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))

Solutions

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 4 months ago

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