,00,000 ´ 12.50 percent = Rs.50,000 Preference Dividends = Rs.2,00,000 ´ 15 percent = Rs.30,000. So, the degree of financial leverage (DFL) will be: DFL = = = 2.00 The degree of financial leverage (DFL) = 2.00 < TOP > 16. A A quote expressed in terms of number of units of domestic currency per unit of foreign currency is known as direct quote. < TOP > 17. A As per Walter ModelP0 = Where, the notations are in their standard use. As the given return on investment (r) > cost of equity (k) the value of the firm will be maximized if the firm does not pay dividends, i.e. maintains a zero payout ratio. < TOP > 18. C Capital Indexed Bond is an instrument designed by RBI to minimize inflation risk < TOP > 19. C Fund management, forex management and risk management are the responsibilities of Treasurer. < TOP > 20. E = 51 days. < TOP > 21. E Storage lag is the time lapsed between the production of goods and their sale. It represents a cost to the firm. Statement (I) is true. The time lapsed between the sale of goods and collection of cash is known as sale lag. Statement (II) is true. Shelf stock refers to items that are stored by the firm and sold with little or no modification to customers. Statement (III) is true. Inventories provide a buffer between purchasing, producing and marketing goods. Statement (IV) is true. Inventories reduce order costs. Statement (V) is not true. Hence (e) is the answer. < TOP > 22. E If the average collection period is found to be consistently higher than the net credit period extended by the company to its customers, then the firm is supposed to have a liquidity crunch. In such a situation, the collection effort has to be made more effective as cash is locked up for a period more than what is warranted by the credit terms extended. < TOP > 23. D Under the letter of credit (LC) arrangement credit is provided by the supplier but the risk is assumed by the bank which opens the LC. Hence it is an indirect form of financing. < TOP > 24. A Liberalizing credit standards will increase investment in receivable while pushing up sales Shortening the credit period will tend to lower sales, as customers decrease investment in receivables, and reduce the incidence of bad debts loss. Rigorous collection program will bring down sales and the amount of receivables and bad debt losses will reduce to a certain extent. A cash discount will decrease the average collection period and will also decrease bad debt losses < TOP > 25. E < TOP > 26. E There are three major reasons for purchasing power parity not holding good: I. Constraints on movements of commodities. II. Price index construction. III. Effect of the statistical method employed. < TOP > 27. A The law of one price assumes that an identical product or service can be sold in different markets with the same price, where there are no restrictions on the sales and no transportation costs. < TOP > 28. A In the currency board system, the board does not have any discretionary powers over the monetary policy; the interest rates are automatically set by the market mechanism. Options (b), (c), (d) and (e) are not true. < TOP > 29. A Current account deficit for a country indicates that gross domestic investment is greater than gross domestic savings. < TOP >30. B The point at which DTL is undefined is called the overall break-even point. At this point the quantity produced can be computed as: Q= , Hence Q = = 1,430 units.Type: Difficult Question Paper Financial Management - II (142) : January 2005 • Answer all questions. • Marks are indicated against each question. 1. A firm’s credit policy consists of which of the following items? (a) Credit period, cash discounts, credit standards, receivables monitoring (b) Credit period, cash discounts, credit standards, collection policy (c) Credit period, cash discounts, receivables monitoring, collection policy (d) Cash discounts, credit standards, receivables monitoring, collection policy (e) Credit period, receivables monitoring, credit standards, collection policy. (1 mark)< Answer > 2. Protective covenants are (a) To protect employees (b) To protect the interests of the company (c) To protect shareholders (d) To protect bondholders (e) To protect customers. (1 mark)< Answer > 3. Which of the following is not an assumption underlying the Modigliani and Miller approach to capital structure? (a) Information is freely available to investors (b) The transaction cost is constant irrespective of the value of the transactions in securities (c) Firms can be divided into classes in such a way that all the firms falling within one class have the same degree of business risk (d) There is no corporate or personal income tax (e) Investors make rational investment decisions. (1 mark)< Answer > 4. The basic EOQ model makes a number of assumptions, including (a) Fluctuating demand (b) Uncertain lead times (c) Zero lead-time (d) Uncertain carrying cost (d) Variable ordering cost. (1 mark)< Answer > 5. All of the following are examples of tax deductible expenses, except (a) Dividends on common shares (b) Interest payments (c) Amortization charges (d) Sales and administrative expenses (e) Salaries and wages paid. (1 mark)< Answer > 6. Which of the following is true with respect to the term ‘capital structure’? (a) It is the mix of long term finances used by the firm (b) It is the manner, in which a firm obtains its long term sources of funding (c) It is the length of time needed to collect the accounts receivable (d) It is the proportion of funds, the firm should invest in long term and short term assets (e) It is the way, in which the company uses the capital at its disposal. (1 mark)< Answer >7. "Capacity," which is one of the traditional "five C's" of credit analysis, refers to (a) The ability of the supplier of the company to extend the credit period offered to the company (b) The willingness of the potential customer to meet his financial obligations (c) The ability of the company to collect receivables from its customers (d) The ability of the potential customer to meet his financial obligations (e) The ability of the company to increase its sales. (1 mark)< Answer > 8. The least expensive form of financing for the firm is (a) Existing common stock (b) Preferred stock (c) Debenture (d) New common stock (e) Retained earnings. (1 mark)< Answer > 9. The earnings-price ratio approach is used for estimating the cost of (a) Debenture capital (b) Preference capital (c) Equity capital (d) Term loan (e) Fixed deposits. (1 mark)< Answer > 10. Which of the following means of financing does not need any collateral security? (a) Cash credit from a private sector bank (b) Overdraft from a public sector bank (c) Cash credit from a co-operative bank (d) Public deposit (e) Term loan from a financial institution. (1 mark)< Answer > 11. Shelf stock refers to (a) Items that are stored by the firm and sold with little or no modification to customers (b) Items that are sold with a major modification to customers (c) Items that are stored by the firm and are not sold at all (d) Items that lost their value and sold as scraps (e) Items that are stored and sold by the firm on installment basis. (1 mark)< Answer > 12. Which of the following is not the assumption of Walter model on dividend policy? (a) Firm has an infinite life (b) Internal rate of return (r) and Cost of capital (k) are assumed to be constant and thus additional investment made by the firm will not change its risk and return profile (c) Retained earning are the only source of finance available to the firm (d) The retention ratio remains constant and hence the growth rate also is constant (e) For a given value of the firm, the dividend per share and the earning per share remain constant. (1 mark)< Answer > 13. Agency costs in the context of capital structure of firms represent the (a) Increase in the cost of production due to the increase in the cost of inputs (b) Increase in the sales commission payable to the sales agents (c) Increase in financial costs due to the rise in interest rates (d) Restrictive conditions imposed by the financial institutions for providing loan to the firm (e) Regulatory requirements to be met by the firm with regard to its human resources. (1 mark)< Answer > 14. Which of the following types of current assets is most likely to be absent in a firm, which undertakes trading business only? (a) Inventory of finished goods (b) Cash (c) Receivables (d) Work-in-process (e) Prepaid expenses. (1 mark)< Answer > 15. The equity investors expect a minimum rate of return on their investment basedI. On the perception of the risk they are undertaking. II. On the company’s past performance. III. On the return they are getting from similar companies. (a) Only (I) above (b) Only (III) above (c) Both (I) and (II) above(d) Both (II) and (III) above (e) All (I), (II) and (III) above. (1 mark)< Answer > 16. Which of the following is/are useful in monitoring both the status and composition of a firm's accounts receivable? I. Days Sales Outstanding. II. Ageing Schedule. III. Collection Matrix. (a) Only (I) above (b) Only (II) above (c) Only (III) above (d) Both (I) and (II) above (e) Both (II) and (III) above. (1 mark)< Answer > 17. Which of the following is true with regard to supplier’s line of credit? (a) It is similar to the letter of credit issued by banks (b) It is the deferred credit facility offered by the suppliers of machineries (c) It is a credit facility offered by the banks to meet the working capital requirements (d) It is an interest free credit offered by the government to promote industrial development in the backward areas (e) It is a credit facility offered by the financial institutions to meet the working capital requirements. (1 mark)< Answer > 18. “Shareholder’s wealth” in a firm is represented by (a) The number of people employed in the firm (b) The book value of the firm’s assets less the book value of its liabilities (c) The amount of salary paid to its employees (d) The market price per share of the firm’s common stock (e) The intrinsic value per share of the firm’s common stock. (1 mark)< Answer > 19. On the basis of Walter’s model on dividend policy, which of the following will logically follow, if the internal rate of return of the firm increases, other things remaining the same, assuming that the dividend payout ratio is less than 100%? (a) The market price per equity share will increase (b) The market price per equity share will decrease (c) The market price per equity share will remain unchanged (d) The return on the retained earnings decreases (e) The return on the retained earnings will remain unchanged. (1 mark)< Answer > 20. Retained earnings are I. An indication of a company’s liquidity. II. The same as cash in the bank. III. Not important while determining dividends. IV. The cumulative earnings of the company after dividends. (a) Only (I) above (b) Only (II) above (c) Only (IV) above (d) Both (I) and (IV) above (e) (I), (III) and (IV) above. (1 mark)< Answer > 21. Overtrading means (a) The firm has disproportionately high amount of working capital with respect to the level of sales(b) The firm has disproportionately low amount of working capital with respect to the level of sales (c) The firm has disproportionately high level of receivables with respect to total assets (d) The firm has disproportionately high level of cash with respect to total assets (e) The firm has been experiencing high turnover of manpower. (1 mark)< Answer > 22. Which of the following would result in an increase in the debt-to-equity ratio? (Assume there are no flotation costs). (a) A firm issues common stock and uses the proceeds to repurchase an equal amount of preferred stock (b) A firm issues preferred stock and uses the proceeds to repurchase an equal amount of bonds (c) A firm with positive additions to retained earnings uses the cash it generates to retire the existing debt (d) A firm uses excess cash to repurchase common stock in an amount equal to additions to retained earnings for the year (e) A firm issues bonds and uses the proceeds to purchase short-term assets. (1 mark)< Answer > 23. Which of the following are subsystems of the inventory management system? I. EOQ subsystem. II. Stock-level subsystem. III. Reorder point subsystem. IV. Safety-stock subsystem. (a) Only (I) above (b) Only (IV) above (c) Both (I) and (IV) above (d) (I), (II) and (III) above (e) All (I), (II), (III) and (IV) above. (1 mark)< Answer > 24. The average collection period measures the (a) Number of days between the day a customer places an order with the firm and the day the firm sends the goods to the customers (b) Number of days it takes a typical cheque to "clear" through the banking system (c) Number of days beyond the end of the credit period and before a typical customer payment is received (d) Number of days between the day a typical credit sale is made and the day a typical account becomes delinquent (e) Number of days between the day when a typical credit sale is made and the day when the firm receives the payment. (1 mark)< Answer > 25. ___________ is used, while evaluating mutually exclusive investments having unequal lives. (a) Equivalent annual annuities method (b) Net present value method (c) Internal rate of return method (d) Accounting rate of return method (e) Discounted payback period method. (1 mark)< Answer > 26. Lead time refers to (a) Work in process time (b) The time gap between placing of the order and procuring the material (c) The period in which a whole lot of inventory is consumed (d) The time finished goods lie as inventories (e) The time gap between two orders. (1 mark)< Answer > 27. The _______ measures the present value return for each rupee of initial investment. (a) Payback period (b) Internal rate of return (c) Net present value (d) Profitability index (e) Accounting rate of return. (1 mark)< Answer >28. Which of the following statements is/are true with respect to cash management? I. A cash management system, which minimizes collection float and maximizes payment float is better than the one with higher collection float and lower payment float. II. A cash management system, which maximizes collection float and minimizes payment float is better than the one with lower collection float and higher payment float. III. If interest rates are increasing; it should be a cause of concern for a finance manager to review his cash management system. (a) Only (I) above (b) Only (II) above (c) Only (III) above (d) Both (I) and (III) above (e) Both (II) and (III) above. (1 mark)< Answer > 29. VED analysis with respect to inventory management is for (a) Monitoring and control of stores and spare parts (b) Monitoring and control of finished goods (c) Monitoring and control of work in process (d) Monitoring and control of production process (e) Monitoring and control of raw materials. (1 mark)< Answer > 30. Which of the following sources of long-term finance arises out of the operations of a profit making business? (a) Preference capital (b) Equity capital (c) Debenture capital (d) Term loan (e) Reserves and surplus. (1 mark)< Answer > 31. If the net present value of a project is negative, (a) The internal rate of return is less than the required return (b) The internal rate of return is more than the required return (c) The internal rate of return is equal to the required return (d) The internal rate of return is less than 0 (e) The internal rate of return is 1+ required return. (1 mark)< Answer > 32. The discount rate that equates the present value of cash flows with the initial outlay is called (a) The net present value (b) The internal rate of return (c) The sum of the present value of cash flows (d) The terminal value of the cash flows (e) The profitability index. (1 mark)< Answer > 33. Which of the following is/are true regarding cumulative preference shares? I. They enjoy a right to participate in surplus profits after equity dividends have been paid. II. They are eligible to get all the arrears of preference dividends before any equity dividend is declared. III. In case there are arrears in dividends on these shares for two or more years, the shareholders will be entitled to voting rights. (a) Only (II) above (b) Only (III) above (c) Both (I) and (II) above(d) Both (I) and (III) above (e) Both (II) and (III) above. (1 mark)< Answer > 34. According to Gordon with respect to dividend policy of a firm, the growth rate of a firm is a product of its (a) Dividend pay out ratio and return on equity(b) Dividend pay out ratio and return on investment (c) Retention ratio and return on investment (d) Retention ratio and return on equity (e) Retention ratio and cost of debt. (1 mark)< Answer > 35. As a general rule, the capital structure that maximizes the market value of a company also (a) Maximizes its average cost of capital (b) Maximizes its earnings per share (c) Maximizes the chance of bankruptcy (d) Minimizes the cost of capital of the company (e) Minimizes the cost of debt capital of the company. (1 mark)< Answer > 36. The advantages of the payback approach include all of the following except (a) It is easy to compute (b) It considers a project's liquidity (c) It considers cash flows, not net income (d) It provides an objective measure of profitability (e) It helps in weeding out risky projects. (1 mark)< Answer > 37. All of the following influence capital budgeting cash flows except __________. (a) Choice of depreciation method for tax purposes (b) Economic length of the project (c) Projected sales (revenues) for the project (d) Sunk costs of the project (e) Opportunity cost of the project. (1 mark)< Answer > 38. Which of the following is a feature of secured premium note (SPN)? (a) It is a kind of non-convertible debenture with an attached warrant (b) It allows the investors to subscribe to the equity of a third firm at a preferential price via-a-vis the market price (c) It is a partly convertible debenture with an attached warrant (d) It is also known as zero coupon convertible note (e) It is an example of a perpetual preference share. (1 mark)< Answer > 39. Which of the following might be attributed to efficient inventory management? I. High inventory turnover ratio. II. Low incidence of production schedule disruptions. III. Low total asset turnover. (a) Only (I) above (b) Only (III) above (c) Both (I) and (II) above(d) Both (I) and (III) above (e) Both (II) and (III) above. (1 mark)< Answer > 40. If the current ratio is less than one, it signifies that I. Net working capital is positive. II. Current assets are more than current liabilities. III. There is a possibility of technical insolvency. (a) Only (I) above (b) Only (II) above (c) Only (III) above (d) Both (I) and (III) above (e) All (I), (II) and (III) above. (1 mark)< Answer >41. Kunwar Ajay Sarees, a popular Indian name in the field of sarees, presently has the annual sales of Rs.100 crore with the credit terms of 1/10, net 30 days. Average collection period of the company is 25 days. It has been observed that fifty percent of the customers in terms of sales revenue avail of the cash discount incentive. The company is contemplating of liberalizing its existing credit terms to 2/10, net 30 days. As a result, sales are likely to increase by Rs.15 crore and average collection period to decline to 15 days. Eighty percent of the customers in terms of sales revenue are expected to avail of the cash discount incentive under liberalization scheme. If the contribution to sales ratio is 20% and the cost of funds to the company is 12%, the total incremental cost to the company due to this collection relaxation program is (Assume 360 days in a year) (a) Rs.106.7 lakh (b) Rs.111.1 lakh (c) Rs.114.2 lakh (d) Rs.129.0 lakh (e) Rs.134.0 lakh. (3 marks) < Answer > 42. Tyco’s business is booming and it needs to raise more capital. The company purchases raw materials from a single supplier on terms of 1/10, net 20 days, and it currently takes the discount. One way of getting the needed funds would be to forgo the discount and Tyco’s owner believes that he could delay payment to 40 days without adverse effects. What is the annual rate of stretching the accounts payable? (Assume 365 days in a year) (a) 10.00% (b) 11.11% (c) 11.75% (d ) 12.29% (e) 13.01%. (1 mark) < Answer > 43. Solana Ltd. follows a policy of fixed dividend payout of 80%. The earning per share for the year 2003- 2004 is Rs.4.50 per share and the same is expected to grow by 20% during the year 2004-2005. The firm earns a return of 18% on its investments. The cost of equity of the company is 15%. The value of the share based on Gorden model would be (approximately) (a) Rs.31.58 (b) Rs.33.85 (c) Rs.35.75 (d) Rs.39.55 (e) Rs.40.00. (1 mark)< Answer > 44. A company has retained earnings of Rs.72 lakh and paid up equity capital of Rs.38 lakh. If the equity investors expect a rate of return of 17% and the cost of issuing fresh equity is 6%, the cost of the retained earnings to the company is (a) 16.4% (b) 17.0% (c) 17.7% (d) 18.1% (e) 19.1%. (1 mark) < Answer > 45. Consider the following information: Rs. Annual consumption of raw material 20,000 Annual cost of production 25,000 Annual cost of sales 1,00,000 Average stock of raw materials 7,500 Average work-in-process 2,000 The average conversion period is (a) 7.2 days (b) 16.0 days (c) 28.8 days (d) 32.4 days (e) 34.2 days. (1 mark) < Answer > 46. Kapur industries places order each time for a lot of 500 units of a particular item. From the available data, the following results are obtained: Inventory carrying cost 40% Ordering cost per order Rs.625 Cost per unit Rs.50 Annual demand 1000 units What is the loss to the organization due to its ordering policy? (a) Rs.1,200 (b) Rs.1,250 (c) Rs.1,400 (d) Rs.1,500 (e) Rs.1,600. (2 marks) < Answer > 47. Calculate the inventory turnover ratio from the following dataParticulars Rs. Sales15,00,000 Purchases 9,66,750 Opening inventory 2,28,750 Closing inventory 2,95,500 (a) 0.17 times (b) 0.29 times (c) 2.28 times (d) 3.43 times (e) 6.72 times. (1 mark) < Answer > 48. LISP Inc. is planning to purchase a new mixer/dubber for Rs.50,000. The new equipment will replace an older mixer that has been fully depreciated but has a market value of Rs.5,000. Compute the net investment required for this project. Assume a marginal tax rate of 40 percent. (a) Rs.43,000 (b) Rs.45,000 (c) Rs.46,000 (d) Rs.47,000 (e) Rs.48,000. (2 marks) < Answer > 49. The following information is given for a project: Year 0 1 2 3 Initial Investment (Rs.) 2,10,000 Net Cash Inflows (Rs.) 30,000 45,000 75,000 Assuming that salvage value at the end of the 3rd year is zero, the accounting rate of return for the project is (a) 59.96% (b) 54.56% (c) 47.62% (d) 43.56% (e) 39.80%. (1 mark) < Answer > 50. Vijaya Dairy Products, located in Gurgaon, receives large remittances from its customers in New Delhi and Jaipur. If the firm deposits these cheques in its local bank, two business days are required for the cheques to clear and the funds to become usable by the firm. However, if it sends an employee to New Delhi or Jaipur and presents the check for payment at the bank upon which it is drawn, the funds are available immediately to the firm. The firm can earn 8% per annum on short-term investments and the cost of sending an employee to New Delhi or Jaipur to present the check for payment is Rs.500. What is the net benefit to the firm of employing this special handling technique for a Rs.50 lakh cheque received on Tuesday from New Delhi (assume 365 days in a year)? (a) Rs.226 (b) Rs.596 (c) Rs.1,096 (d) Rs.1,192 (e) Rs.1,692. (2 marks) < Answer > 51. Miraj Engineering Co. has planned its sales during Oct-Dec 2004 as follows: Month October November December Sales (Rs.) 5,00,000 6,00,000 6,50,000 The products are sold on credit where 50 percent is realized in the month of sale whereas the balance is recovered by the next month. The purchases (amounting to 50% of the month’s sales) are paid in the following month of purchase. Wages and administrative expenses per month amount to Rs.1,50,000 and Rs.80,000 respectively and are paid in the following month in which they are incurred. Depreciation and amortization of preliminary expenses amount to Rs.80,000 and Rs.50,000 respectively. On October 1, a testing equipment worth of Rs.20,000 has been procured with a credit period of 45 days, while on December 31, a fixed deposit will mature (maturity value Rs.1,50,000). If the cash balance at the end of October is Rs.1,00,000, the closing cash balance by the end of the month of November is (a) Rs.20,000 (b) Rs.1,50,000 (c) Rs.2,10,000 (d) Rs.2,20,000 (e) Rs.3,00,000. (3 marks) < Answer > 52. As per the records of Mittal group of companies the following information is available: Total assets Rs.1200 crore Return on assets 15% Cost of equity capital 12% The total market value of the equity of Mittal group of companies as per net income approach is (a) Rs.1,200 crore (b) Rs.1,500 crore (c) Rs.1,800 crore (d) Rs.2,000 crore (e) Rs.2,700 crore. (1 mark) < Answer >53. Subha Enterprises had sales last year of Rs.7,00,000 and 35 percent of its sales are for cash, with the remainder buying on terms of net 30 days. It is following 365 day in a year accounting policy. If the receivables conversion period is actually 38 days, Subha’s accounts receivable are (a) Rs.25,507 (b) Rs.47,370 (c) Rs.55,507 (d) Rs.72,877 (e) Rs.97,370. (2 marks) < Answer > 54. The following details are available regarding the long term sources of finance of M/s. VK Ltd.: Source of finance Range of new financing from the source (Rs. crore) Cost % Equity 0 – 10 14 10 – 20 15 20 & above 16 Preference 0 – 2 13 2 & above 14 Debt 0 – 12 8 12 – 18 9 18 & above 10 The company is considering expanding its operations and requires Rs.50 crore for the same. It is planning to raise in the following proportions: Equity shares 0.4 Debt 0.4 Preference shares 0.2 The weighted marginal cost of capital of new financing in the range of Rs.25 crore – 30 crore is (a) 11.4% (b) 12.0% (c) 12.8% (d) 13.0% (e) 13.2%. (3 marks) < Answer > 55. A firm is presently following EOQ system. The minimum order size stipulated by the supplier is 9000 units for utilizing a cash discount on the purchase price. The annual usage of raw materials is 1,80,000 units, its EOQ is 7,200 units and the cost per order is Rs.100. If the company decides to utilize cash discount, saving in the total ordering cost will be (a) Rs.1,000 (b) Rs.800 (c) Rs.600 (d) Rs.500 (e) Rs.400. (1 mark) < Answer > 56. Radhika Oil Mill is planning for its cash to be maintained during the month of August. The manager has analysed the daily cash outgo for the month of June. Ten largest daily cash outflows are as follows: Date 3rd June 7th June 10th June 12th June 15th June 16th June 18th June 22nd June 26th June 28th June Cash outflow (Rs.) 55,000 40,000 35,000 48,000 23,000 68,000 42,000 33,000 58,000 29,000 It is expected that the pattern of cash outflows in the month of August will remain same as that of the month of June but the magnitude of cash outflows will be 20% more. If the finance manager desires sufficient cash to cover payments of 4 peak days during the month, the safety level of cash to be maintained in the month of August would be (a) Rs.1,72,400 (b) Rs.2,06,880 (c) Rs.2,29,000 (d) Rs.2,74,800 (e) Rs.3,29,760. (2 marks) < Answer >57. Deccan Paints Ltd. had 10 lakh equity shares outstanding at the beginning of July 2004 and these shares were traded in NSE at Rs.150 each. The rate of capitalization appropriate to the risk class to which the firm belongs is 12%. The net income for the year is Rs.2 crore and the investment budget is Rs.4 crore. Assume that no dividend is declared and the additional fund requirement is financed by new issue of equity shares. If Modigliani-Miller hypothesis holds good, the number of equity shares to be issued by the company is (a) 1,09,048 (b) 1,09,248 (c) 1,19,048 (d) 1,19,248 (e) 1,29,348. (2 marks) < Answer > 58. The following figures are extracted from the Books of Lee Vee Enterprises: Profit after tax Rs.30 crore Number of shares outstanding 4 crore P/E ratio 7.2 The total market value of the equity of Lee Vee Enterprises is (a) Rs.120 crore (b) Rs.210 crore (c) Rs.216 crore (d) Rs.220 crore (e) Rs.226 crore. (1 mark) < Answer > 59. The following information regarding the equity shares of M/s. Venus Ltd. is given: Market price per share Rs.17.00 DPS Rs. 3.00 Multiplier 3.40 According to the traditional approach to the dividend policy, the EPS for M/s. Venus Ltd., is (a) Rs.2 (b) Rs.4 (c) Rs.6 (d) Rs.8 (e) Rs.10. (1 mark) < Answer > 60. Consider the following information on sales figure for a firm: Actual Sales (Rs.) Forecasted Sales (Rs.) November 2004 15,65,000 January 2005 20,50,000 December 2004 18,50,000 February 2005 21,00,000 March 2005 19,00,000 April 2005 23,50,000 May 2005 22,75,000 June 2005 19,00,000 • Cash and credit sales are expected to be 20% and 80% respectively. • Receivables from credit sales are expected to be collected as follows: 60% of receivables, on an average, one month from the date of sale and balance 40% of receivables, on an average, two months from the date of sale • Miscellaneous cash purchases of Rs.5000 per month are planned from January to June 2005. • Rs.12,000 is expected from the sale of a machine in February 2005. Total cash receipts forecast for February 2005 would be (a) Rs.18,97,500(b) Rs.19,32,600(c) Rs.20,08,000 (d) Rs.21,42,000 (e) Rs.22,12,000. (2 marks) < Answer > 61. The average daily usage rates of an inventory, lead time and their respective probabilities are as follows: Daily Usage Rate (in units) Probability Lead time (in days)Probability 150 360 450 0.20 0.50 0.30 20 35 – 0.60 0.40 – The possible usage levels at which stock-outs can occur and the probability of stock-out respectively are(a) 3,000 units, 5,250 units and 7,200 units and 50% (b) 5,250 units, 7,200 units and 9,000 units and 56% (c) 9,000 units, 12,600 units and 15,750 units and 50% (d) 5,250 units, 9,000 units and 12,600 units and 46% (e) 7,200 units, 9,000 units and 12,600 units and 68%. (3 marks) < Answer > 62. Ignoring the time value of money, how much does a firm lose on a Rs.5,000 sale that has a 30% profit margin and a 25% probability of default, when the default actually occurs? (a) Rs.875 (b) Rs.1,250 (c) Rs.2,625 (d) Rs.3,500 (e) Rs.5,000. (1 mark) < Answer > 63. Consider the following data regarding a product: Total cost of ordering and carrying inventory Rs.4,00,000 Quantity per order 20,000 units Carrying cost 20% of the purchase price Fixed cost per order Rs.1,000 Purchase price Rs.100. The annual usage of the materials in units is (a) 5 lakh (b) 10 lakh (c) 15 lakh (d) 25 lakh (e) 40 lakh. (2 marks) < Answer > 64. Decisions-Decisions Inc. is evaluating three potential projects. Given the information in the table below, the fact that the firm can invest no more than Rs.30 million and the cost of capital is 10%, the firm should invest in: Year Projects (Rs. in millions) 1 2 3 0 -15-14 -27 1 24 38 65 2 45 60 90 NPV 44.01 70.13 106.47 (a) Only project 1 (b) Only project 3 (c) Projects 1 and 2 (d) Projects 1 and 3 (e) Projects 2 and 3. (1 mark) < Answer > 65. If a project is expected to increase inventory by Rs.15,000, increase accounts payable by Rs.10,000 and decrease accounts receivable by Rs.1,000, what effect does working capital have during the life of the project? (a) Increases investment by Rs.4,000 (b) Increases investment by Rs.5,000 (c) Increases investment by Rs.6,000 (d) Increase investment by Rs.4,500 (e) Working capital has no effect during the life of the project. (1 mark) < Answer > 66. For a profitable firm in 35% marginal tax bracket with Rs.1,00,000 of annual depreciation expense, the depreciation tax shield would be (a) Rs.10,500 (b) Rs.30,000 (c) Rs.35,000 (d) Rs.65,000 (e) Rs.45,000. (1 mark) < Answer > 67. All Advantage Ltd. writes cheques averaging Rs.15,000 a day and it takes 5 days for these cheques to clear. The firm also receives cheques in the amount of Rs.17,000 per day, but the firm loses three days, while its receipts are being deposited and cleared. The firm's net float is (a) Rs.16,000 (b) Rs.24,000 (c) Rs.32,000 (d) Rs.75,000 (e) Rs.1,26,000. (1 mark) < Answer >68. The following information regarding material ‘VIP’ has been collected from the stores register of Sunny Products Ltd. Opening stock 100 units @ Rs.9 per unit Purchases: September 3 50 units @ Rs.12 per unit September 15 150 units @ Rs.15 per unit If 100 units were issued on September 25, according to the weighted average method of pricing, the value of the issue was (a) Rs.900 (b) Rs.1,050 (c) Rs.1,200 (d) Rs.1,250 (e) Rs.1,500. (2 marks) < Answer > 69. The market value of debt and equity of a firm are Rs.80 lakh and Rs.120 lakh and the costs of equity and debt are 16% and 14% respectively. Assuming the firm follows 100% dividend payout ratio and there is no income tax, corporate or personal, the net operating income for the firm is (a) Rs.27.2 lakh (b) Rs.28.4 lakh (c) Rs.30.4 lakh (d) Rs.31.6 lakh (e) Rs.32.4 lakh. (2 marks) < Answer > 70. Consider the following data: Raw-material storage period 50 days Average stock of raw materials Rs.6,51,000 Average balance of trade creditors Rs.2,65,000 Assume 360 days in a year and all purchases are made on credit If the closing stock of raw-materials is 10% higher than the opening stock of raw-materials, the average payment period is (a) 15 days (b) 18 days (c) 20 days (d) 25 days (e) 30 days. (2 marks) < Answer > 71. Average Daily Usage (Units) Probability Lead Time (No. of days) Probability 600 0.6 4 0.3 800 0.4 6 0.7 Normal consumption during lead time will be (a) 1,776 units (b) 2,720 units (c) 3,672 units (d) 4,080 units (e) 4,800 units. (1 mark) < Answer > 72. The following information relates to the sources of long term finance used by Pioneer Industries Ltd.: • Source • Book value • (Rs. in lakh) • Market value • (Rs. in lakh) • Paid-up equity share capital • 200 • 400 • Reserves and surplus • 400 • – • Preference shares • 150 • 159 • Debentures• 250 • 241 Cost of equity share capital = 19.25% Cost of preference share capital = 12.19% Post tax cost of debenture capital = 8% The difference between the weighted average cost using book value weights and market value weights would be (a) 0.52% (b) 0.77% (c) 0.92% (d) 1.23% (e) 1.50%. (2 marks) < Answer > 73. The following figures are collected from annual reports of Hyderabad Textiles: 2003 (in Rs. 000) 2004 (in Rs.000)Raw materials inventory – Closing Balance Work in process inventory – Closing Balance Purchases of raw materials during the year Manufacturing expenses during the year Depreciation 180 25 1085 1165 75 212 45 1192 1280 100 What should be the average conversion period of Hyderabad Textiles for the year 2004? (Assume 360 days in a year) (a) 3 days (b) 5 days (c) 7 days (d) 9 days (e) 11 days. (2 marks) < Answer > 74. Two companies ZED Ltd. and Que Ltd. operate in a same industry and belong to the same group of companies. Both are identical in every respect, except that Zed Ltd. uses debt, while Que Ltd. does not. The levered company has Rs.5,00,000 debentures carrying 10% rate of interest. The cost of capital and the EBIT of both firms are 15% and Rs.4,00,000 respectively. Both the companies pay tax at 40%. The total value of Zed Ltd. and Que Ltd. as per MM approach would be (a) Rs.28,00,000(b) Rs.34,00,000(c) Rs.37,00,000 (d) Rs.40,00,000 (e) Rs.58,33,000. (2 marks) < Answer > 75. Vega India Ltd. is planning to purchase a punching machine having the following details: Cost of machine Rs.30,00,000 Annual cost of operations Rs.2,50,000 for the first four years Rs.3,00,000 for the subsequent years Useful life 10 years The annual capital charge of the machine at a cost of capital of 10 percent is (a) Rs.7,62,082 (b) Rs.7,62,182 (c) Rs.7,62,382 (d) Rs.7,62,582 (e) Rs.7,62,782. (2 marks) < Answer > 76. The wealth ratio for the year 2002, 2003, and 2004 are 1.12, 1.26 and 1.4 respectively. The realized yield would be (a) 21% (b) 23.65% (c) 24.91% (d) 25.48% (e) 26.59%. (1 mark) < Answer > 77. Your firm buys on credit terms of 2/10, net 45 days and it always pays on the 45th day. If you calculate that this policy effectively costs your firm Rs.1,59,621 each year, the firm’s average accounts payable balance is (Assume 365 days in a year) (a) Rs.12,340 (b) Rs.75,000 (c) Rs.1,57,500 (d) Rs.6,25,000 (e) Rs.7,50,000. (1 mark)< Answer > END OF THE QUESTION PAPER Suggested Answers Financial Management - II (142) : January 2005 1. Answer : (b) Reason : A firm’s credit policy consists of credit period, cash discounts, credit standards, collection policy. < TOP >2. Answer : (d) Reason : Protective covenants are used to protect the interest of the bond holders. Hence, alternative (d) is correct. < TOP > 3. Answer : (b) Reason : The MM approach to capital structure assumes that (i) information is freely available to all the investors and there are no transaction costs and all securities are infinitely divisible (ii) firms can be classified in such a way that firms falling within a class have the same degree of business risk (iii) there are no corporate or personal income taxes (iv) investors make rational investment decisions and that there are no transaction costs. < TOP > 4. Answer : (c) Reason : The basic EOQ model makes the following assumptions: i. Constant or unform demand ii. Constant unit price iii. Constant carrying costs iv. Constant ordering costs v. Instantaneous delivery (Zero lead time) vi. Independent orders. Among the given alternatives, instantaneous delivery (zero lead time) is the correct choice. Hence, (c) is the answer. < TOP > 5. Answer : (a) Reason : Dividends on common shares are not tax deductible expenses. All the other mentioned items are tax-deductible expenses. Hence, alternative (a) is correct. < TOP > 6. Answer : (a) Reason : Capital structure refers to the composition of a firm’s long term financing consisting of equity, preference and long term debt. The other alternatives are not best suited to define capital structure. Hence, the correct answer is (a). < TOP > 7. Answer : (d) Reason : ‘Capacity’ in credit analysis refers to the ability of the potential customer to meet his financial obligations. < TOP > 8. Answer : (c) Reason : The debt capital is the cheapest source of financing but it should be used within reasonable limits. < TOP > 9. Answer : (c) Reason : In this case, earnings and price represents the equity earnings and equity prices respectively and hence earnings-price ratio approach is used to estimate the cost of equity capital, not the other types of capitals as mentioned in other alternatives. < TOP > 10. Answer : (d) Reason : Public deposit may be raised by a company by duly following certain norms as per the Companies Act. 1956 without the requirement of any collateral security. While in the other cases, security is to be provided compulsorily. < TOP > 11. Answer : (a) Reason : Shelf stock refers to items that are stored by the firm and sold with little or no modification to customers. < TOP > 12. Answer : (d)Reason : The retention ratio remains constant and hence the growth rate also is constant, this is the assumption of Gordon’s dividend capitalization model not Walter model. All other are the assumptions of Walter model. < TOP > 13. Answer : (d) Reason : In many business entities, the ownership is separated from the management of the company, thereby resulting in agency problems. It does not have any influence on the manufacturing, selling and financial expenses, as well as to meet the several regulatory requirements in order to carry out the business. But considering the safety and security, the lenders generally put some restrictive covenants like, further borrowings, payment of dividends, appointment of the key persons, etc. The implications of these restrictions on the operations are known as agency costs. < TOP > 14. Answer : (d) Reason : A firm which undertakes trading business only will not have work-in-process (d) because work-in-process arises in the context of manufacturing firms. However such a firm will have the finished goods inventory (a), cash (b), receivables (c), if it sells goods on credit and prepaid expenses, if it pays for some services like insurance in advance. < TOP > 15. Answer : (e) Reason : The equity investors expect a minimum return on their investment based on the risk they are undertaking, the company’s past performance and the return they are getting from similar companies they have invested in. So, the correct answer is (e). < TOP > 16. Answer : (b) Reason : DSO tells us about the number of days of sales that is outstanding. It conveys no information about the composition of the accounts receivable. Collection Matrix tells us about the collection pattern of receivables. Ageing schedule not only conveys information about the magnitude of accounts receivables, it also tells us about the age of the accounts receivable. < TOP > 17. Answer : (b) Reason : Through letter of credit (L/C), a bank stands as a guarantee for the buyer to honor the payment obligation. A bank generally disburses funds in the form of cash credit, overdraft, key credit, etc. to finance the working capital requirements of any company. If any business entity cannot afford to pay the purchase price of machinery in lump sum, it may buy the same in installments spread over a period of time; this type of scheme is known as deferred credit facility (also known as supplier’s line of credit), offered by the supplier of machinery. < TOP > 18. Answer : (d) Reason : “Shareholder’s wealth” in a firm is the market price per share of the firm’s common stock not the intrinsic value. Alternative (a) and (c) are no way related to the shareholders wealth. Alternative (b) is not also true. Hence, alternative (d) is the correct. < TOP > 19. Answer : (a) Reason : According to Walter’s model on dividend policy – P = + Given : D < E In the above equation if ‘r’ (internal rate of return) increases then the market price per share increases. < TOP > 20. Answer : (c) Reason : Retained earning are the cumulative earnings of the company after the payment of dividend. All other points are not true in respect of retained earnings. Hence, alternative (c) is the correct choice. < TOP > 21. Answer : (b)Reason : Overtrading means that the firm has disproportionately low level of working capital with respect to the level of sales. To define it as a state in which the firm has disproportionately high level of working capital with respect to sales or a disproportionately high level of receivables with respect to total assets or a disproportionately high level of cash with respect to total assets or low turnover of working capital is incorrect. < TOP > 22. Answer : (e) Reason : If a firm issues bonds and uses the proceeds to purchase short-term assets, the debt equity ratio will increase, for all the other alternatives the debt equity ratio will decrease or remain same. < TOP > 23. Answer : (d) Reason : Subsystems of inventory management system are: i. EOQ subsystem ii. Stock-level subsystem iii. Reorder point subsystem Hence, alternative (d) is the answer. < TOP > 24. Answer : (e) Reason : The average collection period measures the number of days between when a typical credit sale is made and when the firm receives the payment. < TOP > 25. Answer : (a) Reason : Equivalent annual annuities method is used, while evaluating mutually exclusive investments having unequal lives. < TOP > 26. Answer : (b) Reason : The time gap between placing an order and procuring the material is called the lead time. < TOP > 27. Answer : (d) Reason : The profitability index measures the present value return for each rupee of initial investment. < TOP > 28. Answer : (d) Reason : Net float = Payments float – Collections float; therefore the larger the payments float and the lower the collections float the better the cash management system. If interest rates are increasing, it increases the opportunity cost of idle cash and hence should be a cause of concern for a finance manager. So both the statements (I) and (III) are correct. Hence, answer is (d). < TOP > 29. Answer : (a) Reason : VED analysis is for monitoring and control of stores and spare parts.< TOP > 30. Answer : (e) Reason : Preference capital (a) equity capital (b), debenture capital (c) and term loan (d) are all longterm sources of funds which are tapped from outside the firm. Reserves and surplus (e) represent retained earnings, which are generated out of profits of the firm, and they are available to the firm over the long-term. < TOP > 31. Answer : (a) Reason : If the net present value of a project is negative, the internal rate of return is less than the required return. < TOP > 32. Answer : (b) Reason : The discount rate that equates the present value of cash flows with the initial outlay is called. The internal rate of return. < TOP >33. Answer : (e) Reason : For cumulative preference shares, the dividends will be paid on a cumulative basis; In case they remain unpaid in any financial year due to insufficient profits, the company will have to pay all the arrears of preference dividends before declaring any equity dividends. Hence statement II is correct. According to Companies Act, 1956, the cumulative preference shareholders will be entitled to voting rights, if there are arrears in dividends for two or more years. Hence statement III is correct and (e) is the answer. The holder of cumulative preference shares is entitled to receive dividends and any arrears in dividends but they do not have any right to participate in the surplus profits. Hence, I is not true. < TOP > 34. Answer : (c) Reason : The model assumes that retained earnings are the only source of finance available and return on investment is constant throughout the life of the firm. So the growth rate is the multiple of retained earnings and return on investment. So, the correct answer would be (c). < TOP > 35. Answer : (d) Reason : In general when cost of capital of the company is minimum, market value of the firm is maximum. < TOP > 36. Answer : (d) Reason : The payback approach does not provide an objective measure of profitability. < TOP > 37. Answer : (d ) Reason : Choice of depreciation method for tax purposes ,economic length of the project, projected sales (revenues) for the project and opportunity cost of the project all influence the capital budgeting cash flows. But the sunk cost doesn’t influences the capital budgeting cash flows. < TOP > 38. Answer : (a) Reason : Secured premium note is a kind of non-convertible debenture with an attached warrant. The warrant attached to the SPN gives the holder the right to apply for and get allotment of equity shares. Hence, option (a) is the correct choice. < TOP > 39. Answer : (c) Reason : High inventory turnover ratio, low incidence of production schedule disruptions, and high total asset turnover all can be attributed to efficient inventory management. Hence, alternative (c) is the answer. < TOP > 40. Answer : (c) Reason : Current ratio = Net working capital = Current Assets – Current Liabilities From the above equations, the following can be interpreted: (i) Net working capital is negative (ii) Current assets are less than current liabilities (iii) There is a possibility of technical insolvency. < TOP > 41. Answer: (a) Reason: Existing cost of carrying receivables = Cost of carrying receivables after liberalization = Saving in the cost of carrying receivables = 0.833 – 0.5 = Rs.0.333 crore…………….(A) The cost of funds invested in the receivables arising out of new sales = crore ………(B) Amount of discount presently paid = Rs.100 ´ 0.01 ´ 0.5 = Rs.0.5 crore Amount of discount payable after liberalization= 115 ´ 0.02 ´ 0.80 = Rs.1.84 crore The additional amount of discount payable = 1.84 – 0.50 = Rs.1.34 crore…………(C) Thus the total incremental cost = B + C – A = 0.06 + 1.34 – 0.333 = Rs.1.067 crore < TOP > 42. Answer : (d) Reason : Cost of Credit = (1/99)(365/(40 – 10)) = 12.29%. < TOP > 43. Answer : (a) Reason : Retention ratio of the firm =1- pay out ratio =1-0.80 =0.20 According to the Gordon model, the expected value of the share is = =3.6/0.114 =Rs.31.58. < TOP > 44. Answer : (b) Reason : Retained earnings are the amount due to equity holder which has not been paid to them. Therefore, the cost of retained earnings will be equal to expected return of equity holder. And as there is no cost of issue involved, it will be 17%. < TOP > 45. Answer : (c) Reason : Average conversion period = Average daily cost of production = = Rs.69.44 \ Average conversion period = = 28.8 days. Hence option (c) is the correct choice. < TOP > 46. Answer : (b) Reason : EOQ = = (2x1000x625/20)1/2 = 250 units. Evaluation of ordering policies Existing EOQ Total requirement (units) 1000 1000 Units per order 500 250 Number of orders 2 4 Average inventory (units ) 250 125 Carrying cost @40% 5000 2500 Order cost @ Rs. 625 1250 2500 Total cost 6250 5000 Saving = 6250 –5000 = Rs. 1250 So, the firm is incurring a loss of Rs. 1250 by not following an EOQ model. < TOP > 47. Answer : (d) Reason : Inventory turnover = cost of goods sold/ average inventory = 900,000/262,125 = 3.43 times. Cost of goods sold = opening inventory + purchases – closing inventory = 228,750+ 966,750- 295,500 = Rs. 900,000 Average inventory = (opening inventory+ closing inventory)/2 = 262,125. < TOP > 48. Answer : (d) Reason : Net investment = Rs.50,000 – Rs.5,000 + Rs.5,000 (0.4) = Rs.47,000 < TOP > 49. Answer : (c) Reason : Average investment = = Rs.1,05,000 Average profit = = Rs.50,000Accounting rate of return= = = 47.62% < TOP > 50. Answer : (e) Reason : Benefit = Rs.50,00,000(2)(0.08/365) – 500 = Rs. 1,692 < TOP > 51. Answer : (b) Reason : Cash budget for the month of November 2004 November a. Opening Balance Rs.100,000 b. Inflows: Sales realizations: Current month Previous month Rs.300,000 Rs.250,000 c. Outflows: Purchases Rs.250,000 Wages Rs.150,000 Administrative Expenses Rs.80,000 Payment for the equipment Rs.20,000 Total Rs. 500,000 d. Closing Balance (a + b – c) Rs.150,000 Therefore, the required closing balance by the end of the month of November will be = Rs.150,000. < TOP > 52. Answer : (b) Reason : Net operating income =Total assets × Return on asset =1200 × 0.15 =180 Market value of equity =Net operating income/cost of equity capital =180/0.12 = Rs.1500 crore. < TOP > 53. Answer : (b) Reason : Accounts Receivable = 38[(Rs.700,000)(0.65)]/365) = Rs.47,370 < TOP > 54. Answer : (b) Reason : Calculation of breaking point: Source of finance Cost (%)Range of new financing Breaking point Range of total new financing (Rs. in crore) (Rs. in crore) (Rs. in crore) Equity 14 0 – 10 10/0.4 = 25 0 – 25 15 10 – 20 20/0.4 = 50 25 – 50 16 20 and above – 50 and above Preference 13 0 – 2 2/0.2 = 10 0 – 10 14 2 and above – 10 and above Debt 8 0 – 12 12/0.4 = 30 0 – 30 9 12 – 18 18/0.4 = 45 30 – 45 10 18 and above – 45 and above If the new financing is in the range of Rs.25 – 30 crore Cost of equity = 15% Cost of preference = 14% Cost of debt = 8% Weighted marginal cost of capital in the above range = 0.15 x 0.4 + 0.14 x 0.2 + 0.08 x 0.4 = 12% Hence, answer is (b). < TOP > 55. Answer : (d)Reason : If the U is the annual usage, Q* is the EOQ ; Q’ is the order stipulated by the supplier for availing the discount and F is the cost per order, then the savings in the total ordering costs can be computed as: = Hence option (d) is correct. < TOP > 56. Answer : (d) Reason : The average cash outflow during the 4 peak days in the month of June was As the magnitude of cash out flows in the month of August is 20% more than that in the month of June, the expected average cash out flows during the 4 peak days in the month of August would be Rs.57,250 ´ 1.2 = Rs.68,700 So the safety level of cash to be maintained is 4 ´ 68,700 or Rs. 2,74,800 < TOP > 57. Answer : (c) Reason : The market price per share is given by where symbols are in standard use. If no dividends are declared 150 P1 = Rs.168 Net Income = Rs.2 crore Investments budget = Rs.4 crore Amount to be raised by issue of new shares = Rs.2 crore \ Number of shares to be issued = 1,19,048 shares. < TOP > 58. Answer : (c) Reason : EPS= PAT/ No. of share =30/4 =7.5 P/E =7.2 MPS = 7.2 x 7.5 =54 Total market value is= (MPS) x No of shares =54 x 4 =Rs.216 crore. < TOP > 59. Answer : (c) Reason : The traditional approach to dividend policy establishes a relationship between the market price and the dividends in the following manner: P=m(D+E/3) where, m is a multiplier, D is the Dividend Per Share (DPS) and E is the Earnings Per Share (EPS). Hence, 17 = 3.4 (3+E/3) So EPS = Rs.6. Hence, option (c) is the correct choice. < TOP > 60. Answer : (c) Reason : Cash sales = 21,00,000 ´ 0.20 = Rs. 4,20,000 Collection of Credit sales (January 2005) =20,50,000 ´ 0.60 ´ 0.8 = Rs. 9,84,000 Collection of Credit sales (December 2004) =18,50,000 ´ 0.40 ´ 0.8 = Rs. 5,92,000 Sale of machine = Rs. 12,000 Total = Rs 20,08,000 < TOP > 61. Answer : (c) Reason : The possible levels of usage and their corresponding probabilities are computed in the following table: Daily Usage Rate Lead Time Possible levels of usage Units Probability Number of days Probability Possible Usage Levels = (Column 1 x Column 3) Probability = (Column 2 x Column 4)150 0.220 35 0.6 0.4 3,000 5,250 0.12 0.08 360 0.520 35 0.6 0.4 7,200 12,600 0.30 0.20 450 0.320 35 0.6 0.4 9,000 15,750 0.18 0.12 Normal Usage during lead time = Average Daily Usage rate x Average Lead Time Average Daily Usage rate = 150 x 0.20 + 360 x 0.50 + 450 x 0.30 = 345 units. Average Lead Time = 20 x 0.6 + 35 x 0.4 = 26 days Normal Usage during lead time = 345 x 26 = 8,970 units. Stock outs will occur, if the usage is above 8,970 units. From the table computed above, we can infer that stock-outs will occur when the usage levels are 12,600 (with probability 0.20); 9,000 (with probability 0.18) and 15,750 (with probability 0.12). The total probability of stockout is 0.2 + 0.18 + 0.12 = 50%. Hence, (c) is the answer. < TOP > 62. Answer : (d) Reason : Loss that the company will incur, when the customer actually defaults = Cost of the unit = (1 – 0.30) ´ 5000 = Rs.3,500. < TOP > 63. Answer : (e) Reason : The total cost of ordering and carrying = + 400,000 = or, = 200,000 or, U = 40,00,000 = 40 lakh. < TOP > 64. Answer : (c) Reason: Sum of the net present values of projects 1 and 2 = 44.01+70.13 = Rs.114.14 million. < TOP > 65. Answer : (a ) Reason : 15000 -10,000 – 1000 = Rs.4000 < TOP > 66. Answer : (c ) Reason : Depreciation tax shield = 100,000x 0.35 = Rs.35,000. < TOP > 67. Answer : (b) Reason : Positive payments float = Rs.15,000(5) = Rs.75,000. Negative collections float = Rs.17,000(3) = Rs.51,000. Net float = Rs.75,000 – Rs.51,000 = Rs.24,000. < TOP > 68. Answer : (d) Reason : The weighted average price is given by: Rs.12.50 Hence, the value of the issue will be = Rs.12.50 × 100 = Rs.1,250. < TOP >69. Answer : (c) Reason : Capitalization rate for the company, k0 = , where the notations are in their standard use k0 = = 15.2% Further, k0 = = 0.152 Net operating income = 0.152 ´ 200 = Rs.30.4 lakh. < TOP > 70. Answer : (c) Reason : Raw material storage period = Daily consumption of raw materials = Annual consumption = 13,020 x 360 = Rs.46,87,200 Annual consumption = Opening stock + purchases – closing stock Average stock of raw materials = Where opening stock = S and Closing stock = 1.1 S Rs.6,51,000 = S = Rs.6,20,000 = Opening stock Closing stock = Rs.6,82,000 Annual consumption = 6,20,000 + P – 6,82,000 Rs.46,87,200 = 6,20,000 + P – 6,82,000 P = Rs.47,49,200 Average payment period = < TOP > 71. Answer : (c) Reason : Expected average daily usage = 600 ´ 0.6 + 800 ´ 0.4 = 680 units Expected lead time = 4 ´ 0.3 + 6 ´ 0.7 = 5.4 days Hence, normal consumption during lead-time = 680 ´ 5.4 = 3,672 units. < TOP > 72. Answer : (c) Reason: Weighted Average Cost of Capital (WACC) using book value weights Sum of book values of all sources of capital used is 200 + 400 + 150 + 250 = 1000 \ Weight for equity capital (we) = 200/1000 = 0.2 Weight for reserves and surplus (wr) = 400/1000 = 0.4 Weight for preference capital (wp) = 150/1000 = 0.15 Weight for debenture capital (wd) = 250/1000 = 0.25 \ WACC = we ke + wr kr + wp kp + wd kd = 0.2 ´ 19.25 + 0.4 ´ 19.25 + 0.15 ´ 12.19 + 0.25 ´ 8.00 = 15.38% (approx.) Weighted average cost of capital (WACC) using market value weights Sum of market values of all sources of capital used = 400 + 159 + 241 = 800 Weight of equity capital = 400/800 = 0.5 Weight of preference capital = 159/800 = 0.19875 » 0.20 Weight of debenture capital = 241/800 = 0.30125 » 0.30 \ WAC = 0.5 ´ 19.25 + 0.2 ´ 12.19 + 0.3 ´ 8.00 = 14.46% (approx.) The difference between the WACC using book value weights and market value weights = (15.38-14.46)%=0.92% < TOP > 73. Answer : (b) Reason : The amount of raw materials consumed = Opening balance + Purchases during the year – Closing balance = (180,000 + 1,192,000 – 212,000) = Rs.1,160,000 The average stock of work in process = (25,000 + 45,000)/2 = Rs.35,000Annual cost of production = Opening work in process + Consumption of raw materials + Manufacturing expenses + Depreciation – Closing work in process = 25,000 + 1,160,000 + 1,280,000 + 100,000 – 45,000 = Rs.2,520,000 So, the average daily cost of production = Rs.7,000 Hence, the average conversion period = 35,000/7,000 = 5 days. < TOP > 74. Answer : (b) Reason : The value of Que Ltd. (unlevered firm) = EBIT(1-t)/k = 4,00,000(1-0.4)/0.15 = Rs.16,00,000 The value Zed Ltd. (levered firm) = Value of unlevered firm + (t × value of debt) = 16,00,000 × (0.40 × 5,00,000) = Rs.18,00,000 Total value = Rs.16,00,000 + Rs.18,00,000 = Rs. 34,00,000 < TOP > 75. Answer : (c) Reason : Present value of the costs associated with the machine will be Rs.30,00,000 + Rs.250,000 ´ PVIFA(10 percent, 4 years) + Rs.300,000 ´ PVIFA(10 percent, 6 years) ´ PVIF(10 percent, 4 years) = Rs.30,00,000 + Rs.250,000 ´ 3.170 + Rs.300,000 ´ 4.355 ´ 0.683 = Rs.46,84,839.50 The required annual capital charge will be = = = Rs.762,382 (approximately) < TOP > 76. Answer : (d) Reason : Realized yield = = 1.2548-1 = 25.48% < TOP > 77. Answer : (e) Reason : Approximate percentage cost = ´ = 0.212828. Accounts payable = = Rs.750,000. < TOP > Corporate Finance If you invest Rs.25,000/- today at a compound interest of 9%, what will be the future value after 15 years?  (a) Rs.91,062/-  (b) Rs.91,260/-  (c) Rs.91,620/-  (d) Rs.91,200/-  (e) None of the above If choice a is selected set score to 2.Finance function involves:-  (a) Safe custody of funds only  (b) Expenditure of funds only  (c) Procurement of finance only  (d) Procurement and effective utilization of funds  (e) None of the above If choice d is selected set score to 2. The primary objective of corporate management is:-  (a) Maximization of wealth of shareholders  (b) Maximization of EBIT  (c) Maximization of market share price  (d) Maximization of EPS  (e) All of the above If choice e is selected set score to 2. What is the payback period on cash flow (non discounted) of the following project?  (a) 2.5 years  (b) 3 years  (c) 3.5 years  (d) 2 years  (e) None of the above If choice b is selected set score to 2. The goal of wealth maximization takes into consideration:-  (a) Risk related to uncertainty of returns  (b) Timing of expected returns  (c) Amount of returns expected  (d) All of the above  (e) None of the above If choice e is selected set score to 2. Time value of money facilitates comparison of cash flows occurring at different time periods by:-  (a) a) Compounding all cash flows to a common point of time  (b) b) Discounting all cash flows to a common point of time  (c) c) Using either (a) or (b)  (d) d) Neither (a) nor (b)  (e) e) None of the above If choice c is selected set score to 2.'X' Ltd. Company issues Rs.50,000/-, 8% debentures at a premium of 10%. The tax rate applicable to the company is 60%. What is the cost of debt?  (a) 3.5%  (b) 4.21%  (c) 2.91%  (d) 4%  (e) None of the above If choice c is selected set score to 2. What is the NPV (approximate), if cost of capital is 10% on cash flow of the following project?  (a) Rs.493.40/-  (b) Rs.-9507.60/-  (c) Rs.9507.60/-  (d) Rs.-493.40/-  (e) None of the above If choice d is selected set score to 2. Money has a time value because:-  (a) a) The individuals prefer future consumption to present consumption  (b) b) A rupee today is worth more than a rupee tomorrow in terms of purchasing power  (c) c) A rupee today can be productively deployed to generate real returns tomorrow  (d) Both (b) and (c)  (e) All of the above If choice d is selected set score to 2. Cash flows occurring in different periods should not be compared unless:-  (a) The flows occur no more than one year from each other  (b) The flows have been discounted to a common date  (c) High rates of interest can be earned on the flows  (d) Interest rates are expected to be stable  (e) All of the above If choice b is selected set score to 2.What is the risk premium of a security, if the market return is 15%, Beta 0.8 and risk-free rate of return is 9%.  (a) 6.0%  (b) 4.8%  (c) 8.4%  (d) 7.2%  (e) None of the above If choice b is selected set score to 2. Relationship between annual effective rate of interest and annual nominal rate of interest is, if frequency of compounding is more than 1:-  (a) Effective Rate ‹ Nominal rate  (b) Effective rate › Nominal rate  (c) Effective Rate = Nominal rate  (d) All of the above  (e) None of the above If choice b is selected set score to 2. If you invest Rs.20,000/- today at a compound interest of 9.25%, what will be the future value after 15 years?  (a) Rs.75,396/-  (b) Rs.75,960/-  (c) Rs.75,930/-  (d) Rs.75,460/-  (e) None of the above If choice a is selected set score to 2. What is the NPV if cost of capital is 10% on cash flow of the following project?  (a) Rs.2,340/-  (b) Rs.2,400/-  (c) Rs.2,450/-  (d) Rs.2,404/-  (e) None of the above If choice d is selected set score to 2.A student takes a loan of Rs.50,000/- from SBI. The rate of interest being charged by SBI is 10 percent per annum. What would be the amount of equal annual installment if he wishes to pay it back in five installments at the end of every year ( PVIF 10%, 5 Years is 0.621 and PVIFA is 3.791 )?  (a) Approx. Rs.15,620/-  (b) Approx. Rs.15,450/-  (c) Approx. Rs.13,190/-  (d) Approx. Rs.11,000/-  (e) None of the above If choice c is selected set score to 2. You have determined the profitability of a planned project by finding the present value of all the cash flows from that project. Which of the following would cause the project to look more appealing in terms of the present value of those cash flows?  (a) The discount rate decreases  (b) The cash flows are extended over a longer period of time, but total amount of the cash flows remains the same  (c) The discount rate increases  (d) All of the above  (e) None of the above If choice a is selected set score to 2. Which of the following statements is correct?  (a) An investment which compounds interest semiannually, and has a nominal rate of 10 pe rcent, will have an effective rate less than 10 percent  (b) The present value of a 3-year $100 annuity due is less than the present value of a 3-year $100 ordinary annuity  (c) The proportion of the payment of a fully amortized loan which goes toward interest decl ines over time  (d) All of the above  (e) None of the above If choice c is selected set score to 2. A company wants to retire a loan Rs.5,00,000/-, 10 years from today. What amount should it invest each year for 10 years if the funds can earn 8 percent per annum. The first investment will be made at the beginning of this year ( FVIF 10%, 10 Years is 2.594 and FVIFA is 15.937.  (a) Approx. Rs.31,950/-  (b) Approx. Rs.40,000/-  (c) Approx. Rs.34,000/-  (d) Approx. Rs.28,000/-  (e) None of the above If choice e is selected set score to 2.Find out the weighted average cost of capital from the following data:-  (a) 8.0%  (b) 8.11%  (c) 8.2%  (d) 7.5%  (e) None of the above If choice b is selected set score to 2. A company has 10 percent perpetual debt of Rs.1,00,000/-. The tax rate is 35 percent. Determine the cost of debt if the company issued at discount of 10 percent.  (a) 5.0 percent  (b) 5.91 percent  (c) 7.22 percent  (d) 6.5 percent  (e) None of the above If choice c is selected set score to 2. Which of the following bank accounts has the highest effective annual return?  (a) An account which pays 9 percent nominal interest with daily compounding  (b) An account which pays 10 percent nominal interest with daily compounding  (c) An account which pays 10 percent nominal interest with annual compounding  (d) An account which pays 10 percent nominal interest with monthly compounding  (e) None of the above If choice b is selected set score to 2. What is the NPV (approximate), if cost of capital is 10% on cash flow of the following project?  (a) Approx. Rs.-5,500/-  (b) Approx. Rs.5,500/-  (c) Approx. Rs. 4,600/-  (d) Approx. Rs.4,600/-  (e) None of the above If choice c is selected set score to 2.If you invest Rs.30,000/- today at a compound interest of 9.50%, what will be the future value after 10 years?  (a) Rs.74,734/-  (b) Rs.74,897/-  (c) Rs.74,347/-  (d) Rs.74,934/-  (e) None of the above If choice c is selected set score to 2. You are interested in investing your money in a bank account. Which of the following banks provides you with the highest effective rate of interest?  (a) Bank 1; 8 percent with monthly compounding  (b) Bank 2; 8 percent with annual compounding  (c) Bank 4; 8 percent with daily (365-day) compounding  (d) Bank 3; 8 percent with quarterly compounding  (e) None of the above If choice c is selected set score to 2. What is the NPV if cost of capital is 12% on cash flow of the following project?  (a) Rs.657/-  (b) Rs.-765/-  (c) Rs.567/-  (d) Rs.-756/-  (e) None of the above If choice d is selected set score to 2. Which of the following is not considered a capital component for the purpose of calculating the weighted average cost of capital as it applies to capital budgeting?  (a) Accounts payable  (b) Long term debt  (c) Common stock  (d) Preferred stock  (e) None of the above If choice a is selected set score to 2.A company has determined that its optimal capital structure consists of 40 percent debt and 60 percent equity. Given the following information, calculate the firm's weighted average cost of capital, where rd = 6%, Tax rate = 40%, Share Price = $25, Growth = 0%, Dividend = $2.00.  (a) 7.2%  (b) 7%  (c) 6.2%  (d) 6%  (e) 8% If choice c is selected set score to 2. Find out the weighted average cost of capital from the following data:-  (a) 9.26%  (b) 12.0%  (c) 11.15%  (d) 10.3%  (e) None of the above If choice d is selected set score to 2. Which of the following is not considered a capital component?  (a) Long term debt  (b) Common stock  (c) Permanent short term debt  (d) All of the above are considered capital components  (e) None of the above If choice d is selected set score to 2. The common stock of Anthony Steel has a beta of 1.20. The risk-free rate is 5 percent and the market risk premium (rM - rRF) is 6 percent. What is the companys cost of common stock, rs?  (a) 7%  (b) 12.4%  (c) 7.2%  (d) 12.2%  (e) 11% If choice d is selected set score to 2.Equity shares of Phonex Ltd. are quoted in the market at Rs.17.00/-. The dividend expected a year hence is Rs.1.50/-. The expected rate of dividend growth is 8%. The cost of equity capital to the company is:-  (a) 13.88%  (b) 16.82%  (c) 15.46%  (d) 11.08%  (e) None of the above If choice b is selected set score to 2. Which of the following statements is correct?  (a) a) If a company's tax rate increases but the yield to maturity of its non callable bonds re mains the same, the company's marginal cost of debt capital used to calculate its weighted ave rage cost of capital will fall  (b) b) All else equal, an increase in a company's stock price will increase the marginal cost o f common stock,re.  (c) c) All else equal, an increase in interest rates will decrease the marginal cost of common stock, re.  (d) d) Both (a) and (b)  (e) e) None of the above If choice a is selected set score to 2. A stock split will cause a change in the total rupee amounts shown in which of the following balance sheet accounts?  (a) Cash  (b) Common stock  (c) Paid-in capital  (d) Retained earnings  (e) None of the above If choice e is selected set score to 2. Which of the following statements is correct?  (a) a) The WACC is a measure of the before-tax cost of capital  (b) b) Typically the after-tax cost of debt financing exceeds the after-tax cost of equity finan cing  (c) c) The WACC measures the marginal after-tax cost of capital  (d) d) Both (a) and (b)  (e) e) None of the above If choice c is selected set score to 2.Which of the following actions will enable a company to raise additional equity capital (that is, which of the following will raise the total book value of equity)?  (a) a) The establishment of a new-stock dividend reinvestment plan  (b) b) A stock split  (c) c) The establishment of an open-market purchase dividend reinvestment plan  (d) d) A stock repurchase  (e) e) Both (a) and (d) If choice a is selected set score to 2. A company has a capital structure which consists of 50 percent debt and 50 percent equity. Which of the following statements is correct?  (a) The WACC represents the cost of capital based on historical averages. In that sense, it d oes not represent the marginal cost of capital  (b) The cost of equity financing is greater than or equal to the cost of debt financing  (c) The WACC exceeds the cost of equity financing  (d) The WACC is calculated on a before-tax basis  (e) None of the above If choice b is selected set score to 2. Which of the following statements is correct?  (a) a) The weighted average cost of capital for a given capital budget level is a weighted ave rage of the marginal cost of each relevant capital component which makes up the firm's target capital structure  (b) b) The weighted average cost of capital is calculated on a before-tax basis  (c) c) An increase in the risk-free rate is likely to increase the marginal costs of both debt an d equity financing  (d) d) Both (a) and (c)  (e) e) All of the above If choice d is selected set score to 2. Which of the following is not an advantage of using book value weights for computing the cost of capital?  (a) The calculation of the weights is very simple  (b) Book value weights are likely to fluctuate less over a period as these are not affected by the fluctuations in market prices  (c) Book value weights are consistent with the concept of cost of capital  (d) Book value weights are the only usable basis when market values are not obtainable or reliable  (e) None of the above If choice d is selected set score to 2.Which of the following are examples of a primary market transaction?  (a) a) A company issues new common stock  (b) b) A company issues new bonds  (c) c) An investor asks his broker to purchase 1,000 shares of Microsoft common stock  (d) d) All of the above  (e) e) Both (a) and (b) If choice e is selected set score to 2. If the expected rate of return on a stock exceeds the required rate:-  (a) The company is probably not trying to maximize price per share  (b) The stock is a good buy  (c) The stock should be sold  (d) Dividends are not being declared  (e) The stock is experiencing supernormal growth If choice b is selected set score to 2. Which of the following is/are true about NPV?  (a) a) It considers all the cash flows  (b) b) It gives more weightage to distant flows than to near-term flows  (c) c) It considers time value of money  (d) Both (a) and (c)  (e) None of the above If choice d is selected set score to 2. Cash flows occurring from a project in different period are comparable unless:-if:  (a) Interest rates are expected to be stable  (b) The flows have been discounted to a single date  (c) The flows occur periodically every year  (d) Interest can be earned on the cash flows  (e) None of the above If choice b is selected set score to 2.Consider the following data: If the tax rate is 35%, the weighted average cost of funds taking market value as weights is:-  (a) 14.00%  (b) 15.82%  (c) 14.96%  (d) 15.00%  (e) 16.62% If choice c is selected set score to 2. The _________ is the time period that elapses from the point when the firm sells a finished good on account to the point when the receivable is collected..  (a) cash conversion cycle  (b) average payment period  (c ) average collection period  (d) average age of inventory  (e) None of the above If choice c is selected set score to 2. Conflicts in ranking of projects on the basis of NPV and IRR arise due to:-  (a) a) Disparity in the timing of cash inflows  (b) b) Disparity in the size of cash inflows  (c) c) Disparity in the life of cash flows  (d) Both (a) and (b)  (e) None of the above If choice d is selected set score to 2. _________ projects do not compete with each other; the acceptance of one _________ the others from consideration.  (a) Independent; does not eliminate  (b) Capital; eliminates  (c) Replacement; does not eliminate  (d) Mutually exclusive; eliminates  (e) None of the above If choice a is selected set score to 2.The rationale for not including sunk costs in capital budgeting decisions is that they:-  (a) Revert at the end of the investment  (b) Represent nominal, not real, outflows  (c) Are usually small in magnitude  (d) Are historical costs  (e) None of the above If choice d is selected set score to 2. Which of the following events is likely to encourage a company to raise its target debt ratio?  (a) a) An increase in the corporate tax rate  (b) b) An increase in the personal tax rate  (c) c) An increase in the company's operating leverage  (d) Both (a) and (c)  (e) All of the above If choice a is selected set score to 2. Which of the following would increase the likelihood that a company would increase its debt ratio in its capital structure?  (a) a) An increase in costs incurred when filing for bankruptcy  (b) b) An increase in the corporate tax rate  (c) c) A decrease in the firm's business risk  (d) Both (b) and (c)  (e) None of the above If choice b is selected set score to 2. The aggressive financing strategy results in the firm financing its short-term needs with _________ funds and its long-term needs with _________ funds.  (a) long-term; short-term  (b) short-term; long-term  (c) Permanent; seasonal  (d) seasonal; permanent  (e) None of the above If choice b is selected set score to 2.Which of the following statements is correct?  (a) a) A firm can use retained earnings without paying a flotation cost. Therefore, while the cost of retained earnings is not zero, the cost of retained earnings is generally lower than the a fter-tax cost of debt financing  (b) b) The capital structure that minimizes the firm's cost of capital is also the capital struct ure that maximizes the firm's stock price  (c) c) The capital structure that minimizes the firm's cost of capital is also the capital structu re that maximizes the firm's earnings per share  (d) d) If a firm finds that the cost of debt financing is currently less than the cost of equity fi nancing, an increase in its debt ratio will always reduce its cost of capital  (e) Both (a) and (b) If choice b is selected set score to 2. Which of the following statements is correct?  (a) a) Since debt financing raises the firm's financial risk, raising a company's debt ratio will always increase the company's WACC  (b) b) Since debt financing is cheaper than equity financing, raising a company's debt ratio will always reduce the company's WACC  (c) c) Increasing a company's debt ratio will typically reduce the marginal cost of both debt and equity financing; however, it still may raise the company's WACC  (d) Both (a) and (c)  (e) None of the above If choice e is selected set score to 2. According to NI approach:-  (a) a) The total market value of a firm and the cost of capital are dependent on the capital s tructure  (b) b) The total market value of a firm and the cost of capital are independent of capital str ucture  (c) c) The capital structure has no relevance  (d) Both (a) and (c)  (e) None of the above If choice a is selected set score to 2. Under Net Income Approach (NIA), change in the capital structure of a company:-  (a) Does not cause any change either in the overall cost of capital or in the total value of a fi rm  (b) No changes in overall cost of capital  (c) Causes corresponding change in the overall cost of capital as well as the total value of a firm  (d) Causes corresponding change in the overall cost of capital only  (e) None of the above If choice c is selected set score to 2.In Net Operating Income (NOI) approach, market value of a firm:-  (a) Is sometimes affected by capital structure changes  (b) Is affected by capital structure changes  (c) Is affected proportionately  (d) Is not at all affected by capital structure changes  (e) None of the above If choice d is selected set score to 2. Financial structure includes:-  (a) Long term as well as short term sources of funds  (b) Equity share capital of the company  (c) Long term sources of funds  (d) Medium term source of funds  (e) None of the above If choice a is selected set score to 2. The term capital structure:-  (a) Is not part of financial structure  (b) Is part of financial structure  (c) Is part of appropriation account  (d) Is part of profit & loss account  (e) None of the above If choice b is selected set score to 2. Which of the following statement(s) is true?  (a) Risk that can be eliminated by diversification is called specific risk  (b) Risk that cannot be avoided, regardless of how much you diversity is known as market ri sk  (c) The variability of earnings before interest and taxes is referred to as business risk  (d) All of the above  (e) None of the above If choice d is selected set score to 2. Which of the following is not a feature of debt finance?  (a) a) Dilution of control  (b) b) Low cost  (c) c) Financial risk  (d) Both (b) and (c)  (e) None of the above If choice a is selected set score to 2.Which of the following factors has an effect on business risk?  (a) Demand for products manufactured by the firm  (b) Volatility in prices of the products manufactured by the firm  (c) Variability in input prices  (d) All of the above  (e) None of the above If choice d is selected set score to 2. The Modigliani-Miller argument is that:-  (a) a) The value of the levered firm will be more than that of unlevered firm  (b) b) The value of the unlevered firm will be more than the levered firm  (c) c) Levered firms cannot enjoy a premium over unlevered firms as the investors will aboli sh the difference through personal leverage  (d) Either (a) or (b) may be true depending on other circumstances  (e) None of the above If choice c is selected set score to 2. Business risk refers to:-  (a) a) Variability of sales  (b) b) Variability of the market value of the firm  (c) c) Variability of cost of raw materials  (d) Both (a) and (c)  (e) None of the above If choice d is selected set score to 2. Which of the following is true?  (a) Operating leverage measures the sensitivity of EBT to changes in the quantity produced and sold  (b) Operating leverage measures the sensitivity of EBIT to changes in quantity produced an d sold  (c) Operating leverage measures the sensitivity of PAT to changes in quantity produced and sold  (d) Operating leverage measures the sensitivity of PBDT to changes in quantity produced an d sold  (e) None of the above If choice b is selected set score to 2. Total or Combined leverage measures the relationship between:-  (a) PAT and sales  (b) Sales and EPS  (c) EBIT and sales  (d) EPS and EBIT  (e) None of the above If choice b is selected set score to 2.Which of the following is/are correct?  (a) a) Value of the firm and cost of capital are directly related  (b) b) Value of the firm and cost of capital are inversely related  (c) c) The claim of preference shareholders is prior to that of equity shareholders  (d) Both (b) and (c)  (e) None of the above If choice d is selected set score to 2. The ultimate objective of any company is:-  (a) Wealth maximization  (b) Sale maximization  (c) Profit maximization  (d) Improving its reputation  (e) None of the above If choice a is selected set score to 2. Which of the following best describes a firm's cost of capital?  (a) a) It is the weighted arithmetic average of the cost of various sources of long term finan ce used by it  (b) b) The rate of return the firm must earn on its investments in order to satisfy the expect ations of investors who provide long term funds to it  (c) c) It is the weighted arithmetic average of the cost of various sources of long term financ e and short term finance used by it  (d) Both (a) and (b)  (e) None of the above If choice d is selected set score to 2. Which of the following statements is true?  (a) Retained earnings is the only principal source of finance for growing firms  (b) Retained earnings represent the profits ploughed back into the business  (c) Retained earnings represent the extent to which the firm has invested in liquid assets ou t of its profits  (d) Retained earnings are given lesser importance when a firm follows a residual dividend p olicy  (e) None of the above If choice b is selected set score to 2. Which of the following long term sources of finance puts maximum restraint on managerial freedom?  (a) Retained earnings  (b) Preference capital  (c) Equity capital  (d) Term loans  (e) None of the above If choice d is selected set score to 2.The cost of debt remains more or less constant up to a certain degree of leverage but rises thereafter at an increasing rate. This proposition is based on:-  (a) Net income approach on capital structure  (b) Miller-Modigliani approach  (c) Net operating income approach on capital structure  (d) Traditional position/Traditional approach on capital structure  (e) None of the above If choice d is selected set score to 2. Which of the following is true regarding sound capital market structure of a company?  (a) The capital structure should be determined within the debt capacity of the company an d this capacity should not be exceeded  (b) Use of debt should be avoided as it adds to financial risk of the company  (c) Minimum use of leverage at minimum cost  (d) The risk of loss of control of the company due to capital structure is a major concern in a closely held company  (e) The capital structure should not change over a period of time If choice a is selected set score to 2. Which of the following concepts explains the relationship between shareholders and Managers?  (a) Valuation  (b) Value based management  (c) Agency consideration  (d) Shareholder wealth maximization  (e) Miller-Modigliani If choice c is selected set score to 2. A significant assumption of the net operating income is that:-  (a) Debt and equity levels do not change  (b) Dividend increase at a constant rate  (c) It remains constant regardless of changes in leverage  (d) Interest expense and taxes are included in the calculation  (e) It decreases up to a certain point of time, and then increases at an increasing rate, with i ncreasing levels of leverage If choice c is selected set score to 2. Which of he following best describes the situation in which a firm is having problem meeting its financial obligations?  (a) Business risk  (b) Legal bankruptcy  (c) Technical bankruptcy  (d) Financial risk  (e) Financial distress If choice e is selected set score to 2.Which of the following risks is revealed by capital structure ?  (a) a) Liquidity risk  (b) b) Financial risk  (c) c) Market risk  (d) d) Firm's total risk  (e) Both (b) and (d) If choice a is selected set score to 2. Trade creditors of a company are mostly interested in the company's:-  (a) Activity ratios  (b) Liquidity ratio  (c) Profitability ratios  (d) Valuation ratios  (e) Leverage ratios If choice b is selected set score to 2. A decrease in a firm's willingness to pay dividends is likely to result from an increase in its:-  (a) Profitable investment opportunities  (b) Stock price  (c) Access to capital markets  (d) Earnings stability  (e) None of the above If choice a is selected set score to 2. A stock split will cause a change in the total dollar amounts shown in which of the following balance sheet accounts?  (a) Cash  (b) Common stock  (c) Paid in capital  (d) All of the above  (e) None of the above If choice e is selected set score to 2. Which of the following statements is correct?  (a) a) If a company puts in place a 2-for-1 stock split, its stock price should roughly double  (b) b) Share repurchases are taxed less favorably than dividends; this explains why compani es typically pay dividends and avoid share repurchases  (c) c) On average, a company's stock price tends to rise when it announces that it is initiatin g a share repurchase program  (d) Both (a) and (b) If choice c is selected set score to 2.Longer the manufacturing period  (a) Greater is the requirement of working capital  (b) There is no change in the operating cycle  (c) Shorter is the requirements of working capital  (d) Lesser is the requirement of working capital  (e) None of the above If choice a is selected set score to 2. Which of the following factors influence the pay out ratio of a firm?  (a) a) Funds requirement  (b) b) Liquidity position of the firm  (c) c) Access to external sources of financing  (d) All of the above  (e) Both (a) and (b) If choice d is selected set score to 2. Which of the following sources cannot be used for payment of dividend?  (a) a) Current profits after providing for depreciation  (b) b) Profits for any previous financial year to years  (c) c) Capital  (d) Both (b) and (c)  (e) Either (b) or (c) If choice c is selected set score to 2. Net working capital denotes:-  (a) Total liabilities  (b) Excess of fixed assets over current assets  (c) Excess of current liabilities over current assets  (d) Excess of current assets over current liabilities  (e) None of the above If choice d is selected set score to 2. Other things held constant, which of the following will cause an increase in working capital?  (a) Merchandize is sold at a profit, but the sale is on credit  (b) A cash dividend is declared and paid  (c) Cash is used to buy marketable securities  (d) Long term bonds are retired with the proceeds of a preferred stock issue  (e) None of the above If choice a is selected set score to 2.Which of the following statements is correct?  (a) Trade credit is provided to a business only when purchases are made  (b) Commercial paper is a form of short term financing that is primarily used by large, finan cially stable companies  (c) Short term debt, while often cheaper than long term debt, exposes a firm to the potenti al problems associated with rolling over loans  (d) All of the above  (e) None of the above If choice d is selected set score to 2. Which of the following is not a current asset?  (a) a) Prepaid expenses  (b) b) Short term loans and advances  (c) c) Marketable securities  (d) Both (a) and (b)  (e) None of the above If choice b is selected set score to 2. Which of the following is the least liquid among current assets?  (a) Inventories  (b) Prepaid expenses  (c) Cash  (d) Short term securities  (e) Debtors If choice a is selected set score to 2. The current ratio is obtained by:-  (a) Dividing quick assets by total liabilities  (b) Dividing quick assets by long term liabilities  (c) Dividing current assets by current liabilities  (d) Dividing current assets by total liabilities  (e) Dividing quick assets by current liabilities If choice c is selected set score to 2. Which of the following best describes working capital gap?  (a) Quick assets less current liabilities other than bank  (b) Current assets less short term bank borrowings  (c) Current assets less current liabilities other than bank borrowings  (d) Quick assets less current liabilities  (e) Current assets less current liabilities If choice c is selected set score to 2.Financial risk involves:-  (a) a) Fluctuations in exchange rates  (b) b) Different interest and inflation rates  (c) c) Balance of payments position  (d) All of the above  (e) Both (a) and (b) If choice d is selected set score to 2. Which of the following features of preference shares is/are similar to those of equity shares?  (a) a) Redeemability  (b) b) No obligation to pay dividend  (c) c) Voting rights  (d) d) Charge over assets  (e) e) Both (b) and (c) If choice b is selected set score to 2. Euro-Convertible Bonds (ECBs) issued by Indian Companies refer to bonds issued in foreign currency in:-  (a) India and any country in Europe  (b) European countries only  (c) Europe and North America  (d) India or any country outside India  (e) Any country other than India If choice e is selected set score to 2. Which of the following is a/are feature(s) of equity capital?  (a) a) The payment of dividend is compulsory, irrespective of the company's financial perfor mance  (b) b) The dividend, if not paid during a year, becomes payable in the next year  (c) c) Dividend becomes payable only if recommended by the BoD and passed by the comp any in the AGM  (d) d) Both (a) and (b)  (e) e) None of the above If choice c is selected set score to 2. The major advantages of privately placing the securities are:-  (a) Faster access to funds  (b) Fewer procedural formalities  (c) Lower issue cost  (d) Easy access for any company  (e) All of the above If choice e is selected set score to 2.Which of the following is not a source of long term finance?  (a) Equity capital  (b) Term loan  (c) Debenture capital  (d) Commercial paper  (e) Preference capital If choice d is selected set score to 2. Which of the following statements is true?  (a) Equity shareholders enjoy the rewards of ownership and bear the risks of the ownership  (b) Post-tax cost of debentures is always less than the post-tax cost of the term loans  (c) The par value and issue price of an equity share are always capital  (d) All outstanding issues of shares are traded in the primary markets  (e) None of the above If choice a is selected set score to 2. The costliest of long term source of finance is:-  (a) Preference share capital  (b) Equity share capital  (c) Debentures  (d) Retained earnings  (e) Capital raised through private placement If choice b is selected set score to 2. Which of the following statements is/are true? With the commencement of the Companies Act, 1956, the issue of preference shares with voting rights has been restricted only to the following cases:-  (a) There are arrears in dividends for two or more years incase of cumulative preference sh ares  (b) Preference dividend is due for a period of two or more consecutive preceding years  (c) In the preceding six years including the immediately preceding financial year, if the com pany has not paid the preference dividend for a period of three or more years  (d) All of the above  (e) None of the above If choice d is selected set score to 2.A cumulative preference share is one:-  (a) In which all the unpaid dividends are carried forward and payable  (b) Which allows the issuing company the right to call the preference shares wholly or partl y at a certain price  (c) Which can be redeemed  (d) Which can be converted into equity shares  (e) None of the above If choice a is selected set score to 2. Which of the following is/are true about equity capital as a source of finance?  (a) a) Using equity capital to finance working capital may lead to a situation of 'technical ins olvency'  (b) b) Assessing the cost of equity capital is a difficult and complex task  (c) c) Equity capital provides tax benefits to the issuing company  (d) d) Cost of retained earnings is lesser than the cost of debt capital  (e) e) Both (b) and (d) If choice b is selected set score to 2. Rights issue is the method of raising funds:-  (a) a) In which secur ities are simultaneously issued to the existing shareholders and the public  (b) b) Generally issued to the existing shareholders at a price lower than the current market price  (c) c) Generally entailing lower costs of issue  (d) d) Generally made to high net worth individuals  (e) e) Both (b) and (c) If choice e is selected set score to 2. Which of the following, from the firm's point of view, can be considered as the advantage(s) of using equity capital as a source of long term funds?  (a) a) It does not involve any fixed obligation for payment of dividends  (b) b) Equity dividends are payable from post-tax earnings. They are not tax deductible exp enses  (c) c) It enhances the creditworthiness of the company  (d) d) Both (a) and (c)  (e) e) None of the above If choice d is selected set score to 2. Which of the following characteristics is/are true, with reference to preference capital?  (a) a) Preference dividend is payable only out of distributable profits  (b) b) Preference dividend is tax deductible  (c) c) The claim of preference shareholders is prior to the claim of equity shareholders  (d) d) Both (a) and (c)  (e) e) All of the above If choice d is selected set score to 2.What is/are the factor(s) which make(s) debentures attractive to investors?  (a) a) They enjoy a high order of priority in the event of liquidation  (b) b) Stable rate of return  (c) c) Protected by the provisions of Debenture Trust Deed  (d) d) All of the above  (e) e) Both (a) and (b) If choice d is selected set score to 2. The major advantage(s) of entering into a Buy Out Deal (BOD) is/are:-  (a) An advantage accruing to the investor is that the issue price usually reflects the compan y's intrinsic value  (b) Companies, both existing and new, which do not satisfy conditions laid down by the SEB I for premium issues, may issue at a premium through the BOD method  (c) There is less issue cost  (d) The procedural complexities are reduced considerably and the funds reach the firm upfr ont  (e) All of the above If choice e is selected set score to 2. If you invest Rs.25,000/- today at a compound interest of 9%, what will be the future value after 15 years?  (a) Rs.91,062/-  (b) Rs.91,260/-  (c) Rs.91,620/-  (d) Rs.91,200/-  (e) None of the above Finance function involves:-  (a) Safe custody of funds only  (b) Expenditure of funds only  (c) Procurement of finance only  (d) Procurement and effective utilization of funds What is the payback period on cash flow (non discounted) of the following project?  (a) 2.5 years  (b) 3 years  (c) 3.5 years  (d) 2 years  (e) None of the aboveThe goal of wealth maximization takes into consideration:-  (a) Risk related to uncertainty of returns  (b) Timing of expected returns  (c) Amount of returns expected  (d) All of the above  (e) None of the above What is the NPV (approximate), if cost of capital is 10% on cash flow of the following project?  (a) Rs.493.40/-  (b) Rs.-9507.60/-  (c) Rs.9507.60/-  (d) Rs.-493.40/-  (e) None of the aboveIf the nominal rate of interest is 10 percent per annum and frequency of compounding is 4 i.e. quarterly compounding, the effective rate of interest will be:-  (a) 10.25% p.a.  (b) 10% p.a.  (c) 10.75% p.a.  (d) 010.38% p.a.  (e) None of the above What is the risk premium of a security, if the market return is 15%, Beta 0.8 and risk-free rate of return is 9%.  (a) 6.0%  (b) 4.8%  (c) 8.4%  (d) 7.2%  (e) None of the above A student takes a loan of Rs.50,000/- from SBI. The rate of interest being charged by SBI is 10 percent per annum. What would be the amount of equal annual installment if he wishes to pay it back in five installments at the end of every year?  (a) Approx. Rs.15,620/-  (b) Approx. Rs.15,450/-  (c) Approx. Rs.13,190/-  (d) Approx. Rs.11,000/-  (e) None of the above You have determined the profitability of a planned project by finding the present value of all the cash flows from that project. Which of the following would cause the project to look more appealing in terms of the present value of those cash flows?  (a) The discount rate decreases  (b) The cash flows are extended over a longer period of time, but the total amount of the cash flows remains the same  (c) The discount rate increases  (d) Both (b) and (c)  (e) None of the above A company wants to retire a loan Rs.5,00,000/-, 10 years from today. What amount should it invest each year for 10 years if the funds can earn 8 percent per annum. The first investment will be made at the beginning of this year.  (a) Approx. Rs.31,950/-  (b) Approx. Rs.40,000/-  (c) Approx. Rs.34,000/-  (d) Approx. Rs.50,000/-  (e) None of the aboveFind out the weighted average cost of capital from the following data:-  (a) 8.0%  (b) 8.11%  (c) 8.2%  (d) 7.5%  (e) None of the above From the following information: Find out, Operating Leverage & Financial Leverage:-  (a) 2.5 & 2.0  (b) 3.5 & 2.5  (c) 3.0 & 2.0  (d) 3.0 & 2.5  (e) None of the above You are interested in investing your money in a bank account. Which of the following banks provides you with the highest effective rate of interest?  (a) Bank 1; 8 percent with monthly compounding  (b) Bank 2; 8 percent with annual compounding  (c) Bank 4; 8 percent with daily (365-day) compounding  (d) Bank 3; 8 percent with quarterly compounding  (e) None of the above Which of the following is most correct statement? (a) The present value of a 5-year annuity due will exceed the present value of a 5-year ordinary ann uity (Assume that both annuities pay $100 per period and there is no chance of default) (b) If a loan has a nominal rate of 10 percent, then the effective rate can never be less than 10 perc ent (c) If there is annual compounding, then the effective, periodic and nominal rates of interest are all the same (d) All of the above (e) None of the aboveCompute the cost of equity using CAPM where risk-free rate of return is 9%, Beta co-efficient of the firm is 1.1 and assuming a market return of 15% next year.  (a) 16.5%  (b) 15.8%  (c) 16.6%  (d) 15.6%  (e) None of the above Which of the following is not considered a capital component for the purpose of calculating the weighted average cost of capital as it applies to capital budgeting?  (a) Accounts payable  (b) Long term debt  (c) Common stock  (d) Preferred stock  (e) None of the above Terms in this set (100) 1. The present value of $100 expected in two years from today at a discount rate of 6% is: A. $116.64 B. $108.00 C. $100.00 D. $89.00 D PV = 100/(1.06^2) = 89.00 2. Present Value is defined as: A. Future cash flows discounted to the present at an appropriate discount rate B. Inverse of future cash flows C. Present cash flow compounded into the future D. None of the above A 3. If the interest rate is 12%, what is the 2-year discount factor? A. 0.7972 B. 0.8929 C. 1.2544 D. None of the above A DF2 = 1/(1.12^2) = 0.7972 4. If the present value of the cash flow X is $240, and the present value cash flow Y $160, then the present value of the combined cash flow is: A. $240 B. $160 C. $80 D. $400 D PV (x + y) = PV (x) + PV (y) = 240 + 160 = 4005. The rate of return is also called: I) discount rate; II) hurdle rate; III) opportunity cost of capital A. I only B. I and II only C. I, II, and III D. None of the given ones C 6. Present value of $121,000 expected to be received one year from today at an interest rate (discount rate) of 10% per year is: A. $121,000 B. $100,000 C. $110,000 D. None of the above C PV = (121,000)/(1.1) = 110,000 7. One year discount factor at a discount rate of 25% per year is: A. 1.25 B. 1.0 C. 0.8 D. None of the above Discount Factor = 1/1.25 = 0.8 8. The one-year discount factor at an interest rate of 100% per year is: A. 1.5 B. 0.5 C. 0.25 D. None of the above B Discount factor = 1/(1 + 1) = 0.5 9. Present Value of $100,000 that is, expected, to be received at the end of one year at a discount rate of 25% per year is: A. $80,000 B. $125,000 C. $100,000 D. None of the above A PV = (100,000)/(1 + 0.25) = 80,000 10. If the one-year discount factor is 0.8333, what is the discount rate (interest rate) per year? A. 10% B. 20% C. 30% D. None of the above B 1 + r = 1/(0.8333) = 1.20; r = 20% 11. If the present value of $480 to be paid at the end of one year is $400, what is the one-yeardiscount factor? A. 0.8333 B. 1.20 C. 0.20 D. None of the above A Discount factor is = 400/480 = 0.8333 12. If the present value of $250 expected to be received one year from today is $200, what is the discount rate? A. 10% B. 20% C. 25% D. None of the above C 1 + r = 250 /200 = 1.25; r = 25% 13. If the one-year discount factor is 0.90, what is the present value of $120 to be received one year from today? A. $100 B. $96 C. $108 D. None of the above C PV = (120)(0.90) = 108 14. If the present value of $600 expected to be received one year from today is $400, what is the one-year discount rate? A. 15% B. 20% C. 25% D. 50% D 1 + r = (600)/(400) = 1.5; r = 50% 15. The present value formula for one period cash flow is: A. PV = C1(1 + r) B. PV = C1/(1 + r) C. PV = C1/r D. None of the above B 16. The net present value formula for one period is: I) NPV = C0 + [C1/(1 + r)]; II) NPV = PV required investment; and III) NPV = C0/C1 A. I only B. I and II only C. III only D. None of the above B 17. An initial investment of $400,000 will produce an end of year cash flow of $480,000. What is the NPV of the project at a discount rate of 20%?A. $176,000 B. $80,000 C. $0 (zero) D. None of the above C NPV = -400,000 + (480,000/1.2) = 0 18. If the present value of a cash flow generated by an initial investment of $200,000 is $250,000, what is the NPV of the project? A. $250,000 B. $50,000 C. $200,000 D. None of the above B NPV = -200,000 + 250,000 = 50,000 19. What is the present value of the following cash flow at a discount rate of 9%? Year 1: 100k, Year 2: 150k, Year 3: 200k A. $372,431.81 B. $450,000 C. $405,950.68 D. None of the above A PV = (100,000/1.09) + (150,000/(1.09^2)) + 200,000/(1.09^3) = 372,431.81 20. At an interest rate of 10%, which of the following cash flows should you prefer? A: Year 1 - 500, Year 2 - 300, Year 3 - 100 B: Year 1 - 100, Year 2 - 300, Year 3 - 500 A: Year 1 - 300, Year 2 - 300, Year 3 - 300 D: Any of the above as they all add up to 900 A. Option A B. Option B C. Option C D. Option D A PV(A) = 777.61; PV(B) = 714.50; PV(C) = 746.05; A is preferred 21. What is the net present value of the following cash flow at a discount rate of 11%? t = 0: -120k, t = 1: 300k, t = 2: -100k A. $69,108.03 B. $231,432.51 C. $80,000 D. None of the above A NPV = -120,000 + (300,000/1.11) -(100,000/(1.11^2)) = 69,108.03 22. What is the present value of the following cash flow at a discount rate of 16% APR? t = 1: -100k, t = 2: -300k A. $136,741.97 B. $122,948.87C. $158,620.69 D. None of the above A PV = (-100,000/1.16) + (300,000/(1.16^2)) = 136,741.97 23. What is the net present value (NPV) of the following cash flows at a discount rate of 9%? t = 0: -250k, t = 1: 100k, t = 2: 150k, t = 3: 200k A. $122,431.81 B. $200,000 C. $155,950.68 D. None of the above A NPV = -250,000 + (100,000/1.09) + (150,000/(1.09^2)) + (200,000/(1.09^3)) NPV = 122,431.81 24. The following statements regarding the NPV rule and the rate of return rule are true except: A. Accept a project if its NPV > 0 B. Reject a project if the NPV < 0 C. Accept a project if its rate of return > 0 D. Accept a project if its rate of return > opportunity cost of capital C 25. An initial investment of $500 produces a cash flow $550 one year from today. Calculate the rate of return on the project A. 10% B. 15% C. 25% D. none of the above A Rate of return = (550 - 500)/500 = 10% 26. According to the net present value rule, an investment in a project should be made if the: A. Net present value is greater than the cost of investment B. Net present value is greater than the present value of cash flows C. Net present value is positive D. Net present value is negative C 27. Which of the following statements regarding the net present value rule and the rate of return rule is not true? A. Accept a project if NPV > cost of investment B. Accept a project if NPV is positive C. Accept a project if return on investment exceeds the rate of return on an equivalent investment in the financial market D. Reject a project if NPV is negative A 28. The opportunity cost of capital for a risky project is A. The expected rate of return on a government security having the same maturity as the project B. The expected rate of return on a well-diversified portfolio of common stocks C. The expected rate of return on a portfolio of securities of similar risks as the projectD. None of the above C 29. A perpetuity is defined as: A. Equal cash flows at equal intervals of time for a specific number of periods B. Equal cash flows at equal intervals of time forever C. Unequal cash flows at equal intervals of time forever D. None of the above B 30. Which of the following is generally considered an example of a perpetuity: A. Interest payments on a 10-year bond B. Interest payments on a 30-year bond C. Consols D. None of the above C 31. You would like to have enough money saved to receive $100,000 per year perpetuity after retirement so that you and your family can lead a good life. How much would you need to save in your retirement fund to achieve this goal (assume that the perpetuity payments start one year from the date of your retirement. The interest rate is 12.5%)? A. $1,000,000 B. $10,000,000 C. $800,000 D. None of the above C PV = (100,000/0.125) = 800,000 32. What is the present value of $10,000 per year perpetuity at an interest rate of 10%? A. $10,000 B. $100,000 C. $200,000 D. None of the above B PV = (10,000/0.1) = 100,000 33. You would like to have enough money saved to receive $80,000 per year perpetuity after retirement so that you and your family can lead a good life. How much would you need to save in your retirement fund to achieve this goal (assume that the perpetuity payments start one year from the date of your retirement. The interest rate is 8%)? A. $7,500,000 B. $750,000 C. $1,000,000 D. None of the above C PV = (80,000/0.08) = 1,000,000 34. You would like to have enough money saved to receive a $50,000 per year perpetuity after retirement so that you and your family can lead a good life. How much would you need to save in your retirement fund to achieve this goal (assume that the perpetuity payments starts on the day of retirement. The interest rate is 8%)? A. $1,000,000 B. $675,000C. $625,000 D. None of the above B PV = [(50,000/0.08)](1.08) = 675,000 35. You would like to have enough money saved to receive an $80,000 per year perpetuity after retirement so that you and your family can lead a good life. How much would you need to save in your retirement fund to achieve this goal (assume that the perpetuity payments starts on the day of retirement. The interest rate is 10%)? A. $1,500,000 B. $880,000 C. $800,000 D. None of the above B PV = [(80,000/0.1)] * (1.1) = 880,000 36. An annuity is defined as A. Equal cash flows at equal intervals of time for a specified period of time B. Equal cash flows at equal intervals of time forever C. Unequal cash flows at equal intervals of time forever D. None of the above A 37. If you receive $1,000 payment at the end each year for the next five years, what type of cash flow do you have? A. Uneven cash flow stream B. An annuity C. An annuity due D. None of the above B 38. If the three-year present value annuity factor is 2.673 and two-year present value annuity factor is 1.833, what is the present value of $1 received at the end of the 3 years? A. $1.1905 B. $0.84 C. $0.89 D. None of the above B PV = (2.673 - 1.833) * (1) = 0.84 39. If the five-year present value annuity factor is 3.60478 and four-year present value annuity factor is 3.03735, what is the present value at the $1 received at the end of five years? A. $0.63552 B. $1.76233 C. $0.56743 D. None of the above C PV = (3.60478 - 3.03735) * (1) = 0.56743 40. What is the present value annuity factor at a discount rate of 11% for 8 years? A. 5.7122 B. 11.8594C. 5.1461 D. None of the above C PV annuity factor = (1/0.11) - (1/((0.11)(1.11^8))) = 5.1461 41. What is the present value annuity factor at an interest rate of 9% for 6 years? A. 7.5233 B. 4.4859 C. 1.6771 D. None of the above B PV annuity factor = (1/0.09) - (1/((0.09)(1.09^6))) = 4.4859 42. What is the present value of $1000 per year annuity for five years at an interest rate of 12%? A. $6,352.85 B. $3,604.78 C. $567.43 D. None of the above B PV annuity factor = [(1/0.12) - (1/((0.12)(1.12^ 5)))] * 1000 = 3,604.78 43. What is the present value of $5000 per year annuity at a discount rate of 10% for 6 years? A. $21,776.30 B. $3,371.91 C. $16,760.78 D. None of the above C PV = [(1/0.10) - (1/((0.10)(1.10^6)))] * 5000 = 16,760.78 44. After retirement, you expect to live for 25 years. You would like to have $75,000 income each year. How much should you have saved in the retirement to receive this income, if the interest is 9% per year (assume that the payments start on the day of retirement)? A. $736,693.47 B. $802,995.88 C. $2,043,750 D. None of the above B PV = [[(1/0.09) - (1/((0.09)(1.09^25)))] 75,000] (1.09) = 802,995.88 45. After retirement, you expect to live for 25 years. You would like to have $75,000 income each year. How much should you have saved in the retirement to receive this income, if the interest is 9% per year (assume that the payments start one year after the retirement)? A. $736,693.47 B. $6,352,567.22 C. $1,875,000 D. None of the above A PV = [(1/0.09) - (1/((0.09)(1.09^25)))] * 75,000 = 736,693.4746. For $10,000 you can purchase a 5-year annuity that will pay $2504.57 per year for five years. The payments are made at the end of each year. Calculate the effective annual interest rate implied by this arrangement: (approximately) A. 8% B. 9% C. 10% D. None of the above A Using a financial calculator: N = 5; PV = -10,000; PMT = 2504.57; FV = 0 Compute: I = 8.0% [calculator setting: END] 47. If the present value annuity factor for 10 years at 10% interest rate is 6.1446, what is the present value annuity factor for an equivalent annuity due? A. 6.1446 B. 7.38 C. 6.759 D. None of the above C Annuity due: 6.1446 * 1.1 = 6.759 48. If the present annuity factor is 3.8896, what is the present value annuity factor for an equivalent annuity due if the interest rate is 9%? A. 3.5684 B. 4.2397 C. 3.8896 D. None of the above. B annuity due factor = 3.8896 * 1.09 = 4.2397 49. For $10,000 you can purchase a 5-year annuity that will pay $2358.65 per year for five years. The payments are made at the beginning of each year. Calculate the effective annual interest rate implied by this arrangement: (approximately) A. 8% B. 9% C. 10% D. none of the above B Using a financial calculator: N = 5; PV = -10,000; PMT = 2358.65; FV = 0 Compute: I = 9.0% [Calculator setting: BEGIN (BGN)] 50. John House has taken a $250,000 mortgage on his house at an interest rate of 6% per year. If the mortgage calls for twenty equal annual payments, what is the amount of each payment? A. $21,796.14 B. $10,500.00 C. $16,882.43 D. None of the above A (Use a financial calculator) PV = 250,000; I - = 6%; N = 20; FV = 0; Compute PMT = $21,796.14 51. John House has taken a 20-year, $250,000 mortgage on his house at an interest rate of 6%per year. What is the value of the mortgage after the payment of the fifth annual installment? A. $128,958.41 B. $211,689.53 C. $141,019.50 D. None of the above B Step 1: I = 6%; N = 20; PV = 250,000; FV = 0; Compute PMT = 21,796.14 Step 2: I = 6%; N = 15; PMT = 21,796.14; Compute PV = 211,689. 53 52. If the present value of $1.00 received n years from today at an interest rate of r is 0.3855, then what is the future value of $1.00 invested today at an interest rate of r% for n years? A. $1.3855 B. $2.594 C. $1.70 D. Not enough information to solve the problem B FV = 1/(0.3855) = 2.594 53. If the present value of $1.00 received n years from today at an interest rate of r is 0.621, then what is the future value of $1.00 invested today at an interest rate of r% for n years? A. $1.00 B. $1.61 C. $1.621 D. Not enough information to solve the problem B FV = 1/(0.621) = 1.61 54. If the future value of $1 invested today at an interest rate of r% for n years is 9.6463, what is the present value of $1 to be received in n years at r% interest rate? A. $9.6463 B. $1.00 C. $0.1037 D. None of the above C PV = 1/9.6463 = 0.1037 55. If the future value annuity factor at 10% and 5 years is 6.1051, calculate the equivalent present value annuity factor A. 6.1051 B. 3.7908 C. 6.7156 D. None of the given ones B PV = 6.1051/(1.1)^5 = 3.7908 56. If the present value annuity factor at 10% APR for 10 years is 6.1446, what is the equivalent future value annuity factor? A. 3.108 B. 15.9374 C. 2.5937 D. None of the aboveB FV annuity factor = 6.1446 * (1.1^10) = 15.9374 57. If the present value annuity factor at 12% APR for 5 years is 3.6048, what is the equivalent future value annuity factor? A. 2.0455 B. 6.3529 C. 1.7623 D. None of the above B FV annuity factor = 3.6048 * (1.12^5) = 6.3529 58. If the present value annuity factor at 8% APR for 10 years is 6.71, what is the equivalent future value annuity factor? A. 3.108 B. 14.487 C. 2.159 D. None of the above B FV annuity factor = 6.71 * (1.08^10) = 14.487 59. You are considering investing in a retirement fund that requires you to deposit $5,000 per year, and you want to know how much the fund will be worth when you retire. What financial technique should you use to calculate this value? A. Future value of a single payment B. Future value of an annuity C. Present value of an annuity D. None of the above B 60. Mr. Hopper is expected to retire in 25 years and he wishes accumulate $750,000 in his retirement fund by that time. If the interest rate is 10% per year, how much should Mr. Hopper put into the retirement fund each year in order to achieve this goal? [Assume that the payments are made at the end of each year] A. $4,559.44 B. $2,500 C. $7,626.05 D. None of the above C Future value annuity factor = [(1.1^25) - 1]/(0.1) = 98.347; payment = 750,000/98.347 = 7626.05 61. Mr. Hopper is expected to retire in 30 years and he wishes accumulate $1,000,000 in his retirement fund by that time. If the interest rate is 12% per year, how much should Mr. Hopper put into the retirement fund each year in order to achieve this goal? A. $4,143.66 B. $8,287.32 C. $4,000 D. None of the above A Future value annuity factor = [(1.12^30 - 1]/(0.12) = 241.3327;payment = 1,000,000/241.3327 = 4143.66 62. You would like to have enough money saved to receive a growing annuity for 20 years, growing at a rate of 5% per year, the first payment being $50,000 after retirement. That way, you hope that you and your family can lead a good life after retirement. How much would you need to save in your retirement fund to achieve this goal.(assume that the growing annuity payments start one year from the date of your retirement. The interest rate is 10%)? A. $1,000,000 B. $425,678.19 C. $605,604.20 D. None of the above C PV = (50,000)[(1/(0.1 - 0.05)) - {(1/(0.1 - 0.05)}{(1.05^20)/(1.10^20)}] = 605,604.20 63. You would like to have enough money saved to receive a growing annuity for 25 years, growing at a rate of 4% per year, the first payment being $60,000 after retirement, so that you and your family can lead a good life. How much would you need to save in your retirement fund to achieve this goal? (assume that the growing perpetuity payments start one year from the date of your retirement. The interest rate is 12%)? A. $1,500,000 B. $632,390 C. $452,165 D. None of the above B PV = (60,000) [(1/(0.12 - 0.04)) - {(1/(0.12 - 0.04)}{(1.04^25)/(1.12^25)}] = 632,390 64. The discount rate is used for calculating the NPV is: A. Determined by the financial markets B. Found by the government C. Found by the CEO D. None of the above A 65. The managers of a firm can maximize stockholder wealth by: A. Taking all projects with positive NPVs B. Taking all projects with NPVs greater than the cost of investment C. Taking all projects with NPVs greater than present value of cash flow D. All of the above A 66. If you invest $100 at 12% APR for three years, how much would you have at the end of 3 years using simple interest? A. $136 B. $140.49 C. $240.18 D. None of the above A FV = 100 + (100 0.12 3) = $136 67. If you invest $100 at 12% APR for three years, how much would you have at the end of 3 years using compound interest?A. $136 B. $140.49 C. $240.18 D. None of the above B FV = 100 * (1.12^3) = $140.49 68. Which of the following statements is true? A. The process of discounting is the inverse of the process of compounding. B. Ending balances using simple interest is always greater than the ending balance using compound interest at positive interest rates. C. Present value of an annuity due is always less than the present value of an equivalent annuity at positive interest rates. D. All of the above are true. A 69. The concept of compound interest is most appropriately described as: A. Interest earned on an investment B. The total amount of interest earned over the life of an investment C. Interest earned on interest D. None of the above C 70. Ms. Colonial has just taken out a $150,000 mortgage at an interest rate of 6% per year. If the mortgage calls for equal monthly payments for twenty years, what is the amount of each payment? (Assume monthly compounding or discounting.) A. $1254.70 B. $1625.00 C. $1263.06 D. None of the above are true A PMT = 150,000/[(1/0.005) - 1/((0.005 * ((1 + 0.005)^240)))] = $1254.70 71. An investment at 10.47% effective rate compounded monthly is equal to a nominal (annual) rate of: A. 10.99% B. 9.57% C. 10% D. None of the above C NOM = [(1.1047)^(1/12) - 1] * 12 = 0.1 = 10.00% 72. An investment at 12% nominal rate compounded monthly is equal to an annual rate of: A. 12.68% B. 12.36% C. 12% D. None of the above A EAR = ((1.01)^12) - 1 = 0.12681 = 12.68% 73. Mr. William expects to retire in 30 years and would like to accumulate $1 million in the pension fund. If the annual interest rate is 12% per year, how much should Mr. Williams putinto the pension fund each month in order to achieve his goal? Assume that Mr. Williams will deposit the same amount each month into his pension fund and also use monthly compounding. A. $286.13 B. $771.60 C. $345.30 D. None of the above A PMT = 1,000,000/{[(1/0.01) - (1/(0.01 (1.01^360)))] (1.01^360)} = $286.13 74. An investment at 10% nominal rate compounded continuously is equal to an equivalent annual rate of: A. 10.250% B. 10.517% C. 10.381% D. None of the above B (e^(0.1)) - 1 = 0.10517 = 10.517% 75. The present value of a $100 per year perpetuity at 10% per year interest rate is $1000. What would be the present value if the payments were compounded continuously? A. $1000.00 B. $1049.21 C. $1024.40 D. None of the above B (e^r) = 1.1 r = ln(1.1) = 0.09531; PV = 100/0.09531 = $1049.21 76. The rate of return, discount rate, hurdle rate or opportunity cost of capital all means the same. TRUE 77. A dollar today is worth more than a dollar tomorrow if the interest rate is positive. TRUE 78. The present value of a future cash flow can be found by dividing it by an appropriate discount factor. FALSE 79. Net present value is found by subtracting the required investment from the present value of future cash flows. TRUE 80. The opportunity cost of capital is higher for safe investments than for risky ones. FALSE 81. A safe dollar is always worth less than a risky dollar because the rate of return on a safe investment is generally low and the rate of return on a risky investment is generally high. FALSE 82. "Accept investments that have positive net present values" is called the net present value rule. TRUE83. "Accept investments that offer rates of return in excess of opportunity cost of capital". TRUE 84. The rate of return on any perpetuity is equal to the cash flow multiplied by the price. FALSE 85. An annuity is an asset that pays a fixed sum each year for a specified number of years. TRUE 86. The value of a five-year annuity is equal to the sum of two perpetuities. One makes its first payment in year 1, and the other makes its first payment in year 6. FALSE 87. An equal-payment home mortgage is an example of an annuity. TRUE 88. In the amortization of a mortgage loan with equal payments, the fraction of each payment devoted to interest steadily increases over time and the fraction devoted to reducing the loan decreases steadily. TRUE 89. In the case of a growing perpetuity, the present value of the cash flow is given by: [C1/(r - g)] where r > g. TRUE 90. Compound interest assumes that you are reinvesting the interest payments at the rate of return. TRUE 91. Briefly explain the term "discount rate." Discount rate is the rate of return used for discounting future cash flows to obtain the present value. The discount rate can be obtained by looking at the rate of return, an equivalent investment opportunity in the capital market. 92. Intuitively explain the concept of the present value. If you have $100 today, you can invest it and start earning interest on it. On the other hand, if you have to make a payment of $100 one year from today, you do not need to invest $100 today but a lesser amount. The lesser amount invested today plus the interest earned on it should add up to $100. The present value of $100 one year from today at an interest rate of 10% is $90.91. [PV = 100/1.1 = 90.91] 93. State the "net present value rule." Invest in projects with positive net present values. Net present value is the difference between the present value of future cash flows from the project and the initial investment. 94. Briefly explain the concept of risk. If the future cash flows from an investment are not certain then we call it a risky cash flow. That means there is an uncertainty about the future cash flows or future cash flows could be different from expected cash flows. The degree of uncertainty varies from investment to investment. Generally, uncertain cash flows are discounted using a higher discount rate than certain cash flows. This is only one method of dealing with risk. There are many ways to take risk into consideration while making financial decisions. 95. State the "rate of return rule." Invest as long as the rate of return on the investment exceeds the rate of return on equivalentinvestments in the capital market. 96. Discuss why a dollar tomorrow cannot be worth less than a dollar the day after tomorrow. If a dollar tomorrow is worth less than a dollar a day after tomorrow, it would be possible to earn a very large amount of money through "money machine" effect. This is only possible, if someone else is losing a very large amount of money. These conditions can only exist for a short period of time, and cannot exist in equilibrium as the source of money is quickly exhausted. Thus a dollar tomorrow cannot be worth less than a dollar the day after tomorrow. 97. Define the term "perpetuity." A perpetuity is defined as the same cash flow occurring each year forever. 98. Describe how you would go about finding the present value of any annuity given the formula for the present value of a perpetuity. The present value of any annuity can be thought of as the difference between two perpetuities one payment stating in year-1 (immediate) and one starting in year (n + 1) (delayed). By calculating difference between the present values of these two perpetuities today we can find the present value of an annuity. 99. What is the difference between simple interest and compound interest? When money is invested at compound interest, each interest payment is reinvested to earn more interest in subsequent periods. In the simple interest case, the interest is paid only on the initial investment. 100. Briefly explain, "continuous compounding." As frequency of compounding increases, the effective rate on an investment also increases. In case of continuous compounding the frequency of compounding is infinity. In this case, the nature of the function also changes. The effective interest rate is given by (er - 1), where the value of e = 2.718. e is the base for natural logarithms. CAIIB - FINANCIAL MANAGEMENT – MODULE - A MODEL QUESTIONS - (SET-I) 1)What is sampling for groups with considerable variation within but similar to each other called ? a) cluster b) stratified c) systematic d) random 2)What are sampling groups which are very similar within but dissimilar without are called ? a) cluster b) stratified c) systematic d) random 3)In which of the situations would σ¯x = σ not be the correct formula for Sampling √n a) infinite population b) finite population with replacement c) finite population without replacement d) none of the above4) What does the Central tendency theorem state ? a) as the sample size increases the sampling distribution of the mean will approach normality irrespective of the shape of the population distribution b) the mean of the sampling distribution of the mean will equal the population mean even if the population is not normal c) uses of sample statistics to make inferences of the the population parameters without knowledge of the of the frequency distribution d) all of the above 5) What variation does moving average method eliminate.? a) seasonal b) Cyclical c) Irregular d) secular trend 6) What Stream of cash flows continue indefinitely ? a) perpetuity, b) annuity c) futurity d) none of the above 7) What is the difference between real & nominal cash flows due to ? a) compounding b) discounting c) annuity d) inflation 8) On what is the magnitude of discount rate dependent upon ? a) inflation b) preference or consumption c) risk d) all of them 9) While positive cash flows are good for an enterprise what do negative cash flows indicate. a) losses b) a or c or d c) investments d) cash crunch 10) Of what is sinking fund an example of ? a) perpetuity b) annuity c) gratuity d) none of the above 11) What is a scatter diagram ? a) diagram which scatters all elements of the variable. b) A graphic representation of the relationship of the variables c) Helps plot observed values d) b& c 12) In what range does correlation coefficient lie ?a. 0 to +1 b. -1 to 0 c. -1 to +1 d. > 1 13) Point estimate is often insufficient. Why ? e. decision is inversely proportional to the number of estimates f. difficult to pinpoint the correct single estimate g. because it does not provide the extent of error h. a & c 14) If a standard error of a statistic is less than that of another then what is the former is said to be. a ) efficient b) unbiased c) consistent d) sufficient 15) What is interest on a bond known as ? i. return j. yield k. coupon l. maturity value 16) Overstating the return on premium bonds and understating the return on discount bonds is generally true when we use one of the following as an indicator. Which one is it ? a. yield to maturity b. current yield c. rate of return d. discount rate 17) Yield to maturity is that rate which makes the Present Value of the bond payments equal to its buying price. Which of the following is it.? e. coupon rate f. discount rate g. compound rate h. rate of return 18) What does the rate of return equal to if interest rates do not change during the pendency of the bond ? a. yield to maturity b. coupon rate c. compounded rate d. current yield 19)) What is a survey of parliamentarians, seeking their opinion on revision of perks, called? a) biased sampling b) stratified sampling c) random sampling d) systematic sampling20) How is stratified sampling carried out? a)divide the population into homogenous groups and select equally but randomly. b) assigning numbers to the population & selecting the numbers c) sample is made up of elements which are say 10th from the previous selection d)population divides itself into groups and we select equally but randomly from each 21) Why do sampling errors occur ? a) differences between sample and population b) differences among samples themselves c) choice of elements of sampling d) all of the above 22) If σx = standard error of mean, σ = standard deviation of the mean, n = ˉ sample size, N = population size, µ = population mean, sample mean = xˉ What is the standard error of the mean for finite populations ? a) σx = ˉˉ σ. √n b) σx¯ = σ √(N-n) √n √(n-1) c) z = x¯ µ σx¯ d)σx = ˉ σ√(N-n) √n 23) Which variation does moving average method eliminate? a. Seasonal b. Cyclical c. Irregular d) secular trend 24) Why is a discount rate used to calculate net present value? a) money has value b) money has enhancing value c) money has diminishing value d) money has constant value 25) What does net present value give? a) future values of present cash flows b) present value of present cash flow c) present value of future cash flows d) future values of future cash flows 26) What is repayment of entire loan principal at the end of the loan period called ? a) balloon payment b) compounded payment c) annuity d) term payment27) What is the rule of 72 ? a) 12 times table b) rule for calculating future cash flows c) rule for compounding present cash flows d) rule for knowing how quickly money doubles 28) If prices double, what happens to real value of rupee?. a) remains same b) doubles c) halves d) changes in unlike proportions 29) Which method which helps draw a line between the set of scattered points e) regression method f) correlation method g) least square method h) least fit method 30) Out of the following, which 3 measures are used in correlation analysis: a)standard error, b)covariance, c)standard deviation, d)coefficient of correlation, e) coefficient of determination. 1) a, b, c 2) a, c, e 3) b, d, e 4) b, c, e 31)The value of a statistic tends towards the value of the population as size increases. What is it said to be ? a) sufficient b) consistent c) efficient d) unbiased 32) In a normal distribution 95.5% of all the sample statistics are within _____standard errors of the population parameter a) ± 5% b) ± 2.25% c) ± 3% d) none of the above 33) ‘As the output increases, the productivity per worker increases.’ What relationship does it lead to ? a) direct linear relationship b) curvilinear relationship c) inverse relationship d)none of the above34) If the maturity of a bond is long into the future the interest rate is higher. Why? a)longer term maturity is more sensitive to price fluctuation than shorter term b) the attractiveness of longer term is related to interest only c) longer term bonds are generally issued by institutions of lesser rating d) longer term maturity is less sensitive to fluctuation than shorter term 35) What is a zero coupon bond? a) there is gain only in price b) gain in coupon c) no gain at all d) none of these 36) If coupon = C , face value = F , current price = P, discount rate = R , balance period = 3 ,then which of the following is yield to maturity a) C + P-F P(1+R)³ b) ∑C + F ∑(1+R)² (1 + R)³ c) C P d) F P(1+R)³ 37) A company manufactures Radios(x) and Tape recorders(y). Cost of making radio & tape recorder is Rs. 225 and Rs. 375 respectively. The company works in 2 shift totaling 14 hrs. The production and assembly time for a radio is 2hrs while that for tape recorder is 3 hrs. The radio sells for Rs.250 while the tape recorder sells for Rs.410. The company spends an amount of Rs. 75,000 per day on production. Maximize the production in terms of optimum number of radios and tape recorders. Pick the correct constraint equation from the choice given against each type. i) capacity constraint a) 3x + 2y ≤ 14 (machine time) b) 2x + 3y ≤ 14 c) 2x + 3y ≥14 d) 3x + 2y ≥14 ii) financial constraint a) 250x + 410y ≤ 75000 (amount available) b) 3x + 5y ≤ 75000 c) 3x + 5y ≤ 1000 d) 3x + 5y ≥ 1000 iii) non – negativity a) x > 0 ; y > 0 (minimum number) b) x = 0 ; y = 0 c) x ≤ 0 ; y ≤ 0 d) a & b iv) objective function a) P = 25x + 35y (to maximize profit) b) P = 20x + 35y c) P = 25x + 30yd) P = 20x + 35y 38)A firm makes chairs (x) and tables(y). Each table costs Rs.400 in material and Rs.150 in labor . each chair costs Rs.175 in material and Rs.75 in labor. The price of table and chair is Rs.625 and Rs. 300 respectively. The firm has 12 hours of time per day. The production time for each table and chair is 4 hrs, 1.5 hrs respectively. The firm has liquidity of Rs.7000 per day to pay for the material and labor. The objective is to maximize the production for the firm by optimizing the production of tables and chairs. Pick out the correct option for each of the constraint equation. a) capacity constraint : a) 4x + 1.5y ≤ 12 (machine time) b) 1.5x + 4y ≤ 12 c) 4x + 1.5y ≥ 12 d) 1.5x + 4y ≥ 12 b) financial constraint : a) 5x + 11y ≤ 7000 (amount available) b) 5x + 11y ≥ 700 c) 12x + 25y ≤ 7000 d) 12x + 25y ≥ 7000 c) non – negativity : a) x ≥ 0 ; y ≥ 0 (minimum number) b) x = 0 ; y = 0 c) x < 0 ; y < 0 d) b & c d) objective function :a) P = 75x + 50y (To maximize profit) b) P = 50x + 75y c) P = 55x + 75y d) P = 75x + 50y 39) An amount of Rs.1,15,000 is expected to be received one year from today at an interest rate (discount rate) of 10% per year. What is its present value ? a. Rs.121,000 b. RS. 100,500c. Rs.110,000 d. Rs.104,545 40) What is the two-year discount factor at a discount rate of 10% per year ? a. 0.826 b. 1.000 c. 0.909 d. 0.814 41) What is the opportunity cost of capital for a risky project ? a. The expected rate of return on a government security having the same maturity as the project b. The expected rate of return on a well diversified portfolio of common stocks c. The expected rate of return on a portfolio of securities of similar risks as the project d. a or b or c 42) If the one year discount factor is 0.8333, what is the discount rate (interest rate) per year? a . 10% b. 20% c. 30% d. None of the above 43) If the present value of a cash flow generated by an initial investment of Rs.100,000 is Rs.120,000, what is the NPV of the project? a. Rs.120,000 b. Rs.20,000 c. Rs.100,000 d. None of the above 44) The following statements regarding the NPV rule and the rate of return rule are true with one exception. Which one is it : a. Accept a project if its NPV > 0 b. Reject a project if its NPV < 0 c. Accept a project if its rate of return > 0 d. Accept a project if its rate of return > opportunity cost of capital 45) What is the concept of compound interest:? a. Earning interest on the principal b. Earning interest on previously earned interestc. Investing for a number of years d. None of the above 46) If there is a indirect relationship between rainfall & yield of crops then a) yield is higher if rainfall is less b) yield is lower if rainfall is less c) yield is higher if rainfall is higher d) none of the above 47) If a = 2 , b = 1 , independent variable = 4 then dependent variable for an estimating line is a) 2 b) 4 c) 6 d) none of the above 48) If the estimating equation is Y = a – b X which of the following is true a) the y intercept is b b) slope of line is negative c) there is inverse relationship d) all of these e) b & c 49) The value of r2 is 0.49 then coefficient of correlation is a) 0.49 b) 0.7 c) 0.07 d) cannot be determined 50) If the dependent variable increases with the independent variable then the coeff. of correlation is a) 0 to -1 b) 0 to – 0.5 c) 0 to -2 d) none of these 51) The method of least squares finds the best fit line that _______ the error between observed & estimated points on the line a) maximises b) minimizes c) reduces to zero d) b & c 52) If sign of r is negative then it indicates a) direct relationship between X & Y b) indirect relationship between X & Y c) inverse relationship between X & Y d) b or c 53) For Y = a - b X we say that relationship betweenY and X is a) direct & linear b) indirect & linear c) indirect & curvilinear d) direct & curvilinear 54) In the relationship between height and educational qualification a) the height is independent and education is dependent variable b) the height is dependent and education is independent variable c) there is inverse relationship between the two d) none of the above 55) In given Qrtly. data the first step in computing seasonal index is calculating a) 4 qtr moving average b) discard highest and lowest values c) 4 qtr. Moving total d) none of the above 56)For a data of 8 half year periods the code for the 7th half is a) 2 b) 3 c) 6 d) 5 57)When coding for odd number of periods The following is done a) subtract each value from the smallest value b) subtract each value from the highest value c) subtract each value from the middlemost term d) none of the above 58)A time series of annual data will contain which of the following components e) secular trend f) cyclical fluctuation g) seasonal variation h) a & c i) a & b 59)Removing the highest & lowest actual-to-moving average values when computing seasonal index for annual data reduces j) extreme cyclical variations k) secular trend l) seasonal variations m) all of these 60) the repetitive movement around a trend line in a 4- month period is best described byn) seasonal variation o) secular trend p) cyclical fluctuation q) irregular variation 61) the result of discarding extreme values before averaging is called ________ . r) residual mean s) modified mean t) extreme mean u) none of the above 62) For a given year if an adjusted seasonal index is > 100 then for some other period it is v) < 100 w) > 100 x) = 100 y) none of the above 63) Present Value is defined as: A. Future cash flows discounted to the present at an appropriate discount rate B. Inverse of future cash flows C. Present cash flow compounded into the future D. None of the above 64) If the interest rate is 15%, what is the 2 year discount factor? A. 0.7561 B. 0.8697 C. 1.3225 D. 0.658 65) An annuity is defined as A. Equal cash flows at equal intervals of time forever B. Equal cash flows at equal intervals of time for a specific period C. Unequal cash flows at equal intervals of time forever D. None of the above 66) If the present value of the cash flow X is Rs.200, and the present value cash of the flow Y is Rs.150, than the present value of the combined cash flow is: A. 200B. 150 C. 50 D. 350 E. None of the above 67) What is the present value annuity due factor of Re.1at a discount rate of 15% for 15 years? A. 5.8474 B. 8.514 C. 8.13 D. 7.002 68) An investment at 12% nominal rate compounded monthly is equal to an annual rate of: A. 12.68% B. 12.36% C. 12% D. None of the above 69) A 5-year Govt. bond with a compound rate of 8% has a face value of 1000. What is the annual interest payment? A. 80 B. 40 C. 100 D. None of the above 70) If the present value of Rs.444 to be paid at the end of one year isRs. 400, what is the one year discount factor? A. 0.909 B. 1.11 C. 0.11 D. None of the above 71) If you invest Rs.100,000 today at 12% interest rate for one year, what is the amount you will have at the end of the year? A. Rs.90,909 B. Rs.112,000 C. Rs.100,000D. None of the above CAIIB - FINANCIAL MANAGEMENT – MODULE - A MODEL QUESTIONS - (SET-II) 1. Current Price of a share is Rs. 100. The economic state is as follows Economy Probability Price Growth 0.6 130 Recession 0.4 90 Calculate the expected return for the stock a) 10% b) 15% c) 14% d) 16% 2. What is the N P V of the following at 15% C A S H F L O W S t = 0 t = 1 t = 2 -120,000 -100,000 300,000 a) 19,887 b) 80,000 c) 26,300 d) 40,000 3. An investment at 12% compound monthly is equal to annual rate a) 12.68% b) 12.26% c) 12% d) 12.36% 4. In theory of Sampling “ the larger the size of the sample the greater the accuracy” is based on a) law of Statistical regularity b) law of Inertia of large numbers c) law of Statistical imperfection d) law of large numbers 5. If P = 0.5 Q = 0.5 σ = 0.05 Find the sample size a) 1000 b) 100,000 c) 100d) 10,000 6. In finding a sample of good & bad students asking students themselves whether they are good or bad is a case of bias. Which of the following does the bias fall into a) faulty process of selection b) faulty work during collection of data c) faulty method of analysis d) wrong choice of subject 7. When we want to study some unknown traits of a population , we use a) cluster sampling b) stratified sampling c) judgment sampling d) systematic sampling 8. Which of the following is not a restricted random sample a) judgment sampling b) stratified sampling c) systematic sampling d) cluster sampling 9. Which one of the following is not true a) probability sampling depends upon existence of detailed information about the universe for its existence b) probability sampling provides estimates which are essentially unbiased & have reasonable precision c) probability sampling requires a high level of skill and experience for its use d) it is possible to evaluate the relative efficiency of various sample designs of various sample is used 10. In Correlation analysis which of the following is true a) the correlation may be due to pure chance in a small sample b) correlation analysis tell us about cause & effect of relationship c) correlation analysis does not tell us about degree of relationship d) correlated variables cannot be influenced other variables 11. From the following data identify the correct alternative X 10 20 30 40 50 Y 20 35 50 75 90 a) positive & linear b) positive & curvilinear c) negative & linear d) negative & curvilinear 12. In the following X and Y are independent & dependent variables. Read the figures and answer. X 1 2 3 4 Y 5 13 12 25 a) there is no correlation between X & Y b) there is +ve correlation between X & Yc) there is –ve correlation between X & Y d) there partial correlation between X & Y 13. In a study it was noticed that average height of sons of tall fathers is less than that of the fathers and vice versa . This is due to a) extension b) progression c) regression d) hypertension 14. Co-efficient of determination = r2 = explained variation Total variation Co-efficient of correlation = r while r explains completely the relationship between the variables, r2 does not , because a) r2 is less than 1 b) r2 is always +ve c) r2 is always -ve d) r2 as per formula cannot explain direction 15. For a normal distribution which of the following is true a) mode < mean < median b) mode > mean > median c) mean < median < mode d) mean = median = mode 16. Under a normal curve mean + 1.96σ is an area. Choose the correct one from the following a) 95.45% area b) 68.27% area c) 95.00% area d) 99.73% area 17. In a normal curve the area between z = -0.4 & z = 0.6 is a) 0.1554 b) 0.2257 c) 0.3811 d) 0.4267 18. In a normal distribution 7% of items are under 35 then what % are between mean and 35 a) 93% b) 65% c) 43% d) 86% 19. In a normal distribution for incomes mean = 750 Std deviation = 50 Population = 10,000 What is z value for income exceeding 650 a) -2.00 b) -1.50 c) -1.25 d) - 1.75 A) In an aptitude test administered to 1000 students the average scores was 42 & Std. Dev. = 24. Answer the following questions( 24 to 27)20) The number of students exceeding 50 marks a) 370 b) 670 c) 500 d) 250 21) Students lying between 30 & 54 marks a) 383 b) 463 c) 373 d) 293 22) Value of scores exceeded by top 100 students a) 70% b) 60% c) 73% d) 75% 23) No. of students getting scores < 50 a) 600 b) 540 c) 630 d) 660 24) Seasonal variations do not appear in annual figures since e) they occur infrequently f) they are cycles which occur repeatedly over relatively short duration g) figures may not be of requisite accuracy h) it is difficult to index the figures 25) The fall in demand for automobiles causing closure of factory is case of i) seasonal variation j) cyclical variation k) irregular variation l) secular trend 26) In the analysis of time series which of the following adjustments is not done while drawing up an index for de-seasonalising m) calendar variation n) population changes o) price changes p) coding 27) Read the following data and fill in the blank Year production moving average for 3 years 1990 10 1991 20 20 1992 30 30 1993 40 40 1994 50 __ 1995 75 a) 50 b) 55 c) 60 d) 6528) A sampling ratio of 0.10 was used in a sample survey when population Size was 50. What is the finite population multiplier . a) 0.968 b) 0.10 c) 1.10 d) cannot be calculated from the given data. 29) As the confidence level increases for a confidence interval the width of the interval a) Increases b) decreases c) remains unchanged d) a) or b) 30) Trend equation is Y = 25 + 0.4X, where Y is production figures, X is 1 year unit. Origin is 1960; shift origin to 1st Jan. 1961. The trend eqn. will now read as a) Y = 12.5 + 0.4X b) Y = 25 + 0.2X c) Y = 25 + 0.8X d) Y = 12.5 + 0.2X 31) A bond holder of a company has one of the following relationship with It .Identify a) shareholder b) depositor c) creditor d) employee 32) The relationship between the bond prices and interest rates is one of the Following a) direct & linear b) inverse & linear c) direct and curvilinear d) no relationship A) A toy manufacturer produces bicycles(x) & scooters(y). Read the following data and answer: Max. availability of machines is 12 hrs and x takes 2 hrs. and y takes 4 hrs to make. The total cost of x & y is Rs. 400 & 12000 respectively. The sale prices of x & y are Rs. 700 & 16000 respectively. The amount available for daily production is Rs. 28000. Labour available is for 16 hrs. labour requirement for x & y is 4 & 12 hrs respectively Choose the correct option from each of the following ( 38 to 41 ) 33) production constraint a) x + 2y ≤ 6 b) 4x + 2y ≤ 12 c) 2x + y ≤ 6 d) 9x = 6y ≤ 1234) Financial constraint a) 4x + 120y ≤ 280 b) 4x + 12y ≤ 28 c) 12y + 4x ≤ 28 d) 120x + 4y ≤ 280 35) Labour constraint a) 12x + 4y ≤ 16 b) x + 3y ≤ 4 c) 3y + x ≤ 4 d) 4x + 12y ≤ 16 36) Profit equation a) 7x + 160y b) 160x + 7y c) 700x + 1600y d) 70x + 160y B) The trend equation is Y = a + b X If N = 7, ∑Y = 619, ∑X = 0, ∑XY = 141, ∑X2 = 28 Answer the following( 42 to 45) 37) Value of a is a) 66.27 b) 85.55 c) 88.43 d) 74.27 38) Value of b is a) 2.67 b) 5.04 c) 3.45 d) 5.75 39) Equation Y = a + bX is a) Y = 66.27 + 2.67X b) Y = 85.55 + 3.45X c) Y = 88.43 + 5.04X d) Y = 85.55 + 5.75X 40) The monthly trend eqn. is a) Y = 5.52 + 0.2225X b) Y = 7.37 + 0.2875X c) Y = 7.37 + 0.035X d) Y = 7.13 + 0.40X Personal Finance: Turning Money into Wealth, 7e (Keown) Chapter 3 Understanding and Appreciating the Time Value of Money 3.1 Compound Interest and Future Values1) Compounding is when the interest you have already earned on an investment earns interest. Answer: TRUE Diff: 2 Topic: Compounding AACSB: Analytical Thinking 2) Your money grows faster as the compounding period becomes longer. Answer: FALSE Diff: 3 Topic: Compounding AACSB: Analytical Thinking 3) An investment earning 12 percent interest per year should double in value in approximately four years. Answer: FALSE Diff: 2 Topic: Rule of 72 AACSB: Analytical Thinking 4) The present value of a financial asset is what you should be willing to pay today for that financial asset. Answer: TRUE Diff: 2 Topic: Time Value of Money AACSB: Analytical Thinking 5) Time Value of Money calculations can be made much easier through the use of a financial calculator. Answer: TRUE Diff: 1 Topic: Calculator Skills AACSB: Information Technology 6) If you set your calculator to the "end" mode your calculator will assume cash flows occur at the end of each time period. Answer: TRUE Diff: 1 Topic: Calculator Skills AACSB: Information Technology 7) The I/Y key on a financial calculator stores the information for the interest rate or the discount rate per period. Answer: TRUE Diff: 1 Topic: Calculator Skills AACSB: Information Technology 8) You currently have $11,167 in your savings account. What interest rate do you need to earn in order to have $20,000 in the account in 10 years? A) 6% B) 8% C) 10% D) There is not enough information to solve this question. Answer: A Diff: 2 Topic: Calculator Skills AACSB: Analytical Thinking9) The ________ Principle states that a dollar today is worth more than a dollar in the future. A) Future value of money B) Discounted value of money C) Adjusted value of money D) Time value of money E) Annuity value of money Answer: D Diff: 1 Topic: Time Value of Money AACSB: Analytical Thinking 10) The current value in today's dollars of a future sum of money is called A) future value. B) adjusted value. C) compounded value. D) present value. E) discounted value. Answer: D Diff: 1 Topic: Present Value AACSB: Analytical Thinking 11) The dollar value of an investment at some future point in time is also known as A) future value. B) present value. C) compounded annuity. D) the time value of money. E) calculated value. Answer: A Diff: 1 Topic: Future Value AACSB: Analytical Thinking 12) Allowing the interest that you earn on an investment to stay in the investment and to earn interest on the interest you have already earned is called what? A) The power of of present value B) The power of compound interest C) The power of simple interest D) The power of time E) The power of future value Answer: B Diff: 1 Topic: Compounding AACSB: Analytical Thinking 13) A one-time investment of $1,500 at a 10 percent annual rate of return yields $2,196 in two years. The $2,196 is known as the A) present value. B) compound value. C) principal plus interest. D) future value. E) annuity value Answer: D Diff: 3 Topic: Future Value AACSB: Analytical Thinking14) John Madrid put $1,000 into a mutual fund yielding an 18% annual rate of return. Using the Rule of 72, calculate approximately how long it will take for the investment to double in value. A) Three years, four months B) Three years and seven months C) Four years D) Four years and four months E) Five years Answer: C Diff: 2 Topic: Rule of 72 AACSB: Analytical Thinking 15) Samantha Jee put $3,000 into a mutual fund yielding a 12 percent annual rate of return. Using the Rule of 72, calculate approximately how long it will take for the investment to double in value. A) Two years B) Two years and four months C) Six years D) Seven years and four months Answer: C Diff: 2 Topic: Rule of 72 AACSB: Analytical Thinking 16) This helpful investment rule-of-thumb tells you approximately how many years it takes for a sum of money to double in size. A) Rule of compound interest B) Rule of 72 C) Rule of 100 D) Rule of future value E) Rule of annuity doubling Answer: B Diff: 1 Topic: Rule of 72 AACSB: Diverse and Multicultural Work Environments 17) By the Rule of 72, what annual interest rate would be required to turn $100 into $200 in approximately six years? A) 4% B) 8% C) 12% D) 16% Answer: C Diff: 2 Topic: Rule of 72 AACSB: Analytical Thinking 18) Suppose that you invested $100 in a bank account that earned an annual rate of return of 10%. How much would you have in that bank account at the end of 10 years? A) $259.37 B) $238.55 C) $293.74 D) $214.46 E) $279.23 Answer: A Diff: 2 Topic: Future ValueAACSB: Analytical Thinking 19) You have just placed $500 in a bank account that earns an annual rate of return of 6%. How much will you have in that bank account after 6 years? A) $652.48 B) $709.26 C) $787.66 D) $758.66 E) $801.68 Answer: B Diff: 2 Topic: Future Value AACSB: Analytical Thinking 20) As a future graduation present, you uncle has just placed $6,000 in a bank account that will earn an annual rate of return of 6%. How much will be in that account when you graduate in four years? A) $7,731.55 B) $6,752.56 C) $6,247.70 D) $7,790.63 E) $7,574.86 Answer: E Diff: 3 Topic: Future Value AACSB: Analytical Thinking 21) Suppose that you placed $500 in a bank account at the end of each year for the next 10 years. How much would be in that account at the end of the tenth year if the deposits earned an annual rate of return of 8% each year? A) $8,079.46 B) $5,400.00 C) $7,243.28 D) $6,355.04 E) $7,774.51 Answer: C Diff: 3 Topic: Future Value AACSB: Analytical Thinking 22) Suppose that you want to create a "college fund" for your newborn child and place $300 in a bank account at the end of each of the next 20 years. If that account earns an annual rate of return of 7%, how much will be in that account at the end of the twentieth year? A) $13,420.00 B) $12,977.53 C) $13,178.20 D) $11,828.32 E) $12,298.65 Answer: E Diff: 3 Topic: Future Value AACSB: Analytical Thinking 23) Your great-uncle placed $500 a year in a bank account for your "college fund" for each of the last 18 years. How much is now in your college account (at the end of the eighteenth year) if your account earned an annual rate of return of 6%? A) $15,452.83B) $15,175.17 C) $16,427.17 D) $15,413.80 E) $15,546.18 Answer: A Diff: 3 Topic: Future Value AACSB: Analytical Thinking 24) Which financial planning concepts should be helpful to a couple planning for how much money to start saving for their retirement? A) Reinvesting B) Compound interest C) Future values D) Present values E) All of the above Answer: E Diff: 3 Topic: Time Value of Money AACSB: Analytical Thinking 25) A method by which one can compare cash flows across time—either as what a future cash flow is worth today (present value) or what an investment made today will be worth in the future (future value)—is called A) time-value of money. B) compounding. C) simple interest. D) opportunity cost. Answer: A Diff: 2 Topic: Time Value of Money AACSB: Analytical Thinking 26) You have been saving toward the purchase of a new mountain bike. Five years ago, you placed $600 in a bank account, and you have since earned an annual rate of return of 12 percent. How much do you now have in your account? A) $1,057.41 B) $1,293.71 C) $978.70 D) $1,138.70 Answer: A Diff: 2 Topic: Future Value AACSB: Analytical Thinking 27) You have just remembered that four years ago you placed $1,000 in a bank account. If the bank was paying an annual rate of return of 8% during that time, how much should you have in your forgotten account? A) $1,253.03 B) $1,360.49 C) $1,321.92 D) $1,301.92 Answer: B Diff: 2 Topic: Future Value AACSB: Analytical Thinking28) Your great-aunt wants to help with your college graduation party. She has just placed $5,000 dollars in a bank account that will earn an annual rate of return of 6%. If you graduate in four years, how much will be in your party account? A) $7,120.89 B) $6,142.96 C) $5,960.47 D) $6,312.38 Answer: D Diff: 3 Topic: Future Value AACSB: Analytical Thinking 29) Suppose that you place $450 in a bank account each year for the next 20 years. How much would be in your bank account at the end of the twentieth year if the deposits earned an annual rate of return of 6% each year? A) $9,540.00 B) $10,876.31 C) $14,729.44 D) $16,553.52 Answer: D Diff: 3 Topic: Future Value AACSB: Analytical Thinking 30) Suppose that you want to create a "retirement party fund" for yourself and place $50 in a bank account for each of the next 20 years. If that account earns an annual rate of return of 7%, how much will be in your retirement party fund at the end of the twentieth year? A) $1,529.70 B) $2,679.22 C) $1,032.57 D) $2,049.77 Answer: D Diff: 3 Topic: Future Value AACSB: Analytical Thinking 31) Your daughter has been saving $500 a year for each of the last 10 years for her "sweet sixteen" party. How much is now in her party account (at the end of the tenth year) if she earned an annual rate of return of 6%? A) $6,590.40 B) $7,680.04 C) $5,300.00 D) $8,714.84 Answer: A Diff: 3 Topic: Future Value AACSB: Analytical Thinking 32) If your bank pays you interest in the form of an annual rate of return of 10% over each of the next five years, how much will your balance be if you make annual deposits of $400? A) $2,248.37 B) $2,644.20 C) $2,516.31 D) $2,442.04 Answer: D Diff: 3 Topic: Future Value AACSB: Analytical Thinking33) Using the Rule of 72, approximately how long will it take to double your money if you invest it at 8% compounded annually? A) 6 months B) 9 months C) 6 years D) 9 years E) It depends on the amount of the initial investment. Answer: D Diff: 3 Topic: Time Value of Money AACSB: Analytical Thinking 34) Using the Rule of 72, if it will take approximately 12 years for your money to double, at what annually compounded interest rate is it invested? A) 6% B) 8% C) 9% D) 12% Answer: A Diff: 3 Topic: Time Value of Money AACSB: Analytical Thinking 35) You invest $1,000 at age 20 at an annual rate of return of 12%. By the time you are 62 you will have amassed approximately A) $47,040. B) $67,214. C) $116,723. D) $504,000. Answer: C Diff: 3 Topic: Time Value of Money AACSB: Analytical Thinking 36) Describe the effects and benefits of compound interest. Answer: Compounding interest means that interest earned on the principal of an investment or savings vehicle is reinvested and will itself earn interest. Should the interest earned be removed and not reinvested then you won't accumulate a very large amount. Diff: 2 Topic: Compounding AACSB: Analytical Thinking 37) Why is the time value of money an important concept in financial planning? Answer: The time value of money allows us to see the relationship between time and the value of accumulated sums of money. We can clearly understand that starting a savings or retirement plan at a younger age will create much more wealth than waiting to start it at a later time. It also becomes clear that starting younger means saving a smaller monthly amount and having the option of skipping some months or years later if it becomes necessary to do so. Diff: 1 Topic: Time Value of Money AACSB: Reflective Thinking 38) What are some practical uses of present and future values? Answer: There are basically two practical uses for these values. Present values will tell you how much must be saved or invested annually to achieve a future financial goal. It also works for determining the monthlypayment on a loan of a specified amount to be paid back in the future. Future values show the total future accumulated values of specified sums of money saved or invested now and into the future. Budgeting and financial planning would be very difficult if not impossible without the time value of money skills. Diff: 2 Topic: Time Value of Money AACSB: Reflective Thinking 39) A compound interest table is useful in solving a time value of money problem. Name the variables involved. Answer: The interest rate, the period of time involved, the sum of money involved, and the frequency of compounding are variables to consider when using a compound interest table. Diff: 1 Topic: Compounding AACSB: Analytical Thinking 3.2 Compounding and the Power of Time an Interest 1) A dollar received in the future is worth more than a dollar received today. Answer: FALSE Diff: 1 Topic: Time Value of Money AACSB: Analytical Thinking 2) The earlier you begin saving for your retirement, the easier it will be to reach your financial goals for retirement. Answer: TRUE Diff: 1 Topic: Time Value of Money AACSB: Reflective Thinking 3) It is really pretty easy to create a valuable personal financial plan without understanding the time value of money principle. Answer: FALSE Diff: 2 Topic: Time Value of Money AACSB: Reflective Thinking 4) Charlie is starting to save for his retirement now at age 20. If inflation averages 4% annually until his retirement age and he earns an annual rate of return of 4% on his investments during this period, then he should be able to enjoy a very comfortable retirement when he is retired. Answer: FALSE Diff: 3 Topic: Inflation AACSB: Analytical Thinking 5) Small changes in the interest rate can have a dramatic impact on future values. Answer: TRUE Diff: 3 Topic: Time Value of Money AACSB: Diverse and Multicultural Work Environments 6) At the age of 20, James is starting to save for retirement. If inflation averages 4 percent annually until his retirement age and he earns an average annual rate of return of 13 percent on his investments during this period, he should be able to enjoy a comfortable retirement. Answer: FALSE Diff: 3Topic: Time Value of Money AACSB: Analytical Thinking 7) Two of the most important factors in reaching your financial goals are the return on your investments and the length of time you have until you need your money. Answer: TRUE Diff: 2 Topic: Time Value of Money AACSB: Reflective Thinking 8) Generally speaking, regularly saving a little money when you are young can result in a large final payoff. Answer: TRUE Diff: 2 Topic: Time Value of Money AACSB: Reflective Thinking 9) It is not realistic for a 20-year-old to accumulate $1 million by the age of 65. Answer: FALSE Diff: 3 Topic: Time Value of Money AACSB: Reflective Thinking 10) Most people achieve comfortable retirements by postponing saving until after age 50, when they are able to save a large amount on a regular basis. Answer: FALSE Diff: 3 Topic: Time Value of Money AACSB: Reflective Thinking 11) Your money will grow or compound ________ as the number of compounding periods per year becomes ________. A) faster; smaller B) faster; larger C) slower; larger D) slower; compounded E) none of the above are correct Answer: B Diff: 3 Topic: Compounding AACSB: Analytical Thinking 12) Who will end up with the largest amount of money invested at an annual rate of return of 9% over the next 42 years? A) Jim saves $1,200 per year for the first 14 years and then stops putting any new money into the account for the remaining 28 years. B) Jeremy saves nothing for the first 14 years and saves $1,200 per year for the next 14 years and then puts no more money into the account during the last 14 years. C) Jerry saves nothing for the first 14 years and then saves $1,200 per year for the remaining 28 years. D) Joey saves nothing for the first 14 years and then saves $1,500 per year for 14 years then stops putting any new money into the account for the remaining 14 years. E) John saves nothing for the first 10 years and saves $1,500 per year for the remaining 32 years. Answer: A Diff: 3 Topic: Calculator Skills AACSB: Analytical Thinking13) Why should you care about the power of compounding and the time value of money? A) It is critical to obtaining your future financial goals. B) The sooner you start saving for retirement, the less you have to save each year. C) You may outlive your Social Security and employer's retirement plan. D) It is possible to build a large estate for yourself, spouse, and children. E) All of the above Answer: E Diff: 3 Topic: Compounding AACSB: Reflective Thinking 14) Is it possible to save $585,000 for retirement instead of $310,000 without requiring much more to be invested every month? A) Probably not with inflation working against you B) Depends upon the interest rate or return you earn on the investment as well as the number of years until retirement C) Absolutely not D) There is not enough information to answer this question. Answer: B Diff: 2 Topic: Time Value of Money AACSB: Diverse and Multicultural Work Environments 15) What is the annual interest rate earned on a deposit that grew from $250 to $502.84 over the last 5 years? A) 15% B) 13% C) 11% D) 9% Answer: A Diff: 3 Topic: Time Value of Money AACSB: Analytical Thinking 16) Suppose that you had deposited $100 in a bank account for each of the last 5 years. What annual interest rate is attached to this account if there is now (at the end of the fifth year) $758.92 in the account? A) 10% B) 16% C) 19% D) 21% E) 23% Answer: D Diff: 3 Topic: Time Value of Money AACSB: Analytical Thinking 17) What is the annual interest rate earned on a deposit that grew from $60 to $111.06 over the last 8 years? A) 14% B) 12% C) 8% D) 6% Answer: C Diff: 3 Topic: Time Value of Money AACSB: Analytical Thinking18) One day as you were going through some old memorabilia, you discovered an old savings account in which you placed $100 twenty years ago. When you checked out the account, it currently had a balance of $320.71. What annual rate of interest did you earn? A) 12% B) 10% C) 8% D) 6% Answer: D Diff: 3 Topic: Time Value of Money AACSB: Analytical Thinking Arnold Diaz Arnold learned something very valuable as a teenager from his dad. He was told to invest $1,000 at 12% interest at age 20 and leave it alone until age 65. Arnold's dad knew that one strategy that wealthy people use is to exercise self-discipline to never touch this long-term plan. Arnold is very happy he applied his dad's advice. 