CFA 35: Capital Budgeting
Given the following cash flows for a capital project, calculate the NPV and IRR. The required rate of return is 8 percent.
Year 0 1 2 3 4 5
Cash flow −50,000 15,000 15,000 20,000 10
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CFA 35: Capital Budgeting
Given the following cash flows for a capital project, calculate the NPV and IRR. The required rate of return is 8 percent.
Year 0 1 2 3 4 5
Cash flow −50,000 15,000 15,000 20,000 10,000 5,000
NPV IRR
A $1,905 10.9%
B $1,905 26.0%
C $3,379 10.9% Correct answer- C is correct.
NPV=−50,000+15,0001.08+15,0001.082+20,0001.083+10,0001.084+5,0001.085NPV=−50,000+13,888.89+12,860.08+15,876.64+7,350.30+ 3,402.92NPV=−50,000+53,378.83=3,378.83
The IRR, found with a financial calculator, is 10.88 percent.
Given the following cash flows for a capital project, calculate its payback period and discounted payback period. The required rate of return is 8 percent.
Year 0 1 2 3 4 5
Cash flow −50,000 15,000 15,000 20,000 10,000 5,000
The discounted payback period is:
0.16 years longer than the payback period.
0.51 years longer than the payback period.
1.01 years longer than the payback period. Correct answer- C is correct.
Year 0 1 2 3 4 5
Cash flow −50,000 15,000 15,000 20,000 10,000 5,000
Cumulative cash flow −50,000 −35,000 −20,000 0 10,000 15,000
Discounted cash flow −50,000 13,888.89 12,860.08 15,876.64 7,350.30 3,402.92
Cumulative DCF −50,000 −36,111.11 −23,251.03 −7,374.38 −24.09 3,378.83
As the table shows, the cumulative cash flow offsets the initial investment in exactly three years. The payback period is 3.00 years. The discounted payback period is between four and five years. The discounted payback period is 4 years plus 24.09/3,402.92 = 0.007 of the fifth year cash flow, or 4.007 = 4.01 years. The discounted payback period is 4.01 − 3.00 = 1.01 years longer than the payback period.
An investment of $100 generates after-tax cash flows of $40 in Year 1, $80 in Year 2, and $120 in Year 3. The required rate of return is 20 percent. The net present value is closest to:
$42.22.
$58.33.
$68.52. Correct answer- B is correct.
NPV=∑t=03CFt(1+r)t=−100+401.20+801.202+1201.203=$58.33
An investment of $150,000 is expected to generate an after-tax cash flow of $100,000 in one year and another $120,000 in two years. The cost of capital is 10 percent. What is the internal rate of return?
28.39 percent.
28.59 percent.
28.79 percent. Correct answer- C is correct. The IRR can be found using a financial calculator or with trial and error. Using trial and error, the total PV is equal to zero if the discount rate is 28.79 percent.
Present Value
Year Cash Flow 28.19% 28.39% 28.59% 28.79%
0 −150,000 −150,000 −150,000 −150,000 −150,000
1 100,000 78,009 77,888 77,767 77,646
2 120,000 73,025 72,798 72,572 72,346
Total 1,034 686 338 −8
A more precise IRR of 28.7854 percent has a total PV closer to zero.
Kim Corporation is considering an investment of 750 million won with expected after-tax cash inflows of 175 million won per year for seven years. The required rate of return is 10 percent. What is the project's:
NPV? IRR?
A 102 million won 14.0%
B 157 million won 23.3%
C 193 million won 10.0% Correct answer- A is correct.
TheNPV=−750+∑t=171751.10t=−750+851.97=101.97millionwon.
The IRR, found with a financial calculator, is 14.02 percent. (The PV is −750, N = 7, and PMT = 175.)
Kim Corporation is considering an investment of 750 million won with expected after-tax cash inflows of 175 million won per year for seven years. The required rate of return is 10 percent. Expressed in years, the project's payback period and discounted payback period, respectively, are closest to:
4.3 years and 5.4 years.
4.3 years and 5.9 years.
4.8 years and 6.3 years. Correct answer- B is correct.
Year 0 1 2 3 4 5 6 7
Cash flow −750 175 175 175 175 175 175 175
Cumulative cash flow −750 −575 −400 −225 −50 125 300 475
The payback period is between four and five years. The payback period is four years plus 50/175 = 0.29 of the fifth year cash flow, or 4.29 years.
Year 0 1 2 3 4 5 6 7
Cash flow −750 175 175 175 175 175 175 175
Discounted cash flow −750 159.09 144.63 131.48 119.53 108.66 98.78 89.80
Cumulative DCF −750 −590.91 −446.28 −314.80 −195.27 −86.61 12.17 101.97
The discounted payback period is between five and six years. The discounted payback period is five years plus 86.61/98.78 = 0.88 of the sixth year cash flow, or 5.88 years.
An investment of $20,000 will create a perpetual after-tax cash flow of $2,000. The required rate of return is 8 percent. What is the investment's profitability index?
1.08.
1.16.
1.25. Correct answer- C is correct.
ThepresentvalueoffuturecashflowsisPV=2,0000.08=25,000TheprofitabilityindexisPI=PVInvestment=25,00020,000=1.25
Hermann Corporation is considering an investment of €375 million with expected after-tax cash inflows of €115 million per year for seven years and an additional after-tax salvage value of €50 million in Year 7. The required rate of return is 10 percent. What is the investment's PI?
1.19.
1.33.
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