Question

If the required rate of return on the stock is 15 percent, what should the fair value be four years from today? 4 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. (LG 3-4)

If interest rates rise by 1 percent (100 basis points), how do the values of the assets and liabilities of each bank change?

What accounts for the differences between the two banks’ accounts?

Answer 1

Bank 1:

Market Value of the assets currently = Same as par value as the YTM is same as coupon rate = $ 1 million

Market value of the assets when interest rate rises by 1 % = - PV (Rate, Nper, PMT, FV) = - PV (12% + 1%, 10, 12% x 1, 1) = $ 0.9457 million

Hence, assets' value will reduce by = 1 - 0.9457 = $ 0.0543 million = $ 54,262.43

Market value of liabilities currently = Same as par value as the YTM is same as coupon rate = $ 1 million

Market value of the liabilities when interest rate rises by 1 % = - PV (Rate, Nper, PMT, FV) = - PV (10% + 1%, 10, 10% x 1, 1) = $ 0.9411 million

Hence, liabilities' value will reduce by = 1 - 0.9411 = $ 0.0589 million = $ 58,892.32

Bank 2:

Market Value of the assets currently = $894,006.20

Market value of the assets when interest rate rises by 1 % = - PV (Rate, Nper, PMT, FV) = - PV (12% + 1%, 7, 0, 1976362.88) = $  840,074.08

Hence, assets' value will reduce by = 894,006.20 - 840,074.08 = $  53,932.12

Market value of liabilities currently = = - PV (Rate, Nper, PMT, FV) = - PV (10%, 10, 8.275% x 1000000, 1000000) = $ 894,006.22

Market value of the liabilities when interest rate rises by 1 % = - PV (Rate, Nper, PMT, FV) = - PV (10% + 1%, 10, 8.275% x 1000000, 1000000) = $  839,518.43

Hence, liabilities' value will reduce by = 894,006.22 - 839,518.43 = $ 54,487.79

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What accounts for the differences between the two banks’ accounts?

The two banks have assets and liabilities of different duration.

The assets and liabilities have duration mismatch and hence the changes in value of the assets is not exactly same as that in liabilities.