19) Approximately how long will it take Arnold's savings to grow into $2,000? A) 60 months B) 5 years C) 8.5 years D) 6 years Answer: D Diff: 2 Topic: Time Value of Money AACSB: Analytical Thinking 20) If he sticks to this plan, Arnold's savings will have grown to approximately ________ by age 62. A) $116,723 B) $163,987 C) $9,646 D) $1,125,945 Answer: A Diff: 3 Topic: Time Value of Money AACSB: Analytical Thinking 21) If Arnold were to leave his money in the account until he was 68, by approximately what amount would the balance increase between his 62nd and 68th years? A) $113,667 B) $1,096,471 C) $160,457 D) $1,973 Answer: A Diff: 3 Topic: Time Value of Money AACSB: Analytical Thinking 22) If his savings account had earned a more conservative 9% annual rate of return, Arnold's savings would be approximately ________ less by age 68. A) $4,132 B) $62,585 C) $167,805 D) $1,871,663Answer: C Diff: 3 Topic: Time Value of Money AACSB: Analytical Thinking 23) Suppose the investment rate of return were 18%. At this rate, when would Arnold reach the $1,000,000 mark? A) at age 42 B) at age 54 C) at age 62 D) at age 68 Answer: C Diff: 3 Topic: Future Value AACSB: Analytical Thinking Enrique Martinez As a teenager, Enrique learned a valuable lesson from his dad, who told him to invest $1,000 at 8 percent interest at age 20 and leave the money alone until age 65. Enrique's dad knew that one strategy used by wealthy people is to exercise self-discipline and never touch a long-term savings plan. Enrique is happy to apply his dad's advice. 24) Approximately how long will it take Enrique's investment to grow into $2,000? A) Seventy-two months B) Six years C) Nine years D) Twelve years Answer: C Diff: 2 Topic: Time Value of Money AACSB: Analytical Thinking 25) If he sticks to the plan, Enrique's savings will grow to approximately ________ by age 62. A) $25,339 B) $31,920 C) $4,660 D) $148,780 Answer: A Diff: 3 Topic: Time Value of Money AACSB: Analytical Thinking 26) If Enrique leaves the money in the account until he is 68, by approximately what amount would the balance increase between his 62nd and 68th years? A) $14,872 B) $108,569 C) $8,291 D) $35,551 Answer: A Diff: 3 Topic: Time Value of Money AACSB: Analytical Thinking 27) If his savings account earns a more aggressive 14 percent annual rate of return, Enrique's savings will be worth approximately ________ more by age 68.A) $4,145 B) $245,473 C) $498,596 D) $538,807 Answer: C Diff: 3 Topic: Time Value of Money AACSB: Analytical Thinking 28) Suppose the annual rate of return is 15 percent. At this rate, when will Enrique reach the $500,000 mark? A) Age 45 B) Age 58 C) Age 65 D) Age 70 Answer: C Diff: 3 Topic: Time Value of Money AACSB: Analytical Thinking 29) Describe the two factors that affect how much we need to save to achieve financial goals. Answer: The two variable factors that affect total accumulation are the interest rate received and the time period the savings/investment is allowed to accumulate. Increasing the interest rate and/or the period of time to accumulate will create a much larger end product. By decreasing either of these two factors, total accumulation will be decreased. Experiment with increasing either of these factors and the results will be both apparent and amazing. Diff: 2 Topic: Time Value of Money AACSB: Diverse and Multicultural Work Environments 30) List four reasons why you should care about the power of compounding and the time value of money. Answer: The concepts are critical to your efforts to achieve financial goals. The sooner you start saving for retirement, the less you have to save each year. You may outlive your Social Security benefits and employer retirement plans. The concepts will help you develop a large estate for yourself, spouse, and children. Diff: 3 Topic: Compounding AACSB: Analytical Thinking 3.3 Present Value-What's It Worth in Today's Dollars? 1) The present value interest factor is the inverse of the corresponding future value interest factor. Answer: TRUE Diff: 3 Topic: Time Value of Money AACSB: Analytical Thinking 2) Present value lets us compare dollar values from different time periods. Answer: TRUE Diff: 3 Topic: Time Value of Money AACSB: Reflective Thinking 3) The future value of a current investment earning a positive rate of return is always greater than the present value of the investment. Answer: TRUE Diff: 2Topic: Time Value of Money AACSB: Analytical Thinking 4) The discount rate is the interest rate used to bring ________ back to ________. A) current dollars; present dollars B) future dollars; present dollars C) current interest rate; present present interest rate D) future interest rate; present interest rate Answer: B Diff: 1 Topic: Present Value AACSB: Analytical Thinking 5) Which one of the following is the "enemy" of compound interest and makes it very difficult to reach your financial goals? A) Inflation B) Annuity factor C) Simple interest D) Compound frequency E) None of the above Answer: A Diff: 3 Topic: Compounding AACSB: Analytical Thinking 6) What is the present value today of $150 that will be received in four years from now if the discount rate is 12%? A) $76.03 B) $95.33 C) $116.90 D) $105.60 E) $83.39 Answer: B Diff: 3 Topic: Present Value AACSB: Analytical Thinking 7) Rasheed can afford a monthly car payment of $550 for 72 months at an annual interest rate of 7.5 percent. Which of the following is closest to the amount he will be able to borrow for a new car? A) $3,984 B) $6,550 C) $31,810 D) $49,818 Answer: C Diff: 3 Topic: Time Dimension of Investing AACSB: Analytical Thinking 8) What is the present value of an IOU for $1,000 due to be paid in two years, if the discount rate is 8%? A) $857.34 B) $766.40 C) $885.00 D) $683.26 E) $810.77 Answer: A Diff: 3Topic: Present Value AACSB: Analytical Thinking 9) What is the price you would be willing to pay today for an IOU for $500 due in one year if you want to earn at least 16%? A) $480.00 B) $431.03 C) $450.00 D) $395.33 E) $418.23 Answer: B Diff: 3 Topic: Present Value AACSB: Analytical Thinking 10) At the end of each year for ten years you deposit $750 in an account that earns an annual rate of return of 12%. What is the present value of these deposits? A) $4,329.39 B) $5,241.48 C) $3,161.55 D) $4,237.67 E) $4,482.63 Answer: D Diff: 3 Topic: Present Value AACSB: Analytical Thinking 11) Sam's uncle promised to give him $7,000 when he graduates from college three years from now. Assuming an interest rate of 8 percent compounded annually, what is the value of Sam's gift right now? A) $5,504.22 B) $5,510.78 C) $5,556.83 D) $5,555.55 Answer: C Diff: 3 Topic: Present Value AACSB: Analytical Thinking 12) Someone has offered you the opportunity to purchase an IOU. The IOU will pay back a total of $500 in three years. How much would you be willing to pay for that IOU today if you want to earn an annual rate of return of 16%? A) $320.33 B) $422.63 C) $292.63 D) $380.45 Answer: A Diff: 3 Topic: Present Value AACSB: Analytical Thinking 13) What is the maximum that you would be willing to loan your brother for a $100 IOU if he promises to pay you back at the end of the year? You want to earn an annual rate of return of 12%. A) $82.00 B) $89.29 C) $92.73 D) $88.00Answer: B Diff: 3 Topic: Present Value AACSB: Analytical Thinking 3.4 Annuities 1) A perpetuity is an annuity that continues forever. Answer: TRUE Diff: 2 Topic: Annuity AACSB: Analytical Thinking 2) A compound annuity involves depositing or investing an equal sum of money at the end of each time period for a certain number of time periods and allowing it to grow. Answer: TRUE Diff: 1 Topic: Annuity AACSB: Diverse and Multicultural Work Environments 3) An annuity is a series of unequal dollar payments coming at the end of each time period for a specified number of time periods. Answer: FALSE Diff: 2 Topic: Annuity AACSB: Diverse and Multicultural Work Environments 4) With a mortgage loan of $150,000 at an annual percentage rate of 6% for 30 years, you will pay over $150,000 in interest before your loan ends. Answer: TRUE Diff: 3 Topic: Compounding AACSB: Analytical Thinking 5) With a 30-year mortgage loan of $100,000 at an annual interest rate of 7 percent, you will pay less $135,000 in interest before your loan ends. Answer: FALSE Diff: 3 Topic: Compounding AACSB: Analytical Thinking 6) In an amortized loan the earlier payments have a larger portion of the payment going to pay interest and a smaller portion of the payment to pay down the principle. Answer: TRUE Diff: 3 Topic: Amortized Loan AACSB: Analytical Thinking 7) A compound annuity uses the principles of A) reinvesting and present value. B) compound interest and future value. C) reinvesting and compound interest. D) compound interest and present value. E) amortization and reinvesting. Answer: C Diff: 3 Topic: AnnuityAACSB: Analytical Thinking 8) A series of equal dollar payments at the end of each period for "x" number of time periods is A) an annuity. B) a complex annuity. C) an annuity due. D) a deferred annuity. E) an equal installment annuity. Answer: A Diff: 1 Topic: Annuity AACSB: Analytical Thinking 9) What is the present value of $500 received at the end of each of the next five years worth to you today at the appropriate discount rate of 6 percent? A) $1,105 B) $1,850 C) $2,106 D) $2,778 Answer: C Diff: 3 Topic: Annuity AACSB: Analytical Thinking 10) What is the present value of an annual payment of $1,500 discounted back 15 years at an annual rate of return of 3%? A) $10,663.87 B) $12,334.56 C) $13,449.87 D) $17,906.90 Answer: D Diff: 3 Topic: Annuity AACSB: Analytical Thinking 11) What is the present value of an annual payment of $3,600 discounted back 12 years at an annual rate of return of 5 percent? A) $12,977.19 B) $31,907.71 C) $45,360.00 D) $57,301.66 Answer: B Diff: 3 Topic: Annuity AACSB: Analytical Thinking 12) What is the future value of a series of $500 annual payments received at the end of each of the next 5 years' worth if they are invested at an annual rate of return of 6%? A) $1,223.44 B) $2,176.65 C) $2,818.50 D) $3,309.76 Answer: C Diff: 3 Topic: Annuity AACSB: Analytical Thinking13) What is the future value of a stream of $800 annual payments worth to the investor at the end of 10 years if these payments are invested at an annual rate of return of 8.5%? A) $11,868.08 B) $12,195.22 C) $13,334.90 D) $13,667.88 Answer: A Diff: 3 Topic: Annuity AACSB: Analytical Thinking 14) What is the present value of a $1,000 payment at the end of each of the next 10 years discounted back to the present at 5%? A) $5,098 B) $7,722 C) $8,775 D) $9,112 Answer: B Diff: 3 Topic: Annuity AACSB: Analytical Thinking 15) Suppose that you want to purchase a car today. You can afford payments of $400 per month and want to pay the loan back over the next five years. Assuming no down payment is required, how much can you borrow if the bank will charge you an annual percentage rate of 12% compounded monthly? A) $16,726.68 B) $18,220.18 C) $24,667.87 D) $25,008.90 E) $17,982.02 Answer: E Diff: 3 Topic: Present Value AACSB: Analytical Thinking 16) How much can you borrow today if you can make payments of $3,600 a year for the next five years and the interest rate is 10%? A) $13,646.83 B) $12,235.32 C) $18,978.36 D) $15,797.84 E) $17,949.67 Answer: A Diff: 3 Topic: Present Value AACSB: Analytical Thinking 17) Sly's Used Cars just sold you a clunker (you need it to get to class on time). You financed the $4,728.48 purchase price for 24 months. They said your payment would be $250. What interest rate did they charge you (assume monthly compounding)? A) 10% B) 12% C) 16% D) 19% E) 24%Answer: E Diff: 3 Topic: Time Value of Money AACSB: Analytical Thinking 18) What would be the interest rate on a loan of $9,981.78 that you paid off with annual payments of $2,500 for each of the next five years? A) 8.0% B) 10% C) 15% D) 21% E) 26% Answer: A Diff: 3 Topic: Time Value of Money AACSB: Analytical Thinking 19) You just purchased a premier lot in an exclusive neighborhood for your future home. The lot cost $50,000, an amount you financed with a 96-month loan. If your interest rate is 9.25 percent compounded monthly, which of the following is closest to your monthly payment? A) $744.55 B) $853.60 C) $767.23 D) $739.02 E) $810.92 Answer: D Diff: 3 Topic: Time Value of Money AACSB: Analytical Thinking 20) If Monica invests $15,750 at 8 percent annual interest, how much would she have after eight years? A) $29,152.15 B) $17,010.08 C) $32,354.22 D) $39,678.92 Answer: A Diff: 3 Topic: Future Value AACSB: Analytical Thinking 21) How much did you borrow if your annual payments are $5,000 for the next seven years and the interest rate is 9%? A) $25,164.76 B) $36,002.17 C) $19,140.20 D) $27,797.84 Answer: A Diff: 3 Topic: Present Value AACSB: Analytical Thinking 22) Suppose that you want to purchase some land to build a homestead in the future. You can afford payments of $5,000 each year and want to pay the loan back over the next 20 years. Assuming no down payment is required, how much can you borrow if the bank will charge you an annual interest rate of 12%? A) $100,985.45 B) $48,231.47C) $37,347.22 D) $160,262.21 Answer: C Diff: 3 Topic: Present Value AACSB: Analytical Thinking 23) What would be the interest rate on a loan of $39,927.10 that you paid off with annual payments of $10,000 for each of the next five years? A) 8% B) 10% C) 15% D) 21% E) 26% Answer: A Diff: 3 Topic: Present Value AACSB: Analytical Thinking 24) Car loans and mortgage loans are typical annuities in the form of A) maturity loans. B) compound loans. C) amortized loans. D) payment loans. Answer: C Diff: 2 Topic: Amortized Loan AACSB: Analytical Thinking 25) A perpetuity is an annuity where the payments A) stop at maturity. B) are delayed until maturity. C) increase due to inflation. D) never stop. E) accrue until maturity. Answer: D Diff: 2 Topic: Perpetuity AACSB: Analytical Thinking 26) You just purchased a vacant lot for your future son-in-law's home for $30,000. You financed that amount over 120 months. What would your monthly payment be if your interest rate was 12% compounded monthly? A) $430.41 B) $389.21 C) $231.22 D) $189.02 Answer: A Diff: 3 Topic: Time Value of Money AACSB: Analytical Thinking 27) When a loan is paid off in equal installments, this is called a(n) ________ loan. A) amortized B) discounted C) balloon D) reverse annuity E) none of the aboveAnswer: A Diff: 1 Topic: Amortized Loan AACSB: Analytical Thinking 28) Consider that you are paying back a fully amortized loan. Which of the following statements is most correct? A) Later loan payments involve larger amounts of principal repayment. B) The actual loan payments vary from year to year. C) After the last loan payment is made, there is still a large principal repayment remaining. D) Early loan payments include smaller amounts of interest payments. E) None of the above statements are true. Answer: A Diff: 3 Topic: Amortized Loan AACSB: Analytical Thinking 29) Suppose you borrowed $12,000 at an annual rate of 6 percent interest to buy a car and wish to repay it in five equal payments at the end of each of the next five years. Which of the following is the closest to the amount of each of these payments? A) $2,364 B) $2,849 C) $2,544 D) $2,436 Answer: B Diff: 3 Topic: Amortized Loan AACSB: Analytical Thinking 30) Assuming that you can afford a car payment of $400 for 36 months, which of the following is closest to the annual interest rate you would need on a loan to borrow $12,000 for a new car? A) 10.99 percent B) 11.26 percent C) 12.25 percent D) 12.99 percent Answer: C Diff: 3 Topic: Time Value of Money AACSB: Analytical Thinking 31) Jah-Malya can afford a car payment of $400 per month for 48 months at an annual rate of 8.25 percent interest. Which of the following is closest to the amount she will be able to borrow for a new car? A) $16,306 B) $4,741 C) $22,656 D) $12,997 Answer: A Diff: 3 Topic: Time Value of Money AACSB: Analytical Thinking 32) Mark borrows $15,000 to buy a new car. His loan has an annual interest rate of 6.5%, compounded monthly, and his monthly payment is $293.49. How much will he have paid in interest when he has finished repaying his loan in 60 months? A) $43.49 B) $1,575.50C) $2,609.40 D) $17,609.40 Answer: C Diff: 3 Topic: Amortized Loan AACSB: Analytical Thinking 33) Mark borrows $15,000 to buy a new car. His loan has an interest rate of 6.5%, compounded monthly, and his monthly payment is $293.49. If instead his loan had an interest rate of 8%, how much more would he have paid in interest by the time he finished repaying his loan in 60 months? A) $225.00 B) $304.15 C) $639.60 D) $3,249.00 Answer: C Diff: 3 Topic: Amortized Loan AACSB: Analytical Thinking Adrian Clemons Adrian, a single man who wants to buy a house in five years, read an article that recommended a down payment of 20 percent. With a large income and little debt, Adrian can afford to save a substantial amount of money every month. He is asking you for advice to help him reach his goal. 34) Adrian found a nice house today that is selling for $150,000. Assuming an inflation rate of 5 percent in the local real estate market, how much will this house sell for in five years? A) $187,500 B) $191,442 C) $204,650 D) $157,500 Answer: B Diff: 2 Topic: Time Value of Money AACSB: Analytical Thinking 35) Assume that Adrian will need $30,000 for his 20 percent down payment in five years. If he locates an investment with a 9 percent rate of return that compounds annually, which of the following is closest to the amount that he will have to save each year? A) $6,003 B) $4,884 C) $5,187 D) $5,013 Answer: D Diff: 2 Topic: Time Value of Money AACSB: Analytical Thinking 36) It is now five years later, and Adrian has saved enough money for a 20 percent down payment on a house. He will have to borrow $135,000 in a 30-year loan with an annual interest rate of 6 percent compounded monthly. What will his monthly mortgage payment be? A) $1,199.55 B) $809.39 C) $779.98 D) $397.50 Answer: B Diff: 2Topic: Time Value of Money AACSB: Analytical Thinking 37) Define an amortized loan and give two common examples. Answer: An amortized loan is a loan paid off in equal installments. The loan amount is paid back by spreading or amortizing the payments out over a certain time period based on a specific interest rate. Two common examples are auto loans and home mortgages. Diff: 1 Topic: Amortized Loan AACSB: Diverse and Multicultural Work Environments 38) List at least five common examples of annuities. Answer: a one year lease on an apartment, your five year car loan, your parents' mortgage payments, monthly savings to reach a college education expense goal, a monthly paycheck if you are on salary, and constant monthly contributions to retirement plans are all examples of annuities. Diff: 1 Topic: Annuity AACSB: Reflective Thinking 39) For someone who has $100,000 to save for 20 years, would a 4% Certificate of Deposit that compounds annually be a better deal than a 3.94% Certificate of Deposit that compounds quarterly? Why? Answer: With the 4% annual compounding, your $100,000 would compound into $219,112.31. There would be 20 compounding periods at 4% per year and the interest would be calculated at the end of every year. Your $4,000 in interest from year one would not earn any interest until the end of year two ($160). With the quarterly compounding your interest would start earning interest itself starting with the second quarter of year one. There would be a total of 80 compounding periods (4 quarters per year times 20 years) and this would mean that even with the lower interest rate, your money would grow to $219,053.19 for a slight difference of $59.12! Diff: 3 Topic: Time Value of Money AACSB: Analytical Thinking 40) What recommendations would you offer to someone who is trying to break poor financial habits and save money in order to achieve his or her financial goals? Answer: Recommendation one: First, gain an understanding of how compounding works–that as the number of years and the interest rate you earn go up, so does the future value of an investment. Recommendation two: Think of savings as a "snowball effect." You earn interest on your initial investment, and those interest earnings and the initial investment both continue to earn interest. When these earnings are extended over multiple decades, your money can really add up. In other words, you want to start investing as soon as possible. Recommendation three: Pay yourself–your future self, that is–first. To make this process as painless as possible, automate the payments so that when your paycheck is deposited into your bank account, a percentage is automatically transferred to a separate investment account–perhaps your retirement account. Or ask your employer's payroll department about a mandatory payroll deduction. It is much easier to save the money that you never really see! Diff: 3 Topic: Financial Goals AACSB: Reflective Thinking Terms in this set (32) The amount of simple interest is equal to the product of the principal times ____ times ____. a. (1 + rate per time period), the number of time periods b. (1 + rate per time period), (the number of time periods -1)c. rate per time period, the number of time periods d. rate per time period, (the number of time periods - 1) c. rate per time period, the number of time periods The present value of a single amount can be represented as a. PV0 = FVn(PVIFi,n) b. PV0 = FVn(PVIFAi,n) c. PV0 = FVn[1/(1 + i)n] d. a and c d. a and c The basic future value equation is given by a. FVn = PV0(PVIFi,n) b. FVn = PV0(FVIFAi,n) c. FVn = PV0(1/(1+ i)n) d. FVn = PV0(FVIFi,n) d. FVn = PV0(FVIFi,n) The process of finding present values is frequently called a. annualizing b. compounding c. discounting d. leasing c. discounting The values shown in ordinary annuity tables (either present value or compound value) can be adjusted to the annuity due form by ____ the ordinary annuity interest factor by ____. a. dividing, (1 + i) b. dividing, (1 + i)n c. multiplying, (1 + i) d. multiplying, (1 + i)n c. multiplying, (1 + i) A(n) ____ is a financial instrument that agrees to pay an equal amount of money per period into the indefinite future (i.e. forever) a. annuity b. annuity due c. sinking fund d. perpetuity d. perpetuity Finding the discounted current value of $1,000 to be received at the end of each of the next 5 years requires calculating the a. future value of an annuity b. future value of an annuity due c. present value of an annuity d. present value of an annuity due c. present value of an annuity Finding the compound sum of $1,000 to be received at the beginning of each of the next 5 years requires calculating the a. future value of an annuity b. present value of an annuity c. future value of an annuity due d. present value of an annuity duec. future value of an annuity due When using a present value of an annuity table(e.g.,Table IV at the back of the book), a. payments are assumed to be made at the beginning of each period b. PVIFA factors decrease with an increase in the interest rate c. PVIFA factors increase with an increase in the number of periods d. b and c only d. b and c only When using a future value of an annuity table (e.g., Table III at the back of the book), a. payments are assumed to be made at the end of each period b. FVIFA factors increase with an increase in the interest rate c. FVIFA factors increase with an increase in the number of periods d. all of the above d. all of the above An annuity due is one in which a. payments or receipts occur at the end of each period. b. payments or receipts occur at the beginning of each period. c. payments or receipts occur forever. d. cash flows occur continuously. b. payments or receipts occur at the beginning of each period. You have just won a $5 million lottery to be received in twenty annual equal payments of $250,000. What will happen to the present value of your winnings if the interest rate increases during the next 20 years. a. it will be worth less b. it will be worth more c. it will not change d. it will increase during the first ten years a. it will be worth less You have just calculated the present value of the expected cash flows of a potential investment. Management thinks your figures are too low. Which of the following actions would improve the present value of your cash flows? a. extend the cash flows over a longer period of time b. increase the discount rate c. decrease the discount rate d. extend the cash flows over a longer period of time, and decrease the discount rate d. extend the cash flows over a longer period of time, and decrease the discount rate If the present value of a given sum is equal to its future value, then a. the discount rate must be very high b. there is no inflation c. the discount rate must be zero d. none of the answers is correct c. the discount rate must be zero Using the "Rule of 72," about how long will it take a sum of money to double in value if the annual interest rate is 9 percent? a. 9 years b. 7 years c. 8 years d. 10 years c. 8 years The present value of an ordinary annuity is thea. sum of the present value of a series of equal periodic payments b. future value of an equal series of payments c. receipt of equal cash flows for a specified amount of time d. sum of the future value of an equal series of payments a. sum of the present value of a series of equal periodic payments When a loan is amortized over a five year term, the a. rate of interest is reduced each year b. amount of interest paid is reduced each year c. payment is reduced each year d. balance is paid as a balloon payment in the fifth year b. amount of interest paid is reduced each year Annuity due calculations are especially important when dealing with a. term loans b. lease contracts c. capital investments d. capital recovery problems b. lease contracts The more frequent the compounding the a. greater the present value b. greater the amount deposited c. greater the effective interest rate d. lesser the future value c. greater the effective interest rate The effective rate of interest will always be ____ the nominal rate. a. greater than b. equal to c. less than d. equal to or greater than d. equal to or greater than ____ is interest that is paid not only on the principal, but also on any interest earned but not withdrawn during earlier periods. a. basic interest b. simple interest c. future interest d. compound interest d. compound interest Which of the following is worth more? a. Future value of an ordinary annuity of PMT dollars per year for n years discounted at i percent. b. Future value of an annuity due of PMT dollars per year for n years discounted at i percent. c. Both are worth the same amount. d. Cannot be determined from the information given. b. Future value of an annuity due of PMT dollars per year for n years discounted at i percent. The annual effective rate of interest (ieff ) is a function of: a. the annual nominal rate of interest (inom) b. the number of compounding intervals per year (m) c. the number of years (n) d. a and b d. a and bMore frequent compounding results in ____ future values and ____ present values than less frequent compounding at the same interest rate. a. higher, higher b. lower, higher c. higher, lower d. lower, lower c. higher, lower The present value of a(n) ____ is determined by dividing the annual cash flow by the interest rate. a. annuity b. annuity due c. perpetuity d. lease c. perpetuity An annuity that begins more than 1 year in the future is referred to as a(n) ____. a. perpetuity b. annuity due c. uneven annuity d. deferred annuity d. deferred annuity The ____ of a perpetual stream of equal, annual returns (PMT) discounted at i% per year is equal to ____. a. present value; PMT/i b. present value; PMT ⋅ i c. future value; PMT/i d. future value; PMT ⋅ i a. present value; PMT/i Annuity due calculations are most common when dealing with: a. cash dividends b. loan repayments c. lease contracts d. interest payments c. lease contracts The payment or receipt of a series of equal cash flows per period, at the end of each period, for a specified amount of time is called a(n): a. annuity due b. perpetuity c. ordinary annuity d. simple interest c. ordinary annuity The difference between an ordinary annuity and an annuity due is: a. the interest rate b. the timing of the payments c. the amount of the payments d. the number of periods b. the timing of the payments ____ is the return earned by someone who has forgone current consumption. a. the present value b. principle c. an annuityd. interest d. interest Determine how much $1,000 deposited in a savings account paying 8% (compounded annually) will be worth after 5 years. a. $5,526 b. $ 784 c. $1,400 d. $1,469 d. $1,469 Terms in this set (7) Most people prefer to receive money today rather than ten years from now because Receiving cash today enables one to take advantage of current investment opportunities. The primary difference between simple and compound interest is that: Compound interest entails receiving interest payments on previously earned interest The amount of money that would have to be invested today at a given interest rate over a specific period in order to equal a future amount is called: Present value Given some amount to be received several years in the future, if the interest rate increases, the present value of the future amount will be Lower You have determined the profitability of a planned project by finding the present value of all the cash flows from that project. Which of the following would cause the project to look more appealing in terms of the present value of those cash flows? The discount rate decreases. Current assets values may be estimated by calculating: The present value of all future cash flows expected from the asset Terms in this set (70) Cash flow time lines are used primarily for decisions involving paying off debt or investing in financial securities. They cannot be used when making decisions about investments in physical assets. a. True b. False False One of the potential benefits of investing early for retirement is that an investor can receive greater benefits from the compounding of interest. a. True b. False True Of all the techniques used in finance, the least important is the concept of the time value of money. a. True b. FalseFalse Compounding is the process of converting today's values, which are termed present value, to future value. a. True b. False True The coupon rate is the rate of return you could earn on alternative investments of similar risk. a. True b. False False A perpetuity is an annuity with perpetual payments. a. True b. False True An amortized loan is a loan that requires equal payments over its life; its payments include both interest and repayment of the debt. a. True b. False True The greater the number of compounding periods within a year, the greater the future value of a lump sum invested initially, and the greater the present value of a given lump sum to be received at maturity. a. True b. False False Suppose an investor can earn a steady 5% annually with investment A, while investment B will yield a constant 12% annually. Within 11 years time, the compounded value of investment B will be more than twice the compounded value of investment A (ignore risk). a. True b. False True Solving for the interest rate associated with a stream of uneven cash flows, without the use of a calculator, usually involves a trial and error process. a. True b. False True When a loan is amortized, the largest portion of the periodic payment goes to reduce principal in the early years of the loan such that the accumulated interest can be spread out over the life of the loan. a. True b. False False The effective annual rate is always greater than the simple rate as a result of compounding effects. a. True b. False False Because we usually assume positive interest rates in time value analyses, the present value of a three-year annuity will always be less than the future value of a single lump sum, if the sum of the annuity payments equals the original lump sum investment.a. True b. False False All else equal, a dollar received sooner is worth more than a dollar received at some later date, because the sooner the dollar is received the more quickly it can be invested to earn a positive return. a. True b. False True An annuity is a series of equal payments made at fixed equal-length intervals for a specified number of periods. a. True b. False True The difference between an ordinary annuity and an annuity due is that each of the payments of the annuity due earns interest for one additional year (period). a. True b. False True The difference between the PV of an annuity due and the PV of an ordinary annuity is that each of the payments of the annuity due is discounted by one more year. a. True b. False True The effective annual rate is less than the simple rate when we have monthly compounding. a. True b. False False Given some amount to be received several years in the future, if the interest rate increases, the present value of the future amount will a. Be higher. b. Be lower. c. Stay the same. d. Cannot tell. e. Be variable. b. Be lower. You have determined the profitability of a planned project by finding the present value of all the cash flows form that project. Which of the following would cause the project to look more appealing in terms of the present value of those cash flows? a. The discount rate decreases. b. The cash flows are extended over a longer period of time, but the total amount of the cash flows remains the same. c. The discount rate increases. d. Answers b and c above. e. Answers a and b above. a. The discount rate decreases. As the discount rate increases without limit, the present value of the future cash inflows a. Gets larger without limit. b. Stays unchanged.c. Approaches zero. d. Gets smaller without limit, i.e., approaches minus infinity. e. Goes to ern. c. Approaches zero. Which of the following statements is most correct? a. If annual compounding is used, the effective annual rate equals the simple rate. b. If annual compounding is used, the effective annual rate equals the periodic rate. c. If a loan has a 12 percent simple rate with semiannual compounding, its effective annual rate is equal to 11.66 percent. d. Both answers a and b are correct. e. Both answers a and c are correct. d. Both answers a and b are correct. RATIONALE: Statement d is correct. The equation for EAR is as follows: : If annual compounding is used, m = 1 and the equation above reduces to EAR = rSIMPLE. The equation for the periodic rate is: . If annual compounding is used then m = 1 and rPER = rSIMPLE and since EAR = rSIMPLE then rPER = EAR. Why is the present value of an amount to be received (paid) in the future less than the future amount? a. Deflation causes investors to lose purchasing power when their dollars are invested for greater than one year. b. Investors have the opportunity to earn positive rates of return, so any amount invested today should grow to a larger amount in the future. c. Investments generally are not as good as those who sell them suggest, so investors usually are not willing to pay full face value for such investments, thus the price is discounted. d. Because investors are taxed on the income received from investments they never will buy an investment for the amount expected to be received in the future. e. None of the above is a correct answer. b. Investors have the opportunity to earn positive rates of return, so any amount invested today should grow to a larger amount in the future. By definition, what type of annuity best describes payments such as rent and magazine subscriptions (assuming the costs do not change over time)? a. ordinary annuity b. annuity due c. nonconstant annuity d. annuity in arrears b. annuity due What is the effective annual return (EAR) for an investment that pays 10 percent compounded annually? a. equal to 10 percent b. greater than 10 percent c. less than 10 percent d. This question cannot be answered without knowing the dollar amount of the investment. e. None of the above is correct. a. equal to 10 percent What is the term used to describe an annuity with an infinite life? a. perpetuityb. infinuity c. infinity due d. There is no special term for an infinite annuity. a. perpetuity Everything else equal, which of the following conditions will result in the lowest present value of an amount to be received in the future? a. annual compounding b. quarterly compounding c. monthly compounding d. daily compounding d. daily compounding . Suppose someone offered you your choice of two equally risky annuities, each paying $5,000 per year for 5 years. One is an annuity due, while the other is a regular (or deferred) annuity. If you are a rational wealthmaximizing investor which annuity would you choose? a. The annuity due. b. The deferred annuity. c. Either one, because as the problem is set up, they have the same present value. d. Without information about the appropriate interest rate, we cannot find the values of the two annuities, hence we cannot tell which is better. e. The annuity due; however, if the payments on both were doubled to $10,000, the deferred annuity would be preferred. a. The annuity due. Which of the following statements is correct? a. For all positive values of r and n, FVIFr, n ≥ 1.0 and PVIFAr, n ≥ n. b. You may use the PVIF tables to find the present value of an uneven series of payments. However, the PVIFA tables can never be of use, even if some of the payments constitute an annuity (for example, $100 each year for Years 3, 4, and 5), because the entire series does not constitute an annuity. c. If a bank uses quarterly compounding for saving accounts, the simple rate will be greater than the effective annual rate. d. The present value of a future sum decreases as either the simple interest rate or the number of discount periods per year increases. e. All of the above statements are false d. The present value of a future sum decreases as either the simple interest rate or the number of discount periods per year increases. Which of the following statements is correct? a. Other things held constant, an increase in the number of discounting periods per year increases the present value of a given annual annuity. b. Other things held constant, an increase in the number of discounting periods per year increases the present value of a lump sum to be received in the future. c. The payment made each period under an amortized loan is constant, and it consists of some interest and some principal. The later we are is the loan's life, the smaller the interest portion of the payment. d. There is an inverse relationship between the present value interest factor of an annuity and the future value interest factor of an annuity, (i.e., one is the reciprocal of the other). e. Each of the above statements is true. c. The payment made each period under an amortized loan is constant, and it consists of some interest and some principal. The later we are is the loan's life, the smaller the interest portion of the payment. A $10,000 loan is to be amortized over 5 years, with annual end-of-year payments. Given the following facts, which of these statements is correct? a. The annual payments would be larger if the interest rate were lower.b. If the loan were amortized over 10 years rather than 5 years, and if the interest rate were the same in either case, the first payment would include more dollars of interest under the 5-year amortization plan. c. The last payment would have a higher proportion of interest than the first payment. d. The proportion of interest versus principal repayment would be the same for each of the 5 payments. e. The proportion of each payment that represents interest as opposed to repayment of principal would be higher if the interest rate were higher. e. The proportion of each payment that represents interest as opposed to repayment of principal would be higher if the interest rate were higher. RATIONALE: If the interest rate were higher, the payments would all be higher, and all of the increase would be attributable to interest. So, the proportion of each payment that represents interest would be higher. Note that statement b is false because interest during Year 1 would be the interest rate times the beginning balance, which is $10,000. With the same interest rate and the same beginning balance, the Year 1 interest charge will be the same, regardless of whether the loan is amortized over 5 or 10 years. Which of the following statements is correct? a. Simple rates can't be used in present value or future value calculations because they fail to account for compounding effects. b. The periodic interest rate can be used directly in calculations as long as the number of payments per year is greater than or equal to the number of compounding periods per year. c. In all cases where interest is added or payments are made more frequently than annually, the periodic rate is less than the annual rate. d. Generally, the APR is greater than the EAR as a result of compounding effects. e. If the compounding period is semiannual then the periodic rate will equal the effective annual rate divided by two. c. In all cases where interest is added or payments are made more frequently than annually, the periodic rate is less than the annual rate. All else equal, if you expect to receive a certain amount in the future, say, $500 in ten (10) years, the present value of that future amount will be lowest if the interest earned on such investments is compounded a. daily b. weekly c. monthly d. quarterly e. annually a. daily Which of the following payments (receipts) would probably not be considered an annuity due? Based on your knowledge and using logic, think about the timing of the payments. a. rent payments associated with a five-year lease b. payments for a magazine subscription for a two-year period where the payments are made annually c. interest payments associated with a corporate bond that was issued today d. annual payments associated with lottery winnings that are paid out as an annuity c. interest payments associated with a corporate bond that was issued today All else equal, the future value of a lump-sum amount invested today will increase if the a. interest rate that is earned is lowered. b. number of compounding periods is increased. c. investment time period is shortened. d. amount initially invested is lowered. e. Two or more of the above answers are correct. b. number of compounding periods is increased. Susan just signed a long-term lease on a townhouse in New York City (near Central Park) that requires her to makeequal monthly payments for the next five years. The payments Susan has promised to make represent a(n) the landlord. a. ordinary annuity b. annuity due c. series of uneven cash flows d. perpetuity b. annuity due Suppose that the present value of receiving a guaranteed $450 in two years is $385.80. The opportunity rate of return on similar risk investments is 8 percent. According to this information, all else equal, which of the following statements is correct? a. It always would be preferable to wait two years to receive the $450 because this value is greater than the present value. b. Risk averse investors always would prefer to take the $385.80 today because it is a guaranteed amount whereas there is uncertainty as to whether the future amount will be paid. c. No investor should be willing to pay more than $385.80 for such an investment. d. It is apparent the present value was computed incorrectly because the present value of a future amount always should be greater than the future value. e. None of the above is a correct answer. c. No investor should be willing to pay more than $385.80 for such an investment. You plan to invest an amount of money in five-year certificate of deposit (CD) at your bank. The stated interest rate applied to the CD is 12 percent, compounded monthly. How much must you invest if you want the balance in the CD account to be $8,500 in five years? a. $4,678.82 b. $4,823.13 c. $13,600.00 d. $14,979.90 e. $7,589.29 a. $4,678.82 Vegit Corporation needs to borrow funds to support operations during the summer. Vegit's CFO is trying to decide whether to borrow from the Bank of Florida or the Bank of Georgia. The loan offered by Bank of Florida has a 12.5 percent simple interest rate with annual interest payments, whereas the loan offered by the Bank of Georgia has a 12 percent simple interest rate with monthly payments. Which bank should Vegit use for the loan? a. Bank of Georgia, because the 12 percent simple interest is cheaper than the 12.5 percent simple interest at Bank of Florida. b. Bank of Georgia, because the effective interest rate on the loan is less than 12 percent, whereas the effective interest rate on the loan at the Bank of Florida is greater than 12.5 percent. c. Bank of Florida, because the simple interest rate is higher, which means that Vegit will be able to invest the proceeds from the loan at a higher rate of return. d. Bank of Florida, because the effective interest rate on the loan is 12.5 percent, which is less than the 12.7 percent effective interest rate on the loan offered by the Bank of Georgia. e. There is not enough information to answer this question. d. Bank of Florida, because the effective interest rate on the loan is 12.5 percent, which is less than the 12.7 percent effective interest rate on the loan offered by the Bank of Georgia. Alice's investment advisor is trying to convince her to purchase an investment that pays $250 per year. The investment has no maturity; therefore the $250 payment will continue every year forever. Alice has determined that her required rate of return for such an investment should be 14 percent and that she would hold the investment for 10 years and then sell it. If Alice decides to buy the investment, she would receive the first $250 payment one year from today. How much should Alice be willing to pay for this investment?a. $1,304.03, because this is the present value of an ordinary annuity that pays $250 a year for 10 years at 14 percent. b. $1,486.59, because this is the present value of an annuity due that pays $250 a year for 10 years at 14 percent. c. $1,785.71, because this is the present value of a $250 perpetuity at 14 percent. d. There is not enough information to answer this question, because the selling price of the investment in 10 years is not known today. e. None of the above is correct. c. $1,785.71, because this is the present value of a $250 perpetuity at 14 percent. At approximately what rate would you have to invest a lump-sum amount today if you need the amount to triple in six years? Assume interest is compounded annually. a. 20% b. 12% c. 24% d. Not enough information is provided to answer the question. e. None of the above is a correct answer. a. 20% Sarah is thinking about purchasing an investment from HiBond Investing. If she buys the investment, Sarah will receive $100 every three months for five years. The first $100 payment will be made as soon as she purchases the investment. If Sarah's required rate of return is 16 percent, to the nearest dollar, how much should she be willing to pay for this investment? a. $1,359 b. $1,413 c. $1,112 d. $1,519 e. $1,310 b. $1,413 Which of the following statements is most correct? a. The first payment under a 3-year, annual payment, amortized loan for $1,000 will include a smaller percentage (or fraction) of interest if the interest rate is 5 percent than if it is 10 percent. b. If you are lending money, then, based on effective interest rates, you should prefer to lend at a 10 percent simple, or quoted, rate but with semiannual payments, rather than at a 10.1 percent simple rate with annual payments. However, as a borrower you should prefer the annual payment loan. c. The value of a perpetuity (say for $100 per year) will approach infinity as the interest rate used to evaluate the perpetuity approaches zero. d. Statements a, b, and c are all true. e. Only statements b and c are true. d. Statements a, b, and c are all true. A recent advertisement in the financial section of a magazine carried the following claim: "Invest your money with us at 14 percent, compounded annually, and we guarantee to double your money sooner than you imagine." Ignoring taxes, how long would it take to double your money at a simple rate of 14 percent, compounded annually? a. Approximately 3.5 years b. Approximately 5 years c. Exactly 7 years d. Approximately 10 years e. Exactly 14 years b. Approximately 5 years Tabular solution: $1 (FVIF14%, n) = $2FVIF14%, n = 2.000 n = 5+ years. Financial calculator solution: Inputs: I =14; PV = −1; FV =2. Output: N = 5.29 years. At an effective annual interest rate of 20 percent, how many years will it take a given amount to triple in value? (Round to the closest year.) a. 5 b. 8 c. 6 d. 10 e. 9 c. 6 Tabular solution: $1 = $3 (PVIF20%, n) PVIF20%, n = 0.3333 n = 6 periods (years). Financial calculator solution: Inputs: I = 20; PV = −1; FV =3. Output: N = 6.026 = 6 years. You deposited $1,000 in a savings account that pays 8 percent interest, compounded quarterly, planning to use it to finish your last year in college. Eighteen months later, you decide to go to the Rocky Mountains to become a ski instructor rather than continue in school, so you close out your account. How much money will you receive? a. $1,171 b. $1,126 c. $1,082 d. $1,163 e. $1,008 b. $1,126 Tabular solution: FV = $1,000 (FVIF2%, 6) = $1,000 (1.1262) = $1,126.20 ≈ $1,126. F Financial calculator solution: Inputs: N = 6; I = 2; PV = −1,000. Output: FV = $1,126.16 ≈ $1,126. What is the future value of a 5-year ordinary annuity with annual payments of $200, evaluated at a 15 percent interest rate? a. $670.44 b. $842.91 c. $1,169.56 d. $1,522.64 e. $1,348.48 e. $1,348.48 Tabular solution: FB = $200 (FVIFA15%, 5) = $200 × 6.7424 = $1,348.48. Financial calculator solution: Inputs: N = 5; I = 15; PMT = −200. Output: FV = $1,348.48.If a 5-year regular annuity has a present value of $1,000, and if the interest rate is 10 percent, what is the amount of each annuity payment? a. $240.42 b. $263.80 c. $300.20 d. $315.38 e. $346.87 b. $263.80 Tabular solution: $1,000 = PMT (PVIFA10%, 5) PMT = $1,000/3.7908 = $263.80. Financial calculator solution: Inputs: N = 5; I = 10; FV = −1,000. Output: PMT = $263.80. You have the opportunity to buy a perpetuity which pays $1,000 annually. Your required rate of return on this investment is 15 percent. You should be essentially indifferent to buying or not buying the investment if it were offered at a price of a. $5,000.00 b. $6,000.00 c. $6,666.67 d. $7,500.00 e. $8,728.50 c. $6,666.67 RATIONALE: V = PMT/I = $1,000/0.15 = $6,666.67. Assume that you will receive $2,000 a year in Years 1 through 5, $3,000 a year in Years 6 through 8, and $4,000 in Y all cash flows to be received at the end of the year. If you require a 14 percent rate of return, what is the present val cash flows? a. $9,851 b. $13,250 c. $11,714 d. $15,129 e. $17,353 c. $11,714 Tabular solution: PV = $2,000 (PVIFA14%, 5) + $3,000 (PVIFA14%, 5) (PVIF14%, 9) = $2,000 (3.4331) + $3,000 (2.3216) (0.5194) + $4,000 (0.3075) = $6,866.20 + $3,617.52 + $1,230.00 = $11,713.72 ≈ $11,714. Financial calculator solution: Using cash flows Inputs: CF0 = 0; CF1 = 2,000; Nj = 5; CF2 = 3,00 CF3 = 4,000; I = 14. Output: NPV = $11,713.54 ≈ $11,714. If $100 is placed in an account that earns a simple 4 percent, compounded quarterly, what will it be worth in 5 years? a. $122.02 b. $105.10 c. $135.41 d. $120.90 e. $117.48 a. $122.02 Tabular solution:$100 (FVIF1%, 20) = $100 (1.2202) = $122.02. Financial calculator solution: Inputs: N = 1; PV = −100. Output: FV = $122.02. . In 1958 the average tuition for one year at an Ivy League school was $1,800. Thirty years later, in 1988, the average cost was $13,700. What was the growth rate in tuition over the 30-year period? a. 12% b. 9% c. 6% d. 7% e. 8% d. 7% Tabular solution: $13,700 = $1,800 (FVIFi, 30) FVIFi, 30 = 7.6111 I ≈ 7% Financial calculator solution: Inputs: N = 30; PV = −1,800; FV = 13,700. Output: I = 7.0% At an inflation rate of 9 percent, the purchasing power of $1 would be cut in half in 8.04 years. How long to the nearest year would it take the purchasing power of $1 to be cut in half if the inflation rate were only 4%? a. 12 years b. 15 years c. 18 years d. 20 years e. 23 years c. 18 years Tabular solution: 0.5 = $1 (PVIF4%, n) PVIF4%, n = 0.5 PVIF4%, 18 = 0.4936; PVIF4%, 17 =0.5134 n ≈ 18 years. Although a financial calculator or interpolation might be used to solve precisely, Response c is clearly the closest and best answer of those given. Financial calculator solution: Inputs: I = 4; PV = 1; PV = −0.50. Output: N = −17.67 = 18 years. Gomez Electronics needs to arrange financing for its expansion program. Bank A offers to lend Gomez the required funds on a loan where interest must be paid monthly, and the quoted rate is 8 percent. Bank B will charge 9 percent, with interest due at the end of the year. What is the difference in the effective annual rates charged by the two banks? a. 0.25% b. 0.50% c. 0.70% d. 1.00% e. 1.25% c. 0.70% Assume that you can invest to earn a stated annual rate of return of 12 percent, but where interest is compounded semiannually. If you make 20 consecutive semiannual deposits of $500 each, with the first deposit being made today, what will your balance be at the end of Year 20? a. $52,821.19 b. $57,900.83c. $58,988.19 d. $62,527.47 e. $64,131.50 d. $62,527.47 Tabular solution: Periodic (six-month) rate = 12%/2 = 6%. First, calculate the FV as of Year 10 FV10 yr. = ($500) (FVIFA6%, 19) 1.06 + ($500) (FVIF6%, 20) = $500 (33.760) (1.06) + $500 (3.2071) = $19,496.35. Calculate FV as of Year 20 using FV10 as the PV FV20 yr. = ($19,496.35) (FVIF6%, 20) = $19,496.35 (3.2071) = $62,526.74. Financial calculator solution: Calculate the FV as of Year 10 BEGIN mode. Inputs: N = 20; I = 6; PMT = −500. Output: FV = $19,496.36. Calculate the FV as of Year 20 using FV10 as the PV END mode. Inputs: N = 20; I = 6; PMT = −19,496.36. Output: FV = $62,527.47. Assume you are to receive a 20-year annuity with annual payments of $50. The first payment will be received at the end of Year 1, and the last payment will be received at the end of Year 20. You will invest each payment in an account that pays 10 percent. What will be the value in your account at the end of Year 30? a. $6,354.81 b. $7,427.83 c. $7,922.33 d. $8,591.00 e. $6,752.46 b. $7,427.83 Tabular solution: FVYear 20 = $50 (FVIFA10$, 20) = $50 (57.275) = $2,863.75. FVYear 30 = $2,863 (FVIFA10$, 10) = $2,863.75 (2.5937) = $7,427.71. Financial calculator solution: Calculate FV at Year 20, then take that lump sum forward 10 years to Year 30 at 10%. Inputs: N = 20; I = 10; PMT = −50. OutputYear 20: FV = $2,863.75. At Year 30 Inputs: N = 10; I = 10; PV = −2,863.75. OutputYear 30: FV = $7,427.83. You expect to receive $1,000 at the end of each of the next 3 years. You will deposit these payments into an account which pays 10 percent compounded semiannually. What is the future value of these payments, that is, the value at the end of the third year? a. $3,000 b. $3,310 c. $3,318 d. $3,401 e. $3,438 c. $3,318 Tabular solution: FV = $1,000(FVIF5%,4) + $1,000(FVIF5%,2) + $1,000= $1,000(1.2155) + $1,000(1.1025) + $1,000 = $1,215.50 + $1,102.50 + $1,000 = $3,318.00. Financial calculator solution: Convert rSIMPLE to EAR using interest rate conversion Inputs: P/YR = 2; NOM% =10. Output: EFF% = EAR = 10.25%. Solve for FV on annual basis using EAR Inputs: N = 3; I = 10.25; PMT = −1,000. Output: FV = $3,318.006 ≈ $3,318.00. You just graduated, and you plan to work for 10 years and then to leave for the Australian "Outback" bush country. You figure you can save $1,000 a year for the first 5 years and $2,000 a year for the next 5 years. These savings cash flows will start one year from now. In addition, your family has just given you a $5,000 graduation gift. If you put the gift now, and your future savings when they start, into an account which pays 8 percent compounded annually, what will your financial "stake" be when you leave for Australia 10 years from now? a. $21,432 b. $28,393 c. $16,651 d. $31,148 e. $20,000 d. $31,148 Tabular solution: FV = (FVIFA8%, 10) + $1,000 (FVIFA8%, 5) + $5,000 (FVIF8%, 10) = $1,000 (14.487) + $1,000 (5.866) + $5,000 (.1589) = $14,487 + $5,866 + $10,794.50 = $31,147.50 ≈ $31,148 Financial calculator solution: Solution using NFV (Note: Some calculators do not have net future value function. Cash flows can be grouped and carried forward or PV can be used; see alternative solution below.) Inputs: CF0 = 5,000; CF1 = 1,000; Nj = 5; CF2 = 2,000; Nj = 5; I = 8 Output: NFV = $31,147.79 ≈ $31,148 Alternative solution: calculate PV of the cash flows, then bring them forward to FV using the interest rate. Inputs: CF0 = 5,000; CF1 = 1,000; Nj = 5; CF2= 2,000; Nj = 5; I = 8 Output: PV = $14,427.45 Inputs: N = 10; I = 8; PV = −14,427.45 Output: FV= $31,147.79 ≈ $31,148 As the winning contestant in a television game show, you are considering the prizes to be awarded. You must indicate sponsor which of the following two choices you prefer, assuming you want to maximize your wealth. Assume it is no January 1, and there is no danger whatever that the sponsor won't pay off. (1)$1,000 now and another $1,000 at the beginning of each of the 11 subsequent months during the remainder of the year, to be deposited in an account paying 12 percent simple annual rate, but compounded monthly (to be left on deposit for the year). (2) $12,750 at the end of the year. Which one would you choose? a. Choice 1 b. Choice 2 c. Choice 1, if the payments were made at the end of the year. d. The choice would depend on how soon you need the money. e. Either one, since they have the same present value. a. Choice 1 Tabular solution: PVChoice 1 = $1,000 (PVIFA 1%, 11 + 1.0) = $1,000 (11.3676) = $11,367.60 PVChoice 2 = $12,750 (PVIF 1%, 12) = $12,750 (0.8874) = $11,314.35 Financial calculator solution: Choice 1 BEGIN mode, Inputs N = 12; I = 1; PMT = 1,000. Output:−$11,367.63 Choice 2 END mode, Inputs: N = 12; I = 1; FV − 12,750. Output: PV = −$11,314.98 You want to buy a Nissan 350Z on your 27th birthday. You have priced these cars and found that they currently sell for $30,000. You believe that the price will increase by 5 percent per year until you are ready to buy. You can presently invest to earn 14 percent. If you just turned 20 years old, how much must you invest at the end of each of the next 7 years to be able to purchase the Nissan in 7 years? a. $4,945.57 . b. $3,933.93 c. $7,714.72 d. $3,450.82 e. $6,030.43 b. $3,933.93 Tabular solution: Price of car on 27th birthday FV = $30,000 (FVIF 5%, 7) = $30,000 (1.4071) = $42,213. Annual investment required FV of annuity = FVAn = PMT (FVIFA i, n) $42,213 = PMT (FVIFA 14%,7) PMT = $42,213/10.7305 = $3,933.93. Financial calculator solution: Price of car on 27th birthday Inputs: N = 7; I = 5; PV = −30,000. Output: FV = $42,213.01 ≈ $42,213. Annual investment required Inputs: N = 7; I = 14; FV = 42,213.Output: PMT = −$3,933.93. Assume that your required rate of return is 12 percent and you are given the following stream of cash flows: Year Cash Flow 0 $10,000 1 15,000 2 15,000 3 15,000 4 15,000 5 20,000 If payments are made at the end of each period, what is the present value of the cash flow stream? a. $66,909 b. $57,323 c. $61,815 d. $52,345 e. $62,029 a. $66,909 Tabular solution: PV = $10,000 + $15,000 (PVIFA12%, 4) + $20,000 (PVIF12%, 5) = $10,000 + $15,000 (3.0373) + $20,000 (0.5674) = $10,000 + $45,559.50 + $11,348 = $66,907.50. Financial calculator solution: Using cash flows Inputs: CF0 = 10,000; CF1 = 15,000; Nj = 4 times; CF2 = 20,000; I = 12. Output: NPV = $66,908.77 ≈ $66,909. 