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Consider the following two banks: Bank 1 has assets composed solely of a 10-year, 14.00 percent...

Consider the following two banks: Bank 1 has assets composed solely of a 10-year, 14.00 percent coupon, $3.0 million loan with a 14.00 percent yield to maturity. It is financed with a 10-year, 10 percent coupon, $3.0 million CD with a 10 percent yield to maturity. Bank 2 has assets composed solely of a 7-year, 14.00 percent, zero-coupon bond with a current value of $2,677,410.23 and a maturity value of $6,699,600.06. It is financed by a 10-year, 8.25 percent coupon, $3,000,000 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), what is the difference in the value of the assets and liabilities of each bank? (Do not round intermediate calculations. Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places. (e.g., 32.16))

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Expert Solution

As a first step let's calculate the modified duration of each of the two sides of the balance sheet. I have used the excel function namely DURATION and MDURATION to get the output. Please see the table below:

Type Settlement Maturity Coupon Yield Frequency Basis Duration Modified Duration
A B C D E F '=DURATION(A,B,C,D,E,F) '=MDURATION(A,B,C,D,E,F)
Bank 1
Asset 1/1/2019 1/1/2029 14.000% 14.00% 1 1 5.95 5.22
Liabilities 1/1/2019 1/1/2029 10.000% 10.00% 1 1 6.76 6.14
Bank 2
Asset 1/1/2019 1/1/2026 0.000% 14.00% 1 1 7.00 6.14
Liabilities 1/1/2019 1/1/2029 8.250% 10.00% 1 1 7.00 6.37

%age change in the value of a security = - modified duration x %age change in interest rate

%age change in interest rate = + 100 bps = + 1.00%

Since all the instruments of Bank 1 have yield to maturity same as the coupon rate, their market value will be same as their respective face value.

For Bank2, market value of the liability = -PV (Rate, period, pmt, FV) = - PV (10%, 10, 8.25% x 3000000, 3000000) =  2,677,410.23

Type Market value % change New Value
Bank 1 A B C = A x (1 + B)
Asset     3,000,000.00 -5.22% 2,843,516.53
Liabilities     3,000,000.00 -6.14% 2,815,662.99
Difference        27,853.54
Bank 2
Asset     2,677,410.23 -6.14% 2,513,007.85
Liabilities     2,677,410.23 -6.37% 2,506,931.26
Difference          6,076.59

The difference in the value of the assets and liabilities of each bank:

Bank 1 = $ 27,853.54

Bank 2 = $ 6,076.59

jeff jeffy answered 6 months ago
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