# The duration of an 11-year, \$1,000 Treasury bond paying a 10 percent semiannual coupon and selling at par has been estimated at 6.763 years.

Chapter 8:

Problem 9.

Considering the following balance sheet for MMC Bancorp (in millions of dollar):

1. Calculate the value of MMC’s rate-sensitive assets, rate-sensitive liabilities, and repricing gap over the next year.
2. Calculate the expected change in the net interest income for the bank if interest rates rise by 1 percent on both RSAs and RSLs and if interest rates fall by 1 percent on both RSAs and RSLs.
3. Calculate the expected change in the net interest income for the bank if interest rates rise by 1.2 percent on RSAs and by 1 percent on RSLs and if interest rates fall by 1.2 percent on RSAs and by 1 percent on RSLs.

Problem 15.

Consider the following balance sheet for WatchoverU Savings, Inc. (in millions):

 Assets Liabilities and Equity Floating-rate mortgages 1-year time deposits (currently 10% annually) \$50 (currently 6% annually) \$70 30-year fixed-rate loans 3-year time deposits (currently 7% annually) \$50 \$50 (currently 7% annually) \$20 Equity \$10 Total assets \$100 Total liabilities & equity \$100
1. What is WatchoverU’s expected net interest income (for year 2) at year-end?
2. What will expected net interest income (for year 2) be at year-end if interest rates rise by 2 percent?
3. Using the cumulative repricing gap model, what is the expected net interest income (for year 2) for a 2 percent increase in interest rates?
4. What will net interest income (for year 2) be at year-end if interest rates on RSAs increase by 2 percent but interest rates on RSLs increase by 1 percent? Is it reasonable for changes in interest rates on RSAs and RSLs to differ? Why?

Problem 18.

A bank has the following balance sheet:

 Assets Avg. Rate Liabilities/Equity Avg. Rate Rate sensitive \$550,000 7.75% Rate sensitive \$575,000 6.25% Fixed rate 755,000 8.75 Fixed rate 605,000 7.50 Nonearning 265,000 Nonpaying 390,000 Total \$1,570,000 Total \$1,570,000

Suppose interest rates fall such that the average yield on rate-sensitive assets decreases by 15 basis points and the average yield on rate-sensitive liabilities decreases by 5 basis points.

1. Calculate the bank’s CGAP and gap ratio.
2. Assuming the bank does not change the composition of its balance sheet, calculate the resulting change in the bank’s interest income, interest expense, and net interest income.
3. The bank’s CGAP is negative and interest rates decreased, yet net interest income decreased. Explain how the CGAP and spread effects influenced this decrease in net interest income.

Chapter 9:

Problem 17.

The duration of an 11-year, \$1,000 Treasury bond paying a 10 percent semiannual coupon and selling at par has been estimated at 6.763 years.

1. What is the modified duration of the bond? What is the dollar duration of the bond?
2. What will be the estimated price change on the bond if interest rates increase 0.10 percent (10 basis points)? If rates decrease 0.20 percent (20 basis points)?
3. What would the actual price of the bond be under each rate change situation in part (b) using the traditional present value bond pricing techniques? What is the amount of error in each case?

Problem 21.

Two banks are being examined by regulators to determine the interest rate sensitivity of their balance sheets. Bank A has assets composed solely of a 10-year \$1 million loan with a coupon rate and yield of 12 percent. The loan is financed with a 10-year \$1 million CD with a coupon rate and yield of 10 percent. Bank B has assets composed solely of a 7-year, 12 percent zero-coupon bond with a current (market) value of \$894,006.20 and a maturity (principal) value of \$1,976,362.88. The bond is financed with a 10-year, 8.275 percent coupon \$1,000,000 face value CD with a yield to maturity of 10 percent. The loan and the CDs pay interest annually, with principal due at maturity.

1. If market interest rates increase 1 percent (100 basis points), how do the market values of the assets and liabilities of each bank change? That is, what will be the net affect on the market value of the equity for each bank?
2. What accounts for the differences in the changes in the market value of equity between the two banks?
3. Verify your results above by calculating the duration for the assets and liabilities of each bank, and estimate the changes in value for the expected change in interest rates. Summarize your results.

Problem 24.

The balance sheet for Gotbucks Bank, Inc. (GBI), is presented below (\$ millions):

 Assets Liabilities and Equity Cash \$30 Core deposits \$20 Federal funds 20 Federal funds 50 50 Loans (floating) 105 Euro CDs 130 Loans (fixed) 65 Equity 20 Total assets \$220 Total liabilities & equity \$220

Notes to the balance sheet: The fed funds rate is 8.5 percent, the floating loan rate is LIBOR + 4 percent, and currently LIBOR is 11 percent. Fixed rate loans have five-year maturities, are priced at par, and pay 12 percent annual interest. The principal is repaid at maturity. Core deposits are fixed rate for two years at 8 percent paid annually. The principal is repaid at maturity. Euros currently yield 9 percent.