62. You are given the following cash flows. What is the present value (t = 0) if the discount rate is 12 percent? Has a Cash Flow TIme Line Here a. $3,277 b. $4,804 c. $5,302 d. $4,289 e. $2,804 a. $3,277 PV = ? Tabular solution: PV = + $ 1 (PVIF 12%, 1) = $ 1 (0.8929) = $ 0.89 + $2,000 (PVIF 12%, 2) = $2,000 (0.7972) = $1,594.40 + $2,000 (PVIF 12%, 3) = $2,000 (0.7118) = $1,423.60 + $2,000 (PVIF 12%, 4) = $2,000 (0.6355) = −$1,271.00 + −$2,000 (PVIF 12%, 6) = −$2,000 (0.5066) = −$1,013.20 PV = $3,276.69 Financial calculator solution:Inputs: CF0 = 0; CF1 = 1; CF2 = 2,000; Nj = 3 times; CF3 = 0; CF4−2,000; I = 12 Output: NPV = $3,276.615 ≈ $3,277 You are given the following cash flow information. The appropriate discount rate is 12 percent for Years 1-5 and 10 percent for Years 6-10. Payments are received at the end of the year. Year Amount 1-5 $20,000 6-10 $25,000 What should you be willing to pay right now to receive the income stream above? a. $166,866 b. $158,791 c. $225,000 d. $125,870 e. $198,433 d. $125,870 Tabular solution: Years 1-5 PV of annuity Years 1-5 = $$20,000 (PVIFA12%, 5) = $20,000 (3.6048) = $72,096. Years 6-10 Value of annuity Years 6-10 on Day 1 of Year 6 PV5 = $25,000 (PVIFA10%, 5) = $25,000 (3.7908) = $94,770 PV of annuity Years 6-10 at time = 0 PV0 = $94,770 (PVIF 12%, 5) = $94,770 (0.5674) = $53,772.50 PV0 of both annuities $72,096 + $53, 772.50 = $125.868.50 $125.870 Financial calculator solution: Solve for PV at time = 0 of $20,000 annuity Inputs: Solve for PV at time = 5 pf $25,000 annuity using its value at t = 5 Inputs: Solve for PV at time = 0 0f $25,000 annuity Inputs: N = 5; I = 12; FV = -94,769.669. Output: PV = $53,774.855 Add the two PVs together PVBoth annuities = $72,095.524 + $53,774.855 = $125,870.38 $125.870 Note: Tabular solution differs from calculator solution due to interest factor rounding. A project with a 3-year life has the following probability distributions for possible end of year cash flows in each of the next three years: Year 1 Year 2 Year 3 Prob Cash Flow Prob Cash Flow Prob Cash Flow 0.30 $300 0.15 $100 0.25 $200 0.40 500 0.35 200 0.75 800 0.30 700 0.35 600 0.15 900 Using an interest rate of 8 percent, find the expected present value of these uncertain cash flows. (Hint: Find the expected cash flow in each year, then evaluate those cash flows.) a. $1,204.95 b. $835.42 c. $1,519.21 d. $1,580.00 e. $1,347.61e. $1,347.61 Calculate expected cash flows E(CF1) = (0.30) ($300) + (0.40) ($500) + (0.30) ($700) = $500 E(CF2) = (0.15) ($100) + (0.35) ($200) + (0.35) ($600) + (0.15) ($900) = $430 E(CF3) = (0.25) ($200) + (0.75) ($800) = $650 Tabular solution: PV = $500 (PVIF 8%, 1) + $430 (PVIF 8%, 2) + $650 (PVIF 8%, 3) = $500 (0.9259) + $430 (0.8573) + $650 (0.7938) = $462.95 + $368.64 + $515.97 = $1,347.56 Financial Calculator Solution: Using cash flows, Inputs: Output: NPV = $1,347.61 If you buy a factory for $250,000 and the terms are 20 percent down, the balance to be paid off over 30 years at a 1 rate of interest on the unpaid balance, what are the 30 equal annual payments? a. $20,593 b. $31,036 c. $24,829 d. $50,212 e. $6,667 c. $24,829 Tabular solution: Initial balance = 0.8($250,000) = $200,000 $200,000 = PMT (PVIA12%, 30) $200,000 = PMT (8.0552) PMT = $200,00/8.0552 = $24,828.68 ≈ $24,829 Financial calculator solution: Inputs: N = 30; I = 12; PV = −200,000; FV = 0 Output: PMT = $24,828.73 $24,829 In its first year of operations, 2002, the Gourmet Cheese Shoppe had earnings per share (EPS) of $0.26. Four years l in 2006, EPS was up to $0.38, and 7 years after that, in 2013, EPS was up to $0.535. It appears that the first 4 years represented a supernormal growth situation and since then a more normal growth rate has been sustained. What are rates of growth for the earlier period and for the later period? a. 6%; 5% b. 6%; 3% c. 10%; 8% d. 10%; 5% e. 12%; 7% d. 10%; 5% Tabular solution: PV = $0.26 = $0.38 (PVIFi, 4) PVIF i, 4 = $0.26/$0.38 = 0.6842 i1 ≈ 10% PV = $= $0.535 (PVIF i, 7) PFIV i,7 = $0.38/$0.535 = 0.7103 i2 ≈ 5% Financial calculator solution: Inputs: N= 4; PV = −0.26; FV = 0.38. Output: I = 9.95% ≈ 10%Inputs: N = 7; PV = −0.38; FV = 0.535. Output: I = 5.01% ≈ 5% Steaks Galore needs to arrange financing for its expansion program. One bank offers to lend the required $1,000,000 on a loan which requires interest to be paid at the end of each quarter. The quoted rate is 10 percent, and the principal must be repaid at the end of the year. A second lender offers 9 percent, daily compounding (365-day year), with interest and principal due at the end of the year. What is the difference in the effective annual rates (EFF%) charged by the two banks? a. 0.31% b. 0.53% c. 0.75% d. 0.96% e. 1.25% d. 0.96% Difference = 10.38% − 9.42% = 0.96% Alternatively, with a financial calculator, for the quarterly loan enter P/YR = 4, NOM% = 10, and press EFF% to get EAR = 10.38%. For the daily loan, enter P/YR = 365, NOM = 9%, and press EFF% to get EAR = 9.42%. You are currently at time period 0, and you will receive the first payment on an annual payment annuity of $100 in perpetuity at the end of this year. Six full years from now you will receive the first payment on an additional $150 in perpetuity, and at the end of time period 10 you will receive the first payment on an additional $200 in perpetuity. If you require a 10 percent rate of return, what is the combined present value of these three perpetuities? a. $2,349.50 b. $2,526.85 c. $2,685.42 d. $2,779.58 e. $2,975.40 d. $2,779.58 Tabular solution: PV = ($100/0.10) + ($150/0.10)(PVIF 10%, 5) + ($200/0.10)(PVIF 10%, 9) = $1,000 + $1,500 (0.6209) + $2,000 (0.4241) = $1,000 + $931.35 + $848.20 = $2,779.55 Financial calculator solution: Calculate the undiscounted values of each of three perpetuities at the point in time where they begin, using numerical methods, then calculate PV at t = 0 of the combined perpetuity values. PVp1 at Time = 0: $100/0.10 = $1,000 PVp2 at Time = 5; $150/0.10 = $1,500 PVp3 at Time = 9; $200/0.10 = $2,000 Inputs: CF0 = 1,000; CF1 = 0; Nj = 4; CF2 = 1,500; CF3 = 0; Nj = 3; CF4 = 2,000; I = 10. Output: NPV = $2,446.577 ≈ $2,779.58. Note: Tabular solution differs from calculator solution due to interest factor rounding. Find the present value of an income stream which has a negative flow of $100 per year for 3 years, a positive flow o $200 in the 4th year, and a positive flow of $300 per year in Years 5 through 8. The appropriate discount rate is 4 percent for each of the first 3 years and 5 percent for each of the later years. Thus, a cash flow accruing in Year 8 should be discounted at 5 percent for some years and 4 percent in other years. All payments occur at year-end. a. $528.21 b. $1,329.00 c. $792.49d. $1,046.41 e. $875.18 c. $792.49 Tabular solution: PV = −$100 (PVIFA 4%, 3) + $200 (PVIF 5%, 1) (PVIF 4%, 3) + $300 (PVIFA 5%, 4) (PVIF 5%, 1) (PFIV 4%, 3) = −$100 (2.7751) + 200 (0.9524) (0.8890) + $300 (3.35460) (0.9524) (0.8890) = −$277.51 + $169.34 + $900.70 = $792.53. Financial calculator solution: Inputs: CF0 = 0; CF1 = −100; Nj = 3; I = 4. Output: NPV = −277.51 Calculate the PV of CFs 4-8 as of time = 3 at I = 5% Inputs: CF0 = 0; CF1 = 200; CF2 = 300; Nj = I = 5. Output: NPV3 = $1,203.60 Calculate PV of the FV of the positive CFs at Time = 3 Inputs: N=3; I = 4; FV = −1,203.60. Output: PV = $1,070. Total PV = $1,070 − $277.51 = $792.49 Assume that you are graduating, that you plan to work for 4 years, and then to go to law school for 3 years. Right now, going to law school would require $17,000 per year (for tuition, books, living expenses, etc.), but you expect this cost to rise by 8 percent per year in all future years. You now have $25,000 invested in an investment account which pays a simple annual rate of 9 percent, quarterly compounding, and you expect that rate of return to continue into the future. You want to maintain the same standard of living while in law school that $17,000 per year would currently provide. You plan to save and to make 4 equal payments (deposits) which will be added to your account at the end of each of the next 4 years; these new deposits will earn the same rate as your investment account currently earns. How large must each of the 4 payments be in order to permit you to make 3 withdrawals, at the beginning of each of your 3 years in law school? (Note: (1) The first payment is made a year from today and the last payment 4 years from today, (2) the first withdrawal is made 4 years from today, and (3) the withdrawals will not be of a constant amount.) a. $13,242.67 b. $6,562.13 c. $10,440.00 d. $7,153.56 e. $14,922.85 d. $7,153.56 PVCosts = $17,000, I = 8% PVAcct = $25,000, I = 9.31% Financial calculator solution: Step 1: Use the current law school costs and inflation rate to calculate the withdrawals to cover law school costs at T = 4, 5, 6: At T = 4, Inputs: N = 4, PV = −17,000; I = 8. Output: FV4 = $23,128.31 At T = 5, Inputs: N = 5; PV = −17,000; I = 8. Output: FV5 = $24,978.58 At T = 6, Inputs: N = 6; PV = −14,000; I = 8. Output: FV6 = $26,976.86 Step 2: Use interest rate conversion feature to calculate the effective annual rate of the 9% account, compounded quarterly. Inputs: NOM% = 9; P/YR = 4. Output: EFF% = 9.31% Step 3: Use the EAR from Step 2 to determine the PV of law school payments at T = 4, 5, 6 as of T = 4.Inputs: CF0 = 23,128.31; CF1 = 24,978.85; CF2 = 26,976.86; I = 9.31 Output: NPV = $68,556.73 which equals PVT=4, costs Step 4: Determine the VF at T = 4 of the $25,000 in the account as of T = 0: Inputs: N = 4; I = 9.31; PV = −25,000. Output: FV = $35,692.72 Step 5: Calculate shortfall between what the account needs to have and will actually have at T = 4: $68,556.73 − $35,692.72 = $32,864.01 Step 6: Calculate the annuity payments, which will earn 9.31% EAR and accumulate to an FV of $32,864.01 at T = 4: Inputs: N = 4; I = 9.31%; FV = 32,864.01. Output: PMT = $7,153.56 Terms in this set (42) Which of the following is not a role of Finance? a. To ensure the financial statement numbers are accurate. b. To analyze accounting and other data to aid in managerial decisions. c. To determine the present value of cash flows for long term projects for decision making. d. Manage the firm's cash and marketable securities. e. All of the above are roles of finance. a. To ensure the financial statement numbers are accurate. Which of the following mechanisms is not used by shareholders to get managers to act in shareholder's best interests? a. Threat of firing b. Managerial compensation. c. Golden parachute. d. Threat of takeover. e. Payment of stock options. c. Golden parachute Which of the following should be the primary goal pursued by the financial manager of a firm? a. Maximize net income (profits). b. Maximize the firm's net worth, or book value. c. Maximize dividends paid to common stockholders. d. Minimize variable operating expenses. e. Maximize the market value of the firm's stock e. Maximize the market value of the firm's stock Which of the following is an example of an area of business where use of "questionable" ethics is considered a necessity? a. Attracting and sustaining new customers. b. Hiring and keeping skilled employees. c. Keeping up with competition. d. Dealing with firms who use "questionable" ethics.e. None of the above. e. None of the above. Everything else equal, including firm size, dollar sales, type of product sold, and so forth, the primary difference between the proprietorship and partnership business forms is that a. a partnership has more owners than a proprietorship. b. the combined personal liability associated with a partnership is significantly less than the combined personal liability associated with a proprietorship. c. a partnership generally is easier to form than a proprietorship. d. the annual growth rate of a proprietorship is limited by law, whereas the growth rate of a partnership is always potentially unlimited. e. there are many more businesses that are formed as partnerships than proprietorships. a. a partnership has more owners than a proprietorship. Which of the following actions is Which of the following actions is consistent with social responsibility but is necessarily inconsistent with stockholder wealth maximization? a. Investing in a smokestack "scrubber" to reduce the firm's air pollution as mandated by law. b. Voluntarily installing expensive machinery to treat effluent discharge which currently is being dumped into a river where it is ruining the drinking water of the community where the plant is located c. Investing in a smokestack filter to reduce sulphur-dioxide emissions in order to reduce the current tax being levied on the firm by the state for its pollution. d. Making a large corporate donation to the local community in order to fund a recreation complex that will be used by the community and the firm's employees. e. Each of the above actions is consistent with social responsibility and none are necessarily inconsistent with stockholder wealth maximization. e. Each of the above actions is consistent with social responsibility and none are necessarily inconsistent with stockholder wealth maximization. Which of the following statements is correct? a. Given the multi-owner nature of most large corporations, agency costs associated with perquisite consumption are not really a problem. b. Managers may operate in the stockholders' best interests, but they may also operate in their own personal best interests. As long as managers stay within the law, there simply are not any effective controls that stockholders can implement to control managerial decision making. c. Shareholder agency costs include the opportunity costs associated with constraining managerial freedom but do not include managerial salaries. d. An agency relationship exists when one or more persons hire another person to perform some service but withhold decision-making authority from that person. e. All of the above statements are false. c. Shareholder agency costs include the opportunity costs associated with constraining managerial freedom but do not include managerial salaries. Which of the following statements is correct? a. The role of Finance is to use the numbers developed through accounting to aid in decision making. b. The role of Finance is to use the accounting data to make all the decisions of the firm. c. The role of Finance is to make sure the firm shows a profit on its books. d. The role of Finance is to make sure the accountants are doing their job. a. The role of Finance is to use the numbers developed through accounting to aid in decision making. Which of the following statements is correct? a. A hostile takeover is a primary method of transferring ownership interest in a corporation. b. The corporation is a legal entity created by the state and is a direct extension of the legal status of itsowners and managers, that is, the owners and managers are the corporation. c. Unlimited liability and limited life are two key advantages of the corporate form over other forms of business organization. d. In part, due to limited liability and ease of ownership transfer, corporations have less trouble raising money in financial markets than other organizational forms. e. Although stockholders of the corporation are insulated by limited legal liability, the legal status of the corporation does not protect the firm's managers in the same way. d. In part, due to limited liability and ease of ownership transfer, corporations have less trouble raising Which of the following statements about the corporate form of business organization is incorrect? a. The corporation is the easiest form of business organization to establish. b. In the United States, corporations generate a significantly greater percentage of total annual sales than either partnerships or proprietorships. c. Corporations generally are larger than either partnerships or proprietorships. d. One of the most important features of the corporate form of business organization is that stockholders have limited liability. e. None of the above. a. The corporation is the easiest form of business organization to establish. When choosing a business form a. The corporate form is always the best, as evidence by this being the form of the largest organizations! b. Partnerships are the best because they have all the benefits of both corporations and partnerships! c. Sole proprietorships have the advantage of lower agency costs. d. Hybrid forms are always the best - that's why they were developed! a. The corporate form is always the best, as evidence by this being the form of the largest organizations! In the United States, the most common form of business is the __________, and the form of business that generates most of the sales and profits is the __________. a. corporation; corporation b. corporation; proprietorship c. proprietorship; partnership d. proprietorship; corporation e. corporation; partnership d. proprietorship; corporation Paying Payroll Service (PPS) recently declared bankruptcy. The price of PPS's stock has dropped from approximately $10 per share one year ago to $1 today. You can imagine that stockholders are not happy that the value of their stock has dropped so significantly. At the same time the financial position of the firm was deteriorating, PPS executives increased their salaries and perquisites substantially. Nothing they did violated any laws or was considered an unethical act. We would most likely describe this situation as __________. a. an agency problem. b. an accounting glitch. c. an appropriate use of the tax laws. d. an appropriate action, because executive compensation should always be increased substantially each year. e. acceptable, because it is obvious that the executives were trying to maximize the value of the firm, which is what the shareholders want them to do. a. an agency problem 15. Other things held constant, which of the following will not affect the quick ratio? (Assume that current assets equal current liabilities.) a. Fixed assets are sold for cash.b. Cash is used to purchase inventories. c. Cash is used to pay off accounts payable. d. Accounts receivable are collected. e. Long-term debt is issued to payoff a short-term bank loan. b. Cash is used to purchase inventories. All of the following represent cash outflows to the firm except a. Taxes. b. Interest payments. c. Dividends. d. Purchase of plant and equipment. e. Depreciation. e. Depreciation. Other things held constant, which of the following will not affect the quick ratio? (Assume that current assets equal current liabilities.) a. Fixed assets are sold for cash. b. Cash is used to purchase inventories. c. Cash is used to pay off accounts payable. d. Accounts receivable are collected. e. Long-term debt is issued to payoff a short-term bank loan. b. Cash is used to purchase inventories. The annual report contains all of the following financial statements except a. income statement. b. statement of changes in long-term financing. c. statement of cash flows. d. balance sheet. e. statement of retained earnings. b. statement of changes in long-term financing. Which of the following financial statements shows a firm's financing activities (how funds were generated) and investment activities (how funds were used) over a particular period of time? a. balance sheet b. income statement c. statement of retained earnings d. statement of cash flows e. proxy statement d. statement of cash flows Which of the following is not a ratio to assess a firm's liquidity? a. Current Ratio b. Debt ratio c. Quick Ratio d. All of the above assess liquidity. b. Debt ratio When constructing a Statement of Cash Flows, which of the following actions would be considered a source of funds? a. increase in the cash account b. decrease in accounts payablec. increase in inventory d. increase in long-term bonds e. increase in fixed assets d. increase in long-term bonds Which of the following groups probably would not be interested in the financial statement analysis of a firm? a. creditors b. management of the firm c. stockholders d. Internal Revenue Service e. All of the above would be interested in the financial statement analysis. e. All of the above would be interested in the financial statement analysis. Which of the following ratios measures how effectively a firm is managing its assets? a. quick ratio b. times interest earned c. profit margin d. inventory turnover ratio e. price earnings ratio d. inventory turnover ratio Which of the following ratios measures the extent to which operating income can decline before the firm is unable to meet its annual interest costs a. fixed charge coverage ratio b. debt ratio c. times-interest-earned ratio d. return on equity e. profit margin c. times-interest-earned ratio An analysis of a firm's financial ratios over time that is used to determine the improvement or deterioration in its financial situation is called a. sensitivity analysis b. DuPont chart c. ratio analysis d. progress chart e. trend analysis e. trend analysis Which of the following statements is most correct? a. An increase in a firm's debt ratio, with no changes in its sales and operating costs, could be expected to lower its profit margin on sales. b. An increase in DSO, other things held constant, would generally lead to an increase in the total asset turnover ratio. c. An increase on the DSO, other things held constant, would generally lead to an increase in the ROE. d. In a competitive economy, where all firms earn similar returns on equity, one would expect to find lower profit margins for airlines, which require a lot of fixed assets relative to sales, than for fresh fish markets. e. It is more important to adjust the Debt/Asset ratio than the inventory turnover ratio to account for seasonal fluctuations. a. An increase in a firm's debt ratio, with no changes in its sales and operating costs, could be expected to Which of the following statements is correct? a. In the text, depreciation is regarded as a use of cash because it reduces fixed assets, which then must be replaced. b. If a company uses some of its cash to pay off short-term debt, then its current ratio will always decline,given the way ratio is calculated, other things held constant. c. During a recession, it is reasonable to think that most companies inventory turnover ratios will change while their fixed asset turnover ratio will remain fairly constant. d. During a recession, we can be confident that most companies' DSOs (or ACPs) will decline because their sales will probably decline. e. Each of the above statements is false. d. During a recession, we can be confident that most companies' DSOs (or ACPs) will decline because their sales will probably decline. A firm's current ratio has steadily increased over the past 5 years, from 1.9 five years ago to 3.8 today. What would a financial analyst be most justified in concluding? a. The firm's fixed assets turnover probably has improved. b. The firm's liquidity position probably has improved. c. The firm's stock price probably has increased. d. Each of the above is likely to have occurred. e. The analyst would be unable to draw any conclusions from this information. b. The firm's liquidity position probably has improved. Which of the following statements about ratio analysis is incorrect? a. Classifying a large, well-diversified firm into a single industry often is difficult because many of the firm's divisions are involved with different products from different industries. b. As a rule of thumb, it is safe to conclude that any firm with a current ratio greater than 1.0 should be able to meet its current obligations—that is, pay bills that come due in the current period. [Current ratio = (Current assets) / (Current liabilities)] c. Sometimes firms attempt to use "window dressing" techniques to make their financial statements look better than they actually are in the current period. d. Computing the values of the ratios is fairly simple; the toughest and most important part of ratio analysis is interpretation of the values derived from the computations. e. General conclusions about a firm should not be made by examining one or a few ratios—ratio analysis should be comprehensive. b. As a rule of thumb, it is safe to b. As a rule of thumb, it is safe to conclude that any firm with a current ratio greater than 1.0 should be able to meet its current obligations—that is, pay bills that come due in the current period. [Current ratio = (Current assets) / (Current liabilities)] Which of the following statements is most correct? a. firms with relatively low debt ratios have higher expected returns when the business is good. b. firms with relatively low debt ratios are exposed to risk of loss when the business is poor. c. firms with relatively high debt ratios have higher expected returns when the business is bad. d. firms with relatively high debt ratios have higher expected returns when the business is good. e. none of the above. d. firms with relatively high debt ratios have higher expected returns when the business is good. Yesterday, Bicksler Corporation purchased (and received) raw materials on credit from its supplier. All else equal, if Bicksler's current ratio was 2.0 before the purchase, what effect did this transaction have on Bicksler's current ratio? a. Increased. b. Decreased. c. stayed the same. d. There is not enough information to answer this question. e. None of the above is a correct answer.b. Decreased-- The easiest way to see it: assume the have $20 in current assets and $10 in current liabilities. That gives the stated current ratio of 2.0 ($20/$10). Now they buy $5 in materials (inventory) on credit. Both current assets and current liabilities go up by $5. So we get: $25/$15 = 1.67 < 2.0. Which of the following is not a concern in using ratio analysis? a. We don't know an 'optimal' value for ratios.. b. We cannot find adequate industry averages. c. There may be accounting differences. d. Ratios do not give us answers to how to 'fix' an organization. e. All of the above are concerns. e. All of the above are concerns. Given some amount to be received several years in the future, if the interest rate increases, the present value of the future amount will a. Be higher. b. Be lower. c. Stay the same. d. Cannot tell. e. Be variable. c. Stay the same. You have determined the profitability of a planned project by finding the present value of all the cash flows form that project. Which of the following would cause the project to look more appealing in terms of the present value of those cash flows? a. The discount rate decreases. b. The cash flows are extended over a longer period of time, but the total amount of the cash flows remains the same. c. The discount rate increases. d. The cash flows all occur at the end of the year instead of evenly distributed throughout the year. e. Both answers a and b above cause the project to look more appealing. a. The discount rate decreases. As the discount rate increases without limit, the present value of the future cash inflows a. Gets larger without limit. b. Stays unchanged. c. Approaches zero. d. Gets smaller without limit, i.e., approaches minus infinity. e. Goes to one. c. Approaches zero. Why is there a time value of money (cash received today is valued more than cash received a year from now)? a. Interest rates are greater than zero. b. Inflation. c. Consumption needs. d. risk. e. a and b are correct. f. c and d are correct. f. c and d are correct. Why is the present value of an amount to be received (paid) in the future less than the future amount? a. Deflation causes investors to lose purchasing power when their dollars are invested for greater thanone year. b. Investors have the opportunity to earn positive rates of return, so any amount invested today should grow to a larger amount in the future. c. Investments generally are not as good as those who sell them suggest, so investors usually are not willing to pay full face value for such investments, thus the price is discounted. d. Because investors are taxed on the income received from investments they never will buy an investment for the amount expected to be received in the future. e. None of the above is a correct answer. b. Investors have the opportunity to earn positive rates of return, so any amount invested today should grow to a larger amount in the future. By definition, what type of annuity best describes payments such as rent and magazine subscriptions (assuming the costs do not change over time)? a. ordinary annuity b. annuity due c. nonconstant annuity d. annuity in arrears b. annuity due What is the effective annual return (EAR) for an investment that pays 10 percent compounded semiannually? a. equal to 10 percent b. greater than 10 percent c. less than 10 percent d. This question cannot be answered without knowing the dollar amount of the investment. e. None of the above is correct. a. equal to 10 percent Everything else equal, which of the following conditions will result in the lowest present value of an amount to be received in the future? a. annual compounding b. quarterly compounding c. monthly compounding d. daily compounding d. daily compounding What is the term used to describe an annuity with an infinite life? a. perpetuity b. infinity c. infinity due d. There is no special term for an infinite annuity. a. perpetuity Suppose someone offered you your choice of two equally risky annuities, each paying $5,000 per year for 5 years. One is an annuity due, while the other is a regular (or deferred) annuity. If you are a rational wealthmaximizing investor which annuity would you choose? a. The annuity due. b. The deferred annuity. c. Either one, because as the problem is set up, they have the same present value. d. Without information about the appropriate interest rate, we cannot find the values of the two annuities, hence we cannot tell which is better. e. The annuity due; however, if the payments on both were doubled to $10,000, the deferred annuity would be preferred.a. The annuity due. Which of the following statements is correct? a. Other things held constant, an increase in the number of discounting periods per year increases the present value of a given annual annuity. b. Other things held constant, an increase in the number of discounting periods per year increases the present value of a lump sum to be received in the future. c. The payment made each period under an amortized loan is constant, and it consists of some interest and some principal. The later we are in the loan's life, the smaller the interest portion of the payment. d. There is an inverse relationship between the present value interest factor of an annuity and the future value interest factor of an annuity, (i.e., one is the reciprocal of the other). c. The payment made each period under an amortized loan is constant, and it consists of some interest and some principal. The later we are in the loan's life, the smaller the interest portion of the payment. CHAPTER 2 TIME VALUE OF MONEY (Difficulty: E = Easy, M = Medium, and T = Tough) Note: Most problems assume students have a calculator with a yx feature (i.e., an exponential feature). Annuity problems for finding the interest rate or the number of periods are in the financial calculator section at the end of this chapter. Multiple Choice: Conceptual Easy: PV and discount rate Answer: a Diff: E i . You have determined the profitability of a planned project by finding the present value of all the cash flows from that project. Which of the following would cause the project to look more appealing in terms of the present value of those cash flows? a. The discount rate decreases. b. The cash flows are extended over a longer period of time, but the total amount of the cash flows remains the same. c. The discount rate increases. d. Answers b and c above. e. Answers a and b above. PV versus FV Answer: e Diff: E ii . Which of the following statements is most correct? a. If the discount (or interest) rate is positive, the future value of an expected series of payments will always exceed the present value of the same series. b. To increase present consumption beyond present income normally requires either the payment of interest or else an opportunity cost of interest foregone. c. Disregarding risk, if money has time value, it is impossible for the present value of a given sum to be greater than its future value. d. Disregarding risk, if the present value of a sum is equal to its future value, either k = 0 or t = 0. e. Each of the statements above is true. Time value concepts Answer: e Diff: E iii . Which of the following statements is most correct?a. A 5-year $100 annuity due will have a higher present value than a 5- year $100 ordinary annuity. b. A 15-year mortgage will have larger monthly payments than a 30-year mortgage of the same amount and same interest rate. c. If an investment pays 10 percent interest compounded annually, its effective rate will also be 10 percent. d. Statements a and c are correct. e. All of the statements above are correct. Time value concepts Answer: d Diff: E iv . The future value of a lump sum at the end of five years is $1,000. The nominal interest rate is 10 percent and interest is compounded semiannually. Which of the following statements is most correct? a. The present value of the $1,000 is greater if interest is compounded monthly rather than semiannually. b. The effective annual rate is greater than 10 percent. c. The periodic interest rate is 5 percent. d. Both statements b and c are correct. e. All of the statements above are correct. Time value concepts Answer: d Diff: E v . Which of the following statements is most correct? a. The present value of an annuity due will exceed the present value of an ordinary annuity (assuming all else equal). b. The future value of an annuity due will exceed the future value of an ordinary annuity (assuming all else equal). c. The nominal interest rate will always be greater than or equal to the effective annual interest rate. d. Statements a and b are correct. e. All of the statements above are correct. Effective annual rate Answer: d Diff: E vi . Which of the following statements is most correct? a. If annual compounding is used, the effective annual rate equals the nominal rate. b. If annual compounding is used, the effective annual rate equals the periodic rate. c. If a loan has a 12 percent nominal rate with semiannual compounding, its effective annual rate is equal to 11.66 percent. d. Answers a and b are correct. e. Answers a and c are correct.Effective annual rate Answer: b Diff: E vii . Which of the following bank accounts has the highest effective annual return? a. An account which pays 10 percent nominal interest with monthly compounding. b. An account which pays 10 percent nominal interest with daily compounding. c. An account which pays 10 percent nominal interest with annual compounding. d. An account which pays 9 percent nominal interest with daily compounding. e. All of the investments above have the same effective annual return. Effective annual rate Answer: d Diff: E viii . You are interested in investing your money in a bank account. Which of the following banks provides you with the highest effective rate of interest? a. Bank 1; 8 percent with monthly compounding. b. Bank 2; 8 percent with annual compounding. c. Bank 3; 8 percent with quarterly compounding. d. Bank 4; 8 percent with daily (365-day) compounding. e. Bank 5; 7.8 percent with annual compounding. Amortization Answer: b Diff: E ix . Your family recently obtained a 30-year (360-month) $100,000 fixed-rate mortgage. Which of the following statements is most correct? (Ignore all taxes and transactions costs.) a. The remaining balance after three years will be $100,000 less the total amount of interest paid during the first 36 months. b. The proportion of the monthly payment that goes towards repayment of principal will be higher ten years from now than it will be this year. c. The monthly payment on the mortgage will steadily decline over time. d. All of the statements above are correct. e. None of the statements above is correct.Amortization Answer: e Diff: E x . Frank Lewis has a 30-year, $100,000 mortgage with a nominal interest rate of 10 percent and monthly compounding. Which of the following statements regarding his mortgage is most correct? a. The monthly payments will decline over time. b. The proportion of the monthly payment which represents interest will be lower for the last payment than for the first payment on the loan. c. The total dollar amount of principal being paid off each month gets larger as the loan approaches maturity. d. Statements a and c are correct. e. Statements b and c are correct. Medium: Annuities Answer: c Diff: M xi . Suppose someone offered you the choice of two equally risky annuities, each paying $10,000 per year for five years. One is an ordinary (or deferred) annuity, the other is an annuity due. Which of the following statements is most correct? a. The present value of the ordinary annuity must exceed the present value of the annuity due, but the future value of an ordinary annuity may be less than the future value of the annuity due. b. The present value of the annuity due exceeds the present value of the ordinary annuity, while the future value of the annuity due is less than the future value of the ordinary annuity. c. The present value of the annuity due exceeds the present value of the ordinary annuity, and the future value of the annuity due also exceeds the future value of the ordinary annuity. d. If interest rates increase, the difference between the present value of the ordinary annuity and the present value of the annuity due remains the same. e. Answers a and d are correct.Time value concepts Answer: e Diff: M xii . A $10,000 loan is to be amortized over 5 years, with annual end-of-year payments. Given the following facts, which of these statements is most correct? a. The annual payments would be larger if the interest rate were lower. b. If the loan were amortized over 10 years rather than 5 years, and if the interest rate were the same in either case, the first payment would include more dollars of interest under the 5-year amortization plan. c. The last payment would have a higher proportion of interest than the first payment. d. The proportion of interest versus principal repayment would be the same for each of the 5 payments. e. The proportion of each payment that represents interest as opposed to repayment of principal would be higher if the interest rate were higher. Time value concepts Answer: e Diff: M xiii . Which of the following is most correct? a. The present value of a 5-year annuity due will exceed the present value of a 5-year ordinary annuity. (Assume that both annuities pay $100 per period and there is no chance of default.) b. If a loan has a nominal rate of 10 percent, then the effective rate can never be less than 10 percent. c. If there is annual compounding, then the effective, periodic, and nominal rates of interest are all the same. d. Answers a and c are correct. e. All of the answers above are correct. Time value concepts Answer: c Diff: M xiv . Which of the following statements is most correct? a. An investment which compounds interest semiannually, and has a nominal rate of 10 percent, will have an effective rate less than 10 percent. b. The present value of a three-year $100 annuity due is less than the present value of a three-year $100 ordinary annuity. c. The proportion of the payment of a fully amortized loan which goes toward interest declines over time. d. Statements a and c are correct. e. None of the answers above is correct.Tough: Time value concepts Answer: d Diff: T xv . Which of the following statements is most correct? a. The first payment under a 3-year, annual payment, amortized loan for $1,000 will include a smaller percentage (or fraction) of interest if the interest rate is 5 percent than if it is 10 percent. b. If you are lending money, then, based on effective interest rates, you should prefer to lend at a 10 percent nominal, or quoted, rate but with semiannual payments, rather than at a 10.1 percent nominal rate with annual payments. However, as a borrower you should prefer the annual payment loan. c. The value of a perpetuity (say for $100 per year) will approach infinity as the interest rate used to evaluate the perpetuity approaches zero. d. Statements a, b, and c are all true. e. Statements b and c are true. Multiple Choice: Problems Easy: Solving for N for an annuity Answer: b Diff: E xvi . You are currently investing your money in a bank account which has a nominal annual rate of 9 percent, compounded monthly. If you invest $900 at the end of each month, how many months will it take for your account to grow to $301,066.27 (rounded to the nearest month)? a. 40 months b. 168 months c. 175 months d. 221 months e. 335 months Nominal and effective rates Answer: b Diff: E xvii . An investment pays you 9 percent interest compounded semiannually. A second investment of equal risk, pays interest compounded quarterly. What nominal rate of interest would you have to receive on the second investment in order to make you indifferent between the two investments? a. 8.71% b. 8.90% c. 9.00% d. 9.20% e. 9.31% Effective annual rate Answer: c Diff: E xviii . You want to borrow $1,000 from a friend for one year, and you propose to pay her $1,120 at the end of the year. She agrees to lend you the $1,000, but she wants you to pay her $10 of interest at the end of each of the first 11 months plus $1,010 at the end of the 12th month. How much higher is the effective annual rate under your friend's proposal than under your proposal? a. 0.00% b. 0.45% c. 0.68% d. 0.89% e. 1.00%Time for a sum to double Answer: d Diff: E xix . You are currently investing your money in a bank account which has a nominal annual rate of 7 percent, compounded monthly. How many years will it take for you to double your money? a. 8.67 years b. 9.15 years c. 9.50 years d. 9.93 years e. 10.25 years Monthly payments on loan Answer: c Diff: E xx . You are considering buying a new car. The sticker price is $15,000 and you have $2,000 to put toward a down payment. If you can negotiate a nominal annual interest rate of 10 percent and you wish to pay for the car over a 5-year period, what are your monthly car payments? a. $216.67 b. $252.34 c. $276.21 d. $285.78 e. $318.71 Interest rate of an annuity Answer: b Diff: E xxi . South Penn Trucking is financing a new truck with a loan of $10,000 to be repaid in 5 annual end-of-year installments of $2,504.56. What annual interest rate is the company paying? a. 7% b. 8% c. 9% d. 10% e. 11% Medium: Effective annual rate Answer: b Diff: M xxii . If it were evaluated with an interest rate of 0 percent, a 10-year regular annuity would have a present value of $3,755.50. If the future (compounded) value of this annuity, evaluated at Year 10, is $5,440.22, what effective annual interest rate must the analyst be using to find the future value? a. 7% b. 8% c. 9% d. 10% e. 11%FV of a sum Answer: d Diff: M xxiii . Suppose you put $100 into a savings account today, the account pays a nominal annual interest rate of 6 percent, but compounded semiannually, and you withdraw $100 after 6 months. What would your ending balance be 20 years after the initial $100 deposit was made? a. $226.20 b. $115.35 c. $ 62.91 d. $ 9.50 e. $ 3.00 FV of annuity due Answer: d Diff: M xxiv . You are contributing money to an investment account so that you can purchase a house in five years. You plan to contribute six payments of $3,000 a year--the first payment will be made today (t = 0), and the final payment will be made five years from now (t = 5). If you earn 11 percent in your investment account, how much money will you have in the account five years from now (at t = 5)? a. $19,412 b. $20,856 c. $21,683 d. $23,739 e. $26,350Effective annual rate Answer: a Diff: M xxv . You have just borrowed $20,000 to buy a new car. The loan agreement calls for 60 monthly payments of $444.89 each to begin one month from today. If the interest is compounded monthly, then what is the effective annual rate on this loan? a. 12.68% b. 14.12% c. 12.00% d. 13.25% e. 15.08% Effective annual rate Answer: e Diff: M xxvi . You have just taken out a 10-year, $12,000 loan to purchase a new car. This loan is to be repaid in 120 equal end-of-month installments. If each of the monthly installments is $150, what is the effective annual interest rate on this car loan? a. 6.5431% b. 7.8942% c. 8.6892% d. 8.8869% e. 9.0438% NPV and non-annual discounting Answer: b Diff: M xxvii . Your lease calls for payments of $500 at the end of each month for the next 12 months. Now your landlord offers you a new 1-year lease which calls for zero rent for 3 months, then rental payments of $700 at the end of each month for the next 9 months. You keep your money in a bank time deposit that pays a nominal annual rate of 5 percent. By what amount would your net worth change if you accept the new lease? (Hint: Your return per month is 5%/12 = 0.4166667%.) a. -$509.81 b. -$253.62 c. +$125.30 d. +$253.62 e. +$509.81FV under monthly compounding Answer: d Diff: M xxviii . Steven just deposited $10,000 in a bank account which has a 12 percent nominal interest rate, and the interest is compounded monthly. Steven also plans to contribute another $10,000 to the account one year (12 months) from now and another $20,000 to the account two years from now. How much will be in the account three years (36 months) from now? a. $57,231 b. $48,993 c. $50,971 d. $49,542 e. $49,130 FV under daily compounding Answer: a Diff: M xxix . You have $2,000 invested in a bank account that pays a 4 percent nominal annual interest with daily compounding. How much money will you have in the account at the end of July (i.e., in 132 days)? (Assume there are 365 days in each year.) a. $2,029.14 b. $2,028.93 c. $2,040.00 d. $2,023.44 e. $2,023.99 PV under monthly compounding Answer: b Diff: M xxx . You have just bought a security which pays $500 every six months. The security lasts for ten years. Another security of equal risk also has a maturity of ten years, and pays 10 percent compounded monthly (that is, the nominal rate is 10 percent). What should be the price of the security that you just purchased? a. $6,108.46 b. $6,175.82 c. $6,231.11 d. $6,566.21 e. $7,314.86 PV under non-annual compounding Answer: c Diff: M xxxi . You have been offered an investment that pays $500 at the end of every 6 months for the next 3 years. The nominal interest rate is 12 percent; however, interest is compounded quarterly. What is the present value of the investment? a. $2,458.66 b. $2,444.67 c. $2,451.73 d. $2,463.33 e. $2,437.56 Value of missing payments Answer: d Diff: M xxxii . You recently purchased a 20-year investment which pays you $100 at t = 1, $500 at t = 2, $750 at t = 3, and some fixed cash flow, X, at the end of each of the remaining 17 years. The investment cost you $5,544.87. Alternative investments of equal risk have a required return of 9 percent. What is the annual cash flow received at the end of each of the final 17 years, that is, what is X? a. $600 b. $625 c. $650 d. $675 e. $700Value of missing payments Answer: c Diff: M xxxiii . A ten-year security generates cash flows of $2,000 a year at the end of each of the next three years (t = 1, 2, 3). After three years, the security pays some constant cash flow at the end of each of the next six years. (t = 4, 5, 6, 7, 8, 9). Ten years from now (t = 10) the security will mature and pay $10,000. The security sells for $24,307.85, and has a yield to maturity of 7.3 percent. What annual cash flow does the security pay for years 4 through 9? a. $2,995 b. $3,568 c. $3,700 d. $3,970 e. $4,296 Value of missing payments Answer: d Diff: M xxxiv . An investment costs $3,000 today and provides cash flows at the end of each year for 20 years. The investment’s expected return is 10 percent. The projected cash flows for years 1, 2, and 3 are $100, $200, and $300 respectively. What is the annual cash flow received for each of the years 4 through 20 (17 years)? (Assume the same payment for each of these years.) a. $285.41 b. $313.96 c. $379.89 d. $417.87 e. $459.66 Amortization Answer: d Diff: M xxxv . You have just bought a house and have a $125,000, 25-year mortgage with a fixed interest rate of 8.5 percent with monthly payments. Over the next five years, what percentage of your mortgage payments will go toward the repayment of principal? a. 8.50% b. 10.67% c. 12.88% d. 14.93% e. 17.55% Amortization Answer: a Diff: M xxxvi . You have just taken out an installment loan for $100,000. Assume that the loan will be repaid in 12 equal monthly installments of $9,456 and that the first payment will be due one month from today. How much of your third monthly payment will go toward the repayment of principal? a. $7,757.16 b. $6,359.12 c. $7,212.50 d. $7,925.88 e. $8,333.33 Amortization Answer: c Diff: Mxxxvii . A homeowner just obtained a $90,000 mortgage. The mortgage is for 30 years (360 months) and has a fixed nominal annual rate of 9 percent, with monthly payments. What percentage of the total payments made the first two years will go toward repayment of interest? a. 89.30% b. 91.70% c. 92.59% d. 93.65% e. 94.76% Remaining balance on mortgage Answer: d Diff: M xxxviii . Your family purchased a house three years ago. When you bought the house you financed it with a $160,000 mortgage with an 8.5 percent nominal interest rate (compounded monthly). The mortgage was for 15 years (180 months). What is the remaining balance on your mortgage today? a. $ 95,649 b. $103,300 c. $125,745 d. $141,937 e. $159,998 Tough: Required annuity payments Answer: d Diff: T xxxix . Your father, who is 60, plans to retire in 2 years, and he expects to live independently for 3 years. Suppose your father wants to have a real income of $40,000 in today's dollars in each year after he retires. His retirement income will start the day he retires, 2 years from today, and he will receive a total of 3 retirement payments. Inflation is expected to be constant at 5 percent. Your father has $100,000 in savings now, and he can earn 8 percent on savings now and in the future. How much must he save each year, starting today, to meet his retirement goals? a. $1,863 b. $2,034 c. $2,716 d. $5,350 e. $6,102 Required annuity payments Answer: a Diff: T xl . Your client just turned 75 years old and plans on retiring in 10 years on her 85th birthday. She is saving money today for her retirement and is establishing a retirement account with your office. She would like to withdraw money from her retirement account on her birthday each year until she dies. She would ideally like to withdraw $50,000 on her 85th birthday, and increase her withdrawals 10 percent a year through her 89th birthday (i.e., she would like to withdraw $73,205 on her 89th birthday). She plans to die on her 90th birthday, at which time she would like to leave $200,000 to her descendants. Your client currently has $100,000. You estimate that the money in the retirement account will earn 8 percent a year over the next 15 years. Your client plans to contribute an equal amount of money each year until her retirement. Her first contribution will come in 1 year; her 10th and final contribution will come in 10 years (on her 85th birthday). How much should she contribute each year to meet her objectives? a. $12,401.59 b. $12,998.63 c. $13,243.18 d. $13,759.44e. $14,021.53Required annuity payments Answer: c Diff: T xli . You are considering an investment in a 40-year security. The security will pay $25 a year at the end of each of the first three years. The security will then pay $30 a year at the end of each of the next 20 years. The nominal interest rate is assumed to be 8 percent, and the current price (present value) of the security is $360.39. Given this information, what is the equal annual payment to be received from Year 24 through Year 40 (i.e., for 17 years)? a. $35 b. $38 c. $40 d. $45 e. $50 Required annuity payments Answer: a Diff: T xlii . Joe and Jane are interested in saving money to put their two children, John and Susy through college. John is currently 12 years old and will enter college in six years. Susy is 10 years old and will enter college in 8 years. Both children plan to finish college in four years. College costs are currently $15,000 a year (per child), and are expected to increase at 5 percent a year for the foreseeable future. All college costs are paid at the beginning of the school year. Up until now, Joe and Jane have saved nothing but they expect to receive $25,000 from a favorite uncle in three years. To provide for the additional funds that are needed, they expect to make 12 equal payments at the beginning of each of the next twelve years--the first payment will be made today and the final payment will be made on Susy’s 21st birthday (which is also the day that the last payment must be made to the college). If all funds are invested in a stock fund which is expected to earn 12 percent, how large should each of the annual contributions be? a. $ 7,475.60 b. $ 7,798.76 c. $ 8,372.67 d. $ 9,675.98 e. $14,731.90Required annuity payments Answer: b Diff: T xliii . Jim and Nancy are interested in saving money for their son's education. Today is their son's 8th birthday. Their son will enter college ten years from now on his 18th birthday, and will attend for four years. All college costs are due at the beginning of the year, so Jim and Nancy will have to make payments on their son's 18th, 19th, 20th and 21st birthdays (t = 10, 11, 12, 13). They estimate that the college their son wants to attend will cost $35,000 the first year (t = 10) and that the costs will increase 7 percent each year (the final college payment will be made 13 years from now). Currently, Jim and Nancy have $20,000 in an investment account. They also plan to contribute a fixed amount at the end of each of the next ten years (t = 1, 2, 3, ... 10). Their invested money will be in an account which pays 9 percent interest compounded annually. How much money do Jim and Nancy need to contribute to the account in each of the next ten years? a. $5,638 b. $5,848 c. $6,052 d. $6,854 e. $7,285 FV of annuity due Answer: a Diff: T xliv . To save money for a new house, you want to begin contributing money to a brokerage account. Your plan is to make ten contributions to the brokerage account. Each contribution will be for $1,500. The contributions will come at the beginning of each of the next 10 years, i.e., the first contribution will be made at t = 0 and the final contribution will be made at t = 9. Assume that the brokerage account pays a 9 percent return with quarterly compounding. How much money do you expect to have in the brokerage account nine years from now (t = 9)? a. $23,127.49 b. $25,140.65 c. $25,280.27 d. $21,627.49 e. $19,785.76 FV of investment account Answer: b Diff: T xlv . Kelly and Brian Johnson are a recently married couple whose parents have counseled them to start saving immediately in order to have enough money down the road to pay for their retirement and their children’s college expenses. Today (t = 0) is their 25th birthday (the couple shares the same birthday). The couple plans to have two children (Dick and Jane). Dick is expected to enter college 20 years from now (t = 20); Jane is expected to enter college 22 years from now (t = 22). So in years t = 22 and t = 23 there will be two children in college. Each child will take 4 years to complete college, and college costs are paid at the beginning of each year of college. College costs per child will be as follows: Year Cost per child Children in college 20 $ 58,045 Dick 21 $ 62,108 Dick 22 $ 66,456 Dick and Jane 23 $ 71,108 Dick and Jane 24 $ 76,086 Jane 25 $ 81,411 JaneKelly and Brian plan to retire forty years from now at age 65 (at t = 40). They plan to contribute $12,000 per year at the end of each year for the next 40 years into an investment account that earns 10 percent per year. This account will be used to pay for the college costs, and also to provide a nest egg for Kelly and Brian’s retirement at age 65. How big will Kelly and Brian’s nest egg (the balance of the investment account) be when they retire at age 65 (t = 40)? a. $1,854,642 b. $2,393,273 c. $2,658,531 d. $3,564,751 e. $4,758,333 Effective annual rate Answer: c Diff: T xlvi . You have some money on deposit in a bank account which pays a nominal (or quoted) rate of 8.0944 percent, but with interest compounded daily (using a 365-day year). Your friend owns a security which calls for the payment of $10,000 after 27 months. The security is just as safe as your bank deposit, and your friend offers to sell it to you for $8,000. If you buy the security, by how much will the effective annual rate of return on your investment change? a. 1.87% b. 1.53% c. 2.00% d. 0.96% e. 0.44% Non-annual compounding Answer: a Diff: T xlvii . A financial planner has offered you three possible options for receiving cash flows. You must choose the option that has the highest present value. (1) $1,000 now and another $1,000 at the beginning of each of the 11 subsequent months during the remainder of the year, to be deposited in an account paying a 12 percent nominal annual rate, but compounded monthly (to be left on deposit for the year). (2) $12,750 at the end of the year (assume a 12 percent nominal interest rate with semiannual compounding). (3) A payment scheme of 8 quarterly payments made over the next two years. The first payment of $800 is to be made at the end of the current quarter. Payments will increase by 20 percent each quarter. The money is to be deposited in an account paying a 12 percent nominal annual rate, but compounded quarterly (to be left on deposit for the entire 2-year period). Which one would you choose? a. Choice 1. b. Choice 2. c. Choice 3. d. Any one, since they all have the same present value. e. Choice 1, if the payments were made at the end of each month. PMT and quarterly compounding Answer: b Diff: T xlviii . Your employer has agreed to make 80 quarterly payments of $400 each into a trust account to fund your early retirement. The first payment will be made 3 months from now. At the end of 20 years (80 payments), you will be paid 10 equal annual payments, with the first payment to be made at the beginning of Year 21 (or the end of Year 20). The funds will be invested at a nominal rate of 8 percent, quarterly compounding, during both the accumulation and the distribution periods. How large will each of your 10 receipts be? (Hint: You must find the EAR and use it in one of your calculations.) a. $ 7,561 b. $10,789 c. $11,678d. $12,342 e. $13,119 PV of an uneven CF stream Answer: d Diff: T xlix . Hillary is trying to determine the cost of health care to college students, and parents' ability to cover those costs. She assumes that the cost of one year of health care for a college student is $1,000 today, that the average student is 18 when he or she enters college, that inflation in health care cost is rising at the rate of 10 percent per year, and that parents can save $100 per year to help cover their children's costs. All payments occur at the end of the relevant period, and the $100/year savings will stop the day the child enters college (hence 18 payments will be made). Savings can be invested at a nominal rate of 6 percent, annual compounding. Hillary wants a health care plan which covers the fully inflated cost of health care for a student for 4 years, during Years 19 through 22 (with payments made at the end of years 19 through 22). How much would the government have to set aside now (when a child is born), to supplement the average parent's share of a child's college health care cost? The lump sum the government sets aside will also be invested at 6 percent, annual compounding. a. $1,082.76 b. $3,997.81 c. $5,674.23 d. $7,472.08 e. $8,554.84CHAPTER 2 ANSWERS AND SOLUTIONSi. PV and discount rate Answer: a Diff: E ii. PV versus FV Answer: e Diff: E iii. Time value concepts Answer: e Diff: E iv. Time value concepts Answer: d Diff: E Statements b and c are correct; therefore, statement d is the correct choice. The present value is smaller if interest is compounded monthly rather than semiannually. v. Time value concepts Answer: d Diff: E Statements a and b are correct; therefore, statement d is the correct choice. The nominal interest rate will be less than the effective rate when the number of periods per year is greater than one. vi . Effective annual rate Answer: d Diff: E Statement d is correct. The equation for EAR is as follows: EAR = 1 m r 1 m Nom           If annual compounding is used, m = 1 and the equation above reduces to EAR = rNom. The equation for the periodic rate is: m r r Nom PER = . If annual compounding is used then m = 1 and rPER = rNom, and since EAR = rNom then rPER = EAR. vii. Effective annual rate Answer: b Diff: E The bank account which pays the highest nominal rate with the most frequent rate of compounding will have the highest EAR. Consequently, statement b is the correct choice. viii. Effective annual rate Answer: d Diff: E Statement d is correct; the other statements are incorrect. Looking at responses a through d, you should realize the choice with the greatest frequency of compounding will give you the highest EAR. This is statement d. Now, compare choices d and e. We know EARd > 7.8%; therefore, statement d is the correct choice. The EAR of each of the statements is shown below. EARa = 8.30%; EARb = 8%; EARc = 8.24%; EARd = 8.328%; EARe = 7.8%. ix. Amortization Answer: b Diff: E Statement b is true; the others are false. The remaining balance after three years will be $100,000 less the total amount of repaid principal during the first 36 months. On a fixed-rate mortgage the monthly payment remains the same. x. Amortization Answer: e Diff: E Statements b and c are correct; therefore, statement e is the correct choice. Monthly payments will remain the same over the life of the loan.xi. Annuities Answer: c Diff: M By definition, an annuity due is received at the beginning of the year while an ordinary annuity is received at the end of the year. Because the payments are received earlier, both the present and future values of the annuity due are greater than those of the ordinary annuity. xii. Time value concepts Answer: e Diff: M If the interest rate were higher, the payments would all be higher, and all of the increase would be attributable to interest. So, the proportion of each payment that represents interest would be higher. Note that statement b is false because interest during Year 1 would be the interest rate times the beginning balance, which is $10,000. With the same interest rate and the same beginning balance, the Year 1 interest charge will be the same, regardless of whether the loan is amortized over 5 or 10 years. xiii. Time value concepts Answer: e Diff: M xiv. Time value concepts Answer: c Diff: M Statement c is correct; the other statements are false. The effective rate of the investment in statement a is 10.25%. The present value of the annuity due is greater than the present value of the ordinary annuity. xv . Time value concepts Answer: d Diff: T xvi. Solving for N for a single payment Answer: b Diff: E Financial calculator solution: PV = 0 FV = 301,066.27 PMT = -900 I = 9/12 = 0.75 N = ? = 168 months. xvii . Nominal and effective rates Answer: b Diff: E 1st investment Enter the following: NOM% = 9 P/YR = 2 Solve for EFF% = 9.2025%. 2nd investment Enter the following: EFF% = 9.2025 P/YR = 4 Solve for NOM% = 8.90%. xviii . Effective annual rate Answer: c Diff: E Your proposal: EAR1 = $120/$1,000 EAR1 = 12%.Your friend's proposal: Interest is being paid each month ($10/$1,000 = 1% per month), so it compounds, and the EAR is higher than rNom = 12%: EAR2 =     12 0.12 1 + 12 - 1 = 12.68%. Difference = 12.68% - 12.00% = 0.68%. You could also visualize your friend's proposal in a time line format: 0 i=? 1 2 11 12 ┼_____________┼____________┼____ . . . ___┼____________┼ 1,000 -10 -10 -10 -1,010 Insert those cash flows in the cash flow register of a calculator and solve for IRR. The answer is 1%, but this is a monthly rate. The nominal rate is 12(1%) = 12%, which converts to an EAR of 12.68% as follows: Input into a financial calculator the following: P/YR = 12, NOM% = 12, and solve for EFF% = 12.68%. xix. Time for a sum to double Answer: d Diff: E PV = -1 FV = 2 PMT = 0 I = 7/12 N = ? = 119.17 months = 9.93 years. xx . Monthly payments on loan Answer: c Diff: E First, find the monthly interest rate = 0.10/12 = 0.8333%/month. Now, enter in your calculator N = 60, I/YR = 0.8333, PV = -13,000, FV = 0, and solve for PMT = $276.21. xxi . Interest rate of an annuity Answer: b Diff: E Time Line: 0 i = ? 1 2 3 4 5 Years ┼___________┼____________┼____________┼____________┼____________┼ 10,000 -2,504.56 -2,504.56 -2,504.56 -2,504.56 -2,504.56 Tabular solution: $10,000 = $2,504.56(PVIFAi,5) PVIFAi,5 = $10,000/$2,504.56 = 3.9927 i= 8%. Financial calculator solution: Inputs: N = 5; PV = 10,000; PMT = -2,504.56; FV = 0. Output: I = 8%. xxii . Effective annual rate Answer: b Diff: M Time Line: i B = ? 0 i A = 0% 1 2 3 4 10 Years | | | | | . . . | PV = 3,755.50 PMT PMT PMT PMT PMT PMTB = PMTA = 375.55 FV = 5,440.22 Financial calculator solution: Calculate the PMT of the annuity Inputs: N = 10; I = 0; PV = -3,755.50; FV = 0. Output: PMT = $375.55. Calculate the effective annual interest rateInputs: N = 10; PV = 0; PMT = -375.55; FV = 5,440.22. Output: I = 7.999  8.0%. xxiii . FV of a sum Answer: d Diff: M Time Line: 0 3% 1 2 3 4 40 6-months | | | | | ... | Periods 100 -100 FV = ? Tabular/Numerical solution: Solve for amount on deposit at the end of 6 months. Step 1 FV = $100(FVIF3%,1) - $100 = $3.00. FV = $100(1 + 0.06/2) - $100 = $3.00. Step 2 Compound the $3.00 for 39 periods at 3% FV = $3.00(FVIF3%,39) = $9.50. Since table does not show 39 periods, use numerical/calculator exponent method. FV = $3.00(1.03)39 = $9.50. Financial calculator solution: (Step 2 only) Inputs: N = 39; I = 3; PV = -3.00; PMT = 0. Output: FV = $9.50. xxiv. FV of annuity due Answer: d Diff: M There are a few ways to do this. One way is shown below. To get the value at t = 5 of the first 5 payments: BEGIN mode N = 5 I = 11 PV = 0 PMT = -3,000 FV = $20,738.58 Now add on to this the last payment that occurs at t = 5. $20,738.58 + $3,000 = $23,738.58  $23,739. xxv . Effective annual rate Answer: a Diff: M Time Line: EAR = ? 0 i = ? 1 2 60 Months | | | ... | PV = -20,000 444.89 444.89 444.89 Tabular solution: $20,000 = $444.89(PVIFAi,60)PVIFAi,60 = 44.9549 i = 1%. EAR = (1.01)12 - 1.0 = 1.12681 - 1.0 = 0.1268 = 12.68%. Financial calculator solution: Calculate periodic rate and nominal rate Inputs: N = 60; PV = -20,000; PMT = 444.89; FV = 0. Output: I = 1.0. NOM% = 1.0%  12 = 12.00%. Use interest rate conversion feature Inputs: P/YR = 12; NOM% = 12.0. Output: EFF% = EAR = 12.68%. xxvi. Effective annual rate Answer: e Diff: M Given: Loan Value = $12,000; Loan Term = 10 years (120 months); Monthly Payment = $150. N = 120 PV = -12,000 PMT = 150 FV = 0 Solve for I/YR = 0.7241  12 = 8.6892%. However, this is a nominal rate. To find the effective rate, enter the following: NOM% = 8.6892 P/YR = 12 Solve for EFF% = 9.0438%. xxvii . NPV and non-annual discounting Answer: b Diff: M Current 0 5%/12 = 0.4167% 1 2 3 12 lease | | | | . . . | 0 -500 -500 -500 -500 5/12 = 12 0.4167 500 0 -5,840.61 N I PV PMT FV New 05%/12 = 0.4167% 1 2 3 4 12 lease | | | | |    | 0 0 0 0 -700 -700 CF0 = 0 CF1-3 = 0 CF4-12 = -700 I = 0.4167 Solve for NPV = -$6,094.23. Therefore, the PV of payments under the proposed lease would be greater than the PV of payments under the old lease by $6,094.23 - $5,840.61 = $253.62. Thus, your net worth would decrease by $253.62. xxviii. FV under monthly compounding Answer: d Diff: M Step 1 Calculate the FV at t = 3 of the first deposit. Enter N = 36, I/YR = 12/12 = 1, PV = -10000, and PMT = 0. Solve for FV = $14,308. Step 2 Calculate the FV at t = 3 of the second deposit.Enter N = 24, I/YR = 12/12 = 1, PV = -10000, and PMT = 0. Solve for FV = $12,697. Step 3 Calculate the FV at t = 3 of the third deposit. Enter N = 12, I/YR = 12/12 = 1, PV = -20000, and PMT = 0. Solve for FV = $22,537. Step 4 The sum of the future values gives you the answer, $49,542. xxix . FV under daily compounding Answer: a Diff: M The answer is a. Solve for FV as N = 132, I = 4/365 = 0.0110, PV = -2,000, PMT = 0, and solve for FV = ? = $2,029.14. xxx. PV under monthly compounding Answer: b Diff: M Start by calculating the effective rate on the second security: P/YR = 12 NOM% = 10 Solve for EFF% = 10.4713%. Then, convert this effective rate to a semiannual rate: EFF% = 10.4713 P/YR = 2 NOM% = 10.2107%. Now, calculate the value of the first security as follows: N = 10  2 = 20, I = 10.2107/2 = 5.1054, PMT = 500, FV = 0, thus, PV = - $6,175.82. xxxi . PV under non-annual compounding Answer: c Diff: M First, find the effective annual rate for a nominal rate of 12% with quarterly compounding: P/YR = 4, NOM% = 12, and EFF% = ? = 12.55%. In order to discount the cash flows properly, it is necessary to find the nominal rate with semiannual compounding that corresponds to the effective rate calculated above. Convert the effective rate to a semiannual nominal rate as P/YR = 2, EFF% = 12.55, and NOM% = ? = 12.18%. Finally, find the PV as N = 2  3 = 6, I = 12.18/2 = 6.09, PMT = 500, FV = 0, and PV = ? = -$2,451.73. xxxii . Value of missing payments Answer: d Diff: M Find the FV of the price and the first three cash flows at t = 3. To do this first find the present value of them. CF0 = -5,544.87 CF1 = 100 CF2 = 500 CF3 = 750 I = 9; solve for NPV = -$4,453.15. N = 3 I = 9PV = -4,453.15 PMT = 0 FV = $5,766.96. Now solve for X. N = 17 I = 9 PV = -5,766.96 FV = 0 Solve for PMT = $675. xxxiii. Value of missing payments Answer: c Diff: M There are several different ways of doing this. One way is: Find the future value of the first three years of the investment at Year 3. N = 3 I = 7.3 PV = -24,307.85 PMT = 2,000 FV = $23,580.68. Find the value of the final $10,000 at Year 3. N = 7 I = 7.3 PMT = 0 FV = 10,000 PV = -$6,106.63. Add the two Year 3 values (remember to keep the signs right). $23,580.68 + -$6,106.63 = $17,474.05. Now solve for the PMTs over years 4 through 9 (6 years) that have a PV of $17,474.05. N = 6 I = 7.3 PV = -17,474.05 FV = 0 PMT = $3,700.00. xxxiv . Value of missing payments Answer: d Diff: M The project’s cost should be the PV of the future cash flows. Use the cash flow key to find the PV of the first 3 years of cash flows. CF0 = 0, CF1 = 100, CF2 = 200, CF3 = 300, I/YR = 10, NPV = $481.59. The PV of the cash flows for Years 4 - 20 must be: $3,000 - $481.59 = $2,518.41. Take this amount forward in time 3 years: N = 3, I/YR = 10, PV = -2,518.41, PMT = 0, solve for FV = $3,352.00. This amount is also the present value of the 17-year annuity. N = 17, I/YR = 10, PV = -3,352, FV = 0, solve for PMT = $417.87. xxxv . Amortization Answer: d Diff: M N = 25  12 I = 8.5/12 PV = -125,000 FV = 0PMT = $1,006.53 Do amortization: Enter: 1 INPUT 60 AMORT Interest = $51,375.85 Principal = $9,015.95 Balance = $115,984.05 Total Payments = 5  12  $1,006.53 = $60,391.80. of principal % Repayment = $60,391.80 $9,015.95 = 0.1493 = 14.93%. xxxvi . Amortization Answer: a Diff: M Given: Loan Value = $100,000; Repayment Period = 12 months; Monthly Payment = $9,456. N = 12 PV = -100,000 PMT = 9,456 FV = 0 Solve for I/YR = 2.00%  12 = 24.00%. To find the amount of principal paid in the third month (or period), use the calculator’s amortization feature. Enter: 3 INPUT 3 AMORT (to activate the calculator's amortization feature). Interest = $1,698.84 Principal = $7,757.16 Balance = $77,181.86 xxxvii. Amortization Answer: c Diff: M We will use the amortization feature of the HP-10B. Enter the loan details: N = 30  12 = 360 I = 9/12 = 0.75 PV = -90,000 FV = 0 PMT = $724.16. Total payments in the first 2 years are $724.16  24 = $17,379.85. Now get the interest: 1 INPUT 24 AMORT Interest = $16,092.44 Percentage of first two years that is interest is: $16,092.44/$17,379.85 = 0.9259 = 92.59%. xxxviii . Remaining balance on mortgage Answer: d Diff: M Solve for the monthly payment as follows: N = 12  15 = 180 I = 8.5/12 = 0.7083 PV = -160,000FV = 0 PMT = $1,575.58. Use the calculator’s amortization feature to find the remaining principal balance: 1 INPUT 36 AMORT Interest = $ 38,658.34 Principal = $ 18,062.54 Balance = $141,937.46 xxxix . Required annuity payments Answer: d Diff: T Goes on Infl. = 5% Retires Welfare 0 i = 8% 1 2 3 4 5 ┼__________________┼_______________┼_________________┼________________┼_______________┼ 40,000 44,100 46,305 48,620 │_________________________________│ 128,659 ◄___________ │ 100,000 ____________________► (116,640) PMT PMT 12,019 Step 1 The retirement payments, which begin at t = 2, must be: t = 2: $40,000(1.05)2 = $44,100. t = 3: $44,100(1.05) = $46,305. t = 4: $46,305(1.05) = $48,620. Step 2 Now we need enough at t = 2 to make the 3 retirement payments as calculated in Step 1. We cannot use the annuity method, but we can enter, in the cash flow register, the following: CF0 = 44,100. CF1 = 46,305. CF2 = 48,620. Then enter I = 8, and press NPV to find NPV = PV = $128,659. Step 3 The $100,000 now on hand will compound at 8% for 2 years: $100,000(1.08)2 = $116,640. Step 4 The net funds needed is: Need at t = 2 $ 128,659 Will have ( 116,640) Net needed $ 12,019 Step 5 Find the payments needed to accumulate $12,019. Set the calculator to "Begin" and then enter: N = 2; I = 8; PV = 0; FV = 12,019. Solve for PMT = $5,350. xl. Required annuity payments Answer: a Diff: T 75 i=8% 76 84 85 86 87 88 89 90 ┼ ┼__ . . . __┼_________┼__________┼__________┼___________┼__________┼__________┼ +100,000 __________________► +215,892.50 PMT PMT PMT (50,000) (55,000) (60,500) (66,550) (73,205) (200,000) │_____________________________________________________│ (395,548.96) ◄______________ ┼ (179,656.46) Amount needed Value of cash outflows: Age 85 CF0 = ($ 50,000) CF1 = ( 55,000) = (-50,000)1.1 CF2 = ( 60,500) = (-50,000)(1.1)2 CF3 = ( 66,550) = (-50,000)(1.1)3 CF4 = ( 73,205) = (-50,000)(1.1)4 CF5 = ( 200,000) Solve for NPV at 8% = ($395,548.96). Value of $100,000 at age 85: $100,000(1.08)10 = $215,892.50. Shortfall at age 85 = $215,892.50 - $395,548.96 = ($179,656.46). Calculate annual payments to equal this shortfall: N = 10; I/YR = 8; PV = 0; FV = 179,656.46. Solve for PMT = $12,401.59. xli. Required annuity payments Answer: c Diff: T 0 i = 8% 1 2 3 4 23 24 40 | | | | | .. . . | | . . . | (360.39) 25 25 25 30 30 PMT PMT | | 298.25 | 62.14 364.85 Calculate the NPV of payments in Years 1-23: CF0 = 0 CF1-3 = 25 CF4-23 = 30 I = 8 Solve for NPV = $298.25. Difference between the security's price and PV of payments: $360.39 - $298.25 = $62.14. Calculate the FV of the difference between the purchase price and PV of payments, Years 1-23: N = 23 I = 8PV = -62.14 PMT = 0 Solve for FV = $364.85. Calculate the value of the annuity payments in Years 24-40: N = 17 I = 8 PV = -364.85 FV = 0 Solve for PMT = $40. xlii. Required annuity payments Answer: a Diff: T Step 1 Calculate the cost of tuition in each year: College Cost Today = $15,000, Inflation = 5%. $15,000(1.05)6 = $20,101.43(1) = $20,101.43. $15,000(1.05)7 = $21,106.51(1) = $21,106.51. $15,000(1.05)8 = $22,161.83(2) = $44,323.66. $15,000(1.05)9 = $23,269.92(2) = $46,539.85. $15,000(1.05)10 = $24,433.42(1) = $24,433.42. $15,000(1.05)11 = $25,655.09(1) = $25,655.09. Step 2 Find the present value of college costs at t = 0: CF0 = 0 CF1-5 = 0 CF6 = 20,101.43 CF7 = 21,106.51 CF8 = 44,323.66 CF9 = 46,539.85 CF10 = 24,433.42 CF11 = 25,655.09 I = 12; solve for NPV = $69,657.98. Step 3 Find the PV of the $25,000 gift received in Year 3: N = 3 I = 12 PMT = 0 FV = 25,000 Solve for PV = -$17,794.51. Step 4 Calculate the PV of the net amount needed to fund college costs: $69,657.98 - $17,794.51 = $51,863.47. Step 5 Calculate the annual contributions: BEGIN Mode N = 12 I = 12 PV = -51,863.47 FV = 0 Solve for PMT = $7,475.60. xliii . Required annuity payments Answer: b Diff: T Find the present value of the cost of college at t = 10. Use the cash flow register and remember that college costs increase each year by the rate of inflation. t = 10: CF0 = $35,000. t = 11: CF1 = $35,000  1.07 = $37,450.00. t = 12: CF2 = $35,000  (1.07)2 = $40,071.50. t = 13: CF3 = $35,000  (1.07)3 = $42,876.51. I = 9; solve for NPV = $136,193.71. Now figure out the amount of payments they should make: N = 10 I = 9 PV = 20,000 FV = -136,193.71 PMT = $5,847.88  $5,848.xliv. FV of annuity due Answer: a Diff: T First, convert the 9 percent return with quarterly compounding to an effective rate of 9.308332%. With a financial calculator, NOM% = 9, P/YR = 4, EFF% = 9.308332%. (Don’t forget to change P/YR = 4 back to P/YR = 1.) Then calculate the FV of all but the final payment. BEGIN MODE (1 P/YR) N = 9, I/YR = 9.308332, PV = 0, PMT = 1500, and solve for FV = $21,627.49. You must then add the $1,500 at t = 9 to find the answer, $23,127.49. xlv. FV of investment account Answer: b Diff: T We need to figure out how much money we would have saved if we didn’t pay for the college costs. N = 40 I = 10 PV = 0 PMT = -12,000 Solve for FV = $5,311,110.67. Now figure out how much we would use for college costs. First get the college costs at one point in time, t = 20 using the cash flow register. CF0 = 58,045 CF1 = 62,108 CF2 = 66,456  2 = 132,912 (two kids in school) CF3 = 71,108  2 = 142,216 CF4 = 76,086 CF5 = 81,411 I = 10; NPV = $433,718.02. This is the value of the college costs at year t = 20. What we want is to know how much this is at t = 40 N = 20 I = 10 PV = -433,718.02 PMT = 0 Solve for FV = $2,917,837.96. The amount in the nest egg at t = 40 is the amount saved less the amount spent on college; $5,311,110.67 - $2,917,837.96 = $2,393,272.71  $2,393,273. xlvi. Effective annual rate Answer: c Diff: T Time Line: 0 12 24 27 Months 0 i = ?% 1 2 2.25 | | | | -8,000 10,000 Numerical solution:Step 1 Find the effective annual rate (EAR) of interest on the bank deposit EARDaily = (1 + 0.080944/365)365 - 1 = 8.43%. Step 2 Find the EAR of the investment $8,000 = $10,000/(1 + i)2.25 (1 + i)2.25 = 1.25 1 + i = 1.25(1/2.25) 1 + i = 1.10426 i = 0.10426  10.43% Step 3 Difference = 10.43% - 8.43% = 2.0% Financial calculator solution: Calculate EARDaily using interest rate conversion feature Inputs: P/YR = 365; NOM% = 8.0944; Output: EFF% = EAR = 8.43%. Calculate EAR of the equal risk investment Inputs: N = 2.25; PV = -8,000; PMT = 0; FV = 10,000. Output: I = 10.4259  10.43%. Difference: 10.43% - 8.43% = 2.0%. xlvii. Non-annual compounding Answer: a Diff: T To compare these alternatives, find the present value of each strategy and select the option with the highest present value. Option 1 can be valued as an annuity due. On your financial calculator enter: BEGIN mode (to indicate payments will be received at the start of the period) N = 12 I = 12/12 = 1 PMT = -1,000 FV = 0 Solve for PV = $11,367.63. Option 2 can be valued as a lump sum payment to be received in the future. On your financial calculator enter: END mode (to indicate the lump sum will be received at the end of the year) N = 2 I = 12/2 = 6 PMT = 0 FV = 12,750 Solve for PV = $11,347.45.Option 3 can be valued as a series of uneven cash flows. The cash flows at the end of each period are calculated as follows: CF0 = $ 0.00. CF1 = $ 800.00. CF2 = $ 800.00 x (1.20) = $ 960.00. CF3 = $ 960.00 x (1.20) = $1,152.00. CF4 = $1,152.00 x (1.20) = $1,382.40. CF5 = $1,382.40 x (1.20) = $1,658.88. CF6 = $1,658.88 x (1.20) = $1,990.66. CF7 = $1,990.66 x (1.20) = $2,388.79. CF8 = $2,388.79 x (1.20) = $2,866.54. To find the present value of this cash flow stream using your financial calculator enter: END mode (to indicate the cash flows will occur at the end of each period) 0 CFj; 800 CFj; 960 CFj; 1,152 CFj; 1,382.40 CFj; 1,658.88 CFj; 1,990.66 CFj; 2,388.79 CFj; 2,866.54 CFj (to enter the cash flows);I/YR = 12/4 = 3; solve for NPV = $11,267.37. Choose the alternative with the highest present value, and hence select Choice 1 (Answer a). xlviii. PMT and quarterly compounding Answer: b Diff: T 0 i = 2% 1 80 81 82 83 84 116 Qtrs. | | . . . | | | | | . . . | +400 +400 PMT 0 0 0 PMT PMT Find the FV at t = 80 of $400 quarterly payments: N = 80; I = 2; PV = 0; and PMT = 400. Solve for FV = $77,508.78. Find the EAR of 8%, compounded quarterly, so you can determine the value of each of the receipts: EAR =     4 0.08 1 + 4 - 1 = 8.2432%. Now, determine the value of each of the receipts, remembering that this is an annuity due. With a financial calculator input the following: N = 10; I = 8.2432; PV = -77,508.78; and FV = 0. Solve for PMT = $10,788.78  $10,789. xlix. PV of an uneven CF stream Answer: d Diff: T Parent's savings: Health Care Costs, Years 19-22: N = 18 -$1,000(1.1)19 = -$6,115.91 I = 6 -$1,000(1.1)20 = -$6,727.50 PMT = 100 -$1,000(1.1)21 = -$7,400.25 FV = 0 -$1,000(1.1)22 = -$8,140.27 Solve for PV = $1,082.76. 