Question

30. Consider the following two banks: Bank 1 has assets composed solely of a 10-year, 12 percent coupon, $1 million loan with a 12 percent yield to maturity. It is financed with a 10-year, 10 percent coupon, $1 million CD with a 10 percent yield to maturity. Bank 2 has assets composed solely of a 7-year, 12 percent, zero-coupon bond with a current value of $894,006.20 and a maturity value of $1,976,362.88. It is financed with a 10-year, 8.275 percent coupon, $1,000,000 face value CD with a yield to maturity of 10 percent. All securities except the zero-coupon bond pay interest annually. a. If interest rates rise by 1 percent (100 basis points), how do the values of the assets and liabilities of each bank change? b. What accounts for the differences between the two banks’ accounts?

please do in excel

Answer 1

Solution:

Explanation:

a.

For Bank A:

Loan: $120,000*PVIFA n=10,r=13%+ $1,000,000*PVIFn=10,r=13%= $945,737.57.

CD: $100,000*PVIFAn=10,r=11%+ $1,000,000*PVIFn=10,r=11%= $941,107.68.

The loan value decreases $54,262.43 and the CD value falls $58,892.32. Therefore, the decrease in value of the asset is $4,629.89 less than the liability.

For Bank B:

Bond:$1,976,362.88*PVIFn=7,r=13%= $840,074.08.

CD: $82,750*PVIFAn=10,r=11%+ $1,000,000*PVIFn=10,r=11%= $839,518.43.

The bond value & CD values fall by $53,932.12 & $54,487.79 respectively. Therefore, the decrease in value of the asset is $555.67 less than the liability.

NB;

PVIF = Amount / (1+r)n

PVIFA = (1-[1 + r]-n) / r

Also, when calculating for the value of the PVIF & PVIFA, do not round off the intermittent values but rather use them as they are for accuracy purposes.

b.

The assets and liabilities of Bank A change in value by different amounts because the durations of the assets and liabilities are not the same, even though the face values and maturities are the same. For Bank B, the maturities of the assets and liabilities are different, but the current market values and durations are the same. Consequently, the change in interest rates causes approximately the same change in value for both liabilities and assets.