FIN 434 Chapter 7 Practice problems
7-1. A government bond is currently selling for $1,195 and pays $75 per year in interest for 14 years when it matures. If the redemption value of this bond is $1,000, what is its yiel
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FIN 434 Chapter 7 Practice problems
7-1. A government bond is currently selling for $1,195 and pays $75 per year in interest for 14 years when it matures. If the redemption value of this bond is $1,000, what is its yield to maturity if purchased today for $1,195?
The yield to maturity ( ) equation for this bond would be:
7-2. Suppose the government bond described in problem 1 above is held for five years and then the savings institution acquiring the bond decides to sell it at a price of $940. Can you figure out the average annual yield the savings institution will have earned for its five-year investment in the bond?
7-3. U.S. Treasury bills are available for purchase this week at the following prices (based upon $100 par value) and with the indicated maturities:
a. $97.25, 182 days.
b. $95.75, 270 days.
c. $98.75, 91 days.
Calculate the bank discount rate (DR) on each bill if it is held to maturity. What is the equivalent yield to maturity (sometimes called the bond-equivalent or coupon-equivalent yield) on each of these Treasury Bills?
The discount rates and equivalent yields to maturity (bond-equivalent or coupon-equivalent yields) on each of these Treasury bills are:
7-4. Farmville Financial reports a net interest margin of 2.75 percent in its most recent financial report, with total interest revenue of $95 million and total interest costs of $82 million. What volume of earning assets must the bank hold? Suppose the bank’s interest revenues rise by 5 percent and its interest costs and earnings assets increase by 9 percent. What will happen to Farmville’s net interest margin?
The relevant formula is:
If revenues rise by 5 percent, and interest costs and earnings assets rise by 9 percent, net interest margin is:
7-5. If a credit union’s net interest margin, which was 2.50 percent, increases 10 percent and its total assets, which stood originally at $575 million, rise by 20 percent, what change will occur in the bank's net interest income?
New net interest income:
Change in net interest income = New net interest income – Original net interest income
7-6. The cumulative interest rate gap of Poquoson Savings Bank increases 60 percent from an initial figure of $25 million. If market interest rates rise by 25 percent from an initial level of 3 percent, what changes will occur in this thrift’s net interest income?
New net interest income = New market interest rate × Increase in assets
Initial net interest income = Initial market interest rate × Initial assets
Percent change in net interest income = ($1.5 million – $0.75 million)/ $0.75 million
Thus, the bank's net interest income will increase by 100 percent.
7-7. New Comers State Bank has recorded the following financial data for the past three years (dollars in millions):
What has been happening to the bank’s net interest margin? What do you think caused the changes you have observed? Do you have any recommendations for New Comers’ management team?
Net interest margin (NIM) = Net interest income/Total earning assets
Where,
Net interest income = Net interest revenues - Net interest expenses
Total earning assets = Loans + Investments
The net interest margin has been increasing over the years. As interest revenues and expenses as well as the bank’s assets have increased consistently over the years, there has been a constant increase in the net interest margin. If the bank can further cut down on its interest expenses and increase its assets in the next years, the net interest margin will increase at a higher rate.
7-8 The First National Bank of Dogsville finds that its asset and liability portfolio contains the following distribution of maturities and repricing opportunities:
Coming Week Next 30 Days Next 31-90 Days More Than 90 Days
Loans $200.00 $300.00 $475.00 $525.00
Securities 21.00 26.00 40.00 70.00
Interest-sensitive assets
Transaction deposits $320.00 $ 0.00 $ 0.00 $ 0.00
Time accts. 100.00 290.00 196.00 100.00
Money market borrowings 136.00 140.00 100.00 65.00
Interest-sensitive liabilities
When and by how much is the bank exposed to interest rate risk? For each maturity or repricing interval, what changes in interest rates will be beneficial and which will be damaging, given the current portfolio position?
Coming Week Next 30 Days Next 31-90 Days More Than 90 Days
Loans $200 $300 $475 $525
Securities 21 26 40 70
Total IS Assets $221 $326 $515 $595
Transaction deposits $320 $ − $ − $ −
Time Accts. 100 290 196 100
Money Mkt. Borr. 136 140 100 65
Total IS Liab. $556 $430 $296 $165
GAP −335 −104 +219 +430
Cumulative GAP −335 −439 −220 +210
First National has a negative gap in the nearest period and therefore would benefit if interest rates fall. In the next period it has a slightly negative gap and would therefore benefit of interest rate rise. However, its cumulative gap is still negative. The third period is positive gap and hence the bank would benefit if interest rates rise. In the final period the gap is positive and the bank would benefit if interest rates rise. Its cumulative gap is slightly positive and also shows that rising interest rates would be beneficial to the bank overall.
7-9 Sunset Savings Bank currently has the following interest-sensitive assets and liabilities on its balance sheet with the interest-rate sensitivity weights noted.