0 i = 6%1 2 18 19 20 21 22 | | | . . . | | | | | +100 +100 +100 -6,115.91 -6,727.50 -7,400.25 -8,140.27 -$8,554.84 PV of Health care costs 1,082.76 PV of parents' savings -$7,472.08 Lump sum government must set asideCF0 = 0 CF1-18 = 0 CF19 = -6,115.91 CF20 = -6,727.50 CF21 = -7,400.25 CF22 = -8,140.27 I = 6 Solve for NPV = -8,554.84 = PV of Health care costs. Consequently, the government must set aside $8,554.84 - $1,082.76 = $7,472.08. Alternatively, CF0 = 0 CF1-18 = 100 CF19 = -6,115.91 CF20 = -6,727.50 CF21 = -7,400.25 CF22 = -8,140.27 I = 6 Solve for NPV = -$7,472.08 = Lump sum government must set aside now. Terms in this set (17) The _____ is the financial market in which securities are initially issued. primary market Money markets are markets for short-term debt securities What do we call a market in which the price of a security is an accurate estimate by the market of its true value? efficient market What word do we use for the ease with which assets can be converted into cash? liquidity Shares of _____ are units of ownership interest, or equity, in a corporation. common stock Which of the following is not a financial intermediary? The United States Treasury DepartmentWhich of the following statements best describes mutual funds? They enable many investors with limited funds to buy a diversified portfolio Most people prefer to receive money today rather than ten years from now because Receiving cash today enables one to take advantage of current investment opportunities. The primary difference between simple and compound interest is that: Compound interest entails receiving interest payments on previously earned interest The amount of money that would have to be invested today at a given interest rate over a specific period in order to equal a future amount is called: present value Given some amount to be received several years in the future, if the interest rate increases, the present value of the future amount will be lower You have determined the profitability of a planned project by finding the present value of all the cash flows from that project. Which of the following would cause the project to look more appealing in terms of the present value of those cash flows? The discount rate decreases. Current assets values may be estimated by calculating:The present value of all future cash flows expected from the asset. An ordinary annuity may be defined as: A series of equal payments made at regular intervals that are received at the end of each period. In future value or present value problems, unless stated otherwise, cash flows are assumed to be: At the end of the time period. Suppose someone offered you your choice of two equally risky annuities, each paying $5,000 per year for 5 years. One is an annuity due, while the other is a regular (or deferred) annuity. If you are a rational wealth maximizing investor, which annuity would you choose? The annuity due. _______ is an annuity with an infinite life making continual annual payments. Perpetuity Terms in this set (69) The primary role of a financial system is to: a. enable financial managers to evaluate investment projects with a system that always selects the correct opportunity for their firm b. make savvy investors rich c. channel funds from savers to borrowers who need funds for investment projects d. provide employees in financial institutions with a code of ethics e. regulate the banking system c. channel funds from savers to borrows who need funds for investment projects The largest providers of funds in the financial system are: a. individuals b. businesses c. Bill and Melinda Gatesd. government agencies a. individuals The _____________ is the financial market in which securities are initially issued a. secondary market b. private placement c. OTC d. NASDAQ e. primary market e. primary market Money markets are markets for: a. long-term bonds b. short-term debt securities c. preferred securities d. foreign currency exchanges e. corporate stocks b. short-term debt securities What word do we use for the ease with which assets can be converted into cash? a. solvency b. liquidity c. agency d. efficiency e. accuracy b. liquidity What do we call a market in which the price of a security is an accurate estimate by the market of its try value? a. law of one price b. effective market c. secondary d. efficient market e. primary market d. efficient market $100 today is worth: a. the same as $100 to be received in one year, since the inflation rate has been how low recently and funds received in the near future should have the same purchasing power that they have today b. less than $100 received by someone ten years ago, since many products have been improved over this time period c. the same as a future received in one year, since the physical characteristics of U.S. currency are unchanged for long periods of time d. less than $100 to be received in one year, since many peoplewill spend money foolishly today and will become more careful in their spending habits as they mature e. more than $100 to be received in one year, since you can invest the money received today for this period, leaving you with more than $100 in the future e. more than $100 to be received in one year, since you can invest the money received today for this period, leaving you with more than $100 in the future The relationship between risk and return in finance can best be described by which of the following statements? a. high risk always brings it high returns b. the riskier the security, the lower the return expected from it c. high risk securities always beat low risk securities d. risk and return are inversely related e. the riskier the security, the greater the return the investors expect from it e. the riskier the security, the greater the return the investors expect from it Information Asymmetry is: a. false information spread by competitors b. when information is not reflected properly in the market c. incomplete informationd. when some know more than others e. when two pieces of information counteract each other d. when some know more than others Most people prefer to receive money today rather than ten years from now because: a. most people are afraid they will spend future cash payments foolishly b. receiving cash today enables one to take advantage of current investment opportunities c. people are unsure about their future employment prospects and wish to provide themselves with a source of future income d. U.S. prices have been falling recently and a dollar received today will buy more than one received in the future e. future investment returns are expected to be less variable than current ones b. receiving cash today enables one to take advantage of current investment opportunities The primary difference between simple and compound interest is that: a. simple interest is only paid at the end of the investment period b. simple interest is not taxed by the federal government c. compound interest is paid up front and not when the investment matures d. simple interest earns a higher interest rate on reinvested interest than compound interest e. compound interest entails receiving interest payments on previously earned interest e. compound interest entails receiving interest payments on previously earned interest The amount of money that would have to be invested today at a given interest rate over a specific period in order to equal a future amount is called: a. present value interest factor b. future value c. present value d. future value interest factor c. present value The future value of a dollar _____________ as the interest rate increases and ____________ the farther in the future an initial deposit is to be received. a. increases; increases b. decreases; decreases c. increases; decreases d. decreases; increases a. increases; increases Given some amount to be received several years in the future, if the interest rate increases, the present value of the future amount will be a. higher b. variable c. lower d. cannot tell e. stay the same c. lower You have determined the profitability of a planned project by finding the present value of all the cash flows from the project. Which of the following would cause the project to look more appealing in terms of the present value of those cash flows? a. the cash flows are extended over a longer period of time and the the total amount of the cash flows remains the same, but the cash flows are larger toward the end of the project b. the cash flows are extended over a longer period of time, but the total amount of the cash flows remains the same c. the discount rate decreases d. the cash flows occur over the same time period and total the same amount, but the cash flows are larger toward the end of the project e. the discount rate increases c. the discount rate decreases Current assets values may be estimated by calculating: a. the cash flows expected from the asset without adjusting for the time value of money b. only the present value of the cash flows to be received in the first two years since later cash flows are toouncertain to be considered c. a sum of all cash flows expected from the asset d. the future value of all cash flows expected from the asset e. the present value of all future cash flows expected from the asset e. the present value of all future cash flows expected from the asset Compute the simple interest earned on a 1-year $200 deposit that earns 6% per year. a. $200 b. $60 c. $6 d. $120 e. $12 e. $12 The price of a Wendy's Cheeseburger is $0.99, the same it was 5 years ago. Had the price of this sandwich increases at the same 3% annual rate as U.S. consumer prices did over the last 5 years, what would its price be today? a. $1.15 b. $1.22 c. $1.02 d. $1.12 e. $0.84 a. $1.15 $1,200 is deposited today into an account paying 6% interest compounded semiannually. How much interest will have been earned after 25 years? a. $3,950.24 b. $20,904.19 c. $5,260.69 d. $4,060.69 e. $1,312.53 d. $4,060.69 You plan to invest $2,500 in a money market account which will pay an annual stated (nominal) interest rate of 8.75%, but which compounds interest on a weekly basis. If you leave this money on deposit for one year (52 weeks), what will be your ending balance when you close the account? a. $2,681.00 b. $2,728.40 c. $2,582.28 d. $2,611.72 e. $2,703.46 b. $2,728.40 Today you invested $27,500 in an investment that pays 10% and will mature in 2 years. Once the investment matures, you will reinvest your funds for another 6 years in another investment that pays 6%. What will be the value of your investment after 8 years? a. $47,201.22 b. $83,619.85 c. $72,284.28 d. $61,505.26 a. $47,201.22 $1,200 is received at the beginning of year 1, $2,200 is received at the beginning of year 2, and $3,300 is received at the beginning of year 3. If these cash flows are deposited at 12%, their combined future value at the end of year 3 is: a. $7,504 b. $17,000 c. $12,510 d. $8,141 e. $6,700 d. $8,141 Suppose that the NASDAQ Composite index hit a level of 2,100 in February of 2000. In February of 1991 itwas at a level of 4,688. What was the annual average compound growth rate over the period? -8.54% In 1958, the average tuition for one year at an Ivy League school was $1,800. Thirty years later, in 1988, the average cost was $13,700. What was the growth rate in tuition over the 30 − year period? a. 9% b. 6% c. 7% d. 8% e. 12% c. 7% Julian was given a gold coin originally purchased for $1 by his great grandfather 50 years ago. Today the coin is worth $450. The rate of return realized on the sale of this coin is approximately equal to: A. 13% B. 50% C. 7.5% D. 10% E. 15% A. 13% Henry purchased stock in Nortel Networks for $120 per share. Unfortunately the stock did not perform very well in the 3 years that Henry has owned it as it is now trading at $3.93 per share. Feeling that the value of the stock will only continue to drop, Henry sold his shares today. What annual rate of return did Henry make on his investment? A. −66% B. −67% C. −69% D. −70% E. −68% E. -68% When you turned 20, you deposited $1,500 into an account paying interest that is compounded quarterly. You just turned 30, and there is now $2,233.30 in the account. What nominal annual interest rate is the account paying? A. 4.00% B. 1.00% C. 4.06% D. 16.24% E. 3.75% A. 4.00% In February of 2000 the NASDAQ Composite index peaked at a level of 4,696 (just before the Tech Bubble popped). In February of 2006 it was at a level of 2,028. The NASDAQ index has historically grown at an average annual rate of 9.0%. If the index continues to grow at its historic rate, then how many years will it take for the index to grow from its Feb 2006 level back to the Feb 2000 level? 10 years If you presently have $6,000 invested at a rate of 15%, how many years will it take for you investment to triple? (Round up to obtain a whole number of years if necessary.) A. 2 B. 6 C. 4 D. 10 E. 8 E. 8 Gary has $1,400 to invest with the goal of having $4,000 available to purchase a used car. If he can earn 12% compounded semiannually on his investment, how long will he have to wait to acquire his car? A. Eighteen months B. Nine years C. Nine months D. Four yearsE. Eighteen years C. nine months You have a savings account that pays 3.9% interest compounded semiannually, but you are considering transferring your funds into a savings account that pays 3.7% interest compounded monthly. Calculate the difference in the effective interest rates of the two accounts. What is the difference in the effective interest rates of your existing and potential new accounts? 0.0018 A bank pays a quoted annual (nominal) interest rate of 8%. However, it pays interest (compounded) daily using a 365−day year. What is the effective annual rate of return? A. 7.86% B. 9.21% C. 7.54% D. 8.57% E. 8.33% E. 8.33% If you could borrow at 9.5% compounded semi − annually or at 9.4% compounded monthly, which would you prefer? A. 9.5% compounded semi − annually B. 9.4% compounded monthly C. Indifferent A. 9.5% compounded semi − annually Penny just won the state lottery that offers a choice of payments. She may opt for either receiving $1,000,000 today or $2,000,000 at the end of ten years. If she can invest her funds at 5% annually, which is the better choice? A. The earlier payment since the present value of the $2,000,000 payment is $876,000. B. The earlier payment since the future value of $1,000,000 in ten years is $1,628,894. C. The later payment since $1,000,000 invested at 5% for ten years will be worth $1,500,000. D. The later payment since the present value of the $2,000,000 payment is $1,227,827. E. The immediate payment since the present value of the $2,000,000 payment is $1,200,000. D. The later payment since the present value of the $2,000,000 payment is $1,227,827. You will receive a $90,000 inheritance in 7 years. You could invest that money today at 7% compounded semi annually. What is the present value of your inheritance? $55,600.36 What is the present value of $2,000 to be received in six years if interest rates are 8% compounded semiannually? (Round to the nearest whole dollar) A. $1,258 B. $1,158 C. $1,923 D. $1,249 E. $1,852 D. $1,249 How much does Ralph need to invest today to have $150,000 in five years if he will earn 8% interest compounded quarterly on his investment? Round to the nearest whole dollar. A. $102,041 B. $100,946 C. $73,171 D. $105,453 E. $101,351 B. $100,946 Your grandfather has left you $150,000 in a trust fund that you cannot have for another seven years. You have decided that you really need this money now to pay for your college expenses. Your attorney offers you $80,000 for an assignment of the proceeds of the trust. If you can get a student loan at 10%, should you accept your attorney's offer? A. No, because the $150,000 is worth more than $80,000 today. B. Yes, because the $150,000 is worth more than $80,000 today.C. Yes, because the $150,000 is worth less than $80,000 today. D. No, because the $150,000 is worth less than $80,000 today. C. Yes, because the $150,000 is worth less than $80,000 today. A real estate agent wants you to buy a plot of land today for $60,000 and he promises that you can sell it back to him in 7 years for $100,000. If you can earn 9% on alternative investments, then what is the present value of the sales proceeds? Is this a worthwhile investment? A. $61,294.51 ; it is not a worthwhile investment. B. $61,294.51 ; it is a worthwhile investment. C. $60,000 ; not enough information. D. $54,703.42 ; it is not a worthwhile investment. E. $54,703.42 ; it is a worthwhile investment. D. $54,703.42 ; it is not a worthwhile investment. Suzanne has identified a project with the following cash flows. What is the present value of the cash flows at time 0 if the interest rate is 9%? Year- Cash Flow 1 - $2,000 2 - $650 3 - $375 4 - $1,200 A. $3,488.90 B. $3,521.63 C. $3,230.86 D. $4,225.00 E. $3,838.58 B. $3,521.63 An ordinary annuity may be defined as: A. A series of payments, which may or may not be equal in value, that are received at regular intervals at the end of each period. B. A series of equal payments made any time over the course of a year, extending for a period of several years. C. A series of equal payments made at regular intervals that are received at the end of each period. D. A series of equal payments made at regular intervals that are paid at the beginning of each period. E. Any series of payments that occur in the future. C. A series of equal payments made at regular intervals that are received at the end of each period. In future value or present value problems, unless stated otherwise, cash flows are assumed to be: A. At the end of the time period. B. Spread out evenly over a time period. C. In the middle of the time period. D. At the beginning of the time period. A. At the end of the time period. Suppose someone offered you your choice of two equally risky annuities, each paying $5,000 per year for 5 years. One is an annuity due, while the other is a regular (or deferred) annuity. If you are a rational wealth maximizing investor, which annuity would you choose? A. The deferred annuity. B. The annuity due. C. Either one, because as the problem is set up, they have the same present value. D. Without information about the appropriate interest rate, we cannot find the value of the two annuities, hence we cannot tell which is better. E. The annuity due; however, if the payments on both were doubled to $10,000, the deferred annuity would be preferred. B. The annuity due. _______ is an annuity with an infinite life making continual annual payments. A. Perpetuity B. Principal C. APR D. Amortized loan A. PerpetuityWhat is the future value of a 5 − year ordinary annuity with annual payments of $200, evaluated at a 15% interest rate? A. $670.44 B. $842.91 C. $1,169.56 D. $1,348.48 E. $1,522.64 D. $1,348.48 You are expecting to receive $70 per year at the end of each of the next five years. If you invest the money in account that pays 5%, then how much interest will you earn over the five years? (Round to the nearest whole dollar) A. $37 B. $75 C. $350 D. $387 E. $18 A. $37 Janice would like to send her parents on a cruise for their 25th wedding anniversary. She has priced the cruise at $15,000 and she has 5 years to accumulate this money. How much must Janice deposit annually in an account paying 10 percent interest in order to have enough money to send her parents to cruise? (Round to the nearest whole dollar) A. $1,862 B. $2,234 C. $2,457 D. $3,000 E. $2,135 C. $2,457 Sarah found her dream lakefront home, valued at $250,000. She plans to buy a home just like it when she retires in 15 years. Sarah can earn 11% per year on her investments. The price of the house will increase 3% per year for the next 15 years. How much must she invest at the end of each of the next 15 years to finance the purchase? A. $10,198.81 B. $11,320.67 C. $7,266.31 D. $8,952.82 E. $12,565.95 B. $11,320.67 Ethan sells his car to Seamus. Seamus promises to pay Ethan $1,140 at the end of each year for 8 years. What is the present value of Seamus's promised payments if the interest rate is 7%? $6,807.28 Starting one month from now, you need to withdraw $190 per month from your bank account to help cover the costs of your university education. You will continue the monthly withdrawals for the next four years. If the account pays 0.6% interest per month, how much money must you have in your bank account today to support your future needs? $7,903.78 You are 30 years old today. You want to retire at the age of 65. You expect to live until age 95. You would like to have a monthly income of $14,000 per month in retirement. How much do you have to save per month during your working years in order to achieve your retirement goal? Assume end of period payments. Assume an annual interest rate of 2.5% in retirement and 4% during your working life. $3,877.75 Actively managed mutual funds charge higher management fees than passive funds. Assume that the net return to an active fund (after fees) is 9.5% (0.79% per month) and the net return to a passive fund is 10.5% (0.875% per month). Assume that an investor saves $600 per month (end − of − month) over thirty years. What is the difference in the future value of savings between investing in an active fund and a passive fund? A. $120,519.40B. $295,152.00 C. $301,732.21 D. $247,352.36 B. $295,152.00 Gina has planned to start college education in four years from now. To pay for her college education, she has decided to save $1,000 a quarter for the next four years in a bank account paying 12 percent interest (compounded quarterly). How much will she have at the end of fourth year? (Round to the nearest whole dollar) A. $19,116 B. $20,157 C. $16,000 D. $1,574 B. $20,157 An investor is considering the purchase of 20 acres of land. An analysis indicates that if the land is used for cattle grazing, it will produce a cash flow of $1,000 per year indefinitely. If the investor requires a return of 10% on investments of this type, what is the most he or she should be willing to pay for the land? A. $1,000 B. $150,000 C. $1,000,000 D. $100,000 E. $10,000 E. $10,000 You've graduated from college and landed a good job. You want to replace your car, but don't want to take out a car loan. Instead, you decide to invest $300 per month in the stock market and hope to earn 9%. If the market performs as you're hoping, how many years will it take to accumulate $35,000? Ignore taxes. 7.01 years You are late paying a bill for $14,854.50. You have made arrangements to pay off the bill in installments of $360 per month, and you will be charged monthly interest of 1.4% on the overdue balance. How many months will it take you to pay off the account balance? 62 months You are late paying a bill for $11,200.66. You have made arrangements to pay off the bill in installments of $260 per month, and you will be charged monthly interest of 1.2% on the balance owing. How long will it take you to pay off the account balance? (round your answer to nearest month) A. 62 months B. 60 months C. 63 months D. 64 months E. 61 months E. 61 months In three years you will begin receiving an annual payment of $600 that will be made for two years. If the annual interest rate is 12%, what will be the balance in your account at the end of the fourth year? A. $1,344 B. $2,025 C. $1,260 D. $1,272 E. $1,200 D. $1,272 Francis Scott Key just won a "Name That Tune" contest with a grand prize of $220,000. However, the contest stipulates that the winner will receive $100,000 immediately, and the remainder divided equally at the end of each of the next 12 years. Assuming that he can earn 5% on his money, what is the present value of his winnings? $188,632.52 Wally, president of Wally's Burgers, is considering franchising. He has a potential franchise agreement that would allow him to receive 13 endofyear payments starting one year from now. The first two payments would be $25,000 and $22,000 in one and two years respectively, and then $18,000 per year after that for 11 years. IfWally requires a return of 8.8%, what is the present value of this stream of cash flows? ... Molly, president of Molly's Muffins, is considering franchising. She has a potential franchise agreement that would see her receive payments of $28,000, $24,000, and $20,000 at the end of years 1, 2, and 3 respectively, and then $12,000 per year after that for 17 years. If Molly requires a return of 10%, then what is the present value of this stream of cash flows? (Round answer to the nearest whole dollar) A. $143,354 B. $132,636 C. $156,574 D. $124,440 E. $145,900 B. $132,636 Three years from now you will begin receiving annual payments of $7,200. This will continue for 14 years. At a discount rate of 5.8%, what is the present value of this stream of cash flows? A. $64,045.86 B. $60,534.84 C. $51,253.11 D. $57,216.29 E. $54,523.00 ... If you buy a factory for $250,000 and the terms are 20% down, the balance to be paid off over 30 years at a 12 percent rate of interest on the unpaid balance, what are the 30 equal annual payments? (Round to the nearest whole dollar) A. $50,212 B. $31,036 C. $6,667 D. $24,829 E. $20,593 D. $24,829 A Hummer H3 sells for $96,000 tax included. GMAC lends money at the rate of 8.6% APR. If you buy the car and borrow through GMAC, then what are the monthly (endofmonth) payments for a 6year term? $1,711.45 Sally wants to buy a Ford Mustang. The MSRP is $28,478. Ford offers a purchase financing plan with no money down and 48 endofmonth payments of $690. Should she buy the car for cash or take Ford's purchase financing? Assume that she has the cash and that she could invest her money and earn at least 5%. A. Sally should borrow money to buy the car because its present value is lower. B. Sally should borrow money to buy the car because its present value is higher. C. Sally should pay cash to buy the car because its present value is higher. D. Sally should pay cash to buy the car because its present value is lower. $29,961.84 D. Sally should pay cash to buy the car because its present value is lower. An expected return from a portfolio: A. cannot be computed if there are fewer than three securities in the portfolio. B. can be calculated more accurately than the expected return from any of the securities in the portfolio. C. will be lower than the expected return from the security in the portfolio with the lowest yield because portfolios have less risk than individual securities. D. will lie somewhere between the highest and lowest expected returns from securities in the portfolio. E. will exceed the highest expected return from any of the securities in the portfolio. D. will lie somewhere between the highest and lowest expected returns from securities in the portfolio. Which of the following is a false statement? A. Historical returns can be calculated with more confidence than expected returns. B. Expected returns may differ from actual returns because of an unforeseen recession. C. Although expected returns may differ from actual returns, they seldom do. D. Accurate predictions of expected returns depend on the analyst's ability to estimate probabilities. E. Expected returns are not always predicted accurately.C. Although expected returns may differ from actual returns, they seldom do. Compaq recently adjusted the probabilities for its expected cash flows in light of the Asian currency crisis. It revised the probability of favorable conditions from 32% to 18% and the probability of poor earnings from 7% to 17%. Which of the following is the most likely result from this revision? A. It would lower its historical return. B. It would raise expected returns. C. It would lower expected returns. D. The probabilities cannot be revised once they have been estimated. E. It would have no effect on expected returns. C. It would lower expected returns. You bought stock in your favorite online retail company at a price of $60 per share. You recently sold the stock for a price of $71 per share. While holding the stock, you received dividends of $1.92. What was your holding period return? Ans 21.53 Terms in this set (79) Four main areas of Finance Corporate finance Investments Financial institutions and markets International finance Finance definition A combination of the art and science of managing wealth. Financial management definition Generally defined as those activities that create or preserve the economic value of the assets of an individual, small business, or corporation. What is the cycle of money? A figure eight with lender/ investors on one side, the bank in the middle, and borrowers on the other side. Cash flows from the lenders to the bank to the borrower and back again in an endless loop. Types of financial markets that can be classified by the type of asset/ securities traded: Equity market Debt market Derivative market Foreign currency market Internal stakeholders All departmental managers and other employees External stakeholders Customers Suppliers Government Creditors What long-term investments should the firm take on? Capital budgetingWhere will we get the long-term financing to pay for the investment? Capital structure How will we manage the everyday operational activities of the firm? Working capital management Sole Propietorship Single owner (full responsibility) Advantages: Simple and east to form Subject to few regulations No corporate income taxes Disadvantages: Limited life Unlimited liability Difficult to raise capital Owner pays personal tax on profits Partnership General (full responsibility) Limited (LLP) (present responsibility) Silent (only responsible to investment) Advantages: Agreements between partners are easily formed More individuals= more expertise Larger amount of capital available Disadvantages: Assets of general partners are commingled with the business Profits treated as personal income for tax purposes Difficult to transfer ownership Corporation Legal entity separate from its owners Advantages: Business is separate legal entity Owners have limited liability to obligations of the business Easy to transfer ownership Greater access to capital Owners do not have personal liability Disadvantages: Double taxation (corporate and personal) Cost of set-up and filing are difficult Most regulated Benefits and limitations of LLC Benefits: Limited liability Taxed like a partnership Limitations: Qualifications vary from state to state Cannot appear like a corporation otherwise it will be taxed like one Professional corporation (PC) Joins with licensed professionals such as medical doctors, lawyers, ect. Not personally liable for the malpractice of their partners Name +PC Small corporations S-type corporations Benefits: Limited liability Taxed as a partnership Limitations:Owners must be be people (less than 100) so cannot be used for joint venture between two corporations Joe is deciding whether or not to invest $10,000 in a business that has pending lawsuits against it. If Joe invests and the business loses the lawsuit, the most Joe can lose is ? A) $10,000 if Joe is a general partner. B) $10,000 if Joe is a sole proprietor. C) $10,000 if Joe is a silent partner. D) $10,000 plus his share of the lawsuits if this business is in corporation form. C) $10,000 if Joe is a silent partner. What should be management's primary objective? Stockholder wealth maximization, which translates to maximizing stock price. What do the most admired Fortune 500 companies have in common? They act ethically High quality from customer's view Employees who like working there Three aspects of cash flows affect an investment's value? Amount of expected cash flows (bigger is better) Risk of the cash flows (less risk is better) Timing of the cash flow stream (sooner is better). Principal Owners of the company Agent Managers of the company Conflicts between stockholders and managers Managers may act in their own interests and not on behalf of owners (stockholders) Conflicts between stockholders and creditors Stockholders want return as high as possible, while creditors care about the risk. If you are the only employee, and only your money is invested in the business, would any agency problems exist? No Why might managers want make the financial statements look artificially good? A manager might inflate a firm's reported earnings or make its debt appear to be lower if he or she wanted the firm to look good temporarily. What are the potential consequences of inflating earnings or hiding debt? If the firm is publicly traded, the stock price will probably drop once it is revealed that fraud has taken place. If private, banks may be unwilling to lend to it, and investors may be unwilling to invest more money. Would expansion increase or decrease potential agency problems? Increase. If you expanded to additional locations you could not physically be at all locations at the same time. Consequently, you would have to delegate decision-making authority to others. Might acquiring capital lead to agency problems? If you needed additional capital to buy computer inventory or to develop software then you might end up with agency problems if the capital is acquired from outsiders. Does the source of the capital affect agency problems? Agency problems are less for secured debt than for unsecured debt, and different among various capital providers. So it matters whether the new capital comes in the form of an unsecured bank loan, a bank loan secured by your inventory of computers, or from new stockholders. Corporate Governance The set of rules that control a company's behavior towards its directors, managers, employees, stockholders,creditors, customers, competitors, and community. It can help control agency problems. Example: You win a lottery ticket which offers two options: Option a) receiving $750 today; Option b) receiving $935 in three years. Given 10% rate of return, which option should you choose? Never, never do this!!! Money received or paid at different point of time is not comparable! You win a lottery ticket which offers two options: Option a) receiving $750 today; Option b) receiving $935 in three years. Given 10% rate of return, which option should you choose? Let's compare the future values. Option A ($998.25> $935) You win a lottery ticket which offers two options: Option a) receiving $750 today; Option b) receiving $935 in three years. Given 10% rate of return, which option should you choose? Let's compare the present values. Option A ($750> $702.48) Your retirement goal is $2 million. The bank is offering you a CD that is good for 40 years at 6.0%. What initial deposit do you need to make today to reach your $2 million goal at the end of 40 years? N=40 I/Y= 6.0 PMT= 0 FV= 2000000 The answer is: PV= -194444.38 Bank A offers to pay you a lump sum of $20,000 after 5 years if you deposit $9,500 with them today. Bank B, on the other hand, says that they will pay you a lump sum of $22,000 after 5 years if you deposit $10,700 with them today. Which offer should you accept? You should accept Bank A's offer, since it provides a higher annual rate of return You have decided that you will sell off your house, which is currently valued at $300,000, at a point when it appreciates in value to $450,000. If houses are appreciating at an average annual rate of 4.5% in your neighborhood, for approximately how long will you be staying in the house? 9.21 years or 9 years and 3 months Rule of 72 Estimates the number of years required to double a sum of money at a given rate of interest. Ex: If the rate of interest is 9%, it would take 72/9= 8 years to double a sum of money. It can also be used to calculate the rate of interest needed to double a sum of money by a certain number of years. Ex: Double a sum of money in 4 years, the rate of return would have to be 72/4= 18%. In 1626, 387 years ago, Manhattan's native tribe sold Manhattan Island to Peter Minuit for $24. If the native tribe saved the money in a "bank" and earned 6% annual return what would their future value be? I/Y= 6 N= 387 PV= -24 PMT= 0 so the answer is: FV= 149 billion Ordinary annuity Each payment is made at the end of the period Annuity due Each payment is made in the beginning of the periodGoogle glasses will be for sale in 3 years. In order to buy them, you plan to deposit $400 at the end of each year into US Bank saving account drawing 5% interest rate. How much will you have at the end of 3 years? (What's the FV of a 3-year ordinary annuity of $400 at 5%? ) N= 3 I/Y= 5 PV= 0 PMT= -400 So the answer is: FV= 1261 American Airlines promotes a travel fund which generates 5% return in next 3 years and also allows you to withdraw some money each year for a trip. If you want to get $400 for the airfare in each Christmas, how much should you invest in the beginning? (What's the PV of a 3-year ordinary annuity of $400 at 5%?) N= 3 I/Y= 5 PV= -1089.30 FV= 0 So the answer is: PMT= 400 US Bank loans you $1,089.30 for 3 years with 5% interest rate to buy a car. The loan must be repaid in 3 equal payments at the end of each year. What is your annual payment? N= 3 I/Y= 5 PV= 1089.30 FV= 0 So the answer is: PMT= -400 Your grandfather will sell you a piece of beachfront property for $72,500. He says the price is firm whenever you can pay him cash. You know your finances will only allow you to save $5,000 a year and you can make 8 % on your investment. If you invest faithfully every year at the end of the year, how long will it take for you to accumulate the necessary $72,500 future cash for the beachfront property? I/Y= 8 PV=0 PMT= -5000 FV= 72500 So the answer is: N= 10.01 (years) You currently have $67,000 in an interest−earning account. From this account, you wish to make 20 year−end payments of $5,000 each. What annual rate of return must you make on this account to meet your objective? N= 20 PV= 67000 PMT= -5000 FV=0 So the answer is: I/Y= 4.16 Do one practice of switching between ordinary annuity and annuity due. 2nd BGN 2nd SET 2nd QUIT BGN is displayed 2nd BGN 2nd SET 2nd QUIT Nothing is displayed What's the FV of a 3-year annuity due of $400 at 5%? N= 3 I/Y= 5 PV= 0 PMT= -400 So the answer is: FV= 1324.05FV is higher by: Increasing the number of years for which money is invested. Investing at a higher interest rate. (Positive relationship) PV is higher by: Time period is shorter. Interest rate is lower. (Negative relationship) What is a perpetuity? A special annuity that continues forever. suppose an investment promises to pay $100 per year in perpetuity. What is this investment worth if the interest rate is 5 percent? PV of perpetuity= PMT/ r $100/0.05= $2000 Loan payments can be structured in one of 3 ways: Discount loan: Principal and interest is paid in lump sum at end. Interest-only loan: Periodic interest-only payments, principal due at end. Amortized loan: Equal periodic payments of principal and interest. Roseanne wants to borrow $40,000 for a period of 5 years. The lenders offers her a choice of three payment structures: 1. Pay all of the interest (10% per year) and principal in one lump sum at the end of 5 years; 2. Pay interest at the rate of 10% per year for 4 years and then a final payment of interest and principal at the end of the 5th year; 3. Pay 5 equal payments at the end of each year inclusive of interest and part of the principal. Under which of the three options will Roseanne pay the least interest and why? Calculate the total amount of the payments and the amount of interest paid under each alternative. Method one: $24420.40 Method two: $20000 Method 3: $12759.50 Method 3 is the best one. Amortization Schedule Table PMT- Interest= Principle reduction Beginning bal. - prin reduction= end balance. Move end balance to the next beginning balance. You want to buy a house with $250,000. You pay 20% down payment and finance the remaining from mortgage loan. The bank offers you 30-year, 5% fixed rate. N= 360 I/Y= 0.4167 PV= 200000 FV= 0 So the answer is: PMT= -1073.64 Compounding periods per year C/Y= m Periodic interest rate r= APR/ mExample of quarterly compounding period when the annual percentage rate is 5% Period rate (r) 5/4 = 1.25% The First Common Bank has advertised one of its loan offerings as follows: "We will lend you $100,000 for up to 3 years at an APR of 8.5% (interest compounded monthly." If you borrow $100,000 for 1 year, how much interest will you have paid and what is the bank's EAR? Nominal annual rate = APR = 8.5% Frequency of compounding = m = 12 Periodic interest rate = APR/m = 8.5%/12 = 0.70833% = .0070833 EAR (or APY)= (1.0070833)12 - 1 = 1.08839 - 1 =8.839% Total interest paid after 1 year = .08839*$100,000 = $8,839.09 Which of the following investments has the highest effective annual return (EAR)? (Assume that all CDs are of equal risk.) A) A bank CD that pays 7.30 percent annually. B) A bank CD that pays 7.25 percent compounded semi-annually. B EAR=(1+7.25%/2)^2-1=7.38% > 7.3% One bank offers you 4% interest compounded semiannually. What is the equivalent rate if interest is compounded quarterly? 3.98% (1+4%/2)^2-1=(1+X/4)^4-1, then solve X from this equation. Note: you should set your calculator with at least 4 decimals to get correct answer. ABC Printing Company has just signed to buy a building worth $200,000 to house its operations. ABC Printing paid $10,000 down and must finance (borrow) the remaining $190,000. The bank will loan the firm money at 8% APR, but ABC has an option to make annual payments or monthly payments on the loan. Both options have a thirty-year payment schedule. What are the mortgage payments under the two different plans? Annual Payment (compounding): N= 30 I/Y= 8 PV=190000 FV= 0 PMT= -16877.21 Monthly Payment (compounding): N= 360 I/Y= 0.6666 PV=190000 FV=0 PMT=-1394.15 Kay has just taken out a $200,000, 30-year, 5%, mortgage. She has heard from friends that if she increases the size of her monthly payment by one-tenth of the monthly payment, she will be able to pay off the loan much earlier and save a bundle on interest costs. She is not convinced. Let's help her! Minimum monthly payment: N= 360 I/Y= 0.416 PV= 200000 FV=0 PMT= -1073.64 Now we add 10% to the payment: I/Y= 0.416 PV= 200000 PMT= -1181 FV= 0 N= 293.65 293.65/ 12= 24.50 yearsPay off the loan 5.5 years early! Interest saved: $39709.75 21% drop Fisher Effect r = r + h + (r x h) r*= real rate h= inflation rate r= nominal rate If real interest rate is 10% and inflation rate is 4%, what is the nominal rate? Real rate + Inflation rate + (real rate*inflation rate) 10% + 4% + (10%*4%) = 14.4% The rate of return on all riskier investments (r) have to include a default risk premium (dp) and a maturity risk premium (mp) r = r* + h + dp + mp What has a higher rate: 30-year corporate bond yield or 30-year T-bond yield? 30-year corporate bond yield > 30-year T-bond yield Due to the increased length of time and the higher default risk on the corporate bond investment. Yield curve A graphical depiction of the relationship between the interest rate and the maturity date of a financial instrument. 2017 inflation rate 2.61% Current richest American Jeff Bezos If you sign up for a credit card with a 15.24% APR, and you charge $1,025 to it in the first month, you generally can avoid paying any interest on that debt if you pay the full balance at the first payment due date. However, if you choose to make the minimum payment, $25, you will be charged interest on the rest. How much will the interest be for the unpaid balance in the first month? Use EAR (real interest rate) 15.24% / 365 = 0.04176% (daily compounded rate) $1,000 * (1+0.04176%)30-$1,000 = $12.60 (30-day payment period.) ________ is the area of business that deals with how a company conducts its business and implements controls to ensure proper procedures and ethical behavior. A. Leadership B. Agency Relationship C. Corporate Governance D. None of the above C Which of the following is NOT an example of annuity cash flows? A) The university tuition bill you pay every month that is always the same. B) The grocery bill that changes every week. C) The $3.50 you pay every morning for a bagel and coffee as you run to your first morning class. D) Equal annual deposits into a retirement account. B After winning the lottery, you state that you are indifferent between receiving twenty $500,000 end-of-the-year payments (first payment one year from today), or a lump sum of $5,734,961 today. What interest rate are you using in your decision-making process such that you are indifferent between the two choices?A. 5.00% B. 6.00% C. 7.00% D. 8.00% B Which of the following actions will INCREASE the present value of an investment? A. Decrease the interest rate. B. Increase the amount of time. C. Decrease the future value. D. All of the above will increase the present value. A You are analyzing the value of an investment by calculating the present value of its expected future cash flows. Which of the following would provide a higher present value? A. The discount rate decreases. B. The cash flows are extended over a longer period of time, but the total amount of the cash flows remains the same. C. The discount rate increases. D. The total amount of cash flows remains the same, but more of the cash flows are received in the later years and less are received in the earlier years. A Two rival football fans have made the following wager: if one fan's college football team wins the conference title outright, the other fan will donate $1,800 to the winning school. Both schools have had relatively unsuccessful teams, but are improving each season. If the two fans must put up their potential donation today and the discount rate is 9% for the funds, what is the required upfront deposit if we expect a team to win the conference title in 5 years? N= 5 I/Y= 9 PMT= 0 FV=1800 So the answer is: PV= -1169.88 You have an annuity of equal annual end-of-the-year cash flows of $500 that begin two years from today and last for a total of ten cash flows. Using a discount rate of 4%, what are those cash flows worth in today's dollars? $3899.47 1st step: N=10 I/Y= 4 PMT= 500 FV= 0 PV= -4055.45 2nd step: N=1 I/Y=4 PMT=0 FV= -4055.45 PV= 3899.47Time Value of Money Work book – Section I – True, False type questions State whether the following statements are true (T) or False (F) 1.1 Money has time value because you forgo something certain today for something uncertain tomorrow. 1.2 The uncertainty factor increases with time – the distant the cash flows, the more uncertain they become. 1.3 The lower is the compounding period, the higher is the effective rate of interest. 1.4 With high inflation rate, the interest rates tend to increase. 1.5 One of the reasons for attributing time value to money is that individuals prefer future consumption to current consumption. 1.6 The nominal rate of interest is equal to the effective rate of interest when interest is compounded annually. 1.7 The rule of 72 is more precise (provides a better estimate) than the rule of 69 to find the period required to double your initial amount. 1.8 Financial analysis require an explicit consideration of time value of money because most financial problems at corporate and individual level involves cash flows occurring at different points in time. 1.9 Given a principal amount of Rs. 10,000 to be invested for 9 months, it is better to invest in a scheme that offers 12% annual compound interest than investing in a scheme that earns 12% simple interest. 1.10 A bank that pays 10% interest compounded annually pays a higher effective rate of interest than a bank that pays 10% interest compounded quarterly. 1.11 The formula for effective rate of interest (re) is- re= (1+r/m)n -1 1.12 A regular (deferred) annuity is one in which a series of periodic cash flows of equal amount occur at the beginning of each period. 1.13 The rule of 72 is useful in determining the future value of an annuity given the rate of interest. 1.14 Frequency of compounding has no effect on interest earned. 1.15 Maximum benefit of compounding occurs when money is compounded daily. 1.16 Present value of an uneven stream of cash flows can be calculated with the help of present value of annuity table. 1.17 While investing money it is always better to insist on a higher frequency of compounding. 1.18 Increased frequency of compounding means the same thing as decrease in compounding period. 1.19 The benefits from increased compounding frequency decrease with each successive increase in compounding frequency. 1.20 In case of most of banks, fixed deposit money is compounded quarterly. 1.21 Effective rate of interest depends on the compounding period.1.22 Higher the compounding period, higher is the effective rate of interest. 1.23 In simple interest, interest for each year in same. 1.24 The process of determining present value is often called discounting. 1.25 Continuous compounding results in the maximum possible future value for given rate of interest and time period. 1.26 A perpetuity is an annuity that continues for 100 years. 1.27 In perpetuity, the principal amount remains intact. 1.28 The present value of any future sum is inversely related with rate of interest. 1.29 Continuous compounding occurs when interest is compounding daily. 1.30 Sinking fund factor is used to determine the periodic fixed amount that must be invested regularly to accumulate a specified sum at the end of a given period at a given rate of interest. 1.31 When debt(loan) is amortized in periodic fixed installments, the principal component of installment declines over time. 1.32 The compound value of any sum invested today varies directly with rate of interest (r) and time period (n). 1.33 Money has time value because a sum of money to be received in future is more valuable than the same amount today. 1.34 The process of compounding assumes discounting at same rate. 1.35 An annuity due is one in which periodic cast flows of equal amount occur at the beginning of each period. 1.36 Compounding over the same time period, annuity due will have a higher future value than ordinary annuity. 1.37 An amortization schedule tells us about the interest component and principal repayment component of each fixed installment paid by borrower towards loan repayment. 1.38 Annuity tables can be used far all types of cash flows. 1.39 For a given rate of interest(r) and given number of years(n), the present value annuity factor will be greater than future value annuity factor. 1.40 In present value tables, all values are less than 1. 1.41 Present value of annuity due is equal to present value of ordinary annuity x (1 + r). 1.42 Future value of annuity due = present value of ordinary annuity x (1 + r) 1.43 1 ÷ PVAF (Present value Annuity Factor) is knows as capital recovery factors. 1.44 1 ÷ FVAF (Future value Annuity Factor) is known as sinking fund factors. 1.45 The price of any asset today is the present value of all the future cash flows associated with the asset. 1.46 Bond prices vary inversely with the rate of interest. 1.47 An annuity is a stream of constant cash flows occurring at regular intervals of time.1.48 A perpetuity is an annuity that continues for ever i.e., till infinity. 1.49 The present value of a mixed stream of cash flows is the sum of the present values of the individual cash flows. 1.50 An investment option that comes with specified present value and future value after given period has hidden rate of interest. Solutions : Section – I 1.1 T 1.2. T 1.3. T 1.4 T 1.5 F 1.6 T 1.7 F 1.8 T 1.9 F 1.10 F 1.11 F 1.12 F 1.13 F 1.14 F 1.15 F 1.16 F 1.17 T 1.18 T 1.19 T 1.20 T 1.21 T 1.22 F 1.23 T 1.24 T 1.25 T 1.26 F 1.27 T 1.28 T 1.29 F 1.30 T 1.31 F 1.32 T 1.33 F 1.34 T 1.35 T 1.36 T 1.37 T 1.38 F 1.39 F 1.40 T 1.41 T 1.42 F 1.43 T 1.44 T 1.45 T 1.46 T 1.47 T 1.48 T 1.49 T 1.50 T Time Value of Money Work book – Section II – Fill in the blanks Fill in the blanks with suitable answers 2.1 The process of determining present value is often called ................. and is the reverse of the ................. Process. 2.2 A ................. is an annuity that continues forever. 2.3 An ................. is a series of cash flows of fixed amount occurring at regular intervals of time. 2.4 A ................. is the annual deposit or investment of fixed amount that is necessary to accumulate a specified future sum. 2.5 If a loan is to be repaid in equal periodic amounts, it is said to be an .................. 2.6 Effective annual rate of interest is ................. to nominal rate of interest, when interest is compounded annually. 2.7 Effective annual rate of interest with half-yearly compounding is ................. than, with quarterly compounding. 2.8 The formula for effective annual rate of interest (re) is ................. 2.9 If the repayment of a loan is to start after a gap of few years, it is called an ................. loan. 2.10 The general formula for intra year compounding is ................. 2.11 Using the rule of 72 to find doubling period we ................. 72 by .................. 2.12 Annuity (constant annual cash inflow) ÷ Rate of interest (r) is the formula to find present value of ................. 2.13 Lower is the compounding period, the ................. is the effective annual rate of interest. 2.14 The formula to find the growth of money with continuous compounding is ................. 2.15 Present or future value of annuity due = present or future value of ordinary annuity x ................. 2.16 1 ÷ PVAF (present value annuity factor) refers to ................. 2.17 1 ÷ FVAF (future value annuity factor) refers to .................2.18 When cash flows of constant amount occur at the beginning of each period, the annuity is called an ................. 2.19 Compound interest is more than simple interest because in ................. interest is earned on interest. 2.20 ................. compounding results in maximum possible future value at the end of n periods for a given rate of interest. Answers to section II 2.1 Discounting, compounding 2.2 perpetuity 2.3 Annuity 2.4 sinking fund 2.5 amortized loan 2.6 equal 2.7 less 2.8 re = (1 + r/m)m -1 2.9 deferred 2.10 FVn= (1 + r/m)mn 2.11 divide, r 2.12 perpetuity 2.13 higher 2.14 FVn = Po. × ern 2.15 (1+r) 2.16 capital recovery factor 2.17 sinking fund factor 2.18 annuity due 2.19 compound interest 2.20 continuous. Time Value of Money Work book – Section III – Multiple choice questions Mark () the right answer from given alternatives : 3.1 Money has time value because: a. Individuals prefer future consumption to present consumption. b. Money today is more certain than money tomorrow c. Money today is wroth more than money tomorrow in terms of purchasing power. d. There is a possibility of earning risk free return on money invested today. e. (b), (c) and (d) above. 3.2 Given an investment of Rs. 10,000 to be invested for one year; a. It is better to invest in a scheme that pays 10% simple interest. b. It is better to invest in a scheme that pays 10% annual compound interest. c. Both (a) and (b) provide the same return 3.3 Given an investment of Rs. 10,000 for a period of one year, it is better to invest in a scheme that pays: a. 12% interest compounded annually b. 12% interest compounded quarterly c. 12% interest compounded monthly d. 12% interest compounded daily 3.4 Given an investment of Rs. 10,000 over a period of two years, it is better to invest in a scheme that pays; a. 10% interest in the first year and 12% in second year. b. 12% interest in the first year and 10% in second year. c. Both (a) and (b) above provide the same return 3.5 The rule of 72 is used to find;a. Approximate doubling period, given the interest rate (r) b. Approximate interest rate, given the doubling period (n) c. Both (a) and (b) above. 3.6 The relation between effective annual rate of interest (re) and nominal rate of interest (r) is best represented by; a. re = (1 + r /m)mn –1 b. re = (1 + r/m)m –1 c. r = (1 + re/m) –1 d. None of the above 3.7 To find the present value of a sum of Rs. 10,000 to be received at the end of each year for the next 5 years at 10% rate, we use: a. Present value of a single cash flow table b. Present value of annuity table. c. Future value of a single cash flow table d. Future value of annuity table 3.8 Sinking fund factor is the reciprocal of : a. Present value interest factor of a single cash flow. b. Present value interest factor of an annuity. c. Future value interest factor of a single cash flow. d. Future value interest factor of an annuity. 3.9 According to the 'Rule of 69' doubling period of an investment at an interest rate of 15% is : a. 4.6 years b. 4.2 years c. 4.95 years d. 5.25 years 3.10 If the effective rate of interest compounded quarterly is 16%, then the nominal rate of interest is : a. 14.6% b. 15% c. 14.8% d. 15.12% 3.11 If the interest rate on a loan is 1% per month, the effective annual rate of interest is : a. 12% b. 12.36%c. 12.68% d. 12.84% 3.12 If a loan of Rs. 30,000 is to be paid in 5 annual installments with interest rate of 12% p.a. then the equal annual installment will be; a. Rs. 7400 b. Rs. 8100 c. Rs 7812 d. Rs. 8322 3.13 X took a housing loan of Rs. 25,00,000. The loan is to be redeemed in 120 monthly installments of Rs. 31,000 each to be paid at the end of each month. What is the implied interest rate per annum. a. 8.50% b. 8.1% c. 7.70% d. 9.12% 3.14 The difference between effective annual rate of interest with monthly and quarterly compounding, when nominal rate of interest is 10% is; a. 0.10% b. 0.14% c. 0.21% d. 0.09% 3.15 A bond has a face value of Rs. 1000 and a coupon rate of 10%. It will be redeemed after 4 years at 10% premium. Find the present value of bond at a required rate of 12% : a. Rs. 1002.80 b. Rs. 960.72 c. Rs. 980.84 d. Rs. 1020.12 3.16 Axis bank offers 10% nominal interest for a three year fixed deposit to senior citizens. If the compounding is done quarterly, then effective annual rate of interest is : a. 10.25% b. 10.38% c. 10.46% d. 10.52% 3.17 X deposits Rs. 2500 at the end of every month in a bank for 5 years. If the interest rate offered bybank is 8% p.a. compounded monthly, the accumulated sum X will get after 5 years will be: a. Rs. 1,76,802 b. Rs. 1,83,692 c. Rs. 1,91,507 d. Rs. 1,94,752 3.18 You invest Rs. 1500 at the end of year one and Rs. 2000 at the end of second year and Rs. 5000 each year from third to tenth. Find the present value of stream at discount rate of 10% a. Rs. 25,062 b. Rs. 24,712 c. Rs. 26,502 d. Rs. 24,242 3.19 If you take a loan of Rs 1,00,000 today and return Rs. 1,51,807 after 4 years to clear off the loan, what effective annual interest rate is paid by you: a. 12% b. 13% c. 11% d. 12.4% 3.20 In how much period Rs. 1 becomes Rs. 3 at 12% rate of interest compounded annually. a. 12 years c. 10.42 years b. 8 years d. 9.69 years 3.21 Which of the following statements is true? a. Frequency of compounding, has no effect on rate of interest. b. An annuity is a series of cash flows of variable amount. c. The nominal rate of interest is equal to or more than the effective rate of interest. d. Cash flows occurring in different time periods cannot be compared unless they are discounted to a common date. 3.22 If a 12% loan is to be paid back after 10 years, the sinking fund factor will be equal to: a. 0.03471b. 0.05698 c. 0.04231 d. 0.09109 3.23 Mr X has decided to deposit Rs. 70,000 per year in his public provident fund account for next 15 years. At 8% interest compounded annually, how much money will accumulate in his accounts? a. Rs. 19,00,648 b. Rs. 20,14,340 c. Rs. 16,05,151 d. Rs. 19,91, 243 3.24 If a bank offers to double your money in 8 years, what is the effective rate of interest? a. 8.9% b. 9.7% c. 10.2% d. 9.05% 3.25 An investment of Rs.5000 in a deep discount bond will return Rs. 1,00,000 in 20 years. Find the interest rate implicit in the offer? a. 16.72% b. 15.234% c. 17.121% d. 16.159% 3.26 A machine is to be replaced after 5 years, when it is expected to cost Rs. 10,00,000. How much equal sum should be set aside and invested, at the end of each year at 12% p.a. to accumulate the desired sum? a. Rs. 1,62,416 b. Rs. 1,57,410 c. Rs.1,75,115 d. Rs.1,53,429 Answer to Section III 3.1 e 3.2 c 3.3 d 3.4 c 3.5 c 3.6 b 3.7 b 3.8 d 3.9 c 3.10 d 3.11 c 3.12 d 3.13 a 3.14 d 3.15 a 3.16 b 3.17 b 3.18 a 3.19 c 3.20 d3.21 d 3.22 b 3.23 a 3.24 d 3.25 d 3.26 b Time Value of money Work book – Section IV Practical Sums Based on Future (compound) Value and Present (Discount) Value Equation : 4.1 If you invest Rs. 10,000 today for a period of 5 years, what will be its maturity value if the interest rate p.a. is: (a) 8% (b) 10% (c) 12% (d) 15% 4.2 If you invest Rs. 1000 today at interest rate of 10% p.a., what will be its maturity value after 100 years under: (a) Simple interest (b) Compound interest 4.3 How many years will it take for Rs. 5000 invested today at 12% p.a. rate of interest to grow to Rs. 160,000? Use rule of 72. 4.4 In how much period your Rs. 10,000 becomes Rs. 20,000 at 15% rate of interest, using (a) Rule of 72, (b) Rule of 69. 4.5 How much a deposit of Rs. 50,000 grows at the end of 5 years if the nominal rate of interest is 12% p.a. and money is quarterly compounded? Compare this with the amount you get with annual compounding. 4.6 Nominal rate of interest is 12% p.a. Find the effective annual rate of interest when the money is compounded: (a) Annually (b) Semi-annually (c) Quarterly (d) Monthly (e) Daily 4.7 Find the growth rate of sales from 1998 to 2004 from given data: Year 1998 1999 2000 2001 2002 2004 Sales (in million of Rs.) 50 57 68 79 86 99 4.8 A company currently pays a dividend of Rs. 1 per share which is expected to grow to Rs. 3 per share in 10 years. Find the average annual compound growth rate? 4.9 You invest Rs. 3000 today and get Rs. 10,000 after 6 years. What is the implicit interest rate in this? 4.10 If you are given a choice between Rs. 4000 today and Rs. 15,000 after 10 years. Which one will you choose and what your choice implies? 4.11 Find, how much Rs. 10,000 will grow at 8% p.a. nominal rate ofinterest after 3 years when compounding is done: (a) monthly (b) annually (c) perpetually ( continuously). 4.12 What is the present value of Rs. 1,00,000 to be received 10 years from now if rate of interest is 12% p.a.? 4.13 What is the present value of Rs. 50,000 receivable 40 years from now if rate of interest (r) is 8% p.a.? 4.14 What is the present value of following cash flow stream at 10% p.a. rate of interest. Year 0 1 2 3 4 5 Cash flows (in rupees) -10,000 2000 3000 4000 5000 2000 Answer to section IV 4.1 (a) Rs. 14693 (b) Rs. 16105 (c) Rs. 17623 (d) Rs. 20113 4.2 (a) Rs. 11000 (b) Rs. 1,37,80,612 4.3 30 years 4.4 (a) 4.8 years (b) 4.95 years 4.5 Rs. 90305, Rs. 88117 4.6 (a) 12% (b) 12.36% (c) 12.55% (d) 12.68% (e) 12.75% 4.7 12.058 % 4.8 11.612%4.9 22.22% 4.10 14.13% 4.11 (a) Rs. 12702 (b) Rs. 12597 (c) Rs. 12712 4.12 Rs. 32197 4.13 Rs. 2301.54 4.14 Rs. 1959.68 Time Value of Money Workbook – Section V- Questions based on Annuities Future value and Present value of Annuities 5.1 Mr. X deposits Rs. 10,000 at the end of every year for 5 years in his savings account paying 5% p.a. interest. How much money he will get at the end of 5 years? 5.2 Mr. X is planning to buy a car after 5 years when it is expected to cost Rs. 5 Lakh. How much he should save annually to reach his target if his savings earn a compound annual interest rate of 12%? 5.3 A machine is to be replaced after 10 years when it is expected to cost Rs. 10,00,000. How much money should be set aside and invested in a sinking fund at 12% interest p.a. to accumulate the funds needed for replacement? 5.4 X Ltd has Rs. 10,00,000 worth of debentures outstanding. They are to be redeemed 5 years from now. If the interest rate is 12% p.a., how much money should be set aside and invested each year in a sinking fund to accumulate the funds needed for redemption? 5.5 A finance company advertises that it will pay Rs. 1,00,000 at the end of 5th year to any person, who deposits Rs. 16,000 at the end of every year for 5 years. What interest rate is implicit in this offer? 5.6 A travel operator announces that it can take anybody on a world tour at a price of Rs. 2,00,000. I wish to avail this offer. I can save Rs. 25,000 annually and my savings earn 10% p.a. compound interest. How long I will have to wall? 5.7 You expect to receive Rs. 10,000 annually for 3 years at the end of each year. What is its present value at 10% rate?5.8 You can afford to pay Rs. 10,000 per month for 3 years to a finance company for a housing loan. Finance company charges 1% interest per month. How much I can borrow? 5.9 You have borrowed Rs. 10,00,000 from HDFC to finance a house. It charges interest @ 1.25% per month. You can pay Rs. 15,000 per month. What will be the maturity period of loan? 5.10 Your father deposits Rs. 3,00,000 on retirement in a bank which pays 10% p.a. interest compounded annually. How much fixed amount (annuity) he can withdraw annually at the end of every year for 10 years? 5.11 If you deposit Rs. 1,00,000 today, a bank promises to pay you annually Rs. 20,000 for 6 years. What interest rate is implicit in this offer? 5.12 Firm X borrows Rs. 1,000,000 at 15% p.a. interest. The loan is to be paid back in 5 equal annual installments at the end of each year. Find the amount of each equated installment and also make amortization schedule. Answers to Section V 5.1 Rs. 55256 5.2 Rs. 78705 5.3 Rs. 56984 5.4 Rs. 1,57,409.73 5.5 11.18% 5.6 6.167 years 5.7 Rs. 24869 5.8 Rs. 3,01,075 5.9 144 months 5.10 Rs. 48824 5.11 5.47% 5.12 Rs. 298315 Time Value of Money Workbook – Section VI Advance problems on time value of money 6.1 You invest Rs. 3000 a year for 3 years and Rs. 5000 a year for 7 years thereafter at interest rate of 12% p.a. What will be the maturity value at the end of 10 years? . 6.2 A company is offering to pay Rs. 10,000 annually for a period of 10 years, if you deposit Rs 50,000 now. What is implied interest rate in this offer? 6.3 Mr. X receives Rs. 1000 a year for the first 8 years and Rs. 4000 a year forever thereafter. Calculate the PV if interest rate is 12% p.a. 6.4 You invest Rs. 15000 at the end of year 1, Rs 20,000 at the end of year 2 and Rs 50,000 at the end of each year from 3rd year to 10th. Calculate the PV of this stream if the discount rate is 10%. 6.5 Sunil is due to retire 20 years from now. He wants to invest a lump sum now so as to be able to withdraw Rs. 10,000 every year, beginning from the end of the 20th year. How much he should invest now if r = 12%? 6.6 Sunil has deposited Rs 2,00,000 in a bank which pays interest @ 8% p.a. How much can he withdraw at the end of every year for a period of 25 years, so that there is no balance left in the end? 6.7 Mr X is going to retire soon. His employer gives him two options; (a) an annual pension of Rs 8000 for as long as he lives, and(b) a lump sum amount of Rs 50,000. If he expects to live for 20 years and his time preference rate is 10%, which option is better for X? 6.8 How much do you need to invest now at interest rate of 10% p.a. to have a perpetual income of Rs 20,000 from the beginning of the 15th year? 6.9 In order to accumulate Rs. 25000 at the end of 10th year, how much you should invest at the beginning of each year if r = 10%? 6.10 You require Rs 10,000 at the beginning of each year from 10th to 14th year. How much you should invest at the end of each year from 1st to 5th year if interest rate is 10% p.a.? 6.11 Calculate the PV of an annuity of Rs. 5,000 receivable for 35 years, if the first receipt occurs after 15 years. Take discount rate as 12%. 6.12 Akshay takes a bank loan of Rs 10,000 to purchase a scooter. He has to pay an installment of Rs 500 p.m. for next 2 years. What is the implied interest rate? 6.13 As a potential investor you are considering the purchase of a bond that pays 10% per year on face value of Rs 1000. The bond will mature in 5 years at a premium of 5%. What price you should be willing to pay if you require 12% rate of return. 6.14 You deposit a sum of Rs 10,000 with a bank at 12%. If you want to withdraw Rs 1,500 every year, for how long can you do this? 6.15 A Rs 20,00,000 plant expansion is to be financed as follows; 15% down payment and remainder is borrowed at 9% interest. The loan is to be repaid in 8 equal installments starting 4 years from now. Find the amount of each equal annual installment. 6.16 Ten years from now Mr. X will start receiving a pension of Rs 3,000 a year. The payment will continue for 16 years. How much is the pension worth now at 10%? 6.17 You deposit Rs. 4,500 per year at the end of each year for next 25 years in an account that yields 10% p.a. How much you could withdraw at the end of each of the next twenty years following your last deposit? 6.18 A finance company makes an offer that if you deposit Rs 10,000 today, you can receive annual return of Rs 1,100 perpetually, starting from 5th year. Should this offer be accepted if the rate of interest preference is 8% p.a. ? 6.19 A deposit is made in a bank that earns 10% compounded half yearly. It is desired to withdraw Rs 50,000 three years from now and Rs. 70,000 five years from now. What is the size of initial deposit? 6.20 A loan of Rs 1,00,000 is taken on which interest is payable @ 10%. The repayment is to start at the end of 3rd year from now. What should be the annual payment if loan is to be repaid in 6 equal annual installments? 6.21 You want to buy a house costing Rs. 20 lakh. You approach a housing finance company and finance50% of cost. Finance company charges interest @ 1% per month. You can pay Rs. 12,000 per month towards loan amortization. Calculate maturity period of loan. For installment No. 72, calculate interest portion and principal portion. 6.22 Expected cash flows of a project are as follows : Year 0 1 2 3 4 5 Cash flows (in rupees) -10,000 2000 3000 4000 5000 3000 Calculate the present value and future value of the above cash flows at 10%. Also calculate the implicit rate of return. 6.23 Abhijeet borrows Rs. 80,000 for a music system at a monthly interest rate of 1.25%. The loan is to be repaid in 24 equal monthly installments, payable at the beginning of each month. Calculate the amount of each installment? 6.24 Using a discount rate of 10% calculate present value of given cash flows: Year 1 2 3 4 5 6 7 Stream A 1000 2000 3000 4000 5000 6000 7000 Stream B 10,000 9000 8000 7000 6000 5000 4000 Stream C 5,000 5000 5000 5000 5000 5000 5000 6.25 You deposited Rs. 70,000 in your Public Provident Fund A/C for 15 years at 8% interest. How much you will get on maturity. 6.26 You bought a share for Rs. 96 today. After one year, you received a dividend of Rs. 5 on it and sold it for Rs. 105. What is your return on share over a period of one year? 6.27 A finance company offers to triple your money in 10 years. What is the effective rate of interest implicit in the offer? 6.28 To buy your dream car, you can afford to pay Rs. 10,000 per month for 5 years. You call a finance company for loan. It is ready to offer finance over this period at 1% interest per month. How much you can borrow? 6.29 A Russian company has advertised that it can take any person to moon at a cost of $10 million. I can save $5 lakhs every year. How long I will have to wait if my savings earn interest @ 12% p.a. The cost is not likely to change in monetary terms. 6.30 Mr.X borrows Rs. 1,00,000 at 8% interest. Equal annual payments are to be made for 6 years. However at the time of 4th payment, X decides to pay off the entire loan. Find equal annual installment. Also calculate the amount to be paid at the end of 4th year. Answers to Section VI 6.1 Rs.72824 6.2. 15.1% 6.3. Rs.18431 6.4 Rs.250617 6.5 Rs.96756.6 Rs.18736 6.7 option A 6.8 Rs.57933 6.9 Rs.1426 6.10 Rs.4665 611 Rs.8364 6.12 18.15% 6.13 Rs.956.27 6.14 14.2 years 6.15 Rs.397763 6.16 Rs.9954 6.17 Rs.51983 6.18 Yes 6.19 Rs.80285 6.20 Rs.27782.49 6.21 180 months, Rs.7964, Rs.4054 6.22 Rs.2580.6, Rs.4156, 18.69% 6.23 Rs.3831 6.24 Rs.17631, Rs.35921, Rs.24342 6.25 Rs.19,00,648 6.26 14.58% 6.27 11.61% 6.28 Rs.449550 6.29 10.8 years 6.30 Rs.21631.53, Rs.60206 CHAPTER 6 TIME VALUE OF MONEY (Difficulty: E = Easy, M = Medium, and T = Tough) Multiple Choice: Conceptual Easy: PV and discount rate Answer: a Diff: E . You have determined the profitability of a planned project by finding the present value of all the cash flows from that project. Which of the following would cause the project to look more appealing in terms of the present value of those cash flows? a. The discount rate decreases. b. The cash flows are extended over a longer period of time, but the total amount of the cash flows remains the same. c. The discount rate increases. d. Statements b and c are correct. e. Statements a and b are correct. Time value concepts Answer: e Diff: E . Which of the following statements is most correct? a. A 5-year $100 annuity due will have a higher present value than a 5-year $100 ordinary annuity. b. A 15-year mortgage will have larger monthly payments than a 30-year mortgage of the same amount and same interest rate. c. If an investment pays 10 percent interest compounded annually, its effective rate will also be 10 percent. d. Statements a and c are correct. e. All of the statements above are correct. Time value concepts Answer: d Diff: E . The future value of a lump sum at the end of five years is $1,000. The nominal interest rate is 10 percent and interest is compounded semiannually. Which of the following statements is most correct? a. The present value of the $1,000 is greater if interest is compounded monthly rather than semiannually. b. The effective annual rate is greater than 10 percent. c. The periodic interest rate is 5 percent. d. Statements b and c are correct. e. All of the statements above are correct. Time value concepts Answer: d Diff: E . Which of the following statements is most correct? a. The present value of an annuity due will exceed the present value of an ordinary annuity (assuming all else equal). b. The future value of an annuity due will exceed the future value of an ordinary annuity (assuming all else equal). c. The nominal interest rate will always be greater than or equal to the effective annual interest rate. d. Statements a and b are correct. e. All of the statements above are correct. Time value concepts Answer: e Diff: E. Which of the following investments will have the highest future value at the end of 5 years? Assume that the effective annual rate for all investments is the same. a. A pays $50 at the end of every 6-month period for the next 5 years (a total of 10 payments). b. B pays $50 at the beginning of every 6-month period for the next 5 years (a total of 10 payments). c. C pays $500 at the end of 5 years (a total of one payment). d. D pays $100 at the end of every year for the next 5 years (a total of 5 payments). e. E pays $100 at the beginning of every year for the next 5 years (a total of 5 payments). Effective annual rate Answer: b Diff: E . Which of the following bank accounts has the highest effective annual return? a. An account that pays 10 percent nominal interest with monthly com-pounding. b. An account that pays 10 percent nominal interest with daily com-pounding. c. An account that pays 10 percent nominal interest with annual com-pounding. d. An account that pays 9 percent nominal interest with daily com-pounding. e. All of the investments above have the same effective annual return. Effective annual rate Answer: d Diff: E . You are interested in investing your money in a bank account. Which of the following banks provides you with the highest effective rate of interest? a. Bank 1; 8 percent with monthly compounding. b. Bank 2; 8 percent with annual compounding. c. Bank 3; 8 percent with quarterly compounding. d. Bank 4; 8 percent with daily (365-day) compounding. e. Bank 5; 7.8 percent with annual compounding. Amortization Answer: b Diff: E . Your family recently obtained a 30-year (360-month) $100,000 fixed-rate mortgage. Which of the following statements is most correct? (Ignore all taxes and transactions costs.) a. The remaining balance after three years will be $100,000 less the total amount of interest paid during the first 36 months. b. The proportion of the monthly payment that goes towards repayment of principal will be higher 10 years from now than it will be this year. c. The monthly payment on the mortgage will steadily decline over time. d. All of the statements above are correct. e. None of the statements above is correct. Amortization Answer: e Diff: E . Frank Lewis has a 30-year, $100,000 mortgage with a nominal interest rate of 10 percent and monthly compounding. Which of the following statements regarding his mortgage is most correct? a. The monthly payments will decline over time. b. The proportion of the monthly payment that represents interest will be lower for the last payment than for the first payment on the loan. c. The total dollar amount of principal being paid off each month gets larger as the loan approaches maturity. d. Statements a and c are correct. e. Statements b and c are correct. Quarterly compounding Answer: e Diff: E . Your bank account pays an 8 percent nominal rate of interest. The interest is compounded quarterly. Which of the following statements is most correct? a. The periodic rate of interest is 2 percent and the effective rate of interest is 4 percent. b. The periodic rate of interest is 8 percent and the effective rate of interest is greater than 8 percent. c. The periodic rate of interest is 4 percent and the effective rate of interest is 8 percent. d. The periodic rate of interest is 8 percent and the effective rate of interest is 8 percent. e. The periodic rate of interest is 2 percent and the effective rate of interest is greater than 8 percent.Medium: Annuities Answer: c Diff: M . Suppose someone offered you the choice of two equally risky annuities, each paying $10,000 per year for five years. One is an ordinary (or deferred) annuity, the other is an annuity due. Which of the following statements is most correct? a. The present value of the ordinary annuity must exceed the present value of the annuity due, but the future value of an ordinary annuity may be less than the future value of the annuity due. b. The present value of the annuity due exceeds the present value of the ordinary annuity, while the future value of the annuity due is less than the future value of the ordinary annuity. c. The present value of the annuity due exceeds the present value of the ordinary annuity, and the future value of the annuity due also exceeds the future value of the ordinary annuity. d. If interest rates increase, the difference between the present value of the ordinary annuity and the present value of the annuity due remains the same. e. Statements a and d are correct. Time value concepts Answer: e Diff: M . A $10,000 loan is to be amortized over 5 years, with annual end-of-year payments. Given the following facts, which of these statements is most correct? a. The annual payments would be larger if the interest rate were lower. b. If the loan were amortized over 10 years rather than 5 years, and if the interest rate were the same in either case, the first payment would include more dollars of interest under the 5-year amortization plan. c. The last payment would have a higher proportion of interest than the first payment. d. The proportion of interest versus principal repayment would be the same for each of the 5 payments. e. The proportion of each payment that represents interest as opposed to repayment of principal would be higher if the interest rate were higher. Time value concepts Answer: e Diff: M . Which of the following is most correct? a. The present value of a 5-year annuity due will exceed the present value of a 5-year ordinary annuity. (Assume that both annuities pay $100 per period and there is no chance of default.) b. If a loan has a nominal rate of 10 percent, then the effective rate can never be less than 10 percent. c. If there is annual compounding, then the effective, periodic, and nominal rates of interest are all the same. d. Statements a and c are correct. e. All of the statements above are correct. Time value concepts Answer: c Diff: M . Which of the following statements is most correct? a. An investment that compounds interest semiannually, and has a nominal rate of 10 percent, will have an effective rate less than 10 percent. b. The present value of a 3-year $100 annuity due is less than the present value of a 3-year $100 ordinary annuity. c. The proportion of the payment of a fully amortized loan that goes toward interest declines over time. d. Statements a and c are correct. e. None of the statements above is correct. Tough: Time value concepts Answer: e Diff: T . Which of the following statements is most correct? a. The first payment under a 3-year, annual payment, amortized loan for $1,000 will include a smaller percentage (or fraction) of interest if the interest rate is 5 percent than if it is 10 percent. b. If you are lending money, then, based on effective interest rates, you should prefer to lend at a 10 percent nominal, or quoted, rate but with semiannual payments, rather than at a 10.1 percent nominal rate with annual payments. However, as a borrower you should prefer the annual payment loan. c. The value of a perpetuity (say for $100 per year) will approach infinity as the interest rate used toevaluate the perpetuity approaches zero. d. Statements b and c are correct. e. All of the statements above are correct. Multiple Choice: Problems Easy: FV of a sum Answer: b Diff: E . You deposited $1,000 in a savings account that pays 8 percent interest, com¬pounded quarterly, planning to use it to finish your last year in college. Eighteen months later, you decide to go to the Rocky Mountains to become a ski instructor rather than continue in school, so you close out your account. How much money will you receive? a. $1,171 b. $1,126 c. $1,082 d. $1,163 e. $1,008 FV of an annuity Answer: e Diff: E . What is the future value of a 5-year ordinary annuity with annual payments of $200, evaluated at a 15 percent interest rate? a. $ 670.44 b. $ 842.91 c. $1,169.56 d. $1,522.64 e. $1,348.48 FV of an annuity Answer: a Diff: E N . Today is your 23rd birthday. Your aunt just gave you $1,000. You have used the money to open up a brokerage account. Your plan is to contribute an additional $2,000 to the account each year on your birthday, up through and including your 65th birthday, starting next year. The account has an annual expected return of 12 percent. How much do you expect to have in the account right after you make the final $2,000 contribution on your 65th birthday? a. $2,045,442 b. $1,811,996 c. $2,292,895 d. $1,824,502 e. $2,031,435 FV of annuity due Answer: d Diff: E N . Today is Janet’s 23rd birthday. Starting today, Janet plans to begin saving for her retirement. Her plan is to contribute $1,000 to a brokerage account each year on her birthday. Her first contribution will take place today. Her 42nd and final contribution will take place on her 64th birthday. Her aunt has decided to help Janet with her savings, which is why she gave Janet $10,000 today as a birthday present to help get her account started. Assume that the account has an expected annual return of 10 percent. How much will Janet expect to have in her account on her 65th birthday? a. $ 985,703.62 b. $1,034,488.80 c. $1,085,273.98 d. $1,139,037.68 e. $1,254,041.45 PV of an annuity Answer: a Diff: E . What is the present value of a 5-year ordinary annuity with annual payments of $200, evaluated at a 15 percent interest rate?a. $ 670.43 b. $ 842.91 c. $1,169.56 d. $1,348.48 e. $1,522.64 PV of a perpetuity Answer: c Diff: E . You have the opportunity to buy a perpetuity that pays $1,000 annually. Your required rate of return on this investment is 15 percent. You should be essentially indifferent to buying or not buying the investment if it were offered at a price of a. $5,000.00 b. $6,000.00 c. $6,666.67 d. $7,500.00 e. $8,728.50 PV of an uneven CF stream Answer: b Diff: E . A real estate investment has the following expected