Question

Q1) 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 $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 and a maturity (principal) value of 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? (Use the duration)

Answer 1

Bank A: An increase in 100 basis points in interest rate, the assets and liabilities will decrease Loan : $120 (PVIFA 13%, 10 ) +$1,000 (PVIF 13%, 10th year) = $945,737.57 CD : $100 (PVIFA 11%,10 ) + $1,000 (PVIF 11%, 10th year) = $941, 107.68 The asset value decreased by $4,629.89 which is less than the liability. Bank B: Bond : $1,976,362.88 * (PVIF 13 %, 10th year) = $840,074.08 CD : $82.75 (PVIFA 11%, 10 years) +$1,000 (PVIF 11%, 10th year) = $839,518.43 The decrease in bond value by $53,932.12 The decrease in CD value by $54,487.79 The asset is decreased by $555.67 which is less than liability.