Interest-Sensitive Assets $ Amount Rate Sensitivity Index
Federal fund loans $ 50.00 1.00
Security holdings 50.00 1.20
Loans and leases 350.00 1.45
Interest-Sensitive Liabilities $ Amount Rate Sensitivity Index
Interest-bearing deposits $ 250.00 0.75
Money-market borrowings 90.00 0.95
What is the bank’s current interest-sensitive gap? Adjusting for these various interest rate sensitivity weights what is the bank’s weighted interest-sensitive gap? Suppose the federal funds interest rate increases or decreases 50 basis points. How will the bank’s net interest income be affected (a) given its current balance sheet makeup and (b) reflecting its weighted balance sheet adjusted for the foregoing rate-sensitivity indexes?
a.) Change in Bank’s Income = IS Gap × Change in interest rates
Using the regular IS Gap; net income will change by plus or minus $550,000
b.) Change in Bank’s Income = Weighted IS Gap × Change in interest rates
Using the weighted IS Gap; net income will change by plus or minus $1,722,500.
7-10 Sparkle Savings Association has interest-sensitive assets of $400 million, interest-sensitive liabilities of $325 million, and total assets of $500 million. What is the bank’s dollar interest-sensitive gap? What is Sparkle’s relative interest-sensitive gap? What is the value of its interest-sensitivity ratio? Is it asset sensitive or liability sensitive? Under what scenario for market interest rates will Sparkle experience a gain in net interest income? A loss in net interest income?
Dollar Interest-Sensitive Gap = ISA – ISL = $400 million − $325 million = $75 million
7-11 Snowman Bank, N.A., has a portfolio of loans and securities expected to generate cash inflows for the bank as follows:
Deposits and money market borrowings are expected to require the following cash outflows:
If the discount rate applicable to the previous cash flows is 4.25 percent, what is the duration of the Snowman’s portfolio of earning assets and of its deposits and money market borrowings? What will happen to the bank's total returns, assuming all other factors are held constant, if interest rates rise? If interest rates fall? Given the size of the duration gap you have calculated, in what type of hedging should Snowman engage? Please be specific about the hedging transactions needed and their expected effects.
Because Snowman's Asset Duration is greater than its Liability Duration, the bank has a positive duration gap, which means that the bank's net worth will decrease if interest rates rise, because the value of the liabilities will decline by less than the value of the assets. On the other hand, if interest rates were to fall, this positive duration gap will increase the net worth. In this case, the value of the assets will rise by a greater amount than the value of the liabilities.
7-12. Given the cash inflow and outflow figures in Problem 11 for Snowman Bank, N.A., suppose that interest rates began at a level of 4.25 percent and then suddenly rise to 4.75 percent. If the bank has total assets of $20 billion and total liabilities of $18 billion, by how much would the value of Snowman’s net worth change as a result of this movement in interest rates? Suppose, on the other hand, that interest rates decline from 4.25 percent to 3.5 percent. What happens to the value of Snowman’s net worth in this case and by how much in dollars does it change? What is the size of its duration gap?
7-13. Conway Thrift Association reports an average asset duration of 7 years and an average liability duration of 4 years. In its latest financial report, the association recorded total assets of $1.8 billion and total liabilities of $1.5 billion. If interest rates began at 5 percent and then suddenly climbed to 6 percent, what change will occur in the value of Conway’s net worth? By
how much would Conway’s net worth change if, instead of rising, interest rates fell from 5 percent to 4.5 percent?
7-14. A financial firm holds a bond in its investment portfolio whose duration is 15 years. Its current market price is $975. While market interest rates are currently at 6 percent for comparable quality securities, a decrease in interest rates to 5.75 percent is expected in the coming weeks. What change (in percentage terms) will this bond’s price experience if market interest rates change as anticipated?
7-15. A savings bank’s weighted average asset duration is 8 years. Its total liabilities amount to $925 million, while its assets total 1.25 billion dollars. What is the dollar-weighted duration of the bank’s liability portfolio if it has a zero leverage-adjusted duration gap?
Hence, the dollar-weighted duration of the bank’s liability portfolio is 5.92 years.
7-16 Blue Moon National Bank holds assets and liabilities whose average durations and dollar amounts are as shown in this table:
What is the weighted average duration of Blue Moon’s asset portfolio and liability portfolio? What is the leverage-adjusted duration gap?
The weighted average duration of Blue Moon’s asset portfolio is calculated as follows:
The weighted average duration of the liability portfolio is calculated as follows:
Therefore, the leverage-adjusted duration gap is 4.4055 years.
7-17 A government bond currently carries a yield to maturity of 6 percent and a market price of $1,168.49. If the bond promises to pay $100 in interest annually for five years, what is its current duration?
The duration of the bond is computed as follows:
Therefore, the current duration of the bond is 4.23 years.
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