Question

Consider the following two banks: 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? (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)) Asset Value Liabilities Value Before Interest Rise After Interest Rise Difference Before Interest Rise After Interest Rise Difference Bank 1 Bank 2

Answer 1

Answert Banika Bank 4 hag assets composed solely-Of a 10 years, 12.50 person coupon, $ 2.4 million loan with a 12.50 percent yield to Matturity. Zt is financed with a 10 - Yeary, 10 percent coupon, $2.4 millon CD with a 10 percent yield to Maturity, If interest rates rise by 1 percent (loo ba sis points In case of loan & The yield to Matcerity, y = 12.5%. +1% = 13.5% face value Fitture value, FV = $2.40 mn = $ 2400.000 Annual payment = 12.5%. Coupon x face tolue = 12.97. x $ 2.4 0mn $300,000 period - ID years Hence market value of the locin = pu (rata period, Polyment; Fu ) = pv (13.54.,10,300000, 2400000) = $2,272,332 , } 1

In case of co² The yield to Maturity, y=107.+1% = 11% face value s fittelre value, FV5 $2.40mn $2400,000 Annual payment = 10%. Coupon a Face value = 107.X$ 2.40 mn $ 240,000 period 10 years Hence Merrilet value of the CD = pu (roete, period, Payment, Fv) = A (11%,10, 240000, 2400000) 92,258,657 Hence the difference in the value of the assets of each bank = Market value of locin - value of CD and liabilities = $2,258,658-$2,272,332 - - $3,673 Bani 2 Bank 2 has asets composed solely Ofa a 7-yech, 12.50 percent, zero - coupon bond with a current value of $2068.193.38 and Maturity value of $4,716,923.15, .

It is financed by a 10-year, 7.75 percent carpon, $2,400,000 face value CD with a yield to maturity of 10 percent. 3ero coupon bond t Revised yield, y = 12.54, +1% 13.5 y. New market value Maturity valle (1+y)n 14716,923.15)(1+13.51) 7 = $1943,962 Incase of cot The yield to Mertebrity, y = 109. +1%. = 11% Face value Furterre value, FV $2.40 mn $2,400.000 Annual payment 7.759. Coupon X For = 7.75% 8 $2.40mn $186,000 period 10 years Hence, Merrket velle et CD= Pu Crate, periodi pcement, Er PV (117410,186000,2400000)=$1,940,640 Hence, The difference in the value of the assets and liabilithes = Mamicetvale of icon Coupon bond - Market vuilico $1943.962-1940,640 $3,322 of CD