cash flows: Year Cash Flows 1 $10,000 2 25,000 3 50,000 4 35,000 The discount rate is 8 percent. What is the investment’s present value? a. $103,799 b. $ 96,110 c. $ 95,353 d. $120,000 e. $ 77,592 PV of an uneven CF stream Answer: c Diff: E . Assume that you will receive $2,000 a year in Years 1 through 5, $3,000 a year in Years 6 through 8, and $4,000 in Year 9, with all cash flows to be received at the end of the year. If you require a 14 percent rate of return, what is the present value of these cash flows? a. $ 9,851 b. $13,250 c. $11,714 d. $15,129 e. $17,353 Required annuity payments Answer: b Diff: E . If a 5-year ordinary annuity has a present value of $1,000, and if the interest rate is 10 percent, what is the amount of each annuity payment? a. $240.42 b. $263.80 c. $300.20 d. $315.38 e. $346.87 Quarterly compounding Answer: a Diff: E . If $100 is placed in an account that earns a nominal 4 percent, compounded quarterly, what will it be worth in 5 years? a. $122.02 b. $105.10c. $135.41 d. $120.90 e. $117.48 Growth rate Answer: d Diff: E . In 1958 the average tuition for one year at an Ivy League school was $1,800. Thirty years later, in 1988, the average cost was $13,700. What was the growth rate in tuition over the 30-year period? a. 12% b. 9% c. 6% d. 7% e. 8% Effect of inflationAnswer: c Diff: E . At an inflation rate of 9 percent, the purchasing power of $1 would be cut in half in 8.04 years. How long to the nearest year would it take the purchasing power of $1 to be cut in half if the inflation rate were only 4 percent? a. 12 years b. 15 years c. 18 years d. 20 years e. 23 years Interest rate Answer: b Diff: E . South Penn Trucking is financing a new truck with a loan of $10,000 to be repaid in 5 annual end-ofyear installments of $2,504.56. What annual interest rate is the company paying? a. 7% b. 8% c. 9% d. 10% e. 11% Effective annual rate Answer: c Diff: E . Gomez Electronics needs to arrange financing for its expansion program. Bank A offers to lend Gomez the required funds on a loan in which interest must be paid monthly, and the quoted rate is 8 percent. Bank B will charge 9 percent, with interest due at the end of the year. What is the difference in the effective annual rates charged by the two banks? a. 0.25% b. 0.50% c. 0.70% d. 1.00% e. 1.25% Effective annual rate Answer: b Diff: E . You recently received a letter from Cut-to-the-Chase National Bank that offers you a new credit card that has no annual fee. It states that the annual percentage rate (APR) is 18 percent on outstanding balances. What is the effective annual interest rate? (Hint: Remember these companies bill you monthly.) a. 18.81% b. 19.56% c. 19.25% d. 20.00% e. 18.00% Effective annual rate Answer: b Diff: E . Which of the following investments has the highest effective annual rate (EAR)? (Assume that allCDs are of equal risk.) a. A bank CD that pays 10 percent interest quarterly. b. A bank CD that pays 10 percent monthly. c. A bank CD that pays 10.2 percent annually. d. A bank CD that pays 10 percent semiannually. e. A bank CD that pays 9.6 percent daily (on a 365-day basis). Effective annual rate Answer: c Diff: E . You want to borrow $1,000 from a friend for one year, and you propose to pay her $1,120 at the end of the year. She agrees to lend you the $1,000, but she wants you to pay her $10 of interest at the end of each of the first 11 months plus $1,010 at the end of the 12th month. How much higher is the effective annual rate under your friend’s proposal than under your proposal? a. 0.00% b. 0.45% c. 0.68% d. 0.89% e. 1.00% Effective annual rate Answer: b Diff: E . Elizabeth has $35,000 in an investment account. Her goal is to have the account grow to $100,000 in 10 years without having to make any additional contributions to the account. What effective annual rate of interest would she need to earn on the account in order to meet her goal? a. 9.03% b. 11.07% c. 10.23% d. 8.65% e. 12.32% Effective annual rate Answer: a Diff: E . Which one of the following investments provides the highest effective rate of return? a. An investment that has a 9.9 percent nominal rate and quarterly annual compounding. b. An investment that has a 9.7 percent nominal rate and daily (365) compounding. c. An investment that has a 10.2 percent nominal rate and annual compounding. d. An investment that has a 10 percent nominal rate and semiannual compounding. e. An investment that has a 9.6 percent nominal rate and monthly compounding. Effective annual rate Answer: b Diff: E . Which of the following investments would provide an investor the highest effective annual rate of return? a. An investment that has a 9 percent nominal rate with semiannual compounding. b. An investment that has a 9 percent nominal rate with quarterly compounding. c. An investment that has a 9.2 percent nominal rate with annual compounding. d. An investment that has an 8.9 percent nominal rate with monthly compounding. e. An investment that has an 8.9 percent nominal rate with quarterly compounding. Nominal and effective rates Answer: b Diff: E . An investment pays you 9 percent interest compounded semiannually. A second investment of equal risk, pays interest compounded quarterly. What nominal rate of interest would you have to receive on the second investment in order to make you indifferent between the two investments? a. 8.71% b. 8.90% c. 9.00% d. 9.20% e. 9.31% Time for a sum to double Answer: d Diff: E. You are currently investing your money in a bank account that has a nominal annual rate of 7 percent, compounded monthly. How many years will it take for you to double your money? a. 8.67 b. 9.15 c. 9.50 d. 9.93 e. 10.25 Time for lump sum to grow Answer: e Diff: E N . Jill currently has $300,000 in a brokerage account. The account pays a 10 percent annual interest rate. Assuming that Jill makes no additional contributions to the account, how many years will it take for her to have $1,000,000 in the account? a. 23.33 years b. 3.03 years c. 16.66 years d. 33.33 years e. 12.63 years Time value of money and retirement Answer: b Diff: E . Today, Bruce and Brenda each have $150,000 in an investment account. No other contributions will be made to their investment accounts. Both have the same goal: They each want their account to reach $1 million, at which time each will retire. Bruce has his money invested in risk-free securities with an expected annual return of 5 percent. Brenda has her money invested in a stock fund with an expected annual return of 10 percent. How many years after Brenda retires will Bruce retire? a. 12.6 b. 19.0 c. 19.9 d. 29.4 e. 38.9 Monthly loan payments Answer: c Diff: E . You are considering buying a new car. The sticker price is $15,000 and you have $2,000 to put toward a down payment. If you can negotiate a nominal annual interest rate of 10 percent and you wish to pay for the car over a 5-year period, what are your monthly car payments? a. $216.67 b. $252.34 c. $276.21 d. $285.78 e. $318.71 Remaining loan balance Answer: a Diff: E . A bank recently loaned you $15,000 to buy a car. The loan is for five years (60 months) and is fully amortized. The nominal rate on the loan is 12 percent, and payments are made at the end of each month. What will be the remaining balance on the loan after you make the 30th payment? a. $ 8,611.17 b. $ 8,363.62 c. $14,515.50 d. $ 8,637.38 e. $ 7,599.03 Remaining loan balance Answer: b Diff: E . Robert recently borrowed $20,000 to purchase a new car. The car loan is fully amortized over 4 years. In other words, the loan has a fixed monthly payment, and the loan balance will be zero after the final monthly payment is made. The loan has a nominal interest rate of 12 percent with monthly compounding. Looking ahead, Robert thinks there is a chance that he will want to pay off the loan early, after 3 years (36 months). What will be the remaining balance on the loan after he makes the 36th payment? a. $7,915.56b. $5,927.59 c. $4,746.44 d. $4,003.85 e. $5,541.01 Remaining mortgage balance Answer: c Diff: E . Jerry and Faith Hudson recently obtained a 30-year (360-month), $250,000 mortgage with a 9 percent nominal interest rate. What will be the remaining balance on the mortgage after five years (60 months)? a. $239,024 b. $249,307 c. $239,700 d. $237,056 e. $212,386 Remaining mortgage balance Answer: d Diff: E . You just bought a house and have a $150,000 mortgage. The mortgage is for 30 years and has a nominal rate of 8 percent (compounded monthly). After 36 payments (3 years) what will be the remaining balance on your mortgage? a. $110,376.71 b. $124,565.82 c. $144,953.86 d. $145,920.12 e. $148,746.95 Remaining mortgage balance Answer: d Diff: E . Your family purchased a house three years ago. When you bought the house you financed it with a $160,000 mortgage with an 8.5 percent nominal interest rate (compounded monthly). The mortgage was for 15 years (180 months). What is the remaining balance on your mortgage today? a. $ 95,649 b. $103,300 c. $125,745 d. $141,937 e. $159,998 Remaining mortgage balance Answer: c Diff: E . You recently took out a 30-year (360 months), $145,000 mortgage. The mortgage payments are made at the end of each month and the nominal interest rate on the mortgage is 7 percent. After five years (60 payments), what will be the remaining balance on the mortgage? a. $ 87,119 b. $136,172 c. $136,491 d. $136,820 e. $143,527 Remaining mortgage balance Answer: b Diff: E . A 30-year, $175,000 mortgage has a nominal interest rate of 7.45 percent. Assume that all payments are made at the end of each month. What will be the remaining balance on the mortgage after 5 years (60 monthly payments)? a. $ 63,557 b. $165,498 c. $210,705 d. $106,331 e. $101,942 Amortization Answer: c Diff: E . The Howe family recently bought a house. The house has a 30-year, $165,000 mortgage with monthly payments and a nominal interest rate of 8 percent. What is the total dollar amount of interest the family will pay during the first three years of their mortgage? (Assume that all payments are made at the end of the month.)a. $ 3,297.78 b. $38,589.11 c. $39,097.86 d. $43,758.03 e. $44,589.11 FV under monthly compounding Answer: a Diff: E N . Bill plans to deposit $200 into a bank account at the end of every month. The bank account has a nominal interest rate of 8 percent and interest is compounded monthly. How much will Bill have in the account at the end of 2½ years (30 months)? a. $ 6,617.77 b. $ 502.50 c. $ 6,594.88 d. $22,656.74 e. $ 5,232.43 Medium: Monthly vs. quarterly compounding Answer: c Diff: M . On its savings accounts, the First National Bank offers a 5 percent nominal interest rate that is compounded monthly. Savings accounts at the Second National Bank have the same effective annual return, but interest is compounded quarterly. What nominal rate does the Second National Bank offer on its savings accounts? a. 5.12% b. 5.00% c. 5.02% d. 1.28% e. 5.22% Present value Answer: c Diff: M N . Which of the following securities has the largest present value? Assume in all cases that the annual interest rate is 8 percent and that there are no taxes. a. A five-year ordinary annuity that pays you $1,000 each year. b. A five-year zero coupon bond that has a face value of $7,000. c. A preferred stock issue that pays an $800 annual dividend in perpetuity. (Assume that the first dividend is received one year from today.) d. A seven-year zero coupon bond that has a face value of $8,500. e. A security that pays you $1,000 at the end of 1 year, $2,000 at the end of 2 years, and $3,000 at the end of 3 years. PV under monthly compounding Answer: b Diff: M . You have just bought a security that pays $500 every six months. The security lasts for 10 years. Another security of equal risk also has a maturity of 10 years, and pays 10 percent compounded monthly (that is, the nominal rate is 10 percent). What should be the price of the security that you just purchased? a. $6,108.46 b. $6,175.82 c. $6,231.11 d. $6,566.21 e. $7,314.86 PV under non-annual compoundingAnswer: c Diff: M . You have been offered an investment that pays $500 at the end of every 6 months for the next 3 years. The nominal interest rate is 12 percent; however, interest is compounded quarterly. What is the present value of the investment? a. $2,458.66 b. $2,444.67c. $2,451.73 d. $2,463.33 e. $2,437.56 PV of an annuity Answer: a Diff: M . Your subscription to Jogger’s World Monthly is about to run out and you have the choice of renewing it by sending in the $10 a year regular rate or of getting a lifetime subscription to the magazine by paying $100. Your cost of capital is 7 percent. How many years would you have to live to make the lifetime subscription the better buy? Payments for the regular subscription are made at the beginning of each year. (Round up if necessary to obtain a whole number of years.) a. 15 years b. 10 years c. 18 years d. 7 years e. 8 years FV of an annuity Answer: e Diff: M . Your bank account pays a nominal interest rate of 6 percent, but interest is compounded daily (on a 365-day basis). Your plan is to deposit $500 in the account today. You also plan to deposit $1,000 in the account at the end of each of the next three years. How much will you have in the account at the end of three years, after making your final deposit? a. $2,591 b. $3,164 c. $3,500 d. $3,779 e. $3,788 FV of an annuity Answer: c Diff: M . Terry Austin is 30 years old and is saving for her retirement. She is planning on making 36 contributions to her retirement account at the beginning of each of the next 36 years. The first contribution will be made today (t = 0) and the final contribution will be made 35 years from today (t = 35). The retirement account will earn a return of 10 percent a year. If each contribution she makes is $3,000, how much will be in the retirement account 35 years from now (t = 35)? a. $894,380 b. $813,073 c. $897,380 d. $987,118 e. $978,688 FV of an annuity Answer: d Diff: M N . Today is your 20th birthday. Your parents just gave you $5,000 that you plan to use to open a stock brokerage account. Your plan is to add $500 to the account each year on your birthday. Your first $500 contribution will come one year from now on your 21st birthday. Your 45th and final $500 contribution will occur on your 65th birthday. You plan to withdraw $5,000 from the account five years from now on your 25th birthday to take a trip to Europe. You also anticipate that you will need to withdraw $10,000 from the account 10 years from now on your 30th birthday to take a trip to Asia. You expect that the account will have an average annual return of 12 percent. How much money do you anticipate that you will have in the account on your 65th birthday, following your final contribution? a. $385,863 b. $413,028 c. $457,911 d. $505,803 e. $566,498 FV of annuity due Answer: d Diff: M . You are contributing money to an investment account so that you can purchase a house in five years. You plan to contribute six payments of $3,000 a year. The first payment will be made today (t = 0) and the final payment will be made five years from now (t = 5). If you earn11 percent in your investment account, how much money will you have in the account five years from now (at t = 5)? a. $19,412 b. $20,856 c. $21,683 d. $23,739 e. $26,350 FV of annuity due Answer: e Diff: M . Today is your 21st birthday, and you are opening up an investment account. Your plan is to contribute $2,000 per year on your birthday and the first contribution will be made today. Your 45th, and final, contribution will be made on your 65th birthday. If you earn 10 percent a year on your investments, how much money will you have in the account on your 65th birthday, immediately after making your final contribution? a. $1,581,590.64 b. $1,739,749.71 c. $1,579,590.64 d. $1,387,809.67 e. $1,437,809.67 FV of a sum Answer: d Diff: M . Suppose you put $100 into a savings account today, the account pays a nominal annual interest rate of 6 percent, but compounded semiannually, and you withdraw $100 after 6 months. What would your ending balance be 20 years after the initial $100 deposit was made? a. $226.20 b. $115.35 c. $ 62.91 d. $ 9.50 e. $ 3.00 FV under monthly compounding Answer: e Diff: M . You just put $1,000 in a bank account that pays 6 percent nominal annual interest, compounded monthly. How much will you have in your account after 3 years? a. $1,006.00 b. $1,056.45 c. $1,180.32 d. $1,191.00 e. $1,196.68 FV under monthly compounding Answer: d Diff: M . Steven just deposited $10,000 in a bank account that has a 12 percent nominal interest rate, and the interest is compounded monthly. Steven also plans to contribute another $10,000 to the account one year (12 months) from now and another $20,000 to the account two years from now. How much will be in the account three years (36 months) from now? a. $57,231 b. $48,993 c. $50,971 d. $49,542 e. $49,130 FV under daily compounding Answer: a Diff: M . You have $2,000 invested in a bank account that pays a 4 percent nominal annual interest with daily compounding. How much money will you have in the account at the end of July (in 132 days)? (Assume there are 365 days in each year.) a. $2,029.14 b. $2,028.93 c. $2,040.00d. $2,023.44 e. $2,023.99 FV under daily compounding Answer: d Diff: M N . The Martin family recently deposited $1,000 in a bank account that pays a 6 percent nominal interest rate. Interest in the account will be compounded daily (365 days = 1 year). How much will they have in the account after 5 years? a. $1,000.82 b. $1,433.29 c. $1,338.23 d. $1,349.82 e. $1,524.77 FV under non-annual compoundingAnswer: d Diff: M . Josh and John (2 brothers) are each trying to save enough money to buy their own cars. Josh is planning to save $100 from every paycheck. (He is paid every 2 weeks.) John plans to put aside $150 each month but has already saved $1,500. Interest rates are currently quoted at 10 percent. Josh’s bank compounds interest every two weeks while John’s bank compounds interest monthly. At the end of 2 years they will each spend all their savings on a car. (Each brother will buy a car.) What is the price of the most expensive car purchased? a. $5,744.29 b. $5,807.48 c. $5,703.02 d. $5,797.63 e. $5,898.50 FV under quarterly compounding Answer: c Diff: M . An investment pays $100 every six months (semiannually) over the next 2.5 years. Interest, however, is compounded quarterly, at a nominal rate of 8 percent. What is the future value of the investment after 2.5 years? a. $520.61 b. $541.63 c. $542.07 d. $543.98 e. $547.49 FV under quarterly compounding Answer: d Diff: M . Rachel wants to take a trip to England in 3 years, and she has started a savings account today to pay for the trip. Today (8/1/02) she made an initial deposit of $1,000. Her plan is to add $2,000 to the account one year from now (8/1/03) and another $3,000 to the account two years from now (8/1/04). The account has a nominal interest rate of 7 percent, but the interest is compounded quarterly. How much will Rachel have in the account three years from today (8/1/05)? a. $6,724.84 b. $6,701.54 c. $6,895.32 d. $6,744.78 e. $6,791.02 Non-annual compounding Answer: c Diff: M N . Katherine wants to open a savings account, and she has obtained account information from two banks. Bank A has a nominal annual rate of 9 percent, with interest compounded quarterly. Bank B offers the same effective annual rate, but it compounds interest monthly. What is the nominal annual rate of return for a savings account from Bank B? a. 8.906% b. 8.920% c. 8.933%d. 8.951% e. 9.068% FV of an uneven CF stream Answer: e Diff: M . You are interested in saving money for your first house. Your plan is to make regular deposits into a brokerage account that will earn 14 percent. Your first deposit of $5,000 will be made today. You also plan to make four additional deposits at the beginning of each of the next four years. Your plan is to increase your deposits by 10 percent a year. (That is, you plan to deposit $5,500 at t = 1, and $6,050 at t = 2, etc.) How much money will be in your account after five years? a. $24,697.40 b. $30,525.00 c. $32,485.98 d. $39,362.57 e. $44,873.90 FV of an uneven CF stream Answer: d Diff: M . You just graduated, and you plan to work for 10 years and then to leave for the Australian “Outback” bush country. You figure you can save $1,000 a year for the first 5 years and $2,000 a year for the next 5 years. These savings cash flows will start one year from now. In addition, your family has just given you a $5,000 graduation gift. If you put the gift now, and your future savings when they start, into an account that pays 8 percent compounded annually, what will your financial “stake” be when you leave for Australia 10 years from now? a. $21,432 b. $28,393 c. $16,651 d. $31,148 e. $20,000 FV of an uneven CF stream Answer: c Diff: M N . Erika opened a savings account today and she immediately put $10,000 into it. She plans to contribute another $20,000 one year from now, and $50,000 two years from now. The savings account pays a 6 percent annual interest rate. If she makes no other deposits or withdrawals, how much will she have in the account 10 years from today? a. $ 8,246.00 b. $116,937.04 c. $131,390.46 d. $164,592.62 e. $190,297.04 PV of an uneven CF stream Answer: a Diff: M . You are given the following cash flows. What is the present value (t = 0) if the discount rate is 12 percent? 0 1 2 3 4 5 6 Periods | | | | | | | 0 1 2,000 2,000 2,000 0 -2,000 a. $3,277 b. $4,804 c. $5,302 d. $4,289 e. $2,804 PV of uncertain cash flows Answer: e Diff: M . A project with a 3-year life has the following probability distributions for possible end-of-year cash flows in each of the next three years:Year 1 Year 2 Year 3 Prob Cash Flow Prob Cash Flow Prob Cash Flow 0.30 $300 0.15 $100 0.25 $200 0.40 500 0.35 200 0.75 800 0.30 700 0.35 600 0.15 900 Using an interest rate of 8 percent, find the expected present value of these uncertain cash flows. (Hint: Find the expected cash flow in each year, then evaluate those cash flows.) a. $1,204.95 b. $ 835.42 c. $1,519.21 d. $1,580.00 e. $1,347.61 Value of missing cash flow Answer: d Diff: M . Foster Industries has a project that has the following cash flows: Year Cash Flow 0 -$300.00 1 100.00 2 125.43 3 90.12 4 ? What cash flow will the project have to generate in the fourth year in order for the project to have a 15 percent rate of return? a. $ 15.55 b. $ 58.95 c. $100.25 d. $103.10 e. $150.75 Value of missing cash flow Answer: c Diff: M . John Keene recently invested $2,566.70 in a project that is promising to return 12 percent per year. The cash flows are expected to be as follows: End of Year Cash Flow 1 $325 2 400 3 550 4 ? 5 750 6 800 What is the cash flow at the end of the 4th year? a. $1,187 b. $ 600 c. $1,157 d. $ 655 e. $1,267 Value of missing payments Answer: d Diff: M . You recently purchased a 20-year investment that pays you $100 at t = 1, $500 at t = 2, $750 at t = 3, and some fixed cash flow, X, at the end of each of the remaining 17 years. You purchased the investment for $5,544.87. Alternative investments of equal risk have a required return of 9 percent. What is the annual cash flow received at the end of each of the final 17 years, that is, what is X? a. $600b. $625 c. $650 d. $675 e. $700 Value of missing payments Answer: c Diff: M . A 10-year security generates cash flows of $2,000 a year at the end of each of the next three years (t = 1, 2, and 3). After three years, the security pays some constant cash flow at the end of each of the next six years (t = 4, 5, 6, 7, 8, and 9). Ten years from now (t = 10) the security will mature and pay $10,000. The security sells for $24,307.85 and has a yield to maturity of 7.3 percent. What annual cash flow does the security pay for years 4 through 9? a. $2,995 b. $3,568 c. $3,700 d. $3,970 e. $4,296 Value of missing payments Answer: d Diff: M . An investment costs $3,000 today and provides cash flows at the end of each year for 20 years. The investment’s expected return is 10 percent. The projected cash flows for Years 1, 2, and 3 are $100, $200, and $300, respectively. What is the annual cash flow received for each of Years 4 through 20 (17 years)? (Assume the same payment for each of these years.) a. $285.41 b. $313.96 c. $379.89 d. $417.87 e. $459.66 Amortization Answer: c Diff: M . If you buy a factory for $250,000 and the terms are 20 percent down, the balance to be paid off over 30 years at a 12 percent rate of interest on the unpaid balance, what are the 30 equal annual payments? a. $20,593 b. $31,036 c. $24,829 d. $50,212 e. $ 6,667 Amortization Answer: a Diff: M . You have just taken out an installment loan for $100,000. Assume that the loan will be repaid in 12 equal monthly installments of $9,456 and that the first payment will be due one month from today. How much of your third monthly payment will go toward the repayment of principal? a. $7,757.16 b. $6,359.12 c. $7,212.50 d. $7,925.88 e. $8,333.33 Amortization Answer: c Diff: M . A homeowner just obtained a $90,000 mortgage. The mortgage is for 30 years (360 months) and has a fixed nominal annual rate of 9 percent, with monthly payments. What percentage of the total payments made the first two years will go toward payment of interest? a. 89.30% b. 91.70% c. 92.59% d. 93.65% e. 94.76%Amortization Answer: e Diff: M . You recently obtained a $135,000, 30-year mortgage with a nominal interest rate of 7.25 percent. Assume that payments are made at the end of each month. What portion of the total payments made during the fourth year will go towards the repayment of principal? a. 9.70% b. 15.86% c. 13.75% d. 12.85% e. 14.69% Amortization Answer: b Diff: M . John and Peggy recently bought a house, and they financed it with a $125,000, 30-year mortgage with a nominal interest rate of 7 percent. Mortgage payments are made at the end of each month. What portion of their mortgage payments during the first three years will go towards repayment of principal? a. 12.81% b. 13.67% c. 14.63% d. 15.83% e. 17.14% Amortization Answer: b Diff: M N . The Taylor family has a $250,000 mortgage. The mortgage is for 15 years, and has a nominal rate of 8 percent. Mortgage payments are due at the end of each month. What percentage of the monthly payments during the fifth year goes towards repayment of principal? a. 46.60% b. 43.16% c. 57.11% d. 19.32% e. 56.84% Remaining mortgage balance Answer: b Diff: M N . The Bunker Family recently entered into a 30-year mortgage for $300,000. The mortgage has an 8 percent nominal interest rate. Interest is compounded monthly, and all payments are due at the end of the month. What will be the remaining balance on the mortgage after five years? a. $ 14,790.43 b. $285,209.57 c. $300,000.00 d. $366,177.71 e. $298,980.02 Remaining loan balance Answer: d Diff: M . Jamie and Jake each recently bought a different new car. Both received a loan from a local bank. Both loans have a nominal interest rate of 12 percent with payments made at the end of each month, are fully amortizing, and have the same monthly payment. Jamie’s loan is for $15,000; however, his loan matures at the end of 4 years (48 months), while Jake’s loan matures in 5 years (60 months). After 48 months Jamie’s loan will be paid off. At the end of 48 months what will be the remaining balance on Jake’s loan? a. $ 1,998.63 b. $ 2,757.58 c. $ 3,138.52 d. $ 4,445.84 e. $11,198.55 Effective annual rate Answer: b Diff: M . If it were evaluated with an interest rate of 0 percent, a 10-year regular annuity would have a present value of $3,755.50. If the future (compounded) value of this annuity, evaluated at Year 10, is $5,440.22, what effective annual interest rate must the analyst be using to find the future value?a. 7% b. 8% c. 9% d. 10% e. 11% Effective annual rate Answer: d Diff: M . Steaks Galore needs to arrange financing for its expansion program. One bank offers to lend the required $1,000,000 on a loan that requires interest to be paid at the end of each quarter. The quoted rate is 10 percent, and the principal must be repaid at the end of the year. A second lender offers 9 percent, daily compounding (365-day year), with interest and principal due at the end of the year. What is the difference in the effective annual rates (EFF%) charged by the two banks? a. 0.31% b. 0.53% c. 0.75% d. 0.96% e. 1.25% Effective annual rate Answer: e Diff: M . You have just taken out a 10-year, $12,000 loan to purchase a new car. This loan is to be repaid in 120 equal end-of-month installments. If each of the monthly installments is $150, what is the effective annual interest rate on this car loan? a. 6.5431% b. 7.8942% c. 8.6892% d. 8.8869% e. 9.0438% Nominal vs. effective annual rate Answer: b Diff: M N . Gilhart First National Bank offers an investment security with a 7.5 percent nominal annual return, compounded quarterly. Gilhart’s competitor, Olsen Savings and Loan, is offering a similar security that bears the same risk and same effective rate of return. However, Olsen’s security pays interest monthly. What is the nominal annual return of the security offered by Olsen? a. 7.39% b. 7.45% c. 7.50% d. 7.54% e. 7.59% Effective annual rate and annuities Answer: d Diff: M . You plan to invest $5,000 at the end of each of the next 10 years in an account that has a 9 percent nominal rate with interest compounded monthly. How much will be in your account at the end of the 10 years? a. $ 75,965 b. $967,571 c. $ 84,616 d. $ 77,359 e. $ 80,631 Value of a perpetuity Answer: c Diff: M . You are willing to pay $15,625 to purchase a perpetuity that will pay you and your heirs $1,250 each year, forever. If your required rate of return does not change, how much would you be willing to pay if this were a 20-year annual payment, ordinary annuity instead of a perpetuity? a. $10,342 b. $11,931 c. $12,273 d. $13,922e. $17,157 EAR and FV of an annuityAnswer: b Diff: M . An investment pays you $5,000 at the end of each of the next five years. Your plan is to invest the money in an account that pays 8 percent interest, compounded monthly. How much will you have in the account after receiving the final $5,000 payment in 5 years (60 months)? a. $ 25,335.56 b. $ 29,508.98 c. $367,384.28 d. $304,969.90 e. $ 25,348.23 Required annuity payments Answer: c Diff: M . A baseball player is offered a 5-year contract that pays him the following amounts: Year 1: $1.2 million Year 2: 1.6 million Year 3: 2.0 million Year 4: 2.4 million Year 5: 2.8 million Under the terms of the agreement all payments are made at the end of each year. Instead of accepting the contract, the baseball player asks his agent to negotiate a contract that has a present value of $1 million more than that which has been offered. Moreover, the player wants to receive his payments in the form of a 5-year annuity due. All cash flows are discounted at 10 percent. If the team were to agree to the player’s terms, what would be the player’s annual salary (in millions of dollars)? a. $1.500 b. $1.659 c. $1.989 d. $2.343 e. $2.500 Required annuity payments Answer: b Diff: M . Karen and her twin sister, Kathy, are celebrating their 30th birthday today. Karen has been saving for her retirement ever since their 25th birthday. On their 25th birthday, she made a $5,000 contribution to her retirement account. Every year thereafter on their birthday, she has added another $5,000 to the account. Her plan is to continue contributing $5,000 every year on their birthday. Her 41st, and final, $5,000 contribution will occur on their 65th birthday. So far, Kathy has not saved anything for her retirement but she wants to begin today. Kathy’s plan is to also contribute a fixed amount every year. Her first contribution will occur today, and her 36th, and final, contribution will occur on their 65th birthday. Assume that both investment accounts earn an annual return of 10 percent. How large does Kathy’s annual contribution have to be for her to have the same amount in her account at age 65, as Karen will have in her account at age 65? a. $9,000.00 b. $8,154.60 c. $7,398.08 d. $8,567.20 e. $7,933.83 Required annuity payments Answer: c Diff: M . Jim and Nancy just got married today. They want to start saving so they can buy a house five years from today. The average house in their town today sells for $120,000. Housing prices are expected to increase 3 percent a year. When they buy their house five years from now, Jim and Nancy expect to get a 30-year (360- month) mortgage with a 7 percent nominal interest rate. They want the monthly payment on their mortgage to be $500 a month.Jim and Nancy want to buy an average house in their town. They are starting to save today for a down payment on the house. The down payment plus the mortgage will equal the expected price of the house. Their plan is to deposit $2,000 in a brokerage account today and then deposit a fixed amount at the end of each of the next five years. Assuming that the brokerage account has an annual return of 10 percent, how much do Jim and Nancy need to deposit at the end of each year in order to accomplish their goal? a. $10,634 b. $ 9,044 c. $ 9,949 d. $ 9,421 e. $34,569 Required annuity payments Answer: a Diff: M N . Today is your 25th birthday. Your goal is to have $2 million by the time you retire at age 65. So far you have nothing saved, but you plan on making the first contribution to your retirement account today. You plan on making three other contributions to the account, one at age 30, age 35, and age 40. Since you expect that your income will increase rapidly over the next several years, the amount that you contribute at age 30 will be double what you contribute today, the amount at age 35 will be three times what you contribute today, and the amount at age 40 will be four times what you contribute today. Assume that your investments will produce an average annual return of 10 percent. Given your goal and plan, what is the minimum amount you need to contribute to your account today? a. $10,145 b. $10,415 c. $10,700 d. $10,870 e. $11,160 NPV and non-annual discounting Answer: b Diff: M . Your lease calls for payments of $500 at the end of each month for the next 12 months. Now your landlord offers you a new 1-year lease that calls for zero rent for 3 months, then rental payments of $700 at the end of each month for the next 9 months. You keep your money in a bank time deposit that pays a nominal annual rate of 5 percent. By what amount would your net worth change if you accept the new lease? (Hint: Your return per month is 5%/12 = 0.4166667%.) a. -$509.81 b. -$253.62 c. +$125.30 d. +$253.62 e. +$509.81 Tough: PV of an uneven CF stream Answer: c Diff: T . Find the present value of an income stream that has a negative flow of $100 per year for 3 years, a positive flow of $200 in the 4th year, and a positive flow of $300 per year in Years 5 through 8. The appropriate discount rate is 4 percent for each of the first 3 years and 5 percent for each of the later years. Thus, a cash flow accruing in Year 8 should be discounted at 5 percent for some years and 4 percent in other years. All payments occur at year-end. a. $ 528.21 b. $1,329.00 c. $ 792.49 d. $1,046.41 e. $ 875.18 PV of an uneven CF stream Answer: d Diff: T . Hillary is trying to determine the cost of health care to college students and parents’ ability to cover those costs. She assumes that the cost of one year of health care for a college student is $1,000 today, that the average student is 18 when he or she enters college, that inflation in health care cost is rising at the rate of 10 percent per year, and that parents can save $100 per year to help cover their children’s costs. All payments occur at the end of the relevant period, and the $100/year savings will stop the day the child enters college(hence 18 payments will be made). Savings can be invested at a nominal rate of 6 percent, annual compounding. Hillary wants a health care plan that covers the fully inflated cost of health care for a student for 4 years, during Years 19 through 22 (with payments made at the end of Years 19 through 22). How much would the government have to set aside now (when a child is born), to supplement the average parent’s share of a child’s college health care cost? The lump sum the government sets aside will also be invested at 6 percent, annual compounding. a. $1,082.76 b. $3,997.81 c. $5,674.23 d. $7,472.08 e. $8,554.84 Required annuity payments Answer: b Diff: T . You are saving for the college education of your two children. One child will enter college in 5 years, while the other child will enter college in 7 years. College costs are currently $10,000 per year and are expected to grow at a rate of 5 percent per year. All college costs are paid at the beginning of the year. You assume that each child will be in college for four years. You currently have $50,000 in your educational fund. Your plan is to contribute a fixed amount to the fund over each of the next 5 years. Your first contribution will come at the end of this year, and your final contribution will come at the date when you make the first tuition payment for your oldest child. You expect to invest your contributions into various investments, which are expected to earn 8 percent per year. How much should you contribute each year in order to meet the expected cost of your children’s education? a. $2,894 b. $3,712 c. $4,125 d. $5,343 e. $6,750 Required annuity payments Answer: b Diff: T . A young couple is planning for the education of their two children. They plan to invest the same amount of money at the end of each of the next 16 years. The first contribution will be made at the end of the year and the final contribution will be made at the end of the year the older child enters college. The money will be invested in securities that are certain to earn a return of 8 percent each year. The older child will begin college in 16 years and the second child will begin college in 18 years. The parents anticipate college costs of $25,000 a year (per child). These costs must be paid at the end of each year. If each child takes four years to complete their college degrees, then how much money must the couple save each year? a. $ 9,612.10 b. $ 5,477.36 c. $12,507.29 d. $ 5,329.45 e. $ 4,944.84 Required annuity payments Answer: c Diff: T . Your father, who is 60, plans to retire in 2 years, and he expects to live independently for 3 years. He wants a retirement income that has, in the first year, the same purchasing power as $40,000 has today. However, his retirement income will be a fixed amount, so his real income will decline over time. His retirement income will start the day he retires, 2 years from today, and he will receive a total of 3 retirement payments. Inflation is expected to be constant at 5 percent. Your father has $100,000 in savings now, and he can earn 8 percent on savings now and in the future. How much must he save each year, starting today, to meet his retirement goals? a. $1,863 b. $2,034 c. $2,716d. $5,350 e. $6,102 Required annuity payments Answer: d Diff: T . Your father, who is 60, plans to retire in 2 years, and he expects to live independently for 3 years. Suppose your father wants to have a real income of $40,000 in today’s dollars in each year after he retires. His retirement income will start the day he retires, 2 years from today, and he will receive a total of 3 retirement payments. Inflation is expected to be constant at 5 percent. Your father has $100,000 in savings now, and he can earn 8 percent on savings now and in the future. How much must he save each year, starting today, to meet his retirement goals? a. $1,863 b. $2,034 c. $2,716 d. $5,350 e. $6,102 Required annuity payments Answer: c Diff: T . You are considering an investment in a 40-year security. The security will pay $25 a year at the end of each of the first three years. The security will then pay $30 a year at the end of each of the next 20 years. The nominal interest rate is assumed to be 8 percent, and the current price (present value) of the security is $360.39. Given this information, what is the equal annual payment to be received from Year 24 through Year 40 (for 17 years)? a. $35 b. $38 c. $40 d. $45 e. $50 Required annuity payments Answer: a Diff: T . John and Jessica are saving for their child’s education. Their daughter is currently eight years old and will be entering college 10 years from now (t = 10). College costs are currently $15,000 a year and are expected to increase at a rate of 5 percent a year. They expect their daughter to graduate in four years, and that all annual payments will be due at the beginning of each year (t = 10, 11, 12, and 13). Right now, John and Jessica have $5,000 in their college savings account. Starting today, they plan to contribute $3,000 a year at the beginning of each of the next five years (t = 0, 1, 2, 3, and 4). Then their plan is to make six equal annual contributions at the end of each of the following six years (t = 5, 6, 7, 8, 9, and 10). Their investment account is expected to have an annual return of 12 percent. How large of an annual payment do they have to make in the subsequent six years (t = 5, 6, 7, 8, 9, and 10) in order to meet their child’s anticipated college costs? a. $4,411 b. $7,643 c. $2,925 d. $8,015 e. $6,798 Required annuity payments Answer: a Diff: T . Today is Rachel’s 30th birthday. Five years ago, Rachel opened a brokerage account when her grandmother gave her $25,000 for her 25th birthday. Rachel added $2,000 to this account on her 26th birthday, $3,000 on her 27th birthday, $4,000 on her 28th birthday, and $5,000 on her 29th birthday. Rachel’s goal is to have $400,000 in the account by her 40th birthday. Starting today, she plans to contribute a fixed amount to the account each year on her birthday. She will make 11 contributions, the first one will occur today, and the final contribution will occur on her 40th birthday. Complicating things somewhat is the fact that Rachel plans to withdraw $20,000 from the account on her 35th birthday to finance the down payment on a home. How large does each of these 11 contributions have to befor Rachel to reach her goal? Assume that the account has earned (and will continue to earn) an effective return of 12 percent a year. a. $11,743.95 b. $10,037.46 c. $11,950.22 d. $14,783.64 e. $ 9,485.67 Required annuity payments Answer: c Diff: T . John is saving for his retirement. Today is his 40th birthday. John first started saving when he was 25 years old. On his 25th birthday, John made the first contribution to his retirement account; he deposited $2,000 into an account that paid 9 percent interest, compounded monthly. Each year on his birthday, John contributes another $2,000 to the account. The 15th (and last) contribution was made last year on his 39th birthday. John wants to close the account today and move the money to a stock fund that is expected to earn an effective return of 12 percent a year. John’s plan is to continue making contributions to this new account each year on his birthday. His next contribution will come today (age 40) and his final planned contribution will be on his 65th birthday. If John wants to accumulate $3,000,000 in his account by age 65, how much must he contribute each year until age 65 (26 contributions in all) to achieve his goal? a. $11,892 b. $13,214 c. $12,471 d. $10,388 e. $15,572 Required annuity payments Answer: a Diff: T . Joe and Jane are interested in saving money to put their two children, John and Susy through college. John is currently 12 years old and will enter college in six years. Susy is 10 years old and will enter college in 8 years. Both children plan to finish college in four years. College costs are currently $15,000 a year (per child), and are expected to increase at 5 percent a year for the foreseeable future. All college costs are paid at the beginning of the school year. Up until now, Joe and Jane have saved nothing but they expect to receive $25,000 from a favorite uncle in three years. To provide for the additional funds that are needed, they expect to make 12 equal payments at the beginning of each of the next 12 years--the first payment will be made today and the final payment will be made on Susy’s 21st birthday (which is also the day that the last payment must be made to the college). If all funds are invested in a stock fund that is expected to earn 12 percent, how large should each of the annual contributions be? a. $ 7,475.60 b. $ 7,798.76 c. $ 8,372.67 d. $ 9,675.98 e. $14,731.90 Required annuity payments Answer: b Diff: T . John and Barbara Roberts are starting to save for their daughter’s college education. • Assume that today’s date is September 1, 2002. • College costs are currently $10,000 a year and are expected to increase at a rate equal to 6 percent per year for the foreseeable future. All college payments are due at the beginning of the year. (So for example, college will cost $10,600 for the year beginning September 1, 2003). • Their daughter will enter college 15 years from now (September 1, 2017). She will be enrolled for four years. Therefore the Roberts will need to make four tuition payments. The first payment will be made on September 1, 2017, the final payment will be made on September 1, 2020. Notice that because of rising tuition costs, the tuition payments will increase each year. • The Roberts would also like to give their daughter a lump-sum payment of $50,000 on September 1,2021, in order to help with a down payment on a home, or to assist with graduate school tuition. • The Roberts currently have $10,000 in their college account. They anticipate making 15 equal contributions to the account at the end of each of the next 15 years. (The first contribution would be made on September 1, 2003, the final contribution will be made on September 1, 2017). • All current and future investments are assumed to earn an 8 percent return. (Ignore taxes.) How much should the Roberts contribute each year in order to reach their goal? a. $3,156.69 b. $3,618.95 c. $4,554.83 d. $5,955.54 e. $6,279.54 Required annuity payments Answer: a Diff: T . Joe and June Green are planning for their children’s college education. Joe would like his kids to attend his alma mater where tuition is currently $25,000 per year. Tuition costs are expected to increase by 5 percent each year. Their children, David and Daniel, just turned 2 and 3 years old today, September 1, 2002. They are expected to begin college the year in which they turn 18 years old and each will complete his schooling in four years. College tuition must be paid at the beginning of each school year. Grandma Green invested $10,000 in a mutual fund the day each child was born. This was to begin the boys’ college fund (a combined fund for both children). The investment has earned and is expected to continue to earn 12 percent per year. Joe and June will now begin adding to this fund every August 31st (beginning with August 31, 2003) to ensure that there is enough money to send the kids to college. How much money must Joe and June put into the college fund each of the next 15 years if their goal is to have all of the money in the investment account by the time Daniel (the oldest son) begins college? a. $5,928.67 b. $7,248.60 c. $4,822.66 d. $7,114.88 e. $5,538.86 Required annuity payments Answer: a Diff: T . Jerry and Donald are two brothers with the same birthday. Today is Jerry’s 30th birthday and Donald’s 25th birthday. Donald has been saving for retirement ever since his 20th birthday, when he started his retirement account with a $10,000 contribution. Every year since, Donald has contributed $5,000 to the account on his birthday. He plans to make the 40th, and final, $5,000 contribution on his 60th birthday, after which he plans to retire. In other words, by the time Donald has made all of his contributions he will have made one contribution of $10,000 followed by 40 annual contributions of $5,000. Jerry plans to retire on the same day (which will be his 65th birthday); however, until now, he has saved nothing for retirement. Jerry’s plan is to start contributing a fixed amount each year on his birthday; the first contribution will occur today. Jerry’s 36th, and final, contribution will occur on his 65th birthday. Jerry’s goal is to have the same amount when he retires at age 65 that Donald will have at age 60. Assume that both accounts have an expected annual return of 12 percent. How much does Jerry need to contribute each year in order to meet his goal? a. $ 9,838 b. $ 9,858 c. $ 9,632 d. $10,788 e. $11,041 Required annuity payments Answer: b Diff: T . Bob is 20 years old today and is starting to save money, so that he can get his MBA. He is interested in a 1-year MBA program. Tuition and expenses are currently $20,000 per year, and they are expected to increase by 5 percent per year. Bob plans to begin his MBA when he is 26 years old, and since all tuition and expenses are due at the beginning of the school year, Bob will make his one single payment six years from today. Right now, Bob has $25,000 in a brokerage account, and he plans to contribute a fixed amount to theaccount at the end of each of the next six years (t = 1, 2, 3, 4, 5, and 6). The account is expected to earn an annual return of 10 percent each year. Bob plans to withdraw $15,000 from the account two years from today (t = 2) to purchase a used car, but he plans to make no other withdrawals from the account until he starts the MBA program. How much does Bob need to put in the account at the end of each of the next six years to have enough money to pay for his MBA? a. $1,494 b. $ 580 c. $4,494 d. $2,266 e. $3,994 Required annuity payments Answer: e Diff: T N . Suppose you are deciding whether to buy or lease a car. If you buy the car, it will cost $17,000 today (t = 0). You expect to sell the car four years (48 months) from now for $6,000 (at t = 48). As an alternative to buying the car, you can lease the car for 48 months. All lease payments would be made at the end of the month. The first lease payment would occur next month (t = 1) and the final lease payment would occur 48 months from now (t = 48). If you buy the car, you would do so with cash, so there is no need to consider financing. If you lease the car, there is no option to buy it at the end of the contract. Assume that there are no taxes, and that the operating costs are the same regardless of whether you buy or lease the car. Assume that all cash flows are discounted at a nominal annual rate of 12 percent, so the monthly periodic rate is 1 percent. What is the breakeven lease payment? (That is, at what monthly payment would you be indifferent between buying and leasing the car?) a. $333.00 b. $336.62 c. $339.22 d. $343.51 e. $349.67 Required annuity payments Answer: c Diff: T N . Today is Craig’s 24th birthday, and he wants to begin saving for retirement. To get started, his plan is to open a brokerage account, and to put $1,000 into the account today. Craig intends to deposit $X into the account each year on his subsequent birthdays until the age of 64. In other words, Craig plans to make 40 contributions of $X. The first contribution will be made one year from now on his 25th birthday, and the 40th (and final) contribution will occur on his 64th birthday. Craig plans to retire at age 65 and he expects to live until age 85. Once he retires, Craig estimates that he will need to withdraw $100,000 from the account each year on his birthday in order to meet his expenses. (That is, Craig plans to make 20 withdrawals of $100,000 each-–the first withdrawal will occur on his 65th birthday and the final one will occur on his 84th birthday.) Craig expects to earn 9 percent a year in his brokerage account. Given his plans, how much does he need to deposit into the account for each of the next 40 years, in order to reach his goal? (That is, what is $X?) a. $2,379.20 b. $2,555.92 c. $2,608.73 d. $2,657.18 e. $2,786.98 Required annuity payments Answer: a Diff: T N . Your father is 45 years old today. He plans to retire in 20 years. Currently, he has $50,000 in a brokerage account. He plans to make 20 additional contributions of $10,000 a year. The first of these contributions will occur one year from today. The 20th and final contribution will occur on his 65th birthday. Once he retires, your father plans to withdraw a fixed dollar amount from the account each year on his birthday. The first withdrawal will occur on his 66th birthday. His 20th and final withdrawal will occur on his 85th birthday. After age 85, your father expects you to take care of him. Your father also plans to leave you with no inheritance. Assume that the brokerage account has an annual expected return of 10 percent. How much will your father be able to withdraw from his account each year after he retires? a. $106,785.48 b. $108,683.05 c. $111,131.54 d. $118,638.62e. $119,022.45 Annuity due vs. ordinary annuity Answer: e Diff: T . Bill and Bob are both 25 years old today. Each wants to begin saving for his retirement. Both plan on contributing a fixed amount each year into brokerage accounts that have annual returns of 12 percent. Both plan on retiring at age 65, 40 years from today, and both want to have $3 million saved by age 65. The only difference is that Bill wants to begin saving today, whereas Bob wants to begin saving one year from today. In other words, Bill plans to make 41 total contributions (t = 0, 1, 2, ... 40), while Bob plans to make 40 total contributions (t = 1, 2, ... 40). How much more than Bill will Bob need to save each year in order to accumulate the same amount as Bill does by age 65? a. $796.77 b. $892.39 c. $473.85 d. $414.48 e. $423.09 Amortization Answer: b Diff: T . The Florida Boosters Association has decided to build new bleachers for the football field. Total costs are estimated to be $1 million, and financing will be through a bond issue of the same amount. The bond will have a maturity of 20 years, a coupon rate of 8 percent, and has annual payments. In addition, the Association must set up a reserve to pay off the loan by making 20 equal annual payments into an account that pays 8 percent, annual compounding. The interest-accumulated amount in the reserve will be used to retire the entire issue at its maturity 20 years hence. The Association plans to meet the payment requirements by selling season tickets at a $10 net profit per ticket. How many tickets must be sold each year to service the debt (to meet the interest and principal repayment requirements)? a. 5,372 b. 10,186 c. 15,000 d. 20,459 e. 25,000 FV of an annuity Answer: c Diff: T . John and Julie Johnson are interested in saving for their retirement. John and Julie have the same birthday--both are 50 years old today. They started saving for their retirement on their 25th birthday, when they received a $20,000 gift from Julie’s aunt and deposited the money in an investment account. Every year thereafter, the couple added another $5,000 to the account. (The first contribution was made on their 26th birthday and the 25th contribution was made today on their 50th birthday.) John and Julie estimate that they will need to withdraw $150,000 from the account 3 years from now, to help meet college expenses for their 5 children. The couple plans to retire on their 58th birthday, 8 years from today. They will make a total of 8 more contributions, one on each of their next 8 birthdays with the last payment made on their 58th birthday. If the couple continues to contribute $5,000 to the account on their birthday, how much money will be in the account when they retire? Assume that the investment account earns 12 percent a year. a. $1,891,521 b. $2,104,873 c. $2,289,627 d. $2,198,776 e. $2,345,546 FV of an annuity Answer: e Diff: T . Carla is interested in saving for retirement. Today, on her 40th birthday, she has $100,000 in her investment account. She plans to make additional contributions on each of her subsequent birthdays. Specifically, she plans to: • Contribute $10,000 per year each year during her 40’s. (This will entail 9 contributions--the first will occur on her 41st birthday and the 9th on her 49th birthday.) • Contribute $20,000 per year each year during her 50’s. (This will entail 10 contributions--the first will occur on her 50th birthday and the 10th on her 59th birthday.)• Contribute $25,000 per year thereafter until age 65. (This will entail 6 contributions--the first will occur on her 60th birthday and the 6th on her 65th birthday.) Assume that her investment account has an expected return of 11 percent per year. If she sticks to her plan, how much will Carla have in her account on her 65th birthday after her final contribution? a. $1,575,597 b. $2,799,513 c. $2,877,872 d. $2,909,143 e. $2,934,143 EAR and FV of annuity Answer: c Diff: T N . Today you opened up a local bank account. Your plan is make five $1,000 contributions to this account. The first $1,000 contribution will occur today and then every six months you will contribute another $1,000 to the account. (So your final $1,000 contribution will be made two years from today). The bank account pays a 6 percent nominal annual interest, and interest is compounded monthly. After two years, you plan to leave the money in the account earning interest, but you will not make any further contributions to the account. How much will you have in the account 8 years from today? a. $7,092 b. $7,569 c. $7,609 d. $7,969 e. $8,070 FV of annuity due Answer: a Diff: T . To save money for a new house, you want to begin contributing money to a brokerage account. Your plan is to make 10 contributions to the brokerage account. Each contribution will be for $1,500. The contributions will come at the beginning of each of the next 10 years. The first contribution will be made at t = 0 and the final contribution will be made at t = 9. Assume that the brokerage account pays a 9 percent return with quarterly compounding. How much money do you expect to have in the brokerage account nine years from now (t = 9)? a. $23,127.49 b. $25,140.65 c. $25,280.27 d. $21,627.49 e. $19,785.76 FV of investment account Answer: b Diff: T . Kelly and Brian Johnson are a recently married couple whose parents have counseled them to start saving immediately in order to have enough money down the road to pay for their retirement and their children’s college expenses. Today (t = 0) is their 25th birthday (the couple shares the same birthday). The couple plan to have two children (Dick and Jane). Dick is expected to enter college 20 years from now (t = 20); Jane is expected to enter college 22 years from now (t = 22). So in years t = 22 and t = 23 there will be two children in college. Each child will take 4 years to complete college, and college costs are paid at the beginning of each year of college. College costs per child will be as follows: Year Cost per child Children in college 20 $58,045 Dick 21 62,108 Dick 22 66,456 Dick and Jane 23 71,108 Dick and Jane 24 76,086 Jane 25 81,411 Jane Kelly and Brian plan to retire 40 years from now at age 65 (at t = 40). They plan to contribute $12,000 per year at the end of each year for the next 40 years into an investment account that earns 10 percent per year. Thisaccount will be used to pay for the college costs, and also to provide a nest egg for Kelly and Brian’s retirement at age 65. How big will Kelly and Brian’s nest egg (the balance of the investment account) be when they retire at age 65 (t = 40)? a. $1,854,642 b. $2,393,273 c. $2,658,531 d. $3,564,751 e. $4,758,333 Effective annual rate Answer: c Diff: T . You have some money on deposit in a bank account that pays a nominal (or quoted) rate of 8.0944 percent, but with interest compounded daily (using a 365-day year). Your friend owns a security that calls for the payment of $10,000 after 27 months. The security is just as safe as your bank deposit, and your friend offers to sell it to you for $8,000. If you buy the security, by how much will the effective annual rate of return on your investment change? a. 1.87% b. 1.53% c. 2.00% d. 0.96% e. 0.44% PMT and quarterly compounding Answer: b Diff: T . Your employer has agreed to make 80 quarterly payments of $400 each into a trust account to fund your early retirement. The first payment will be made 3 months from now. At the end of 20 years (80 payments), you will be paid 10 equal annual payments, with the first payment to be made at the beginning of Year 21 (or the end of Year 20). The funds will be invested at a nominal rate of 8 percent, quarterly compounding, during both the accumulation and the distribution periods. How large will each of your 10 receipts be? (Hint: You must find the EAR and use it in one of your calculations.) a. $ 7,561 b. $10,789 c. $11,678 d. $12,342 e. $13,119 Non-annual compounding Answer: a Diff: T . A financial planner has offered you three possible options for receiving cash flows. You must choose the option that has the highest present value. (1) $1,000 now and another $1,000 at the beginning of each of the 11 subsequent months during the remainder of the year, to be deposited in an account paying a 12 percent nominal annual rate, but compounded monthly (to be left on deposit for the year). (2) $12,750 at the end of the year (assume a 12 percent nominal interest rate with semiannual compounding). (3) A payment scheme of 8 quarterly payments made over the next two years. The first payment of $800 is to be made at the end of the current quarter. Payments will increase by 20 percent each quarter. The money is to be deposited in an account paying a 12 percent nominal annual rate, but compounded quarterly (to be left on deposit for the entire 2-year period). Which one would you choose? a. Choice 1 b. Choice 2 c. Choice 3 d. Either one, since they all have the same present value. e. Choice 1, if the payments were made at the end of each month. Value of unknown withdrawal Answer: d Diff: T . Steve and Robert were college roommates, and each is celebrating their 30th birthday today. When they graduated from college nine years ago (on their 21st birthday), they each received $5,000 from familymembers for establishing investment accounts. Steve and Robert have added $5,000 to their separate accounts on each of their following birthdays (22nd through 30th birthdays). Steve has withdrawn nothing from the account, but Robert made one withdrawal on his 27th birthday. Steve has invested the money in Treasury bills that have earned a return of 6 percent per year, while Robert has invested his money in stocks that have earned a return of 12 percent per year. Both Steve and Robert have the same amount in their accounts today. How much did Robert withdraw on his 27th birthday? a. $ 7,832.22 b. $ 8,879.52 c. $10,865.11 d. $15,545.07 e. $13,879.52 Breakeven annuity payment Answer: a Diff: T N . Linda needs a new car and she is deciding whether it makes sense to buy or lease the car. She estimates that if she buys the car it will cost her $17,000 today (t = 0) and that she would sell the car four years from now for $7,000 (at t = 4). If she were to lease the car she would make a fixed lease payment at the end of each of the next 48 months (4 years). Assume that the operating costs are the same regardless of whether she buys or leases the car. Assume that if she leases, there are no up-front costs and that there is no option to buy the car after four years. Linda estimates that she should use a 6 percent nominal interest rate to discount the cash flows. What is the breakeven lease payment? (That is, at what monthly lease payment would she be indifferent between buying and leasing the car?) a. $269.85 b. $271.59 c. $275.60 d. $277.39 e. $279.83 Multiple Part: (The following information applies to the next two problems.) A 30-year, $115,000 mortgage has a nominal annual rate of 7 percent. All payments are made at the end of each month. Required mortgage payment Answer: b Diff: E N . What is the monthly payment on the mortgage? a. $760.66 b. $765.10 c. $772.29 d. $774.10 e. $776.89 Remaining mortgage balance Answer: e Diff: E N . What is the remaining balance on the mortgage after 5 years? a. $106,545.45 b. $106,919.83 c. $107,623.52 d. $107,988.84 e. $108,251.33 (The following information applies to the next two problems.) Today is your 21st birthday and your parents gave you a gift of $2,000. You just put this money in a brokerage account, and your plan is to add $1,000 to the account each year on your birthday, starting on your 22nd birthday. Time to accumulate a lump sum Answer: d Diff: E N. If you earn 10 percent a year in the brokerage account, what is the minimum number of whole years it will take for you to have at least $1,000,000 in the account? a. 41 b. 43 c. 45 d. 47 e. 48 Required annual rate of return Answer: c Diff: E N . Assume that you want to have $1,000,000 in the account by age 60 (39 years from today). What annual rate of return will you need to earn on your investments in order to reach this goal? a. 12.15% b. 12.41% c. 12.57% d. 12.66% e. 12.91% (The following information applies to the next two problems.) Your family recently bought a house. You have a $100,000, 30-year mortgage with a 7.2 percent nominal annual interest rate. Interest is compounded monthly and all payments are made at the end of the month. Monthly mortgage payments Answer: c Diff: E N . What is the monthly payment on the mortgage? a. $639.08 b. $674.74 c. $678.79 d. $685.10 e. $691.32 Amortization Answer: d Diff: M N . What percentage of the total payments during the first three years is going towards the principal? a. 9.6% b. 10.3% c. 11.7% d. 12.9% e. 13.4% (The following information applies to the next two problems.) The Jordan family recently purchased their first home. The house has a 15-year (180-month), $165,000 mortgage. The mortgage has a nominal annual interest rate of 7.75 percent. All mortgage payments are made at the end of the month. Monthly mortgage payments Answer: d Diff: E N . What is the monthly payment on the mortgage? a. $1,065.63 b. $1,283.61 c. $1,322.78 d. $1,553.10 e. $1,581.97 Remaining mortgage balance Answer: c Diff: E N . What will be the remaining balance on the mortgage after one year (right after the 12th payment has been made)? a. $152,879.31 b. $155,362.50 c. $158,937.91d. $160,245.39 e. $160,856.84 (The following information applies to the next two problems.) Victoria and David have a 30-year, $75,000 mortgage with an 8 percent nominal annual interest rate. All payments are due at the end of the month. Amortization Answer: d Diff: M N . What percentage of their monthly payments the first year will go towards interest payments? a. 7.76% b. 9.49% c. 82.17% d. 90.51% e. 91.31% Amortization Answer: a Diff: E N . If Victoria and David were able to refinance their mortgage and replace it with a 7 percent nominal annual interest rate, how much (in dollars) would their monthly payment decline? a. $ 51.35 b. $ 59.78 c. $ 72.61 d. $ 88.37 e. $104.49 (The following information applies to the next two problems.) Karen and Keith have a $300,000, 30-year (360-month) mortgage. The mortgage has a 7.2 percent nominal annual interest rate. Mortgage payments are made at the end of each month. Monthly mortgage payment Answer: c Diff: E N . What is the monthly payment on the mortgage? a. $1,759.41 b. $1,833.33 c. $2,036.36 d. $2,055.29 e. $3,105.25 Amortization Answer: b Diff: M N . What percentage of the total payments the first year (the first twelve months) will go towards repayment of principal? a. 11.88% b. 12.00% c. 13.21% d. 13.55% e. 14.16% (The following information applies to the next three problems.) Bill and Paula just purchased a car. They financed the car with a four-year (48-month) $15,000 loan. The loan is fully amortized after four years (i.e., the loan will be fully paid off after four years). Loan payments are due at the end of each month. The loan has a 12 percent nominal annual rate and the interest is compounded monthly. Monthly loan payments Answer: a Diff: E N . What are the monthly payments on the loan?a. $395.01 b. $401.99 c. $409.16 d. $411.54 e. $418.16 Amortization Answer: e Diff: M N . What percentage of the total payments the first two years are going towards repayment of principal? a. 44.1% b. 50.0% c. 55.9% d. 61.6% e. 69.7% Effective annual rate Answer: e Diff: E N . What is the effective annual rate on the loan? (Hint: Remember to switch your calculator back to P/YR = 1 after working this problem.) a. 12.36% b. 12.49% c. 12.55% d. 12.62% e. 12.68% Web Appendix 6B Multiple Choice: Problems Easy: PV continuous compounding Answer: b Diff: E 6B- . In six years’ time, you are scheduled to receive money from a trust established for you by your grandparents. When the trust matures there will be $100,000 in the account. If the account earns 9 percent compounded continuously, how much is in the account today? a. $ 23,456 b. $ 58,275 c. $171,600 d. $ 59,627 e. $ 61,385 Medium: FV continuous compounding Answer: a Diff: M 6B- . Assume one bank offers you a nominal annual interest rate of 6 percent compounded daily while another bank offers you continuous compounding at a 5.9 percent nominal annual rate. You decide to deposit $1,000 with each bank. Exactly two years later you withdraw your funds from both banks. What is the difference in your withdrawal amounts between the two banks? a. $ 2.25 b. $ 0.09 c. $ 1.12 d. $ 1.58 e. $12.58 Continuous compounded interest rate Answer: a Diff: M 6B- . In order to purchase your first home you need a down payment of $19,000 four years from today. You currently have $14,014 to invest. In order to achieve your goal, what nominal interest rate, compounded continuously, must you earn on this investment?a. 7.61% b. 7.26% c. 6.54% d. 30.56% e. 19.78% Payment and continuous compounding Answer: d Diff: M 6B- . You place $1,000 in an account that pays 7 percent interest compounded continuously. You plan to hold the account exactly three years. Simultaneously, in another account you deposit money that earns 8 percent compounded semiannually. If the accounts are to have the same amount at the end of the three years, how much of an initial deposit do you need to make now in the account that pays 8 percent interest compounded semiannually? a. $1,006.42 b. $ 986.73 c. $ 994.50 d. $ 975.01 e. $ 962.68 Continuous compounding Answer: a Diff: M 6B- . You have the choice of placing your savings in an account paying 12.5 percent compounded annually, an account paying 12.0 percent compounded semiannually, or an account paying 11.5 percent compounded continuously. To maximize your return you would choose: a. 12.5% compounded annually b. 12.0% compounded semiannually c. 11.5% compounded continuously d. You would be indifferent since the effective rate for all three is the same. e. You would be indifferent between choices a and c since their effective rates are the same. Continuous compounding Answer: b Diff: M 6B- . You have $5,438 in an account that has been paying an annual rate of 10 percent, compounded continuously. If you deposited some funds 10 years ago, how much was your original deposit? a. $1,000 b. $2,000 c. $3,000 d. $4,000 e. $5,000 Continuous compounding Answer: d Diff: M 6B- . For a 10-year deposit, what annual rate payable semiannually will produce the same effective rate as 4 percent compounded continuously? a. 2.02% b. 2.06% c. 3.95% d. 4.04% e. 4.12% Continuous compounding Answer: b Diff: M 6B- . How much should you be willing to pay for an account today that will have a value of $1,000 in 10 years under continuous compounding if the nominal rate is 10 percent? a. $354 b. $368 c. $385 d. $376 e. $370Continuous compounding Answer: b Diff: M 6B- . If you receive $15,000 today and can invest it at a 5 percent annual rate compounded continuously, what will be your ending value after 20 years? a. $35,821 b. $40,774 c. $75,000 d. $81,342 e. $86,750 CHAPTER 6 ANSWERS AND SOLUTIONS Terms in this set (132) 1. An ordinary annuity is best defined by which one of the following A. increasing payments paid for a definitive period of time B. increasing payments paid forever ANSWER: equal payments paid at regular intervals over a stated time period D. equal payments paid at regular intervals of time on an ongoing basis E. unequal payments that occur at set intervals for a limited period of time 2. Which one of the following accurately defines a perpetuity A. a limited number of equal payments paid in even time increments B. payments of equal amounts that are paid irregularly but indefinitely C. varying amounts that are paid at even intervals forever ANSWER: unending equal payments paid at equal time intervals E. unending equal payments paid at either equal or unequal time intervals 3. Which one of the following terms is used to identify a British perpetuity A. ordinary annuity B. amortized cash flow C. annuity due D. discounted loan ANSWER: consol 4. The interest rate that is quoted by a lender is referred to as which one of the following ANSWER: stated interest rate B. compound rate C. effective annual rate D. simple rate E. common rate 5. A monthly interest rate expressed as an annual rate would be an example of which one of the following rates A. stated rate B. discounted annual rate ANSWER: effective annual rate D. periodic monthly rate E. consolidated monthly rate 6. What is the interest rate charged per period multiplied by the number of periods per year called A. effective annual rate ANSWER: annual percentage rate C. periodic interest rate D. compound interest rate E. daily interest rate 7. A loan where the borrower receives money today and repays a single lump sum on a future date is called a(n) _____ loan. A. amortized B. continuousC. balloon ANSWER: pure discount E. interest-only ... 8. Which one of the following terms is used to describe a loan that calls for periodic interest payments and a lump sum principal payment A. amortized loan B. modified loan C. balloon loan D. pure discount loan ANSWER: interest-only loan 9. Which one of the following terms is used to describe a loan wherein each payment is equal in amount and includes both interest and principal ANSWER: amortized loan B. modified loan C. balloon loan D. pure discount loan E. interest-only loan 10. Which one of the following terms is defined as a loan wherein the regular payments, including both interest and principal amounts, are insufficient to retire the entire loan amount, which then must be repaid in one lump sum A. amortized loan B. continuing loan ANSWER: balloon loan D. remainder loan E. interest-only loan 11. You are comparing two annuities which offer quarterly payments of $2,500 for five years and pay 0.75 percent interest per month. Annuity A will pay you on the first of each month while annuity B will pay you on the last day of each month. Which one of the following statements is correct concerning these two annuities A. These two annuities have equal present values but unequal futures values at the end of year five. B. These two annuities have equal present values as of today and equal future values at the end of year five. C. Annuity B is an annuity due. D. Annuity A has a smaller future value than annuity B. ANSWER: Annuity B has a smaller present value than annuity A. 12. You are comparing two investment options that each pay 5 percent interest, compounded annually. Both options will provide you with $12,000 of income. Option A pays three annual payments starting with $2,000 the first year followed by two annual payments of $5,000 each. Option B pays three annual payments of $4,000 each. Which one of the following statements is correct given these two investment options A. Both options are of equal value given that they both provide $12,000 of income. B. Option A has the higher future value at the end of year three. ANSWER: Option B has a higher present value at time zero than does option A. D. Option B is a perpetuity. E. Option A is an annuity. 13. You are considering two projects with the following cash flows: Which of the following statements are true concerning these two projects I. Both projects have the same future value at the end of year 4, given a positive rate of return. II. Both projects have the same future value given a zero rate of return. III. Project X has a higher present value than Project Y, given a positive discount rate. IV. Project Y has a higher present value than Project X, given a positive discount rate. A. II only B. I and III only ANSWER: II and III only D. II and IV only E. I, II, and IV only14. Which one of the following statements is correct given the following two sets of project cash flows A. The cash flows for Project B are an annuity, but those of Project A are not. B. Both sets of cash flows have equal present values as of time zero given a positive discount rate. C. The present value at time zero of the final cash flow for Project A will be discounted using an exponent of three. D. The present value of Project A cannot be computed because the second cash flow is equal to zero. ANSWER: As long as the discount rate is positive, Project B will always be worth less today than will Project A. 15. Which one of the following statements related to annuities and perpetuities is correct A. An ordinary annuity is worth more than an annuity due given equal annual cash flows for ten years at 7 percent interest, compounded annually. ANSWER: A perpetuity comprised of $100 monthly payments is worth more than an annuity comprised of $100 monthly payments, given an interest rate of 12 percent, compounded monthly. C. Most loans are a form of a perpetuity. D. The present value of a perpetuity cannot be computed, but the future value can. E. Perpetuities are finite but annuities are not. 16. Which of the following statements related to interest rates are correct I. Annual interest rates consider the effect of interest earned on reinvested interest payments. II. When comparing loans, you should compare the effective annual rates. III. Lenders are required by law to disclose the effective annual rate of a loan to prospective borrowers. IV. Annual and effective interest rates are equal when interest is compounded annually. A. I and II only B. II and III only ANSWER: II and IV only D. I, II, and III only E. II, III, and IV only 17. Which one of the following statements concerning interest rates is correct A. Savers would prefer annual compounding over monthly compounding. B. The effective annual rate decreases as the number of compounding periods per year increases. ANSWER: The effective annual rate equals the annual percentage rate when interest is compounded annually. D. Borrowers would prefer monthly compounding over annual compounding. E. For any positive rate of interest, the effective annual rate will always exceed the annual percentage rate. 18. Which one of these statements related to growing annuities and perpetuities is correct A. The cash flow used in the growing annuity formula is the initial cash flow at time zero. B. Growth rates cannot be applied to perpetuities if you wish to compute the present value. C. The future value of an annuity will decrease if the growth rate is increased. D. An increase in the rate of growth will decrease the present value of an annuity. ANSWER: The present value of a growing perpetuity will decrease if the discount rate is increased. 