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Bank 1 has assets composed solely of a 10-year, 12.50 percent coupon, $2.4 million loan with...

Bank 1 has assets composed solely of a 10-year, 12.50 percent coupon, $2.4 million loan with a 12.50 percent yield to maturity. It is financed with a 10-year, 10 percent coupon, $2.4 million CD with a 10 percent yield to maturity.

Bank 2 has assets composed solely of a 7-year, 12.50 percent, zero-coupon bond with a current value of $2,068,193.38 and a maturity value of $4,716,923.15. It is financed by a 10-year, 7.75 percent coupon, $2,400,000 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?

Solutions

Expert Solution

Bank 1

Bank 1 has assets composed solely of a 10-year, 12.50 percent coupon, $2.4 million loan with a 12.50 percent yield to maturity. It is financed with a 10-year, 10 percent coupon, $2.4 million CD with a 10 percent yield to maturity.

If interest rates rise by 1 percent (100 basis points),

In case of loan:

the yield to maturity, y = 12.5% + 1% = 13.5%

Face value = Future value, FV = $ 2.40 mn = $ 2,400,000

Annual payment = 12.5% coupon x Face value = 12.5% x $ 2.40 mn = $  300,000

Period = 10 years

Hence, market value of the loan = PV (rate, period, payment, FV) = PV(13.5%, 10, 300000, 2400000) =  $ 2,272,332

In case of CD:

the yield to maturity, y = 10% + 1% = 11%

Face value = Future value, FV = $ 2.40 mn = $ 2,400,000

Annual payment = 10% coupon x Face value = 10% x $ 2.40 mn = $ 240,000

Period = 10 years

Hence, market value of the CD = PV (rate, period, payment, FV) = PV(11%, 10, 240000, 2400000) =  $ 2,258,658

Hence, the difference in the value of the assets and liabilities of each bank = Market value of loan - market value of CD = $ 2,258,658 - $ 2,272,332 = - $ 3,673

--------------------

Bank 2

Bank 2 has assets composed solely of a 7-year, 12.50 percent, zero-coupon bond with a current value of $2,068,193.38 and a maturity value of $ 4,716,923.15. It is financed by a 10-year, 7.75 percent coupon, $2,400,000 face value CD with a yield to maturity of 10 percent.

Zero coupon bond:

Revised yield, y = 12.5% + 1% = 13.5%

New market value = Maturity value / (1 + y)n = $ 4,716,923.15 / (1 + 13.5%)7 = $ 1,943,962

In case of CD:

the yield to maturity, y = 10% + 1% = 11%

Face value = Future value, FV = $ 2.40 mn = $ 2,400,000

Annual payment = 7.75% coupon x Face value = 7.75% x $ 2.40 mn = $ 186,000

Period = 10 years

Hence, market value of the CD = PV (rate, period, payment, FV) = PV(11%, 10, 186000, 2400000) =  $ 1,940,640

Hence, the difference in the value of the assets and liabilities = Market value of zero coupon bond - market value of CD = $ 1,943,962  - $ 1,940,640 = $ 3,322


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