19. Which one of the following statements correctly states a relationship A. Time and future values are inversely related, all else held constant. B. Interest rates and time are positively related, all else held constant. C. An increase in the discount rate increases the present value, given positive rates. D. An increase in time increases the future value given a zero rate of interest. ANSWER: Time and present value are inversely related, all else held constant. 20. Which one of the following compounding periods will yield the smallest present value given a stated future value and annual percentage rate A. annual B. semi-annual C. monthly D. daily ANSWER: continuous 21. The entire repayment of which one of the following loans is computed simply by computing a single future value A. interest-only loan B. balloon loanC. amortized loan ANSWER: pure discount loan E. bullet loan 22. How is the principal amount of an interest-only loan repaid A. The principal is forgiven over the loan period so does not have to be repaid. B. The principal is repaid in equal increments and included in each loan payment. ANSWER: The principal is repaid in a lump sum at the end of the loan period. D. The principal is repaid in equal annual payments. E. The principal is repaid in increasing increments through regular monthly payments. 23. An amortized loan: A. requires the principal amount to be repaid in even increments over the life of the loan. ANSWER: may have equal or increasing amounts applied to the principal from each loan payment. C. requires that all interest be repaid on a monthly basis while the principal is repaid at the end of the loan term. D. requires that all payments be equal in amount and include both principal and interest. E. repays both the principal and the interest in one lump sum at the end of the loan term. ... 24. You need $25,000 today and have decided to take out a loan at 7 percent for five years. Which one of the following loans would be the least expensive Assume all loans require monthly payments and that interest is compounded on a monthly basis. A. interest-only loan ANSWER: amortized loan with equal principal payments C. amortized loan with equal loan payments D. discount loan E. balloon loan where 50 percent of the principal is repaid as a balloon payment 25. Your grandmother is gifting you $100 a month for four years while you attend college to earn your bachelor's degree. At a 5.5 percent discount rate, what are these payments worth to you on the day you enter college A. $4,201.16 ANSWER: $4,299.88 C. $4,509.19 D. $4,608.87 E. $4,800.00 26. You just won the grand prize in a national writing contest! As your prize, you will receive $2,000 a month for ten years. If you can earn 7 percent on your money, what is this prize worth to you today ANSWER: $172,252.71 B. $178,411.06 C. $181,338.40 D. $185,333.33 E. $190,450.25 27. Phil can afford $180 a month for 5 years for a car loan. If the interest rate is 8.6 percent, how much can he afford to borrow to purchase a car A. $7,750.00 B. $8,348.03 ANSWER: $8,752.84 D. $9,266.67 E. $9,400.00 28. You are the beneficiary of a life insurance policy. The insurance company informs you that you have two options for receiving the insurance proceeds. You can receive a lump sum of $200,000 today or receive payments of $1,400 a month for 20 years. You can earn 6 percent on your money. Which option should you take and why A. You should accept the payments because they are worth $209,414 to you today. B. You should accept the payments because they are worth $247,800 to you today. C. You should accept the payments because they are worth $336,000 to you today. D. You should accept the $200,000 because the payments are only worth $189,311 to you today. ANSWER: You should accept the $200,000 because the payments are only worth $195,413 to you today.29. Your employer contributes $75 a week to your retirement plan. Assume that you work for your employer for another 20 years and that the applicable discount rate is 7.5 percent. Given these assumptions, what is this employee benefit worth to you today ANSWER: $40,384.69 B. $42,618.46 C. $44,211.11 D. $44,306.16 E. $44,987.74 30. The Design Team just decided to save $1,500 a month for the next 5 years as a safety net for recessionary periods. The money will be set aside in a separate savings account which pays 4.5 percent interest compounded monthly. The first deposit will be made today. What would today's deposit amount have to be if the firm opted for one lump sum deposit today that would yield the same amount of savings as the monthly deposits after 5 years A. $80,459.07 ANSWER: $80,760.79 C. $81,068.18 D. $81,333.33 E. $81,548.20 31. You need some money today and the only friend you have that has any is your miserly friend. He agrees to loan you the money you need, if you make payments of $25 a month for the next six months. In keeping with his reputation, he requires that the first payment be paid today. He also charges you 1.5 percent interest per month. How much money are you borrowing A. $134.09 B. $138.22 C. $139.50 D. $142.68 ANSWER: $144.57 32. You buy an annuity that will pay you $24,000 a year for 25 years. The payments are paid on the first day of each year. What is the value of this annuity today if the discount rate is 8.5 percent A. $241,309 B. $245,621 C. $251,409 D. $258,319 ANSWER: $266,498 33. You are scheduled to receive annual payments of $4,800 for each of the next 7 years. The discount rate is 8 percent. What is the difference in the present value if you receive these payments at the beginning of each year rather than at the end of each year ANSWER: $1,999 B. $2,013 C. $2,221 D. $2,227 E. $2,304 34. You are comparing two annuities with equal present values. The applicable discount rate is 8.75 percent. One annuity pays $5,000 on the first day of each year for 20 years. How much does the second annuity pay each year for 20 years if it pays at the end of each year A. $5,211 B. $5,267 C. $5,309 D. $5,390 ANSWER: $5,438 35. Trish receives $480 on the first of each month. Josh receives $480 on the last day of each month. Both Trish and Josh will receive payments for next three years. At a 9.5 percent discount rate, what is the difference in the present value of these two sets of payments ANSWER: $118.63 B. $121.06 C. $124.30D. $129.08 E. $132.50 36. What is the future value of $1,200 a year for 40 years at 8 percent interest Assume annual compounding. A. $301,115 B. $306,492 ANSWER: $310,868 D. $342,908 E. $347,267 37. What is the future value of $15,000 a year for 30 years at 12 percent interest A. $2,878,406 ANSWER: $3,619,990 C. $3,711,414 D. $3,989,476 E. $4,021,223 38. Alexa plans on saving $3,000 a year and expects to earn an annual rate of 10.25 percent. How much will she have in her account at the end of 45 years A. $1,806,429 B. $1,838,369 C. $2,211,407 ANSWER: $2,333,572 E. $2,508,316 39. Theresa adds $1,000 to her savings account on the first day of each year. Marcus adds $1,000 to his savings account on the last day of each year. They both earn 6.5 percent annual interest. What is the difference in their savings account balances at the end of 35 years ANSWER: $8,062 B. $8,113 C. $8,127 D. $8,211 E. $8,219 40. You are borrowing $17,800 to buy a car. The terms of the loan call for monthly payments for 5 years at 8.6 percent interest. What is the amount of each payment A. $287.71 B. $291.40 C. $301.12 D. $342.76 ANSWER: $366.05 41. You borrow $165,000 to buy a house. The mortgage rate is 7.5 percent and the loan period is 30 years. Payments are made monthly. If you pay the mortgage according to the loan agreement, how much total interest will you pay A. $206,408 B. $229,079 ANSWER: $250,332 D. $264,319 E. $291,406 42. Holiday Tours (HT) has an employment contract with its newly hired CEO. The contract requires a lump sum payment of $10.4 million be paid to the CEO upon the successful completion of her first three years of service. HT wants to set aside an equal amount of money at the end of each year to cover this anticipated cash outflow and will earn 5.65 percent on the funds. How much must HT set aside each year for this purpose A. $3,184,467 ANSWER: $3,277,973 C. $3,006,409 D. $3,318,190 E. $3,466,667 43. Nadine is retiring at age 62 and expects to live to age 85. On the day she retires, she has $348,219 in herretirement savings account. She is somewhat conservative with her money and expects to earn 6 percent during her retirement years. How much can she withdraw from her retirement savings each month if she plans to spend her last penny on the morning of her death A. $1,609.92 B. $1,847.78 C. $1,919.46 D. $2,116.08 ANSWER: $2,329.05 44. Kingston Development Corp. purchased a piece of property for $2.79 million. The firm paid a down payment of 15 percent in cash and financed the balance. The loan terms require monthly payments for 15 years at an annual percentage rate of 7.75 percent, compounded monthly. What is the amount of each mortgage payment ANSWER: $22,322.35 B. $23,419.97 C. $23,607.11 D. $24,878.15 E. $25,301.16 Amount financed = $2,790,000 (1 - 0.15) = $2,371,500 45. You estimate that you will owe $42,800 in student loans by the time you graduate. The interest rate is 4.25 percent. If you want to have this debt paid in full within six years, how much must you pay each month A. $611.09 ANSWER: $674.50 C. $714.28 D. $736.05 E. $742.50 46. You are buying a previously owned car today at a price of $3,500. You are paying $300 down in cash and financing the balance for 36 months at 8.5 percent. What is the amount of each loan payment ANSWER: $101.02 B. $112.23 C. $118.47 D. $121.60 E. $124.40 Amount financed = $3,500 - $300 = $3,200 47. Atlas Insurance wants to sell you an annuity which will pay you $3,400 per quarter for 25 years. You want to earn a minimum rate of return of 6.5 percent. What is the most you are willing to pay as a lump sum today to buy this annuity A. $151,008.24 B. $154,208.16 ANSWER: $167,489.11 D. $173,008.80 E. $178,927.59 48. Your car dealer is willing to lease you a new car for $245 a month for 48 months. Payments are due on the first day of each month starting with the day you sign the lease contract. If your cost of money is 6.5 percent, what is the current value of the lease A. $10,331.03 ANSWER: $10,386.99 C. $12,197.74 D. $12,203.14 E. $13,008.31 49. Your great aunt left you an inheritance in the form of a trust. The trust agreement states that you are to receive $3,600 on the first day of each year, starting immediately and continuing for 20 years. What is the value of this inheritance today if the applicable discount rate is 6.75 percent A. $38,890.88 B. $40,311.16 ANSWER: $41,516.01 D. $42,909.29 E. $43,333.3350. You just received an insurance settlement offer related to an accident you had six years ago. The offer gives you a choice of one of the following three offers: You can earn 7.5 percent on your investments. You do not care if you personally receive the funds or if they are paid to your heirs should you die within the settlement period. Which one of the following statements is correct given this information A. Option A is the best choice as it provides the largest monthly payment. B. Option B is the best choice because it pays the largest total amount. ANSWER: Option C is the best choice because it is has the largest current value. D. Option B is the best choice because you will receive the most payments. E. You are indifferent to the three options as they are all equal in value. 51. Samuelson Engines wants to save $750,000 to buy some new equipment six years from now. The plan is to set aside an equal amount of money on the first day of each quarter starting today. The firm can earn 4.75 percent on its savings. How much does the firm have to save each quarter to achieve its goal ANSWER: $26,872.94 B. $26,969.70 C. $27,192.05 D. $27,419.29 E. $27,911.08 52. Stephanie is going to contribute $300 on the first of each month, starting today, to her retirement account. Her employer will provide a 50 percent match. In other words, her employer will contribute 50 percent of the amount Stephanie saves. If both Stephanie and her employer continue to do this and she can earn a monthly rate of 0.90 percent, how much will she have in her retirement account 35 years from now A. $1,936,264 B. $1,943,286 C. $1,989,312 D. $2,068,418 ANSWER: $2,123,007 53. You are considering an annuity which costs $160,000 today. The annuity pays $18,126 a year at an annual interest rate of 7.50 percent. What is the length of the annuity time period A. 12 years B. 13 years C. 14 years ANSWER: 15 years E. 16 years 54. Today, you borrowed $6,200 on your credit card to purchase some furniture. The interest rate is 14.9 percent, compounded monthly. How long will it take you to pay off this debt assuming that you do not charge anything else and make regular monthly payments of $120 A. 5.87 years B. 6.40 years ANSWER: 6.93 years D. 7.23 years E. 7.31 years 55. Meadow Brook Manor would like to buy some additional land and build a new assisted living center. The anticipated total cost is $23.6 million. The CEO of the firm is quite conservative and will only do this when the company has sufficient funds to pay cash for the entire construction project. Management has decided to save $1.2 million a quarter for this purpose. The firm earns 6.25 percent, compounded quarterly, on the funds it saves. How long does the company have to wait before expanding its operations A. 4.09 years ANSWER: 4.32 years C. 4.46 years D. 4.82 years E. 4.91 years 56. Today, you are retiring. You have a total of $411,016 in your retirement savings and have the fundsinvested such that you expect to earn an average of 7.10 percent, compounded monthly, on this money throughout your retirement years. You want to withdraw $2,500 at the beginning of every month, starting today. How long will it be until you run out of money A. 31.97 years B. 34.56 years C. 42.03 year ANSWER: 48.19 years E. You will never run out of money. 57. Gene's Art Gallery is notoriously known as a slow-payer. The firm currently needs to borrow $27,500 and only one company will even deal with them. The terms of the loan call for daily payments of $100. The first payment is due today. The interest rate is 21.9 percent, compounded daily. What is the time period of this loan Assume a 365 day year. A. 264.36 days B. 280.81 days ANSWER: 300.43 days D. 316.46 days E. 341.09 days 58. The Wine Press is considering a project which has an initial cash requirement of $187,400. The project will yield cash flows of $2,832 monthly for 84 months. What is the rate of return on this project A. 6.97 percent ANSWER: 7.04 percent C. 7.28 percent D. 7.41 percent E. 7.56 percent 59. Your insurance agent is trying to sell you an annuity that costs $200,000 today. By buying this annuity, your agent promises that you will receive payments of $1,225 a month for the next 30 years. What is the rate of return on this investment A. 5.75 percent B. 5.97 percent ANSWER: 6.20 percent D. 6.45 percent E. 6.67 percent 60. You have been investing $250 a month for the last 13 years. Today, your investment account is worth $73,262. What is your average rate of return on your investments ANSWER: 8.94 percent B. 9.23 percent C. 9.36 percent D. 9.41 percent E. 9.78 percent 61. Will has been purchasing $25,000 worth of New Tek stock annually for the past 11 years. His holdings are now worth $598,100. What is his annual rate of return on this stock A. 14.13 percent B. 14.24 percent C. 14.29 percent D. 14.37 percent ANSWER: 14.68 percent 62. Your father helped you start saving $20 a month beginning on your 5th birthday. He always made you deposit the money into your savings account on the first day of each month just to "start the month out right." Today completes your 17th year of saving and you now have $6,528.91 in this account. What is the rate of return on your savings ANSWER: 5.15 percent B. 5.30 percent C. 5.47 percent D. 5.98 percent E. 6.12 percent 63. Today, you turn 23. Your birthday wish is that you will be a millionaire by your 40th birthday. In an attemptto reach this goal, you decide to save $50 a day, every day until you turn 40. You open an investment account and deposit your first $50 today. What rate of return must you earn to achieve your goal A. 10.67 percent ANSWER: 11.85 percent C. 12.90 percent D. 13.06 percent E. 13.54 percent 64. You just settled an insurance claim. The settlement calls for increasing payments over a 10-year period. The first payment will be paid one year from now in the amount of $10,000. The following payments will increase by 4.5 percent annually. What is the value of this settlement to you today if you can earn 8 percent on your investments A. $76,408.28 ANSWER: $80,192.76 C. $82,023.05 D. $84,141.14 E. $85,008.16 65. Your grandfather left you an inheritance that will provide an annual income for the next 10 years. You will receive the first payment one year from now in the amount of $4,000. Every year after that, the payment amount will increase by 6 percent. What is your inheritance worth to you today if you can earn 9.5 percent on your investments ANSWER: $31,699.15 B. $36,666.67 C. $41,121.21 D. $43,464.12 E. $46,908.17 66. You just won a national sweepstakes! For your prize, you opted to receive never-ending payments. The first payment will be $12,500 and will be paid one year from today. Every year thereafter, the payments will increase by 3.5 percent annually. What is the present value of your prize at a discount rate of 8 percent A. $166,666.67 B. $248,409.19 ANSWER: $277,777.78 D. $291,006.12 E. $300,000.00 67. A wealthy benefactor just donated some money to the local college. This gift was established to provide scholarships for worthy students. The first scholarships will be granted one year from now for a total of $35,000. Annually thereafter, the scholarship amount will be increased by 5.5 percent to help offset the effects of inflation. The scholarship fund will last indefinitely. What is the value of this gift today at a discount rate of 8 percent A. $437,500 B. $750,000 C. $1,200,000 ANSWER: $1,400,000 E. $1,450,750 68. Southern Tours is considering acquiring Holiday Vacations. Management believes Holiday Vacations can generate cash flows of $187,000, $220,000, and $245,000 over the next three years, respectively. After that time, they feel the business will be worthless. Southern Tours has determined that a 13.5 percent rate of return is applicable to this potential acquisition. What is Southern Tours willing to pay today to acquire Holiday Vacations ANSWER: $503,098 B. $538,615 C. $545,920 D. $601,226 E. $638,407 69. You are considering two savings options. Both options offer a 7.4 percent rate of return. The first option is to save $900, $2,100, and $3,000 at the end of each year for the next three years, respectively. The other option is to save one lump sum amount today. If you want to have the same balance in your savings account at the end of the three years, regardless of the savings method you select, how much do you need to save today if youselect the lump sum option A. $4,410 B. $4,530 C. $4,600 ANSWER: $5,080 E. $5,260 70. Your parents have made you two offers. The first offer includes annual gifts of $10,000, $11,000, and $12,000 at the end of each of the next three years, respectively. The other offer is the payment of one lump sum amount today. You are trying to decide which offer to accept given the fact that your discount rate is 8 percent. What is the minimum amount that you will accept today if you are to select the lump sum offer ANSWER: $28,216 B. $29,407 C. $29,367 D. $30,439 E. $30,691 71. You are considering changing jobs. Your goal is to work for three years and then return to school full-time in pursuit of an advanced degree. A potential employer just offered you an annual salary of $41,000, $44,000, and $46,000 a year for the next three years, respectively. All salary payments are made as lump sum payments at the end of each year. The offer also includes a starting bonus of $2,500 payable immediately. What is this offer worth to you today at a discount rate of 6.75 percent A. $112,406 B. $115,545 ANSWER: $117,333 D. $121,212 E. $134,697 72. You are considering a project which will provide annual cash inflows of $4,500, $5,700, and $8,000 at the end of each year for the next three years, respectively. What is the present value of these cash flows, given a 9 percent discount rate A. $14,877 ANSWER: $15,103 C. $15,429 D. $16,388 E. $16,847 73. You just signed a consulting contract that will pay you $35,000, $52,000, and $80,000 annually at the end of the next three years, respectively. What is the present value of these cash flows given a 10.5 percent discount rate ANSWER: $133,554 B. $142,307 C. $148,880 D. $151,131 E. $156,910 74. You have some property for sale and have received two offers. The first offer is for $89,500 today in cash. The second offer is the payment of $35,000 today and an additional $70,000 two years from today. If the applicable discount rate is 11.5 percent, which offer should you accept and why A. You should accept the $89,500 today because it has the higher net present value. B. You should accept the $89,500 today because it has the lower future value. C. You should accept the first offer as it has the greatest value to you. ANSWER: You should accept the second offer because it has the larger net present value. E. It does not matter which offer you accept as they are equally valuable. 75. Your local travel agent is advertising an upscale winter vacation package for travel three years from now to Antarctica. The package requires that you pay $25,000 today, $30,000 one year from today, and a final payment of $45,000 on the day you depart three years from today. What is the cost of this vacation in today's dollars if the discount rate is 9.75 percent ANSWER: $86,376 B. $89,695 C. $91,219 D. $91,407E. $93,478 76. One year ago, Deltona Motor Parts deposited $16,500 in an investment account for the purpose of buying new equipment three years from today. Today, it is adding another $12,000 to this account. The company plans on making a final deposit of $20,000 to the account one year from today. How much will be available when it is ready to buy the equipment, assuming the account pays 5.5 interest A. $53,408 B. $53,919 C. $56,211 ANSWER: $56,792 E. $58,021 77. Lucas will receive $6,800, $8,700, and $12,500 each year starting at the end of year one. What is the future value of these cash flows at the end of year five if the interest rate is 7 percent A. $32,418 B. $32,907 ANSWER: $33,883 D. $35,411 E. $36,255 78. You plan on saving $5,200 this year, nothing next year, and $7,500 the following year. You will deposit these amounts into your investment account at the end of each year. What will your investment account be worth at the end of year three if you can earn 8.5 percent on your funds A. $13,528.12 ANSWER: $13,621.57 C. $13,907.11 D. $14,526.50 E. $14,779.40 79. Miley expects to receive the following payments: Year 1 = $60,000; Year 2 = $35,000; Year 3 = $12,000. All of this money will be saved for her retirement. If she can earn an average of 10.5 percent on her investments, how much will she have in her account 25 years after making her first deposit A. $972,373 B. $989,457 C. $1,006,311 D. $1,147,509 ANSWER: $1,231,776 80. Blackwell, Inc. has a $75,000 liability it must pay three years from today. The company is opening a savings account so that the entire amount will be available when this debt needs to be paid. The plan is to make an initial deposit today and then deposit an additional $15,000 each year for the next three years, starting one year from today. The account pays a 4.5 percent rate of return. How much does the firm need to deposit today A. $18,299.95 B. $20,072.91 C. $21,400.33 ANSWER: $24,487.78 E. $31,076.56 81. The government has imposed a fine on the Corner Tavern. The fine calls for annual payments of $150,000, $100,000, $75,000, and $50,000, respectively, over the next four years. The first payment is due one year from today. The government plans to invest the funds until the final payment is collected and then donate the entire amount, including the investment earnings, to help the local community shelter. The government will earn 6.25 percent on the funds held. How much will the community shelter receive four years from today A. $349,674.06 B. $366,875.00 ANSWER: $422,497.56 D. $458,572.71 E. $515,737.67 82. Wicker Imports established a trust fund that provides $90,000 in scholarships each year for needy students. The trust fund earns a fixed 6 percent rate of return. How much money did the firm contribute to the fund assuming that only the interest income is distributed A. $1,150,000B. $1,200,000 C. $1,333,333 ANSWER: $1,500,000 E. $1,600,000 83. A preferred stock pays an annual dividend of $2.60. What is one share of this stock worth today if the rate of return is 11.75 percent A. $18.48 B. $20.00 ANSWER: $22.13 D. $28.80 E. $30.55 84. You would like to establish a trust fund that will provide $120,000 a year forever for your heirs. The trust fund is going to be invested very conservatively so the expected rate of return is only 5.75 percent. How much money must you deposit today to fund this gift for your heirs ANSWER: $2,086,957 B. $2,121,212 C. $2,300,000 D. $2,458,122 E. $2,500,000 85. You just paid $750,000 for an annuity that will pay you and your heirs $45,000 a year forever. What rate of return are you earning on this policy A. 5.25 percent B. 5.50 percent C. 5.75 percent ANSWER: 6.00 percent E. 6.25 percent 86. You grandfather won a lottery years ago. The value of his winnings at the time was $50,000. He invested this money such that it will provide annual payments of $2,400 a year to his heirs forever. What is the rate of return A. 4.75 percent ANSWER: 4.80 percent C. 5.00 percent D. 5.10 percent E. 5.15 percent 87. The preferred stock of Casco has a 5.48 percent dividend yield. The stock is currently priced at $59.30 per share. What is the amount of the annual dividend A. $2.80 B. $2.95 C. $3.10 ANSWER: $3.25 E. $3.40 88. Your credit card company charges you 1.65 percent interest per month. What is the annual percentage rate on your account A. 18.95 percent ANSWER: 19.80 percent C. 20.90 percent D. 21.25 percent E. 21.70 percent 89. What is the annual percentage rate on a loan with a stated rate of 2.25 percent per quarter ANSWER: 9.00 percent B. 9.09 percent C. 9.18 percent D. 9.27 percent E. 9.31 percent 90. You are paying an effective annual rate of 18.974 percent on your credit card. The interest is compoundedmonthly. What is the annual percentage rate on this account ANSWER: 17.50 percent B. 18.00 percent C. 18.25 percent D. 18.64 percent E. 19.00 percent 91. What is the effective annual rate if a bank charges you 9.50 percent compounded quarterly A. 9.62 percent B. 9.68 percent C. 9.72 percent ANSWER: 9.84 percent E. 9.91 percent 92. Your credit card company quotes you a rate of 17.9 percent. Interest is billed monthly. What is the actual rate of interest you are paying A. 19.03 percent B. 19.21 percent ANSWER: 19.44 percent D. 19.57 percent E. 19.72 percent 93. The Pawn Shop loans money at an annual rate of 21 percent and compounds interest weekly. What is the actual rate being charged on these loans A. 23.16 percent ANSWER: 23.32 percent C. 23.49 percent D. 23.56 percent E. 23.64 percent 94. You are considering two loans. The terms of the two loans are equivalent with the exception of the interest rates. Loan A offers a rate of 7.75 percent, compounded daily. Loan B offers a rate of 8 percent, compounded semi-annually. Which loan should you select and why ANSWER: A; the effective annual rate is 8.06 percent. B. A; the annual percentage rate is 7.75 percent. C. B; the annual percentage rate is 7.68 percent. D. B; the effective annual rate is 8.16 percent. E. The loans are equivalent offers so you can select either one. 95. You have $5,600 that you want to use to open a savings account. There are five banks located in your area. The rates paid by banks A through E, respectively, are given below. Which bank should you select if your goal is to maximize your interest income A. 3.26 percent, compounded annually B. 3.20 percent, compounded monthly ANSWER: 3.25 percent, compounded semi-annually D. 3.10 percent, compounded continuously E. 3.15 percent, compounded quarterly EARA = 3.26 percent Bank C offers the highest effective annual rate at 3.276 percent. 96. What is the effective annual rate of 14.9 percent compounded continuously A. 15.59 percent B. 15.62 percent C. 15.69 percent D. 15.84 percent ANSWER: 16.07 percent 97. What is the effective annual rate of 9.75 percent compounded continuously A. 10.17 percent ANSWER: 10.24 percentC. 10.29 percent D. 10.33 percent E. 10.47 percent 98. City Bank wants to appear competitive based on quoted loan rates and thus must offer a 7.75 percent annual percentage rate on its loans. What is the maximum rate the bank can actually earn based on the quoted rate ANSWER: 8.06 percent B. 8.14 percent C. 8.21 percent D. 8.26 percent E. 8.58 percent 99. You are going to loan a friend $900 for one year at a 5 percent rate of interest, compounded annually. How much additional interest could you have earned if you had compounded the rate continuously rather than annually A. $0.97 ANSWER: $1.14 C. $1.23 D. $1.36 E. $1.41 100. You are borrowing money today at 8.48 percent, compounded annually. You will repay the principal plus all the interest in one lump sum of $12,800 two years from today. How much are you borrowing A. $9,900.00 B. $10,211.16 ANSWER: $10,877.04 D. $11,401.16 E. $11,250.00 101. This morning, you borrowed $9,500 at 7.65 percent annual interest. You are to repay the loan principal plus all of the loan interest in one lump sum four years from today. How much will you have to repay ANSWER: $12,757.92 B. $12,808.13 C. $12,911.89 D. $13,006.08 E. $13,441.20 102. On this date last year, you borrowed $3,400. You have to repay the loan principal plus all of the interest six years from today. The payment that is required at that time is $6,000. What is the interest rate on this loan A. 8.01 percent ANSWER: 8.45 percent C. 8.78 percent D. 9.47 percent E. 9.93 percent 103. John's Auto Repair just took out an $89,000, 10-year, 8 percent, interest-only loan from the bank. Payments are made annually. What is the amount of the loan payment in year 10 A. $7,120 B. $8,850 C. $13,264 D. $89,000 ANSWER: $96,120 104. On the day you entered college, you borrowed $18,000 on an interest-only, four-year loan at 5.25 percent from your local bank. Payments are to be paid annually. What is the amount of your loan payment in year 2 ANSWER: $945 B. $1,890 C. $3,600 D. $5,106 E. $6,250 105. On the day you entered college you borrowed $25,000 from your local bank. The terms of the loaninclude an interest rate of 4.75 percent. The terms stipulate that the principal is due in full one year after you graduate. Interest is to be paid annually at the end of each year. Assume that you complete college in four years. How much total interest will you pay on this loan A. $5,266.67 B. $5,400.00 ANSWER: $5,937.50 D. $6,529.00 E. $6,607.11 106. You just acquired a mortgage in the amount of $249,500 at 6.75 percent interest, compounded monthly. Equal payments are to be made at the end of each month for thirty years. How much of the first loan payment is interest (Assume each month is equal to 1/12 of a year.) A. $925.20 B. $1,206.16 ANSWER: $1,403.44 D. $1,511.21 E. $1,548.60 Interest portion of first loan payment = 107. On June 1, you borrowed $212,000 to buy a house. The mortgage rate is 8.25 percent. The loan is to be repaid in equal monthly payments over 15 years. The first payment is due on July 1. How much of the second payment applies to the principal balance (Assume that each month is equal to 1/12 of a year.) ANSWER: $603.32 B. $698.14 C. $1,358.56 D. $1,453.38 E. $2,056.70 108. This morning, you borrowed $150,000 to buy a house. The mortgage rate is 7.35 percent. The loan is to be repaid in equal monthly payments over 20 years. The first payment is due one month from today. How much of the second payment applies to the principal balance (Assume that each month is equal to 1/12 of a year.) A. $268.84 ANSWER: $277.61 C. $917.06 D. $925.83 E. $1,194.67 ANSWER: The APR is a stated rate and is computed as (r n), where r is the rate per period and n is the number of periods per year. The EAR considers compounding and is computed as (1 + r)n - 1, where r is the rate per period and n is the number of periods per year. The effective annual rate will always be higher than the annual percentage rate as long as the account is compounded more than once a year and the interest rate is greater than zero. The EAR is the equivalent rate based on annual compounding. The EAR has greater importance because it is the actual cost of a loan. Feedback: Refer to section 6.3 ... ... ... ... ... 112. Kristie owns a perpetuity which pays $12,000 at the end of each year. She comes to you and offers to sell you all of the payments to be received after the 10th year. Explain how you can determine the value of this offer. ...ANSWER: 113. Western Bank offers you a $21,000, 6-year term loan at 8 percent annual interest. What is the amount of your annual loan payment A. $4,228.50 ANSWER: $4,542.62 C. $4,666.67 D. $4,901.18 E. $5,311.07 114. First Century Bank wants to earn an effective annual return on its consumer loans of 10 percent per year. The bank uses daily compounding on its loans. By law, what interest rate is the bank required to report to potential borrowers A. 9.23 percent B. 9.38 percent ANSWER: 9.53 percent D. 9.72 percent E. 10.00 percent APR = 365 [(1 + 0.10)1/365 - 1] = 9.53 percent 115. Downtown Bank is offering 3.4 percent compounded daily on its savings accounts. You deposit $8,000 today. How much will you have in your account 11 years from now ANSWER: $11,628.09 B. $11,714.06 C. $12,204.50 D. $12,336.81 E. $12,414.14 FV = $8,000 [1 + (0.034/365)]11 365 = $11,628.09 116. You want to buy a new sports coupe for $41,750, and the finance office at the dealership has quoted you an 8.6 percent APR loan compounded monthly for 48 months to buy the car. What is the effective interest rate on this loan A. 8.28 percent B. 8.41 percent C. 8.72 percent D. 8.87 percent ANSWER: 8.95 percent EAR = [1 + (.086/12)]12 - 1 = 8.95 percent 117. Beginning three months from now, you want to be able to withdraw $1,500 each quarter from your bank account to cover college expenses over the next 4 years. The account pays 1.25 percent interest per quarter. How much do you need to have in your account today to meet your expense needs over the next 4 years ANSWER: $21,630.44 B. $21,847.15 C. $22,068.00 D. $22,454.09 E. $22,711.18 118. You are planning to save for retirement over the next 15 years. To do this, you will invest $1,100 a month in a stock account and $500 a month in a bond account. The return on the stock account is expected to be 7 percent, and the bond account will pay 4 percent. When you retire, you will combine your money into an account with a 5 percent return. How much can you withdraw each month during retirement assuming a 20- year withdrawal period A. $2,636.19 B. $2,904.11 C. $3,008.21 ANSWER: $3,113.04 E. $3,406.97 119. You want to be a millionaire when you retire in 40 years. You can earn an 11 percent annual return. How much more will you have to save each month if you wait 10 years to start saving versus if you start saving at the end of this month A. $79.22B. $114.13 C. $168.47 D. $201.15 ANSWER: $240.29 FVA40 years = $1,000,000 = C [{[1 + (0.11/12)]40 12; C = $116.28 FVA30 years = $1,000,000 = C [{[1 + (0.11/12)]30 12; C = $356.57 Difference = $356.57 - $116.28 = $240.29 120. You have just won the lottery and will receive $540,000 as your first payment one year from now. You will receive payments for 26 years. The payments will increase in value by 4 percent each year. The appropriate discount rate is 10 percent. What is the present value of your winnings A. $6,221,407 ANSWER: $6,906,372 C. $7,559,613 D. $7,811,406 E. $8,003.11 121. You are preparing to make monthly payments of $65, beginning at the end of this month, into an account that pays 6 percent interest compounded monthly. How many payments will you have made when your account balance reaches $9,278 A. 97 ANSWER: 108 C. 119 D. 124 E. 131 122. You want to borrow $47,170 from your local bank to buy a new sailboat. You can afford to make monthly payments of $1,160, but no more. Assume monthly compounding. What is the highest rate you can afford on a 48-month APR loan ANSWER: 8.38 percent B. 8.67 percent C. 8.82 percent D. 9.01 percent E. 9.18 percent 123. You need a 25-year, fixed-rate mortgage to buy a new home for $240,000. Your mortgage bank will lend you the money at a 7.5 percent APR for this 300-month loan, with interest compounded monthly. However, you can only afford monthly payments of $850, so you offer to pay off any remaining loan balance at the end of the loan in the form of a single balloon payment. What will be the amount of the balloon payment if you are to keep your monthly payments at $850 A. $738,464 B. $745,316 C. $767,480 ANSWER: $810,220 E. $847,315 Remaining principal = $240,000 - $115,021.67 = $124,978.33 Balloon payment = $124,978.33 [1 + (0.075/12)]25 12 = $810,220 124. The present value of the following cash flow stream is $5,933.86 when discounted at 11 percent annually. What is the value of the missing cash flow A. $1,500 B. $1,750 C. $2,000 D. $2,250 ANSWER: $2,500 PV of missing cash flow = $5,933.86 - ($2,000/1.11) - ($1,750/1.113) - ($1,250/1.114) = $2,029.06 CF2 = $2,029.06 1.112 = $2,500 125. You have just purchased a new warehouse. To finance the purchase, you've arranged for a 30-year mortgage loan for 80 percent of the $2,600,000 purchase price. The monthly payment on this loan will be $11,000. What is the effective annual rate on this loan ANSWER: 4.98 percentB. 5.25 percent C. 5.46 percent D. 6.01 percent E. 6.50 percent Loan amount = $2,600,000 0.80 = $2,080,000 EAR = [1 + (.0487/12)]12 - 1 = 4.98 percent 126. Consider a firm with a contract to sell an asset 3 years from now for $90,000. The asset costs $71,000 to produce today. At what rate will the firm just break even on this contract A. 7.87 percent B. 8.01 percent ANSWER: 8.23 percent D. 8.57 percent E. 8.90 percent $90,000 = $71,000 (1 + r)3; r = 8.23 percent 127. What is the present value of $1,100 per year, at a discount rate of 10 percent if the first payment is received 6 years from now and the last payment is received 28 years from now ANSWER: $6,067.36 B. $6,138.87 C. $6,333.33 D. $6,420.12 E. $6,511.08 PV = $9,771.54/1.15 = $6,067.36 128. You have your choice of two investment accounts. Investment A is a 5-year annuity that features end-ofmonth $2,500 payments and has an interest rate of 11.5 percent compounded monthly. Investment B is a 10.5 percent continuously compounded lump sum investment, also good for five years. How much would you need to invest in B today for it to be worth as much as investment A five years from now A. $108,206.67 ANSWER: $119,176.06 C. $124,318.08 D. $129,407.17 E. $131,008.15 FVA = $2,500 [{[1 + (0.115/12)]5 12 -1}/(0.115/12)] = $201,462.23 PV = $201,462.23 e-1 0.105 5 = $119,176.06 129. Given an interest rate of 8 percent per year, what is the value at date t = 9 of a perpetual stream of $500 annual payments that begins at date t = 17 ANSWER: $3,646.81 B. $4,109.19 C. $4,307.78 D. $6,250.00 E. $6,487.17 PVt = 16 = $500/.08 = $6,250 PVt = 9 = $6,250/1.0816-9 = $3,646.81 130. You want to buy a new sports car for $55,000. The contract is in the form of a 60-month annuity due at a 6 percent APR, compounded monthly. What will your monthly payment be A. $1,047.90 B. $1,053.87 ANSWER: $1,058.01 D. $1,063.30 E. $1,072.11 131. You are looking at a one-year loan of $10,000. The interest rate is quoted as 10 percent plus 5 points. A point on a loan is simply 1 percent (one percentage point) of the loan amount. Quotes similar to this one are very common with home mortgages. The interest rate quotation in this example requires the borrower to pay 5 points to the lender up front and repay the loan later with 10 percent interest. What is the actual rate you arepaying on this loan A. 15.00 percent B. 15.47 percent C. 15.55 percent ANSWER: 15.79 percent E. 15.84 percent Loan amount received = $10,000 (1 - .05) = $9,500 Loan repayment amount = $10,000 1.101 = $11,000 $11,000 = $9,500 (1 + r)1; r = 15.79 percent 132. Your holiday ski vacation was great, but it unfortunately ran a bit over budget. All is not lost. You just received an offer in the mail to transfer your $5,000 balance from your current credit card, which charges an annual rate of 18.7 percent, to a new credit card charging a rate of 9.4 percent. You plan to make payments of $510 a month on this debt. How many less payments will you have to make to pay off this debt if you transfer the balance to the new card A. 0.36 payments ANSWER: 0.48 payments C. 1.10 payments D. 1.23 payments E. 2.49 payments $5,000 = $510 [(1 - {1 + (0.094/12)]}t)/(0.094/12)] t = ln (1/0.9232)/ln 1.007833; t = 10.24 payments Difference = 10.72 - 10.24 = 0.48 payments Terms in this set (132) 1. An ordinary annuity is best defined by which one of the following A. increasing payments paid for a definitive period of time B. increasing payments paid forever ANSWER: equal payments paid at regular intervals over a stated time period D. equal payments paid at regular intervals of time on an ongoing basis E. unequal payments that occur at set intervals for a limited period of time 2. Which one of the following accurately defines a perpetuity A. a limited number of equal payments paid in even time increments B. payments of equal amounts that are paid irregularly but indefinitely C. varying amounts that are paid at even intervals forever ANSWER: unending equal payments paid at equal time intervals E. unending equal payments paid at either equal or unequal time intervals 3. Which one of the following terms is used to identify a British perpetuity A. ordinary annuity B. amortized cash flow C. annuity due D. discounted loan ANSWER: consol 4. The interest rate that is quoted by a lender is referred to as which one of the following ANSWER: stated interest rate B. compound rate C. effective annual rate D. simple rate E. common rate 5. A monthly interest rate expressed as an annual rate would be an example of which one of the following rates A. stated rate B. discounted annual rate ANSWER: effective annual rateD. periodic monthly rate E. consolidated monthly rate 6. What is the interest rate charged per period multiplied by the number of periods per year called A. effective annual rate ANSWER: annual percentage rate C. periodic interest rate D. compound interest rate E. daily interest rate 7. A loan where the borrower receives money today and repays a single lump sum on a future date is called a(n) _____ loan. A. amortized B. continuous C. balloon ANSWER: pure discount E. interest-only ... 8. Which one of the following terms is used to describe a loan that calls for periodic interest payments and a lump sum principal payment A. amortized loan B. modified loan C. balloon loan D. pure discount loan ANSWER: interest-only loan 9. Which one of the following terms is used to describe a loan wherein each payment is equal in amount and includes both interest and principal ANSWER: amortized loan B. modified loan C. balloon loan D. pure discount loan E. interest-only loan 10. Which one of the following terms is defined as a loan wherein the regular payments, including both interest and principal amounts, are insufficient to retire the entire loan amount, which then must be repaid in one lump sum A. amortized loan B. continuing loan ANSWER: balloon loan D. remainder loan E. interest-only loan 11. You are comparing two annuities which offer quarterly payments of $2,500 for five years and pay 0.75 percent interest per month. Annuity A will pay you on the first of each month while annuity B will pay you on the last day of each month. Which one of the following statements is correct concerning these two annuities A. These two annuities have equal present values but unequal futures values at the end of year five. B. These two annuities have equal present values as of today and equal future values at the end of year five. C. Annuity B is an annuity due. D. Annuity A has a smaller future value than annuity B. ANSWER: Annuity B has a smaller present value than annuity A. 12. You are comparing two investment options that each pay 5 percent interest, compounded annually. Both options will provide you with $12,000 of income. Option A pays three annual payments starting with $2,000 the first year followed by two annual payments of $5,000 each. Option B pays three annual payments of $4,000 each. Which one of the following statements is correct given these two investment options A. Both options are of equal value given that they both provide $12,000 of income. B. Option A has the higher future value at the end of year three. ANSWER: Option B has a higher present value at time zero than does option A. D. Option B is a perpetuity. E. Option A is an annuity. 13. You are considering two projects with the following cash flows: Which of the following statements are true concerning these two projects I. Both projects have the same future value at the end of year 4, given a positive rate of return. II. Both projects have the same future value given a zero rate of return. III. Project X has a higher present value than Project Y, given a positive discount rate.IV. Project Y has a higher present value than Project X, given a positive discount rate. A. II only B. I and III only ANSWER: II and III only D. II and IV only E. I, II, and IV only 14. Which one of the following statements is correct given the following two sets of project cash flows A. The cash flows for Project B are an annuity, but those of Project A are not. B. Both sets of cash flows have equal present values as of time zero given a positive discount rate. C. The present value at time zero of the final cash flow for Project A will be discounted using an exponent of three. D. The present value of Project A cannot be computed because the second cash flow is equal to zero. ANSWER: As long as the discount rate is positive, Project B will always be worth less today than will Project A. 15. Which one of the following statements related to annuities and perpetuities is correct A. An ordinary annuity is worth more than an annuity due given equal annual cash flows for ten years at 7 percent interest, compounded annually. ANSWER: A perpetuity comprised of $100 monthly payments is worth more than an annuity comprised of $100 monthly payments, given an interest rate of 12 percent, compounded monthly. C. Most loans are a form of a perpetuity. D. The present value of a perpetuity cannot be computed, but the future value can. E. Perpetuities are finite but annuities are not. 16. Which of the following statements related to interest rates are correct I. Annual interest rates consider the effect of interest earned on reinvested interest payments. II. When comparing loans, you should compare the effective annual rates. III. Lenders are required by law to disclose the effective annual rate of a loan to prospective borrowers. IV. Annual and effective interest rates are equal when interest is compounded annually. A. I and II only B. II and III only ANSWER: II and IV only D. I, II, and III only E. II, III, and IV only 17. Which one of the following statements concerning interest rates is correct A. Savers would prefer annual compounding over monthly compounding. B. The effective annual rate decreases as the number of compounding periods per year increases. ANSWER: The effective annual rate equals the annual percentage rate when interest is compounded annually. D. Borrowers would prefer monthly compounding over annual compounding. E. For any positive rate of interest, the effective annual rate will always exceed the annual percentage rate. 18. Which one of these statements related to growing annuities and perpetuities is correct A. The cash flow used in the growing annuity formula is the initial cash flow at time zero. B. Growth rates cannot be applied to perpetuities if you wish to compute the present value. C. The future value of an annuity will decrease if the growth rate is increased. D. An increase in the rate of growth will decrease the present value of an annuity. ANSWER: The present value of a growing perpetuity will decrease if the discount rate is increased. 19. Which one of the following statements correctly states a relationship A. Time and future values are inversely related, all else held constant. B. Interest rates and time are positively related, all else held constant. C. An increase in the discount rate increases the present value, given positive rates. D. An increase in time increases the future value given a zero rate of interest. ANSWER: Time and present value are inversely related, all else held constant. 20. Which one of the following compounding periods will yield the smallest present value given a stated future value and annual percentage rate A. annual B. semi-annual C. monthly D. daily ANSWER: continuous 21. The entire repayment of which one of the following loans is computed simply by computing a single future value A. interest-only loan B. balloon loan C. amortized loanANSWER: pure discount loan E. bullet loan 22. How is the principal amount of an interest-only loan repaid A. The principal is forgiven over the loan period so does not have to be repaid. B. The principal is repaid in equal increments and included in each loan payment. ANSWER: The principal is repaid in a lump sum at the end of the loan period. D. The principal is repaid in equal annual payments. E. The principal is repaid in increasing increments through regular monthly payments. 23. An amortized loan: A. requires the principal amount to be repaid in even increments over the life of the loan. ANSWER: may have equal or increasing amounts applied to the principal from each loan payment. C. requires that all interest be repaid on a monthly basis while the principal is repaid at the end of the loan term. D. requires that all payments be equal in amount and include both principal and interest. E. repays both the principal and the interest in one lump sum at the end of the loan term. ... 24. You need $25,000 today and have decided to take out a loan at 7 percent for five years. Which one of the following loans would be the least expensive Assume all loans require monthly payments and that interest is compounded on a monthly basis. A. interest-only loan ANSWER: amortized loan with equal principal payments C. amortized loan with equal loan payments D. discount loan E. balloon loan where 50 percent of the principal is repaid as a balloon payment 25. Your grandmother is gifting you $100 a month for four years while you attend college to earn your bachelor's degree. At a 5.5 percent discount rate, what are these payments worth to you on the day you enter college A. $4,201.16 ANSWER: $4,299.88 C. $4,509.19 D. $4,608.87 E. $4,800.00 26. You just won the grand prize in a national writing contest! As your prize, you will receive $2,000 a month for ten years. If you can earn 7 percent on your money, what is this prize worth to you today ANSWER: $172,252.71 B. $178,411.06 C. $181,338.40 D. $185,333.33 E. $190,450.25 27. Phil can afford $180 a month for 5 years for a car loan. If the interest rate is 8.6 percent, how much can he afford to borrow to purchase a car A. $7,750.00 B. $8,348.03 ANSWER: $8,752.84 D. $9,266.67 E. $9,400.00 28. You are the beneficiary of a life insurance policy. The insurance company informs you that you have two options for receiving the insurance proceeds. You can receive a lump sum of $200,000 today or receive payments of $1,400 a month for 20 years. You can earn 6 percent on your money. Which option should you take and why A. You should accept the payments because they are worth $209,414 to you today. B. You should accept the payments because they are worth $247,800 to you today. C. You should accept the payments because they are worth $336,000 to you today. D. You should accept the $200,000 because the payments are only worth $189,311 to you today. ANSWER: You should accept the $200,000 because the payments are only worth $195,413 to you today. 29. Your employer contributes $75 a week to your retirement plan. Assume that you work for your employer for another 20 years and that the applicable discount rate is 7.5 percent. Given these assumptions, what is this employee benefit worth to you today ANSWER: $40,384.69 B. $42,618.46 C. $44,211.11 D. $44,306.16 E. $44,987.7430. The Design Team just decided to save $1,500 a month for the next 5 years as a safety net for recessionary periods. The money will be set aside in a separate savings account which pays 4.5 percent interest compounded monthly. The first deposit will be made today. What would today's deposit amount have to be if the firm opted for one lump sum deposit today that would yield the same amount of savings as the monthly deposits after 5 years A. $80,459.07 ANSWER: $80,760.79 C. $81,068.18 D. $81,333.33 E. $81,548.20 31. You need some money today and the only friend you have that has any is your miserly friend. He agrees to loan you the money you need, if you make payments of $25 a month for the next six months. In keeping with his reputation, he requires that the first payment be paid today. He also charges you 1.5 percent interest per month. How much money are you borrowing A. $134.09 B. $138.22 C. $139.50 D. $142.68 ANSWER: $144.57 32. You buy an annuity that will pay you $24,000 a year for 25 years. The payments are paid on the first day of each year. What is the value of this annuity today if the discount rate is 8.5 percent A. $241,309 B. $245,621 C. $251,409 D. $258,319 ANSWER: $266,498 33. You are scheduled to receive annual payments of $4,800 for each of the next 7 years. The discount rate is 8 percent. What is the difference in the present value if you receive these payments at the beginning of each year rather than at the end of each year ANSWER: $1,999 B. $2,013 C. $2,221 D. $2,227 E. $2,304 34. You are comparing two annuities with equal present values. The applicable discount rate is 8.75 percent. One annuity pays $5,000 on the first day of each year for 20 years. How much does the second annuity pay each year for 20 years if it pays at the end of each year A. $5,211 B. $5,267 C. $5,309 D. $5,390 ANSWER: $5,438 35. Trish receives $480 on the first of each month. Josh receives $480 on the last day of each month. Both Trish and Josh will receive payments for next three years. At a 9.5 percent discount rate, what is the difference in the present value of these two sets of payments ANSWER: $118.63 B. $121.06 C. $124.30 D. $129.08 E. $132.50 36. What is the future value of $1,200 a year for 40 years at 8 percent interest Assume annual compounding. A. $301,115 B. $306,492 ANSWER: $310,868 D. $342,908 E. $347,267 37. What is the future value of $15,000 a year for 30 years at 12 percent interest A. $2,878,406 ANSWER: $3,619,990 C. $3,711,414 D. $3,989,476 E. $4,021,22338. Alexa plans on saving $3,000 a year and expects to earn an annual rate of 10.25 percent. How much will she have in her account at the end of 45 years A. $1,806,429 B. $1,838,369 C. $2,211,407 ANSWER: $2,333,572 E. $2,508,316 39. Theresa adds $1,000 to her savings account on the first day of each year. Marcus adds $1,000 to his savings account on the last day of each year. They both earn 6.5 percent annual interest. What is the difference in their savings account balances at the end of 35 years ANSWER: $8,062 B. $8,113 C. $8,127 D. $8,211 E. $8,219 40. You are borrowing $17,800 to buy a car. The terms of the loan call for monthly payments for 5 years at 8.6 percent interest. What is the amount of each payment A. $287.71 B. $291.40 C. $301.12 D. $342.76 ANSWER: $366.05 41. You borrow $165,000 to buy a house. The mortgage rate is 7.5 percent and the loan period is 30 years. Payments are made monthly. If you pay the mortgage according to the loan agreement, how much total interest will you pay A. $206,408 B. $229,079 ANSWER: $250,332 D. $264,319 E. $291,406 42. Holiday Tours (HT) has an employment contract with its newly hired CEO. The contract requires a lump sum payment of $10.4 million be paid to the CEO upon the successful completion of her first three years of service. HT wants to set aside an equal amount of money at the end of each year to cover this anticipated cash outflow and will earn 5.65 percent on the funds. How much must HT set aside each year for this purpose A. $3,184,467 ANSWER: $3,277,973 C. $3,006,409 D. $3,318,190 E. $3,466,667 43. Nadine is retiring at age 62 and expects to live to age 85. On the day she retires, she has $348,219 in her retirement savings account. She is somewhat conservative with her money and expects to earn 6 percent during her retirement years. How much can she withdraw from her retirement savings each month if she plans to spend her last penny on the morning of her death A. $1,609.92 B. $1,847.78 C. $1,919.46 D. $2,116.08 ANSWER: $2,329.05 44. Kingston Development Corp. purchased a piece of property for $2.79 million. The firm paid a down payment of 15 percent in cash and financed the balance. The loan terms require monthly payments for 15 years at an annual percentage rate of 7.75 percent, compounded monthly. What is the amount of each mortgage payment ANSWER: $22,322.35 B. $23,419.97 C. $23,607.11 D. $24,878.15 E. $25,301.16 Amount financed = $2,790,000 (1 - 0.15) = $2,371,500 45. You estimate that you will owe $42,800 in student loans by the time you graduate. The interest rate is 4.25 percent. If you want to have this debt paid in full within six years, how much must you pay each month A. $611.09 ANSWER: $674.50C. $714.28 D. $736.05 E. $742.50 46. You are buying a previously owned car today at a price of $3,500. You are paying $300 down in cash and financing the balance for 36 months at 8.5 percent. What is the amount of each loan payment ANSWER: $101.02 B. $112.23 C. $118.47 D. $121.60 E. $124.40 Amount financed = $3,500 - $300 = $3,200 47. Atlas Insurance wants to sell you an annuity which will pay you $3,400 per quarter for 25 years. You want to earn a minimum rate of return of 6.5 percent. What is the most you are willing to pay as a lump sum today to buy this annuity A. $151,008.24 B. $154,208.16 ANSWER: $167,489.11 D. $173,008.80 E. $178,927.59 48. Your car dealer is willing to lease you a new car for $245 a month for 48 months. Payments are due on the first day of each month starting with the day you sign the lease contract. If your cost of money is 6.5 percent, what is the current value of the lease A. $10,331.03 ANSWER: $10,386.99 C. $12,197.74 D. $12,203.14 E. $13,008.31 49. Your great aunt left you an inheritance in the form of a trust. The trust agreement states that you are to receive $3,600 on the first day of each year, starting immediately and continuing for 20 years. What is the value of this inheritance today if the applicable discount rate is 6.75 percent A. $38,890.88 B. $40,311.16 ANSWER: $41,516.01 D. $42,909.29 E. $43,333.33 50. You just received an insurance settlement offer related to an accident you had six years ago. The offer gives you a choice of one of the following three offers: You can earn 7.5 percent on your investments. You do not care if you personally receive the funds or if they are paid to your heirs should you die within the settlement period. Which one of the following statements is correct given this information A. Option A is the best choice as it provides the largest monthly payment. B. Option B is the best choice because it pays the largest total amount. ANSWER: Option C is the best choice because it is has the largest current value. D. Option B is the best choice because you will receive the most payments. E. You are indifferent to the three options as they are all equal in value. 51. Samuelson Engines wants to save $750,000 to buy some new equipment six years from now. The plan is to set aside an equal amount of money on the first day of each quarter starting today. The firm can earn 4.75 percent on its savings. How much does the firm have to save each quarter to achieve its goal ANSWER: $26,872.94 B. $26,969.70 C. $27,192.05 D. $27,419.29 E. $27,911.08 52. Stephanie is going to contribute $300 on the first of each month, starting today, to her retirement account. Her employer will provide a 50 percent match. In other words, her employer will contribute 50 percent of the amount Stephanie saves. If both Stephanie and her employer continue to do this and she can earn a monthly rate of 0.90 percent, how much will she have in her retirement account 35 years from now A. $1,936,264 B. $1,943,286 C. $1,989,312D. $2,068,418 ANSWER: $2,123,007 53. You are considering an annuity which costs $160,000 today. The annuity pays $18,126 a year at an annual interest rate of 7.50 percent. What is the length of the annuity time period A. 12 years B. 13 years C. 14 years ANSWER: 15 years E. 16 years 54. Today, you borrowed $6,200 on your credit card to purchase some furniture. The interest rate is 14.9 percent, compounded monthly. How long will it take you to pay off this debt assuming that you do not charge anything else and make regular monthly payments of $120 A. 5.87 years B. 6.40 years ANSWER: 6.93 years D. 7.23 years E. 7.31 years 55. Meadow Brook Manor would like to buy some additional land and build a new assisted living center. The anticipated total cost is $23.6 million. The CEO of the firm is quite conservative and will only do this when the company has sufficient funds to pay cash for the entire construction project. Management has decided to save $1.2 million a quarter for this purpose. The firm earns 6.25 percent, compounded quarterly, on the funds it saves. How long does the company have to wait before expanding its operations A. 4.09 years ANSWER: 4.32 years C. 4.46 years D. 4.82 years E. 4.91 years 56. Today, you are retiring. You have a total of $411,016 in your retirement savings and have the funds invested such that you expect to earn an average of 7.10 percent, compounded monthly, on this money throughout your retirement years. You want to withdraw $2,500 at the beginning of every month, starting today. How long will it be until you run out of money A. 31.97 years B. 34.56 years C. 42.03 year ANSWER: 48.19 years E. You will never run out of money. 57. Gene's Art Gallery is notoriously known as a slow-payer. The firm currently needs to borrow $27,500 and only one company will even deal with them. The terms of the loan call for daily payments of $100. The first payment is due today. The interest rate is 21.9 percent, compounded daily. What is the time period of this loan Assume a 365 day year. A. 264.36 days B. 280.81 days ANSWER: 300.43 days D. 316.46 days E. 341.09 days 58. The Wine Press is considering a project which has an initial cash requirement of $187,400. The project will yield cash flows of $2,832 monthly for 84 months. What is the rate of return on this project A. 6.97 percent ANSWER: 7.04 percent C. 7.28 percent D. 7.41 percent E. 7.56 percent 59. Your insurance agent is trying to sell you an annuity that costs $200,000 today. By buying this annuity, your agent promises that you will receive payments of $1,225 a month for the next 30 years. What is the rate of return on this investment A. 5.75 percent B. 5.97 percent ANSWER: 6.20 percent D. 6.45 percent E. 6.67 percent 60. You have been investing $250 a month for the last 13 years. Today, your investment account is worth $73,262. What is your average rate of return on your investmentsANSWER: 8.94 percent B. 9.23 percent C. 9.36 percent D. 9.41 percent E. 9.78 percent 61. Will has been purchasing $25,000 worth of New Tek stock annually for the past 11 years. His holdings are now worth $598,100. What is his annual rate of return on this stock A. 14.13 percent B. 14.24 percent C. 14.29 percent D. 14.37 percent ANSWER: 14.68 percent 62. Your father helped you start saving $20 a month beginning on your 5th birthday. He always made you deposit the money into your savings account on the first day of each month just to "start the month out right." Today completes your 17th year of saving and you now have $6,528.91 in this account. What is the rate of return on your savings ANSWER: 5.15 percent B. 5.30 percent C. 5.47 percent D. 5.98 percent E. 6.12 percent 63. Today, you turn 23. Your birthday wish is that you will be a millionaire by your 40th birthday. In an attempt to reach this goal, you decide to save $50 a day, every day until you turn 40. You open an investment account and deposit your first $50 today. What rate of return must you earn to achieve your goal A. 10.67 percent ANSWER: 11.85 percent C. 12.90 percent D. 13.06 percent E. 13.54 percent 64. You just settled an insurance claim. The settlement calls for increasing payments over a 10-year period. The first payment will be paid one year from now in the amount of $10,000. The following payments will increase by 4.5 percent annually. What is the value of this settlement to you today if you can earn 8 percent on your investments A. $76,408.28 ANSWER: $80,192.76 C. $82,023.05 D. $84,141.14 E. $85,008.16 65. Your grandfather left you an inheritance that will provide an annual income for the next 10 years. You will receive the first payment one year from now in the amount of $4,000. Every year after that, the payment amount will increase by 6 percent. What is your inheritance worth to you today if you can earn 9.5 percent on your investments ANSWER: $31,699.15 B. $36,666.67 C. $41,121.21 D. $43,464.12 E. $46,908.17 66. You just won a national sweepstakes! For your prize, you opted to receive never-ending payments. The first payment will be $12,500 and will be paid one year from today. Every year thereafter, the payments will increase by 3.5 percent annually. What is the present value of your prize at a discount rate of 8 percent A. $166,666.67 B. $248,409.19 ANSWER: $277,777.78 D. $291,006.12 E. $300,000.00 67. A wealthy benefactor just donated some money to the local college. This gift was established to provide scholarships for worthy students. The first scholarships will be granted one year from now for a total of $35,000. Annually thereafter, the scholarship amount will be increased by 5.5 percent to help offset the effects of inflation. The scholarship fund will last indefinitely. What is the value of this gift today at a discount rate of 8 percent A. $437,500 B. $750,000 C. $1,200,000ANSWER: $1,400,000 E. $1,450,750 68. Southern Tours is considering acquiring Holiday Vacations. Management believes Holiday Vacations can generate cash flows of $187,000, $220,000, and $245,000 over the next three years, respectively. After that time, they feel the business will be worthless. Southern Tours has determined that a 13.5 percent rate of return is applicable to this potential acquisition. What is Southern Tours willing to pay today to acquire Holiday Vacations ANSWER: $503,098 B. $538,615 C. $545,920 D. $601,226 E. $638,407 69. You are considering two savings options. Both options offer a 7.4 percent rate of return. The first option is to save $900, $2,100, and $3,000 at the end of each year for the next three years, respectively. The other option is to save one lump sum amount today. If you want to have the same balance in your savings account at the end of the three years, regardless of the savings method you select, how much do you need to save today if you select the lump sum option A. $4,410 B. $4,530 C. $4,600 ANSWER: $5,080 E. $5,260 70. Your parents have made you two offers. The first offer includes annual gifts of $10,000, $11,000, and $12,000 at the end of each of the next three years, respectively. The other offer is the payment of one lump sum amount today. You are trying to decide which offer to accept given the fact that your discount rate is 8 percent. What is the minimum amount that you will accept today if you are to select the lump sum offer ANSWER: $28,216 B. $29,407 C. $29,367 D. $30,439 E. $30,691 71. You are considering changing jobs. Your goal is to work for three years and then return to school full-time in pursuit of an advanced degree. A potential employer just offered you an annual salary of $41,000, $44,000, and $46,000 a year for the next three years, respectively. All salary payments are made as lump sum payments at the end of each year. The offer also includes a starting bonus of $2,500 payable immediately. What is this offer worth to you today at a discount rate of 6.75 percent A. $112,406 B. $115,545 ANSWER: $117,333 D. $121,212 E. $134,697 72. You are considering a project which will provide annual cash inflows of $4,500, $5,700, and $8,000 at the end of each year for the next three years, respectively. What is the present value of these cash flows, given a 9 percent discount rate A. $14,877 ANSWER: $15,103 C. $15,429 D. $16,388 E. $16,847 73. You just signed a consulting contract that will pay you $35,000, $52,000, and $80,000 annually at the end of the next three years, respectively. What is the present value of these cash flows given a 10.5 percent discount rate ANSWER: $133,554 B. $142,307 C. $148,880 D. $151,131 E. $156,910 74. You have some property for sale and have received two offers. The first offer is for $89,500 today in cash. The second offer is the payment of $35,000 today and an additional $70,000 two years from today. If the applicable discount rate is 11.5 percent, which offer should you accept and why A. You should accept the $89,500 today because it has the higher net present value. B. You should accept the $89,500 today because it has the lower future value. C. You should accept the first offer as it has the greatest value to you.ANSWER: You should accept the second offer because it has the larger net present value. E. It does not matter which offer you accept as they are equally valuable. 75. Your local travel agent is advertising an upscale winter vacation package for travel three years from now to Antarctica. The package requires that you pay $25,000 today, $30,000 one year from today, and a final payment of $45,000 on the day you depart three years from today. What is the cost of this vacation in today's dollars if the discount rate is 9.75 percent ANSWER: $86,376 B. $89,695 C. $91,219 D. $91,407 E. $93,478 76. One year ago, Deltona Motor Parts deposited $16,500 in an investment account for the purpose of buying new equipment three years from today. Today, it is adding another $12,000 to this account. The company plans on making a final deposit of $20,000 to the account one year from today. How much will be available when it is ready to buy the equipment, assuming the account pays 5.5 interest A. $53,408 B. $53,919 C. $56,211 ANSWER: $56,792 E. $58,021 77. Lucas will receive $6,800, $8,700, and $12,500 each year starting at the end of year one. What is the future value of these cash flows at the end of year five if the interest rate is 7 percent A. $32,418 B. $32,907 ANSWER: $33,883 D. $35,411 E. $36,255 78. You plan on saving $5,200 this year, nothing next year, and $7,500 the following year. You will deposit these amounts into your investment account at the end of each year. What will your investment account be worth at the end of year three if you can earn 8.5 percent on your funds A. $13,528.12 ANSWER: $13,621.57 C. $13,907.11 D. $14,526.50 E. $14,779.40 79. Miley expects to receive the following payments: Year 1 = $60,000; Year 2 = $35,000; Year 3 = $12,000. All of this money will be saved for her retirement. If she can earn an average of 10.5 percent on her investments, how much will she have in her account 25 years after making her first deposit A. $972,373 B. $989,457 C. $1,006,311 D. $1,147,509 ANSWER: $1,231,776 80. Blackwell, Inc. has a $75,000 liability it must pay three years from today. The company is opening a savings account so that the entire amount will be available when this debt needs to be paid. The plan is to make an initial deposit today and then deposit an additional $15,000 each year for the next three years, starting one year from today. The account pays a 4.5 percent rate of return. How much does the firm need to deposit today A. $18,299.95 B. $20,072.91 C. $21,400.33 ANSWER: $24,487.78 E. $31,076.56 81. The government has imposed a fine on the Corner Tavern. The fine calls for annual payments of $150,000, $100,000, $75,000, and $50,000, respectively, over the next four years. The first payment is due one year from today. The government plans to invest the funds until the final payment is collected and then donate the entire amount, including the investment earnings, to help the local community shelter. The government will earn 6.25 percent on the funds held. How much will the community shelter receive four years from today A. $349,674.06 B. $366,875.00 ANSWER: $422,497.56 D. $458,572.71E. $515,737.67 82. Wicker Imports established a trust fund that provides $90,000 in scholarships each year for needy students. The trust fund earns a fixed 6 percent rate of return. How much money did the firm contribute to the fund assuming that only the interest income is distributed A. $1,150,000 B. $1,200,000 C. $1,333,333 ANSWER: $1,500,000 E. $1,600,000 83. A preferred stock pays an annual dividend of $2.60. What is one share of this stock worth today if the rate of return is 11.75 percent A. $18.48 B. $20.00 ANSWER: $22.13 D. $28.80 E. $30.55 84. You would like to establish a trust fund that will provide $120,000 a year forever for your heirs. The trust fund is going to be invested very conservatively so the expected rate of return is only 5.75 percent. How much money must you deposit today to fund this gift for your heirs ANSWER: $2,086,957 B. $2,121,212 C. $2,300,000 D. $2,458,122 E. $2,500,000 85. You just paid $750,000 for an annuity that will pay you and your heirs $45,000 a year forever. What rate of return are you earning on this policy A. 5.25 percent B. 5.50 percent C. 5.75 percent ANSWER: 6.00 percent E. 6.25 percent 86. You grandfather won a lottery years ago. The value of his winnings at the time was $50,000. He invested this money such that it will provide annual payments of $2,400 a year to his heirs forever. What is the rate of return A. 4.75 percent ANSWER: 4.80 percent C. 5.00 percent D. 5.10 percent E. 5.15 percent 87. The preferred stock of Casco has a 5.48 percent dividend yield. The stock is currently priced at $59.30 per share. What is the amount of the annual dividend A. $2.80 B. $2.95 C. $3.10 ANSWER: $3.25 E. $3.40 88. Your credit card company charges you 1.65 percent interest per month. What is the annual percentage rate on your account A. 18.95 percent ANSWER: 19.80 percent C. 20.90 percent D. 21.25 percent E. 21.70 percent 89. What is the annual percentage rate on a loan with a stated rate of 2.25 percent per quarter ANSWER: 9.00 percent B. 9.09 percent C. 9.18 percent D. 9.27 percent E. 9.31 percent 90. You are paying an effective annual rate of 18.974 percent on your credit card. The interest is compounded monthly. What is the annual percentage rate on this account ANSWER: 17.50 percent B. 18.00 percentC. 18.25 percent D. 18.64 percent E. 19.00 percent 91. What is the effective annual rate if a bank charges you 9.50 percent compounded quarterly A. 9.62 percent B. 9.68 percent C. 9.72 percent ANSWER: 9.84 percent E. 9.91 percent 92. Your credit card company quotes you a rate of 17.9 percent. Interest is billed monthly. What is the actual rate of interest you are paying A. 19.03 percent B. 19.21 percent ANSWER: 19.44 percent D. 19.57 percent E. 19.72 percent 93. The Pawn Shop loans money at an annual rate of 21 percent and compounds interest weekly. What is the actual rate being charged on these loans A. 23.16 percent ANSWER: 23.32 percent C. 23.49 percent D. 23.56 percent E. 23.64 percent 94. You are considering two loans. The terms of the two loans are equivalent with the exception of the interest rates. Loan A offers a rate of 7.75 percent, compounded daily. Loan B offers a rate of 8 percent, compounded semi-annually. Which loan should you select and why ANSWER: A; the effective annual rate is 8.06 percent. B. A; the annual percentage rate is 7.75 percent. C. B; the annual percentage rate is 7.68 percent. D. B; the effective annual rate is 8.16 percent. E. The loans are equivalent offers so you can select either one. 95. You have $5,600 that you want to use to open a savings account. There are five banks located in your area. The rates paid by banks A through E, respectively, are given below. Which bank should you select if your goal is to maximize your interest income A. 3.26 percent, compounded annually B. 3.20 percent, compounded monthly ANSWER: 3.25 percent, compounded semi-annually D. 3.10 percent, compounded continuously E. 3.15 percent, compounded quarterly EARA = 3.26 percent Bank C offers the highest effective annual rate at 3.276 percent. 96. What is the effective annual rate of 14.9 percent compounded continuously A. 15.59 percent B. 15.62 percent C. 15.69 percent D. 15.84 percent ANSWER: 16.07 percent 97. What is the effective annual rate of 9.75 percent compounded continuously A. 10.17 percent ANSWER: 10.24 percent C. 10.29 percent D. 10.33 percent E. 10.47 percent 98. City Bank wants to appear competitive based on quoted loan rates and thus must offer a 7.75 percent annual percentage rate on its loans. What is the maximum rate the bank can actually earn based on the quoted rate ANSWER: 8.06 percent B. 8.14 percent C. 8.21 percent D. 8.26 percentE. 8.58 percent 99. You are going to loan a friend $900 for one year at a 5 percent rate of interest, compounded annually. How much additional interest could you have earned if you had compounded the rate continuously rather than annually A. $0.97 ANSWER: $1.14 C. $1.23 D. $1.36 E. $1.41 100. You are borrowing money today at 8.48 percent, compounded annually. You will repay the principal plus all the interest in one lump sum of $12,800 two years from today. How much are you borrowing A. $9,900.00 B. $10,211.16 ANSWER: $10,877.04 D. $11,401.16 E. $11,250.00 101. This morning, you borrowed $9,500 at 7.65 percent annual interest. You are to repay the loan principal plus all of the loan interest in one lump sum four years from today. How much will you have to repay ANSWER: $12,757.92 B. $12,808.13 C. $12,911.89 D. $13,006.08 E. $13,441.20 102. On this date last year, you borrowed $3,400. You have to repay the loan principal plus all of the interest six years from today. The payment that is required at that time is $6,000. What is the interest rate on this loan A. 8.01 percent ANSWER: 8.45 percent C. 8.78 percent D. 9.47 percent E. 9.93 percent 103. John's Auto Repair just took out an $89,000, 10-year, 8 percent, interest-only loan from the bank. Payments are made annually. What is the amount of the loan payment in year 10 A. $7,120 B. $8,850 C. $13,264 D. $89,000 ANSWER: $96,120 104. On the day you entered college, you borrowed $18,000 on an interest-only, four-year loan at 5.25 percent from your local bank. Payments are to be paid annually. What is the amount of your loan payment in year 2 ANSWER: $945 B. $1,890 C. $3,600 D. $5,106 E. $6,250 105. On the day you entered college you borrowed $25,000 from your local bank. The terms of the loan include an interest rate of 4.75 percent. The terms stipulate that the principal is due in full one year after you graduate. Interest is to be paid annually at the end of each year. Assume that you complete college in four years. How much total interest will you pay on this loan A. $5,266.67 B. $5,400.00 ANSWER: $5,937.50 D. $6,529.00 E. $6,607.11 106. You just acquired a mortgage in the amount of $249,500 at 6.75 percent interest, compounded monthly. Equal payments are to be made at the end of each month for thirty years. How much of the first loan payment is interest (Assume each month is equal to 1/12 of a year.) A. $925.20 B. $1,206.16 ANSWER: $1,403.44 D. $1,511.21 E. $1,548.60Interest portion of first loan payment = 107. On June 1, you borrowed $212,000 to buy a house. The mortgage rate is 8.25 percent. The loan is to be repaid in equal monthly payments over 15 years. The first payment is due on July 1. How much of the second payment applies to the principal balance (Assume that each month is equal to 1/12 of a year.) ANSWER: $603.32 B. $698.14 C. $1,358.56 D. $1,453.38 E. $2,056.70 108. This morning, you borrowed $150,000 to buy a house. The mortgage rate is 7.35 percent. The loan is to be repaid in equal monthly payments over 20 years. The first payment is due one month from today. How much of the second payment applies to the principal balance (Assume that each month is equal to 1/12 of a year.) A. $268.84 ANSWER: $277.61 C. $917.06 D. $925.83 E. $1,194.67 ANSWER: The APR is a stated rate and is computed as (r n), where r is the rate per period and n is the number of periods per year. The EAR considers compounding and is computed as (1 + r)n - 1, where r is the rate per period and n is the number of periods per year. The effective annual rate will always be higher than the annual percentage rate as long as the account is compounded more than once a year and the interest rate is greater than zero. The EAR is the equivalent rate based on annual compounding. The EAR has greater importance because it is the actual cost of a loan. Feedback: Refer to section 6.3 ... ... ... ... ... 112. Kristie owns a perpetuity which pays $12,000 at the end of each year. She comes to you and offers to sell you all of the payments to be received after the 10th year. Explain how you can determine the value of this offer. ... ANSWER: 113. Western Bank offers you a $21,000, 6-year term loan at 8 percent annual interest. What is the amount of your annual loan payment A. $4,228.50 ANSWER: $4,542.62 C. $4,666.67 D. $4,901.18 E. $5,311.07 114. First Century Bank wants to earn an effective annual return on its consumer loans of 10 percent per year. The bank uses daily compounding on its loans. By law, what interest rate is the bank required to report to potential borrowers A. 9.23 percent B. 9.38 percent ANSWER: 9.53 percent D. 9.72 percent E. 10.00 percent APR = 365 [(1 + 0.10)1/365 - 1] = 9.53 percent 115. Downtown Bank is offering 3.4 percent compounded daily on its savings accounts. You deposit $8,000 today. How much will you have in your account 11 years from now ANSWER: $11,628.09 B. $11,714.06 C. $12,204.50 D. $12,336.81 E. $12,414.14FV = $8,000 [1 + (0.034/365)]11 365 = $11,628.09 116. You want to buy a new sports coupe for $41,750, and the finance office at the dealership has quoted you an 8.6 percent APR loan compounded monthly for 48 months to buy the car. What is the effective interest rate on this loan A. 8.28 percent B. 8.41 percent C. 8.72 percent D. 8.87 percent ANSWER: 8.95 percent EAR = [1 + (.086/12)]12 - 1 = 8.95 percent 117. Beginning three months from now, you want to be able to withdraw $1,500 each quarter from your bank account to cover college expenses over the next 4 years. The account pays 1.25 percent interest per quarter. How much do you need to have in your account today to meet your expense needs over the next 4 years ANSWER: $21,630.44 B. $21,847.15 C. $22,068.00 D. $22,454.09 E. $22,711.18 118. You are planning to save for retirement over the next 15 years. To do this, you will invest $1,100 a month in a stock account and $500 a month in a bond account. The return on the stock account is expected to be 7 percent, and the bond account will pay 4 percent. When you retire, you will combine your money into an account with a 5 percent return. How much can you withdraw each month during retirement assuming a 20-year withdrawal period A. $2,636.19 B. $2,904.11 C. $3,008.21 ANSWER: $3,113.04 E. $3,406.97 119. You want to be a millionaire when you retire in 40 years. You can earn an 11 percent annual return. How much more will you have to save each month if you wait 10 years to start saving versus if you start saving at the end of this month A. $79.22 B. $114.13 C. $168.47 D. $201.15 ANSWER: $240.29 FVA40 years = $1,000,000 = C [{[1 + (0.11/12)]40 12; C = $116.28 FVA30 years = $1,000,000 = C [{[1 + (0.11/12)]30 12; C = $356.57 Difference = $356.57 - $116.28 = $240.29 120. You have just won the lottery and will receive $540,000 as your first payment one year from now. You will receive payments for 26 years. The payments will increase in value by 4 percent each year. The appropriate discount rate is 10 percent. What is the present value of your winnings A. $6,221,407 ANSWER: $6,906,372 C. $7,559,613 D. $7,811,406 E. $8,003.11 121. You are preparing to make monthly payments of $65, beginning at the end of this month, into an account that pays 6 percent interest compounded monthly. How many payments will you have made when your account balance reaches $9,278 A. 97 ANSWER: 108 C. 119 D. 124 E. 131 122. You want to borrow $47,170 from your local bank to buy a new sailboat. You can afford to make monthly payments of $1,160, but no more. Assume monthly compounding. What is the highest rate you can afford on a 48-month APR loan ANSWER: 8.38 percent B. 8.67 percent C. 8.82 percent D. 9.01 percent E. 9.18 percent123. You need a 25-year, fixed-rate mortgage to buy a new home for $240,000. Your mortgage bank will lend you the money at a 7.5 percent APR for this 300-month loan, with interest compounded monthly. However, you can only afford monthly payments of $850, so you offer to pay off any remaining loan balance at the end of the loan in the form of a single balloon payment. What will be the amount of the balloon payment if you are to keep your monthly payments at $850 A. $738,464 B. $745,316 C. $767,480 ANSWER: $810,220 E. $847,315 Remaining principal = $240,000 - $115,021.67 = $124,978.33 Balloon payment = $124,978.33 [1 + (0.075/12)]25 12 = $810,220 124. The present value of the following cash flow stream is $5,933.86 when discounted at 11 percent annually. What is the value of the missing cash flow A. $1,500 B. $1,750 C. $2,000 D. $2,250 ANSWER: $2,500 PV of missing cash flow = $5,933.86 - ($2,000/1.11) - ($1,750/1.113) - ($1,250/1.114) = $2,029.06 CF2 = $2,029.06 1.112 = $2,500 125. You have just purchased a new warehouse. To finance the purchase, you've arranged for a 30-year mortgage loan for 80 percent of the $2,600,000 purchase price. The monthly payment on this loan will be $11,000. What is the effective annual rate on this loan ANSWER: 4.98 percent B. 5.25 percent C. 5.46 percent D. 6.01 percent E. 6.50 percent Loan amount = $2,600,000 0.80 = $2,080,000 EAR = [1 + (.0487/12)]12 - 1 = 4.98 percent 126. Consider a firm with a contract to sell an asset 3 years from now for $90,000. The asset costs $71,000 to produce today. At what rate will the firm just break even on this contract A. 7.87 percent B. 8.01 percent ANSWER: 8.23 percent D. 8.57 percent E. 8.90 percent $90,000 = $71,000 (1 + r)3; r = 8.23 percent 127. What is the present value of $1,100 per year, at a discount rate of 10 percent if the first payment is received 6 years from now and the last payment is received 28 years from now ANSWER: $6,067.36 B. $6,138.87 C. $6,333.33 D. $6,420.12 E. $6,511.08 PV = $9,771.54/1.15 = $6,067.36 128. You have your choice of two investment accounts. Investment A is a 5-year annuity that features end-ofmonth $2,500 payments and has an interest rate of 11.5 percent compounded monthly. Investment B is a 10.5 percent continuously compounded lump sum investment, also good for five years. How much would you need to invest in B today for it to be worth as much as investment A five years from now A. $108,206.67 ANSWER: $119,176.06 C. $124,318.08 D. $129,407.17 E. $131,008.15 FVA = $2,500 [{[1 + (0.115/12)]5 12 -1}/(0.115/12)] = $201,462.23 PV = $201,462.23 e-1 0.105 5 = $119,176.06129. Given an interest rate of 8 percent per year, what is the value at date t = 9 of a perpetual stream of $500 annual payments that begins at date t = 17 ANSWER: $3,646.81 B. $4,109.19 C. $4,307.78 D. $6,250.00 E. $6,487.17 PVt = 16 = $500/.08 = $6,250 PVt = 9 = $6,250/1.0816-9 = $3,646.81 130. You want to buy a new sports car for $55,000. The contract is in the form of a 60-month annuity due at a 6 percent APR, compounded monthly. What will your monthly payment be A. $1,047.90 B. $1,053.87 ANSWER: $1,058.01 D. $1,063.30 E. $1,072.11 131. You are looking at a one-year loan of $10,000. The interest rate is quoted as 10 percent plus 5 points. A point on a loan is simply 1 percent (one percentage point) of the loan amount. Quotes similar to this one are very common with home mortgages. The interest rate quotation in this example requires the borrower to pay 5 points to the lender up front and repay the loan later with 10 percent interest. What is the actual rate you are paying on this loan A. 15.00 percent B. 15.47 percent C. 15.55 percent ANSWER: 15.79 percent E. 15.84 percent Loan amount received = $10,000 (1 - .05) = $9,500 Loan repayment amount = $10,000 1.101 = $11,000 $11,000 = $9,500 (1 + r)1; r = 15.79 percent 132. Your holiday ski vacation was great, but it unfortunately ran a bit over budget. All is not lost. You just received an offer in the mail to transfer your $5,000 balance from your current credit card, which charges an annual rate of 18.7 percent, to a new credit card charging a rate of 9.4 percent. You plan to make payments of $510 a month on this debt. How many less payments will you have to make to pay off this debt if you transfer the balance to the new card A. 0.36 payments ANSWER: 0.48 payments C. 1.10 payments D. 1.23 payments E. 2.49 payments $5,000 = $510 [(1 - {1 + (0.094/12)]}t)/(0.094/12)] t = ln (1/0.9232)/ln 1.007833; t = 10.24 payments Difference = 10.72 - 10.24 = 0.48 payments Questions in Chapter 6 concept.qz 1) A given rate is quoted as 12 percent, but has an effective annual rate of 12.55 percent. What is the rate of compounding during the year? [A] annually [B] semi-annually [C] quarterly [D] monthly [E] continuously [A] :If interest is compounded annually, the effective and annual rates are equal. Review section 6.3. [B] :Twelve percent compounded semi-annually has an effective annual rate of 12.36 percent. Review section 6.3. [C] :You are correct! [D] :Twelve percent compounded monthly has an effective annual rate of 12.68 percent. Review section 6.3. [E] :Twelve percent compounded continuously has an effective annual rate of 12.75 percent. Reviewsection 6.3. 2) You own a bond issued by the Canadian Pacific railroad that promises to pay the holder $100 annually forever. You plan to sell the bond five years from now. If similar investments yield 8 percent at that time, how much will your bond be worth? [A] $918.79 [B] $1,014.28 [C] $1,250.00 [D] $1,489.42 [E] $1,958.20 [A] :Did you use the perpetuity formula? Review section 6.2. [B] :Did you use the perpetuity formula? Review section 6.2. [C] :You are correct! [D] :Did you use the perpetuity formula? Review section 6.2. [E] :Did you use the perpetuity formula? Review section 6.2. 3) The stated interest rate is the same thing as the effective annual rate. [A] True [B] False [A] :You need to review these definitions in section 6.3. [B] :You are correct! 4) You can find the future value of a set of cash flows by finding the future value of each cash flow individually and then summing these future values. [A] True [B] False [A] :You are correct! [B] :This is just one of the ways to find the future value of a stream of cash flows. Review section 6.1. 5) You win the lottery and are given the option of receiving $250,000 now or an annuity of $25,000 at the end of each year for 30 years. Ignoring taxes, which one of the following statements is correct? [A] You cannot choose between the two options without first computing their future values. [B] You will always choose the lump regardless of the interest rate applied. [C] You will choose the annuity payment if the interest rate is 7 percent. [D] You will always choose the annuity. [E] Comparing the future value of each option will lead to a different decision than comparing the present values. [A] :You can compare the two by computing either their future values or their present values. Review section 6.2. [B] :Which option do you prefer at 10 percent? What about 5 percent? Review section 6.2. [C] :You are correct! [D] :This is not true. Verify that for interest rates above 9.31 percent you would prefer the lump sum to the annuity. Review section 6.2. [E] :You will reach the same conclusion whether comparing future values or present values. Review section 6.2. 6) At the end of each year for the next ten years you will receive cash flows of $50. The initial investment is $320. What rate of return are you expecting from this investment?[A] 9.06 percent [B] 10.43 percent [C] 12.01 percent [D] 12.28 percent [E] 13.21 percent [A] :You are correct! [B] :Is the $320 a present value or a future value? Review section 6.2. [C] :This is a present value of an annuity problem. Review section 6.2. [D] :This is a present value of an annuity problem. Review section 6.2. [E] :This is a present value of an annuity problem. Review section 6.2. 7) What annual percentage rate of return allows you to triple your money in 20 years? [A] 5.65 percent [B] 5.98 percent [C] 6.86 percent [D] 6.92 percent [E] 8.99 percent [A] :You are correct! [B] :Can you use a present value of $1 and a future value of $3 to solve this problem? Review section 6.3. [C] :Can you use a present value of $1 and a future value of $3 to solve this problem? Review section 6.3. [D] :Can you use a present value of $1 and a future value of $3 to solve this problem? Review section 6.3. [E] :Can you use a present value of $1 and a future value of $3 to solve this problem? Review section 6.3. 8) You just borrowed $26,000 for five years. The loan is an interest-only loan for five years at 8 percent compounded annually. How much of the first payment is used to reduce the loan principal? [A] $0 [B] $2,080.00 [C] $4,431.87 [D] $5,416.00 [E] $6,511.87 [A] :You are correct! [B] :What type of loan is this? Review section 6.4. [C] :What type of loan is this? Review section 6.4. [D] :What type of loan is this? Review section 6.4. [E] :What type of loan is this? Review section 6.4. 9) You agree to loan your parents $22,000 to buy a new van. They agree to pay you $450 a month for 5 years. The: [A] interest rate is 0.75 percent per month. [B] annual percentage rate is 8.17 percent. [C] effective annual rate is 8.37 percent. [D] annual percentage rate is 8.68 percent. [E] effective annual rate is 8.70 percent. [A] :Is the annual percentage rate 9 percent? Review section 6.3.[B] :You need to review this computation in section 6.3. [C] :The annual percentage rate is 8.37 percent. Review section 6.3. [D] :Try again. Review section 6.3. [E] :You are correct! 10) You hold a winning ticket from your state lottery. It entitles the bearer to receive payments of $50,000 at the end of each of the next 20 years. Given what you know about the time value of money, you should be able to sell this ticket for no less than $1 million in the open market. [A] True [B] False [A] :If the interest rate is greater than zero, what is the present value of your winnings? Review section 6.2. [B] :You are correct! 11) At the end of each year for the next ten years you will receive cash flows of $50. If the appropriate discount rate is 5.5 percent, how much would you pay for this annuity? [A] $259.82 [B] $299.02 [C] $338.99 [D] $376.88 [E] $379.16 [A] :This is a present value of an annuity problem. Review section 6.2. [B] :This is a present value of an annuity problem. Review section 6.2. [C] :This is a present value of an annuity problem. Review section 6.2. [D] :You are correct! [E] :This is a present value of an annuity problem. Review section 6.2. 12) What is the future value in 10 years of $1,000 payments received at the beginning of each year for the next 10 years? Assume an interest rate of 5.625 percent. [A] $12,259.63 [B] $12,950.96 [C] $13,679.45 [D] $14,495.48 [E] $14,782.15 [A] :Did you find the present value of an annuity due? Review section 6.2. [B] :Did you compute the value of an ordinary annuity rather than an annuity due? Review section 6.2. [C] :You are correct! [D] :What is an annuity due? Review section 6.2. [E] :What is an annuity due? Review section 6.2. 13) The company you work for will deposit $600 at the end of each month into your retirement fund. Interest is compounded monthly. You plan to retire 15 years from now and estimate that you will need $2,000 per month out of the account for the next 20 years. If the account pays 8.0 percent compounded monthly, how much do you need to put into the account in addition to your company deposit in order to meet your objective? [A] $0.00 [B] $57.59[C] $90.99 [D] $95.88 [E] $104.49 [A] :Based on what you plan to withdraw in retirement, you must have $239,108.58 in the account when you retire at the end of 15 years from now. How much must be deposited each month to reach that goal? Review section 6.2. [B] :Based on what you plan to withdraw in retirement, you must have $239,108.58 in the account when you retire at the end of 15 years from now. How much must be deposited each month to reach that goal? Review section 6.2. [C] :You are correct! [D] :Based on what you plan to withdraw in retirement, you must have $239,108.58 in the account when you retire at the end of 15 years from now. How much must be deposited each month to reach that goal? Review section 6.2. [E] :Based on what you plan to withdraw in retirement, you must have $239,108.58 in the account when you retire at the end of 15 years from now. How much must be deposited each month to reach that goal? Review section 6.2. 14) An example of an annuity is a stream of payments of $4,000 at the end of each year for 20 years. [A] True [B] False [A] :You are correct! [B] :This is a level stream of cash flows for a fixed period of time. Review section 6.2. 15) Vito will loan you money on a "five-for-six" arrangement. That is, for every $5 he gives you today, you give him $6 one week from now. What is the APR of this loan? [A] 410 percent [B] 540 percent [C] 860 percent [D] 1,040 percent [E] 1,310 percent [A] :Did you get an interest rate per week of 20 percent? Review section 6.3. [B] :Did you get an interest rate per week of 20 percent? Review section 6.3. [C] :Did you get an interest rate per week of 20 percent? Review section 6.3. [D] :You are correct! [E] :Did you get an interest rate per week of 20 percent? Review section 6.3. 16) Suppose you are evaluating two annuities. They are identical in every way, except that one is an ordinary annuity and one is an annuity due. Assuming an interest rate of 10 percent, which one of the following is true? [A] The ordinary annuity must have a higher present value than the annuity due. [B] The annuity due must have the same present value as the ordinary annuity. [C] The ordinary annuity must have a lower future value than the annuity due. [D] The two annuities will differ in present value by the amount of exactly one of the annuity payments. [E] The annuity due will be larger than the ordinary annuity by an amount equal to the present value of the last annuity payment. [A] :The reverse of this statement is true. Can you explain why? Review section 6.2. [B] :The timing of the cash flows is different so they cannot have the same present value. Review section 6.2. [C] :You are correct![D] :This is incorrect. Prove it by constructing an example where the annuity amount is $100 per year and the number of years is 5. Review section 6.2. [E] :This is incorrect. Prove it by constructing an example where the annuity amount is $100 per year and the number of years is 5. Review section 6.2. 17) Your monthly mortgage payment on your house is $593.90. It is a 30-year mortgage at 7.8 percent compounded monthly. How much did you borrow? [A] $75,000 [B] $77,500 [C] $80,000 [D] $82,500 [E] $85,000 [A] :This is a present value of an annuity problem. Review section 6.2. [B] :This is a present value of an annuity problem. Review section 6.2. [C] :This is a present value of an annuity problem. Review section 6.2. [D] :You are correct! [E] :This is a present value of an annuity problem. Review section 6.2. 18) You can afford to pay $125 a month on a car loan. You are willing to make monthly payments for four years at 7.9 percent. How much can you afford to borrow to buy a car? [A] $4,849.53 [B] $5,130.10 [C] $5,150.00 [D] $5,163.75 [E] $5,200.00 [A] :This is a present value of an annuity problem. Review section 6.2. [B] :You are correct! [C] :This is a present value of an annuity problem. Review section 6.2. [D] :This is a present value of an annuity problem. Review section 6.2. [E] :This is a present value of an annuity problem. Review section 6.2. 19) Which of the following can be computed? III. present value of an annuity due IV. future value of an annuity due [A] I and III only [B] II and III only [C] II, III, and IV only [D] I, III, and IV only [E] I, II, III, and IV [A] :These are not the only ones that can be computed. Review section 6.2. [B] :One of these can not be computed. Review section 6.2. [C] :One of these can not be computed. Review section 6.2. [D] :You are correct! [E] :One of these can not be computed. Review section 6.2. 20) You deposit $100,000 into an account today. How much can you withdraw monthly for ten years if you can earn a 5 percent rate of return? You make your first withdrawal today.[A] $1,056.25 [B] $1,058.73 [C] $1,060.66 [D] $1,061.03 [E] $1,061.87 [A] :You are correct! [B] :You need to review section 6.2. [C] :Did you confuse this with an ordinary annuity? Review section 6.2. [D] :You need to review section 6.2. [E] :You need to review section 6.2. 21) You just borrowed $5,000 to buy a car. The loan will be amortized over 36 months at a 3.9 discount rate. What is the amount of each payment? [A] $146.92 [B] $147.03 [C] $147.40 [D] $147.99 [E] $148.13 [A] :Did you confuse this with an annuity due? Review section 6.2. [B] :This is a present value of an annuity problem. Review section 6.2. [C] :You are correct! [D] :This is a present value of an annuity problem. Review section 6.2. [E] :This is a present value of an annuity problem. Review section 6.2. 22) You need to borrow $18,000 to buy a truck. The current loan rate is 9.9 percent compounded monthly and you want to pay the loan off in equal monthly payments over 5 years. What is your monthly payment? [A] $363.39 [B] $374.04 [C] $381.56 [D] $394.69 [E] $455.66 [A] :You need to review this computation in section 6.2. [B] :You need to review this computation in section 6.2. [C] :You are correct! [D] :You do not get the right answer when you compute an annual payment and then divide that amount by 12. Why not? Review section 6.2. [E] :You need to review this computation in section 6.2. 23) You are considering five different loan offers. The terms of all five loans are equivalent with the exception of the interest rate. Of the rates offered, which one should you accept? [A] 8.60 percent compounded annually [B] 8.40 percent compounded semi-annually [C] 8.38 percent compounded monthly [D] 8.35 percent compounded continuously [E] 8.40 percent compounded daily [A] :Which loan has the lowest effective annual rate? Review section 6.3. [B] :You are correct! [C] :Which loan has the lowest effective annual rate? Review section 6.3. [D] :Which loan has the lowest effective annual rate? Review section 6.3. [E] :Which loan has the lowest effective annual rate? Review section 6.3.24) You are considering investing $750 in a 10-year annuity. The rate of return you feel you require is 6.5 percent. What annual cash flow from the annuity will provide the required return? [A] $70.77 [B] $102.96 [C] $104.33 [D] $114.31 [E] $129.27 [A] :This is a present value of an annuity problem. Review section 6.2. [B] :This is a present value of an annuity problem. Review section 6.2. [C] :You are correct! [D] :This is a present value of an annuity problem. Review section 6.2. [E] :This is a present value of an annuity problem. Review section 6.2. 25) You and your spouse have found your dream home in Rapid City, South Dakota. The selling price is $120,000. You will pay $20,000 down and obtain a 30-year fixed-rate mortgage at 8.25 percent for the balance. Assume that monthly payments begin in one month. What is the amount of each payment? [A] $725.01 [B] $751.27 [C] $757.76 [D] $825.45 [E] $901.52 [A] :This is a present value of an annuity problem where the present value is $100,000. Review section 6.2. [B] :You are correct! [C] :This is a present value of an annuity problem where the present value is $100,000. Review section 6.2. [D] :This is a present value of an annuity problem where the present value is $100,000. Review section 6.2. [E] :This is a present value of an annuity problem where the present value is $100,000. Review section 6.2. 26) You make deposits of $500, $200, $300, and $400 respectively on the last day of each year for four years. The account earns 6 percent interest. How much money do you have in your account at the end of the four years? [A] $1,460.12 [B] $1,511.89 [C] $1,538.23 [D] $1,548.02 [E] $1,551.09 [A] :You need to review section 6.1. [B] :You need to review section 6.1. [C] :You are correct! [D] :You need to review section 6.1. [E] :You need to review section 6.1. 27) You just paid $10,000 for an annuity. The annuity will pay you $1,000 a year for 12 years. What is the rate of return on this annuity?[A] 2.92% [B] 3.01% [C] 3.23% [D] 3.50% [E] 3.68% [A] :You are correct! [B] :This is a present value of an annuity problem. Review section 6.2. [C] :This is a present value of an annuity problem. Review section 6.2. [D] :This is a present value of an annuity problem. Review section 6.2. [E] :This is a present value of an annuity problem. Review section 6.2. 28) Suppose you invest $10 for one year, and at the end of the year you receive back $12. Which of the following statements must be true concerning your investment? I. The quoted rate must have been greater than 20 percent. II. To figure the quoted rate, you would need to know how often the investment was compounded. III. The effective annual rate was 20 percent. IV. The continuously compounded effective annual rate has to be 20 percent. [A] I and III only. [B] II and III only [C] I and IV only [D] II, III, and IV only [E] I, II, and III only [A] :Can an effective rate be less than a quoted rate? Review section 6.3. [B] :You are correct! [C] :At least one of these is incorrect. Review section 6.3. [D] :How do you know the investment used continuous compounding? [E] :Can an effective rate be less than a quoted rate? Review section 6.3. 29) You and your spouse have found your dream home in Rapid City, South Dakota. The selling price is $120,000; you will put $20,000 down and obtain a 30-year fixed-rate mortgage at 8.25 percent for the rest. How much interest will you pay over the life of the loan? [A] $135,101 [B] $145,583 [C] $170,457 [D] $190,457 [E] $270,457 [A] :Did you get a monthly payment of $751.27? If you make 360 payments, how much will you pay in total? Review section 6.4. [B] :Did you get a monthly payment of $751.27? If you make 360 payments, how much will you pay in total? Review section 6.4. [C] :You are correct! [D] :Did you get a monthly payment of $751.27? If you make 360 payments, how much will you pay in total? Review section 6.4. [E] :Did you get a monthly payment of $751.27? If you make 360 payments, how much will you pay in total? Review section 6.4. 30) You are in the process of buying a car and are trying to decide which one of three financing options you should select. The amount you are borrowing is $8,500. The first option is 24 monthly payments of $368.73 each. The second option is 36 monthly payments of $252.09 each. The third option is 48 monthly payments of $191.92. If your only concern is selecting the option with the lowest rate of interest, you:[A] can select either the 24 or the 36 monthly payments as their effective annual rates are equal. [B] can select either the 24 or the 48 monthly payments as their effective annual rates are equal. [C] should select the 24 monthly payments. [D] should select the 36 monthly payments. [E] should select the 48 monthly payments. [A] :The effective rates on these two options are different. Review section 6.3. [B] :The effective rates on these two options are different. Review section 6.3. [C] :You are correct! [D] :This option does not have the lowest effective annual rate. Review section 6.3. [E] :This option does not have the lowest effective annual rate. Review section 6.3. 31) A Treasury bill is an example of a pure discount loan. [A] True [B] False [A] :You are correct! [B] :A Treasury bill is a loan on which the borrower, the U.S. government in this case, receives money today and repays a single lump sum at some time in the future. Review section 6.4. 32) You deposit $25,000 in your bank account today. Starting next year, you plan to withdraw equal amounts from the account at the end of each of the next four years. What is the most you can withdraw annually? [A] $ 6,125.43 [B] $ 6,988.91 [C] $ 7,133.84 [D] $ 7,548.02 [E] $ 8,154.71 [A] :This is a present value of an annuity problem. Review section 6.2. [B] :Did you confuse this with an annuity due? Review section 6.2. [C] :This is a present value of an annuity problem. Review section 6.2. [D] :You are correct! [E] :This is a present value of an annuity problem. Review section 6.2. 33) You have $500 that you would like to invest. ABC Co. offers an account which pays 8 percent compounded annually. XYZ Co. has an account which pays 7.75 percent compounded semi-annually. Which account should you choose and why? [A] ABC because it has a higher effective annual rate [B] ABC because the annual percentage rate is higher [C] XYZ because it has a higher effective annual rate [D] XYZ because the stated rate is higher [E] XYZ because it compounds more frequently [A] :You are correct! [B] :Is the annual percentage rate what you actually receive? Review section 6.3. [C] :The effective annual rate of XYZ is only 7.9 percent. Review section 6.3. [D] :You need to review the various types of rates in section 6.3. [E] :XYZ may compound more frequently, but its effective annual rate is only 7.9 percent. Review section 6.3. 34) You ask your banker to loan you $100,000 as a 30-year fixed-rate mortgage at 8.25 percent compounded monthly. Your banker suggests you consider a 15-year loan at 7.75 percent compounded monthly. What is the difference in the monthly payment between these two loans?[A] $9.26 [B] $54.72 [C] $111.57 [D] $190.01 [E] $194.59 [A] :Be sure to take into account both the difference in interest rates and the number of payments. Review section 6.4. [B] :Be sure to take into account both the difference in interest rates and the number of payments. Review section 6.4. [C] :Be sure to take into account both the difference in interest rates and the number of payments. Review section 6.4. [D] :You are correct! [E] :Be sure to take into account both the difference in interest rates and the number of payments. Review section 6.4. 35) A local consumer finance company is offering loans at an annual percentage rate of 20 percent. The interest on the loan is compounded continuously. What is the effective annual rate? [A] 21.21 percent [B] 22.14 percent [C] 23.61 percent [D] 24.97 percent [E] 25.83 percent [A] :Did you use a formula containing eq to solve this problem? Review section 6.3. [B] :You are correct! [C] :Did you use a formula containing eq to solve this problem? Review section 6.3. [D] :Did you use a formula containing eq to solve this problem? Review section 6.3. [E] :Did you use a formula containing eq to solve this problem? Review section 6.3. 36) You want to save $100,000 for five years. You are considering different investments that are equivalent except for the interest rate. Which one of the following rates should you choose? [A] 8.9 percent compounded annually [B] 8.80 percent compounded quarterly [C] 8.75 percent compounded monthly [D] 8.70 percent compounded continuously [E] 8.85 percent compounded semi-annually [A] :Is this the highest effective annual rate? Review section 6.3. [B] :Is this the highest effective annual rate? Review section 6.3. [C] :You are correct! [D] :Is this the highest effective annual rate? Review section 6.3. [E] :Is this the highest effective annual rate? Review section 6.3. 37) You have $1,398.16 in your savings account today. You plan on adding $130 a month to this account for the next five years. The account pays 2.5 percent interest compounded monthly. How much money will you have in your savings account at the end of the five years? [A] $8,003.09 [B] $8,299.27 [C] $8,671.54 [D] $9,883.39 [E] $10,123.92[A] :You need to review sections 6.1.and 6.2. [B] :Did you forget about the balance in the account today? Review sections 6.1 and 6.2. [C] :You need to review sections 6.1 and 6.2. [D] :You are correct! [E] :You need to review sections 6.1.and 6.2. 38) Charlie’s Used Cars will sell you a pre-owned truck for $3,000 with no money down. You agree to make weekly payments of $40.00 for 2 years, beginning one week after you buy the car. What is the EAR of this loan? [A] 34.43 percent [B] 36.55 percent [C] 40.94 percent [D] 42.34 percent [E] 53.01 percent [A] :This is the annual percentage rate, not the effective annual rate. Review section 6.3. [B] :Did you get an annual percentage rate of 34.43 percent? Review section 6.3. [C] :You are correct! [D] :Did you get an annual percentage rate of 34.43 percent? Review section 6.3. [E] :Did you get an annual percentage rate of 34.43 percent? Review section 6.3. 39) You just borrowed $18,500 at 6.5 percent compounded monthly. The loan is to be amortized over five years. What is the amount of each payment? [A] $357.24 [B] $360.02 [C] $360.57 [D] $361.97 [E] $362.03 [A] :You need to review sections 6.2 and 6.4. [B] :Did you confuse this with an annuity due? Review sections 6.2 and 6.4. [C] :You need to review sections 6.2 and 6.4. [D] :You are correct! [E] :You need to review sections 6.2 and 6.4. 40) What would your payment be on a 10-year, $150,000 loan at 10 percent compounded semi-annually assuming payments are made annually? [A] $19,716.67 [B] $20,743.77 [C] $24,411.81 [D] $24,674.60 [E] $25,366.63 [A] :To compute this payment, first calculate the effective annual rate and then use that rate to find the annuity payment. Review section 6.3. [B] :To compute this payment, first calculate the effective annual rate and then use that rate to find the annuity payment. Review section 6.3. [C] :To compute this payment, first calculate the effective annual rate and then use that rate to find the annuity payment. Review section 6.3. [D] :You are correct![E] :To compute this payment, first calculate the effective annual rate and then use that rate to find the annuity payment. Review section 6.3. 41) You work for a furniture store. You normally sell a living room set for $2,500 and finance the full purchase price for 30 monthly payments at an annual percentage rate of 24 percent. You are planning to run a zero-interest financing sale during which you will finance the set over 30 months at 0 percent interest. How much do you need to charge for the living room set during the sale in order to earn your usual rate of return on the set including the financing income? [A] $2,500.00 [B] $2,827.40 [C] $3,348.60 [D] $3,437.20 [E] $3,784.80 [A] :In this case, you need to adjust the price so that the payment per month at 0 percent interest is the same as the payment per month at 24 percent interest and a price of $2,500. Review section 6.2. [B] :In this case, you need to adjust the price so that the payment per month at 0 percent interest is the same as the payment per month at 24 percent interest and a price of $2,500. Review section 6.2. [C] :You are correct! [D] :In this case, you need to adjust the price so that the payment per month at 0 percent interest is the same as the payment per month at 24 percent interest and a price of $2,500. Review section 6.2. [E] :In this case, you need to adjust the price so that the payment per month at 0 percent interest is the same as the payment per month at 24 percent interest and a price of $2,500. Review section 6.2. 42) A stated interest rate is a rate expressed as if it were compounded once per year. [A] True [B] False [A] :This is the definition of an effective annual rate. Review section 6.3. [B] :You are correct! 43) You are considering an investment with a quoted return of 10 percent per year. If interest is compounded daily, what is the effective return on this investment? [A] 9.91 percent [B] 10.00 percent [C] 10.25 percent [D] 10.47 percent [E] 10.52 percent [A] :The effective annual rate cannot be lower than the quoted rate. Review section 6.3. [B] :Since compounding occurs more than once during the year, the effective annual rate must exceed the quoted rate. Review section 6.3. [C] :This effective annual rate corresponds to semi-annual, not daily, compounding. Review section 6.3. [D] :This effective annual rate corresponds to monthly, not daily, compounding. Review section 6.3. [E] :You are correct! 44) The process of providing for a loan to be paid off by making regular principal reductions is called amortizing the loan. [A] True [B] False[A] :You are correct! [B] :This is a correct definition. Review section 6.4. 45) You obtain a $100,000, 30-year fixed-rate mortgage at 8.25 percent compounded monthly. Although you get a 30-year mortgage, you plan to prepay the loan by making an additional payment each month along with your regular payment. How much extra must you pay each month if you wish to pay off the loan in 20 years? [A] $24.56 [B] $54.88 [C] $100.80 [D] $103.28 [E] $106.86 [A] :Did you get a payment of $751.27 for 30 years? How much is the payment for 20 years? Review section 6.4. [B] :Did you get a payment of $751.27 for 30 years? How much is the payment for 20 years? Review section 6.4. [C] :You are correct! [D] :Did you get a payment of $751.27 for 30 years? How much is the payment for 20 years? Review section 6.4. [E] :Did you get a payment of $751.27 for 30 years? How much is the payment for 20 years? Review section 6.4. 46) You are going to withdraw $1,000 at the end of each year for the next three years from an account that pays interest at a rate of 8 percent compounded annually. How much must be in the account today in order for the account to reduce to a balance of zero after the last withdrawal? [A] $793.83 [B] $2,577.10 [C] $2,602.29 [D] $2,713.75 [E] $2,775.67 [A] :This is a present value of an annuity problem. Review section 6.2. [B] :You are correct! [C] :This is a present value of an annuity problem. Review section 6.2. [D] :This is a present value of an annuity problem. Review section 6.2. [E] :This is a present value of an annuity problem. Review section 6.2. 47) You are going to withdraw $1,000 at the end of each year for the next three years from an account that pays interest at a rate of 8 percent compounded annually. The account balance will reduce to zero when the last withdrawal is made. How much money will be in the account immediately after the second withdrawal is made? [A] $925.93 [B] $977.10 [C] $982.29 [D] $1,000.00 [E] $2,000.00 [A] :You are correct! [B] :What is the present value of $1,000 received one year from today? Review section 6.2. [C] :What is the present value of $1,000 received one year from today? Review section 6.2. [D] :What is the present value of $1,000 received one year from today? Review section 6.2.[E] :What is the present value of $1,000 received one year from today? Review section 6.2. 48) You receive $100 at the end of each year for ten years. This is an example of an annuity due. [A] True [B] False [A] :What is the difference between an ordinary annuity and an annuity due? Review section 6.2. [B] :You are correct! 49) Which one of the following is a true statement? [A] It is best not to rely solely on quoted rates when comparing investments. [B] The quoted rate is equivalent to the effective rate regardless of the compounding frequency. [C] The annual percentage rate quoted on a loan requiring monthly payments is the interest rate you actually pay. [D] The annual percentage rate is the interest rate per period divided by the number of periods per year. [E] The annual percentage rate will be larger than the effective annual rate when interest is compounded monthly. [A] :You are correct! [B] :Which rate considers interest on interest? Review section 6.3. [C] :The annual percentage rate is not the interest rate you actually pay. Review section 6.3. [D] :Does the interest rate per period multiplied by the number of periods per year equate to the rate you actually pay? Review section 6.3. [E] :The effective annual rate will be the larger of the two. Review section 6.3. 50) In order to help you through college, your parents just deposited $25,000 into a bank account paying 8 percent interest. Starting tomorrow, you plan to withdraw equal amounts from the account at the beginning of each of the next four years. What is the most you can withdraw annually? [A] $ 6,125.43 [B] $ 6,988.91 [C] $ 7,133.84 [D] $ 7,548.02 [E] $ 8,154.71 [A] :This is a present value of an annuity due problem. Review section 6.2. [B] :You are correct! [C] :This is a present value of an annuity due problem. Review section 6.2. [D] :You are ignoring the fact that this is an annuity due. Review section 6.2. [E] :This is a present value of an annuity due problem. Review section 6.2. 51) Rob and Laura wish to buy a new home. The price is $187,500 and they plan to put 20 percent down. The bank will lend them the remainder at a 10 percent fixed rate for 30 years, with monthly payments to begin in one month. Assuming they pay off the loan over the 30 year period as planned, what will the total cost (principal + interest + down payment) of the house be? [A] $187,500 [B] $271,996 [C] $354,234 [D] $473,760[E] $511,390 [A] :You must first find the monthly payment. Did you get $1,316.36? Be sure to incorporate the down payment into your computation and work with a 360-month loan. Review section 6.4. [B] :You must first find the monthly payment. Did you get $1,316.36? Be sure to incorporate the down payment into your computation and work with a 360-month loan. Review section 6.4. [C] :You must first find the monthly payment. Did you get $1,316.36? Be sure to incorporate the down payment into your computation and work with a 360-month loan. Review section 6.4. [D] :You must first find the monthly payment. Did you get $1,316.36? Be sure to incorporate the down payment into your computation and work with a 360-month loan. Review section 6.4. [E] :You are correct! 52) Loan A requires fixed principal payments each year for five years. Loan B is amortized over five years with the payment amount remaining constant. In year one, the required payment on loan A will exceed the required payment on loan B. [A] True [B] False [A] :You are correct! [B] :In year one, loan A requires a payment equal to 20 percent of the principal plus the first year’s interest. How does this vary from the payment required by loan B? Review section 6.4. 53) You have won a prize which will pay you or your heirs $25,000 a year for fifty years. The first payment is due immediately. What is the present value of this prize given an 8 percent discount rate? [A] $300,000 [B] $305,837 [C] $309,650 [D] $312,500 [E] $330,304 [A] :How do you calculate the present value of an annuity due? Review section 6.2. [B] :How do you calculate the present value of an annuity due? Review section 6.2. [C] :How do you calculate the present value of an annuity due? Review section 6.2. [D] :Is this an annuity due or a perpetuity? Review section 6.2. [E] :You are correct! 54) There is no upper limit to an effective annual rate. That is, as the frequency of compounding increases, the effective annual rate also increases without limit. [A] True [B] False [A] :The highest effective annual rate is derived from continuous compounding. Review section 6.3. [B] :You are correct! 55) What is the effective annual rate of 12 percent compounded continuously? [A] 12.12 percent [B] 12.36 percent [C] 12.55 percent[D] 12.75 percent [E] 12.89 percent [A] :Did you use eq-1 to solve this problem? Review section 6.3. [B] :Did you use eq-1 to solve this problem? Review section 6.3. [C] :Did you use eq-1 to solve this problem? Review section 6.3. [D] :You are correct! [E] :Did you use eq-1 to solve this problem? Review section 6.3. 56) You have just won a lottery prize. You can choose to receive $750,000 today or an annual payment of $50,411.78 at the end of each year for the next twenty years. At any rate higher than 3 percent, you should take the lump sum. [A] True [B] False [A] :You are correct! [B] :Three percent is the rate that makes the present value of the annuity and the lump sum payment equivalent. What happens to the present value as the interest rate increases? Review section 6.2. 57) Bernie just won a contest with a grand prize of $250,000. The contest stipulates that the winner will receive $100,000 immediately plus $15,000 at the end of each of the next 10 years. If Bernie can earn 5 percent on his money, how much is this prize worth to him today? [A] $114,285.71 [B] $166,175.62 [C] $189,345.45 [D] $215,826.02 [E] $250,000.00 [A] :How many $15,000 payments will Bernie receive? Review section 6.2. [B] :This is a present value of an annuity problem. Review section 6.2. [C] :This is a present value of an annuity problem. Review section 6.2. [D] :You are correct! [E] :Since interest compounds at 5 percent, the present value has to be lower than this amount. Review section 6.2. 58) Moe purchases a 30-year annuity that pays $100 per year. Larry purchases a perpetuity that pays $100 a year. In both cases, payments begin one year from today. The appropriate interest rate is 10 percent. What is the present value today of Larry’s payments occurring from year 31 on? [A] $51.15 [B] $57.31 [C] $58.11 [D] $81.21 [E] More than $100 [A] :What is the difference in the present value of these two payment streams? Review section 6.2. [B] :You are correct! [C] :Did you get $942.69 as the present value of Moe’s annuity? Review section 6.2. [D] :Did you get $1,000 as the present value of Larry’s entire perpetuity? Review section 6.2. [E] :What is the difference in the present value of these two payment streams? Review section 6.2. 59) Your brother-in-law borrowed $2,000 from you 4 years ago and then disappeared. Now he has returned and wants to repay the loan, including the interest accrued. You had agreed to charge him 10 percent interest compounded annually. He is offering to make five equal annual payments beginning in one year. How much will your brother-in-law have to pay you annually in order to extinguish this debt?[A] $697.43 [B] $738.63 [C] $751.46 [D] $772.45 [E] $798.24 [A] :Did you compute the current amount he owes you as $2,928.20? Review section 6.2. [B] :Did you compute the current amount he owes you as $2,928.20? Review section 6.2. [C] :Did you compute the current amount he owes you as $2,928.20? Review section 6.2. [D] :You are correct! [E] :Did you compute the current amount he owes you as $2,928.20? Review section 6.2. 60) Suppose you buy a new Toyota for $20,000, paying nothing down. You agree to a repayment schedule of 6 equal annual payments beginning one year from today. The banker's required return is 9 percent, compounded annually. What is the amount of each annual payment? [A] $3,729.03 [B] $4,458.40 [C] $5,121.24 [D] $6,664.91 [E] $7,563.01 [A] :This is a present value of an annuity problem. Review section 6.2. [B] :You are correct! [C] :This is a present value of an annuity problem. Review section 6.2. [D] :This is a present value of an annuity problem. Review section 6.2. [E] :This is a present value of an annuity problem. Review section 6.2. 61) You are going to invest $500 at the end of each year for ten years. Given an interest rate, you can find the future value of this investment by: I. adding the cash flows together and then applying a future value factor to that sum. II. applying the proper future value factor to each cash flow, then adding up these values. III. finding the present value of each cash flow, adding all of the present values together, then finding the future value at the end of year ten of this lump sum. IV. finding the present value of an ordinary annuity. [A] II only [B] III only [C] II and III only [D] I, II, and IV only [E] II, III, and IV only [A] :True, but there is another method that also works. Review section 6.1. [B] :True, but there is another method that also works. Review section 6.1. [C] :You are correct! [D] :At least one of these choices is incorrect. Review section 6.1. [E] :At least one of these choices is incorrect. Review section 6.1. 62) What is the effective annual rate of 12 percent compounded semi-annually? [A] 12.12 percent [B] 12.36 percent [C] 12.55 percent [D] 12.68 percent [E] 12.75 percent[A] :What is the number of compounding periods? Review section 6.3. [B] :You are correct! [C] :What is the number of compounding periods? Review section 6.3. [D] :What is the number of compounding periods? Review section 6.3. [E] :What is the number of compounding periods? Review section 6.3. 63) You are borrowing $1,500 at 6 percent compounded annually. You plan to pay $90 at the end of each year on the loan. How long will it take you to repay the loan in full? [A] 9 years [B] 10 years [C] 11 years [D] 12 years [E] You will never pay off the loan. [A] :How much interest will you owe for year one? Review section 6.2. [B] :How much of the first payment is applied to the loan principal? Review section 6.2. [C] :How much interest will you owe for year one? Review section 6.2. [D] :How much of the first payment is applied to the loan principal? Review section 6.2. [E] :You are correct! 64) You have just won the lottery. You and your heirs will receive $25,000 per year forever, beginning one year from now. What is the present value of this lottery given an 8 percent discount rate? [A] $182,500 [B] $200,000 [C] $287,500 [D] $312,500 [E] $337,500 [A] :This is a present value of a perpetuity problem. Review section 6.2. [B] :This is a present value of a perpetuity problem. Review section 6.2. [C] :This is a present value of a perpetuity problem. Review section 6.2. [D] :You are correct! [E] :This is a present value of a perpetuity problem. Review section 6.2. 65) A consol is a type of perpetuity. [A] True [B] False [A] :You are correct! [B] :You need to review this definition in section 6.2. 66) An annuity is a level stream of cash flows for a fixed period of time. [A] True [B] False [A] :You are correct! [B] :This is the definition of an annuity. Review section 6.2.67) You invest $500 today. You plan on adding annual amounts $500, $600, and $700 to the account at the end of each of the next three years, respectively. What will your account be worth five years from now if you earn a 7 percent rate of return? [A] $2,788.91 [B] $2,893.13 [C] $2,903.14 [D] $2,934.86 [E] $3,006.38 [A] :This is a future value with multiple cash flows. Review section 6.1. [B] :You are correct! [C] :This is a future value with multiple cash flows. Review section 6.1. [D] :This is a future value with multiple cash flows. Review section 6.1. [E] :This is a future value with multiple cash flows. Review section 6.1. 68) In almost all present and future value computations, it is implicitly assumed that the cash flows occur at the end of each period. [A] True [B] False [A] :You are correct! [B] :If the cash flows occur at the beginning of the period that information will be so noted. Review section 6.1. 69) Five years from now you will begin to receive cash flows of $75 per year. These cash flows will continue forever. If the discount rate is 6 percent, what is the present value of these cash flows? [A] $799.68 [B] $894.22 [C] $934.07 [D] $990.12 [E] $1,104.67 [A] :Did you get a value for the perpetuity of $1,250 at the end of four years from now? Did you discount the $1,250 back to today? Review section 6.2. [B] :Did you get a value for the perpetuity of $1,250 at the end of four years from now? Did you discount the $1,250 back to today? Review section 6.2. [C] :Did you get a value for the perpetuity of $1,250 at the end of four years from now? Did you discount the $1,250 back to today? Review section 6.2. [D] :You are correct! [E] :Did you get a value for the perpetuity of $1,250 at the end of four years from now? Did you discount the $1,250 back to today? Review section 6.2. 70) A preferred stock pays an annual dividend of $5.50. If you want to earn 9 percent on your investments, how much are you willing to pay for one share of this stock? [A] $57.50 [B] $58.33 [C] $60.00 [D] $61.11 [E] $62.66 [A] :You need to review perpetuities in section 6.2. [B] :You need to review perpetuities in section 6.2.[C] :You need to review perpetuities in section 6.2. [D] :You are correct! [E] :You need to review perpetuities in section 6.2. 71) You are comparing three investments. Option A pays 9 percent compounded semi-annually. Option B pays 8.9 percent compounded monthly. Option C pays 8.75 percent compounded daily. Which option should you choose if you wish to invest your money for five years? [A] Option A because it has the higher quoted rate [B] Option A because it has the highest effective annual rate [C] Option B because it has the highest effective annual rate [D] Option C because it will pay the most interest on interest over the five years [E] Option C because it will compound a total of 1,825 times over the five years [A] :Is the quoted rate what you actually earn? Review section 6.3. [B] :Did you get an effective annual rate of 9.20 percent for Option A? Review section 6.3. [C] :You are correct! [D] :Option C pays the lowest amount of interest on interest of these three options. Review section 6.3. [E] :There are 1,825 compounding periods but the effective annual rate is the lowest of the three options. Review section 6.3. 72) Joe purchases a $100 perpetuity on which payments begin in one year. Lynn purchases a $100 perpetuity on which payments begin immediately. Both annuities pay annual payments. The applicable discount rate is 10 percent. Which one of the following statements is true? [A] Joe's perpetuity is worth $100 more than Lynn's. [B] Lynn's perpetuity is worth $100 more than Joe's. [C] The perpetuities are of equal value today. [D] Lynn's perpetuity is worth $90.91 more than Joe's. [E] Joe’s perpetuity is worth $90.91 more than Lynn’s. [A] :This compares a perpetuity with a perpetuity due. If it were not for the $100 Lynn gets immediately, the two perpetuities would be worth the same amount. Review section 6.2. [B] :You are correct! [C] :This compares a perpetuity with a perpetuity due. Notice that if not for the $100 Lynn gets immediately, the two perpetuities would be worth the same amount. Review section 6.2. [D] :This compares a perpetuity with a perpetuity due. Notice that if not for the $100 Lynn gets immediately, the two perpetuities would be worth the same amount. Review section 6.2. [E] :This compares a perpetuity with a perpetuity due. Notice that if not for the $100 Lynn gets immediately, the two perpetuities would be worth the same amount. Review section 6.2. 73) Which one of the following is the annuity present value factor? [A] 1-[1/(1+r)t]/r [B] [(1+r)t-1]/r [C] [1- (1+r)t][1+r] [D] 1+[(1+r)t/r]/r [E] 1+[1/(1+r)t]/r [A] :You are correct! [B] :Try again. Review section 6.2. [C] :Try again. Review section 6.2. [D] :Try again. Review section 6.2. [E] :Try again. Review section 6.2.74) The present value of an ordinary annuity and an annuity due will be equal if both annuities have the same payment per period, the same number of periods, and the same discount rate. Assume the discount rate is greater than zero. [A] True [B] False [A] :Is the timing of the payments equal? Review section 6.2. [B] :You are correct! 75) You want to establish a trust fund to give your heirs $100,000 a year forever. The fund is expected to earn a 5.75 percent rate of return. How much money must you deposit today to establish this trust? [A] $1,700,000 [B] $1,716,067 [C] $1,723,049 [D] $1,739,130 [E] $1,800,000 [A] :This is a present value of a perpetuity. Review section 6.2. [B] :This is a present value of a perpetuity. Review section 6.2. [C] :This is a present value of a perpetuity. Review section 6.2. [D] :You are correct! [E] :This is a present value of a perpetuity. Review section 6.2. 76) What is the present value of $1,000 payments received at the beginning of each year for the next 10 years? Assume an interest rate of 5.49 percent compounded monthly. [A] $7,069.13 [B] $7,093.62 [C] $7,492.64 [D] $7,912.58 [E] $7,955.26 [A] :Since the frequency of the compounding differs from the frequency of the payments, you must compute the effective annual rate and use this rate to find the present value of the annuity. Review section 6.3. [B] :Since the frequency of the compounding differs from the frequency of the payments, you must compute the effective annual rate and use this rate to find the present value of the annuity. Review section 6.3. [C] :Since the frequency of the compounding differs from the frequency of the payments, you must compute the effective annual rate and use this rate to find the present value of the annuity. Review section 6.3. [D] :You are correct! [E] :Since the frequency of the compounding differs from the frequency of the payments, you must compute the effective annual rate and use this rate to find the present value of the annuity. Review section 6.3. 77) You are considering various loan offers. The loan terms are equivalent with the exception of the interest rate. Which one of the following rates should you accept? [A] 8.75 percent compounded monthly [B] 8.90 percent compounded semi-annually [C] 8.70 percent compounded continuously [D] 8.99 percent compounded annually[E] 8.95 percent compounded quarterly [A] :Is this the lowest effective annual rate? Review section 6.3. [B] :Is this the lowest effective annual rate? Review section 6.3. [C] :Is this the lowest effective annual rate? Review section 6.3. [D] :You are correct! [E] :Is this the lowest effective annual rate? Review section 6.3. 78) A pure discount loan is a loan on which the borrower receives money today and repays a single lump sum at some time in the future. [A] True [B] False [A] :You are correct! [B] :This is the definition of a pure discount loan. Review section 6.4. 79) Preferred stock is an example of a perpetuity. [A] True [B] False [A] :You are correct! [B] :Doesn’t preferred stock pay a fixed payment per period forever? Review section 6.2. 80) Dom Diego is establishing a $1 million trust fund to provide scholarships for exchange students. The fund will distribute the interest income annually. The principal must remain invested at all times. How much will be available annually for students if the fund can earn a 5 percent rate of return? [A] $25,000 [B] $50,000 [C] $100,000 [D] $125,000 [E] $150,000 [A] :What is 5 percent of $1 million? Review section 6.2. [B] :You are correct! [C] :What is 5 percent of $1 million? Review section 6.2. [D] :What is 5 percent of $1 million? Review section 6.2. [E] :What is 5 percent of $1 million? Review section 6.2. 81) In order to compare equally risky investment opportunities that have interest rates reported in different formats you should convert each rate to a(n): [A] annual nominal rate. [B] monthly nominal rate. [C] effective annual rate. [D] annual percentage rate. [E] stated rate. [A] :Is the nominal rate what you actually pay or earn? Review section 6.3. [B] :Is the nominal rate what you actually pay or earn? Review section 6.3. [C] :You are correct! [D] :Is the annual percentage rate what you actually pay or earn? Review section 6.3.[E] :Is the annual percentage rate what you actually pay or earn? Review section 6.3. 82) An interest rate quoted as six percent compounded monthly means interest is paid at a rate of six percent each month. [A] True [B] False [A] :In this case, interest is paid at a rate of 0.5 percent each month. Review section 6.3. [B] :You are correct! 83) You are planning to save your annual bonuses from work and are comparing savings accounts. Account A compounds semi-annually while Account B compounds monthly. If both accounts have the same effective annual rate of interest and you place only the bonuses in the account, you: [A] should choose Account A because it has a higher annual percentage rate. [B] should choose Account B because it has a higher annual percentage rate. [C] should choose Account B because it is compounded more frequently. [D] should choose Account A because you will pay less in taxes. [E] can choose either account since you are indifferent between the two. [A] :You should not choose based on the annual percentage rate. Review section 6.3. [B] :You should not choose based on the annual percentage rate. Review section 6.3. [C] :Just because an account compounds more frequently does not automatically mean it is the better choice. Review section 6.3. [D] :Taxes are not a part of the problem as it is stated. Review section 6.3. [E] :You are correct! 84) The First National Bank offers one-year certificates of deposit with a stated rate of 5.50 percent compounded quarterly. Which one of the following rates, compounded semi-annually, comes closest to providing you with the same amount of interest? [A] 5.487 percent [B] 5.500 percent [C] 5.507 percent [D] 5.512 percent [E] 5.538 percent [A] :Did you compare effective annual rates? Review section 6.3. [B] :Did you compare effective annual rates? Review section 6.3. [C] :Did you compare effective annual rates? Review section 6.3. [D] :Did you compare effective annual rates? Review section 6.3. [E] :You are correct! 85) You are going to withdraw $1,000 at the end of each year for the next three years from an account that pays interest of 8 percent compounded annually. The account balance will reduce to zero when the last withdrawal is made. How much interest will you earn on the account over the three-year life? [A] $0.00 [B] $240.00 [C] $422.90 [D] $576.24 [E] $3,000.00 [A] :First determine the present value of this annuity, then subtract this number from the total withdrawals. Review section 6.2.[B] :First determine the present value of this annuity, then subtract this number from the total withdrawals. Review section 6.2. [C] :You are correct! [D] :First determine the present value of this annuity, then subtract this number from the total withdrawals. Review section 6.2. [E] :First determine the present value of this annuity, then subtract this number from the total withdrawals. Review section 6.2. 86) What is the effective annual rate of 10 percent compounded monthly? [A] 10.25 percent [B] 10.38 percent [C] 10.47 percent [D] 10.50 percent [E] 10.52 percent [A] :What is the number of compounding periods? Review section 6.3. [B] :What is the number of compounding periods? Review section 6.3. [C] :You are correct! [D] :What is the number of compounding periods? Review section 6.3. [E] :What is the number of compounding periods? Review section 6.3. 87) If interest is compounded annually, the effective annual rate and the annual percentage rate will be the same. [A] True [B] False [A] :You are correct! [B] :These two rates are equal anytime interest is compounded annually. Review section 6.3. 88) You save $350 a month for forty years. Your average rate of return is 8.5 percent. What is your account balance at the end of the forty years? [A] $168,000.00 [B] $789,518.23 [C] $793,004.61 [D] $1,413,528.32 [E] $1,423,540.81 [A] :Did you forget about the interest earned? Review section 6.2. [B] :This is a future value of an ordinary annuity. Review section 6.2. [C] :This is a future value of an ordinary annuity. Review section 6.2. [D] :You are correct! [E] :Did you confuse this with an annuity due? Review section 6.2. 89) If a loan is set up to be fully amortized over a period of ten years but the loan period is only five years, then the borrower will owe a balloon payment at the end of the five-year period. [A] True [B] False [A] :You are correct! [B] :Whenever the number of payments is less than the period over which the loan is amortized there willbe a balloon payment. Review section 6.4. 90) Three years from now, you can afford to make a $6,000 payment to the bank. The bank will give you an 8 percent pure discount loan. How much cash is the bank willing to give you today? [A] $4,762.99 [B] $5,144.03 [C] $5,389.18 [D] $5,401.03 [E] $5,555.56 [A] :You are correct! [B] :What is the present value of the $6,000? Review section 6.4. [C] :What is the present value of the $6,000? Review section 6.4. [D] :What is the present value of the $6,000? Review section 6.4. [E] :What is the present value of the $6,000? Review section 6.4. 91) A perpetuity is the same thing as an annuity due. [A] True [B] False [A] :How long do perpetuity payments continue? Review section 6.2. [B] :You are correct! 92) Which one of the following is the correct formula for computing the future value of an annuity? [A] FVt= C X [(1+r)t-1]/r [B] FVt= C X1/[(1+r)t-1] [C] FVt= C X [(1+r)t-1] X r [D] FVt= C X [(1+r)t+1]/t [E] FVt= C X [(1+r)t+1]/r [A] :You are correct! [B] :Try again. Review section 6.2. [C] :Try again. Review section 6.2. [D] :Try again. Review section 6.2. [E] :Try again. Review section 6.2. 93) The preferred stock of Marble Comics currently sells for $31.25 per share. The annual dividend is $2.50. Assuming a constant dividend forever, what is the rate of return on this stock? [A] 4.5 percent [B] 6.0 percent [C] 8.0 percent [D] 9.5 percent [E] 12.5 percent [A] :Is this a perpetuity? Review section 6.2. [B] :Is this a perpetuity? Review section 6.2. [C] :You are correct! [D] :Is this a perpetuity? Review section 6.2. [E] :This is a perpetuity. Review section 6.2.94) Rob and Laura wish to buy a new home. The price is $187,500 and they plan to put 20 percent down. New Rochelle Savings and Loan will lend them the remainder at 10 percent compounded monthly for 30 years. The first payment is due one month from today. What is the amount of their monthly payment? [A] $1,316.36 [B] $1,325.99 [C] $1,512.56 [D] $1,645.45 [E] $1,760.45 [A] :You are correct! [B] :You cannot find the annual payment and then divide by twelve. This ignores the effects of compounding monthly. Review section 6.4. [C] :Be sure to incorporate the down payment into your computation and work with a 360-month loan. Review section 6.4. [D] :Did you take the down payment into account? Review section 6.4. [E] :Be sure to incorporate the down payment into your computation and work with a 360-month loan. Review section 6.4. 95) An effective annual rate will always be equal to or greater than the annual percentage rate. [A] True [B] False [A] :You are correct! [B] :You need to review these definitions in section 6.3. 96) Daryl wishes to save money to provide for his retirement. Beginning one month from now, he will deposit a fixed amount into a retirement savings account that will earn 12 percent compounded monthly for thirty years. He will make 360 such deposits. Then, one year after making his final deposit, he will withdraw $100,000 annually for 25 years. The account balance will reduce to zero when the last withdrawal is made. The fund will earn 12.68 percent compounded annually during the last twenty-five years. What is the fixed monthly amount that Daryl will be depositing for the first thirty years? [A] $205.28 [B] $209.58 [C] $214.24 [D] $234.89 [E] $249.38 [A] :You first need to compute how much Daryl must have in his account immediately after making his 360th deposit. This amount is the present value of $100,000 per year for 25 years at a rate of 12.68 percent. From this, you can determine how much he must deposit each month. Review section 6.2. [B] :You first need to compute how much Daryl must have in his account immediately after making his 360th deposit. This amount is the present value of $100,000 per year for 25 years at a rate of 12.68 percent. From this, you can determine how much he must deposit each month. Review section 6.2. [C] :You are correct! [D] :You first need to compute how much Daryl must have in his account immediately after making his 360th deposit. This amount is the present value of $100,000 per year for 25 years at a rate of 12.68 percent. From this, you can determine how much he must deposit each month. Review section 6.2. [E] :You first need to compute how much Daryl must have in his account immediately after making his 360th deposit. This amount is the present value of $100,000 per year for 25 years at a rate of 12.68 percent.From this, you can determine how much he must deposit each month. Review section 6.2. 97) A given rate is quoted as 8 percent, but has an effective annual rate of 8.33 percent. What is the rate of compounding during the year? [A] annually [B] semi-annually [C] quarterly [D] monthly [E] continuously [A] :If interest is compounded annually, the effective and quoted rates are equal. Review section 6.3. [B] :Eight percent compounded semi-annually has an effective annual rate of 8.16 percent. Review section 6.3. [C] :Eight percent compounded quarterly has an effective annual rate of 8.24 percent. Review section 6.3. [D] :Eight percent compounded monthly has an effective annual rate of 8.3 percent. Review section 6.3. [E] :You are correct! 98) As a gift from your parents, you and your heirs will receive $25,000 per year forever, beginning one year from now. What discount rate is being used if the present value of this gift is quoted at $416,667? [A] 4.0 percent [B] 5.0 percent [C] 6.0 percent [D] 7.0 percent [E] 8.0 percent [A] :Do you get $25,000 if you multiply the present value by this rate? Review section 6.2. [B] :Do you get $25,000 if you multiply the present value by this rate? Review section 6.2. [C] :You are correct! [D] :Do you get $25,000 if you multiply the present value by this rate? Review section 6.2. [E] :Do you get $25,000 if you multiply the present value by this rate? Review section 6.2. 99) You want to retire 35 years from today and have $5 million in your retirement savings at that time. You expect to earn an average rate of return of 12 percent compounded monthly on your savings. How much must you save at the beginning of each month to achieve this goal if you have nothing saved as of today? [A] $650 [B] $733 [C] $730 [D] $770 [E] $777 [A] :This is a future value of an annuity due problem. Review section 6.2. [B] :This is a future value of an annuity due problem. Review section 6.2. [C] :This is a future value of an annuity due problem. Review section 6.2. [D] :You are correct! [E] :Did you confuse this with an ordinary annuity? Review section 6.2. 100) What is the effective annual rate of 8 percent compounded quarterly? [A] 8.00 percent [B] 8.16 percent [C] 8.24 percent [D] 8.30 percent[E] 8.33 percent [A] :Did you forget about compounding? Review section 6.3. [B] :How many compounding periods are there? Review section 6.3. [C] :You are correct! [D] :How many compounding periods are there? Review section 6.3. [E] :How many compounding periods are there? Review section 6.3. 101) As a general rule, the effective annual rate is more appropriate for financial decision making than is the annual percentage rate. [A] True [B] False [A] :You are correct! [B] :The effective annual rate is what you actually pay or earn, the annual percentage rate is not. Review section 6.3. 102) What is the present value of $1,000 payments received at the end of each year for the next 10 years? Assume an interest rate of 5.625 percent. [A] $7,069.13 [B] $7,093.62 [C] $7,492.64 [D] $7,914.10 [E] $8,165.12 [A] :You need to review annuity computations in section 6.2. [B] :You need to review annuity computations in section 6.2. [C] :You are correct! [D] :Did you treat this as an annuity due? Review section 6.2. [E] :You need to review annuity computations in section 6.2. 103) Which of the following statements are true? I. There is an inverse relationship between present values and interest rates. II. The effective annual rate will be higher than the annual percentage rate for a loan that compounds interest monthly. III. There is an inverse relationship between future values and periods of time. IV. All else equal, the more frequently interest is compounded on a loan, the more interest you will have to pay. [A] I and II only [B] III and IV only [C] II, III, and IV only [D] I, II, and IV only [E] I, II, III, and IV [A] :Yes, but there is another correct statement also. Review section 6.3. [B] :One of these statements is false. Review section 6.1. [C] :One of these statements is false. Review section 6.1. [D] :You are correct! [E] :One of these statements is false. Review section 6.1. 104) Fast Eddie's Used Cars will sell you a pre-owned Honda for $3,000 with no money down. You agree to make weekly payments for 2 years, beginning one week after you buy the car. The stated rate on the loan is26 percent. How much is each payment? [A] $32.96 [B] $37.06 [C] $38.19 [D] $45.90 [E] $69.65 [A] :This is a present value of an annuity problem with weekly compounding. Review section 6.2. [B] :You are correct! [C] :This is a present value of an annuity problem with weekly compounding. Review section 6.2. [D] :This is a present value of an annuity problem with weekly compounding. Review section 6.2. [E] :This is a present value of an annuity problem with weekly compounding. Review section 6.2. [F]