Question

Consider the following two banks:

Bank 1 has assets composed solely of a 10-year, 11.75 percent coupon, $2.1 million loan with a 11.75 percent yield to maturity. It is financed with a 10-year, 10 percent coupon, $2.1 million CD with a 10 percent yield to maturity.

Bank 2 has assets composed solely of a 7-year, 11.75 percent, zero-coupon bond with a current value of $2,229,035.91 and a maturity value of $4,851,206.79. It is financed by a 10-year, 11.00 percent coupon, $2,100,000 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?

Answer 1

Bank 1:Asset value:
Before interest rise=2.1*10^6(since couppon same as YTM)
after interest rise we use pv formuale in excel
=pv(rate,nper,pmt,fv,type)
=pv(12.75%,10,(2.1*10^6*11.75%),(2.1*10^6),0)
=1984901.19
Difference=1984901.19-2.1*10^6=-115098.81
Liabilites value:
Before interest rise=2.1*10^6
after interest rise=
=pv(11%,10,(2.1*10^6*10%),(2.1*10^6),0)
=1976326.13
Difference=1599883.06-2.1*10^6=-123673.87

Bank 2:Asset value:
Before interest rise=2229035.91
after interest rise we use pv formuale in excel
=pv(rate,nper,pmt,fv,type)
=pv(12.75%,7,(0),(4851206.79),0)
=2094276.09
Difference=2094276.09-2229035.91=-134759.82
Liabilites value:
Before interest rise
=pv(10%,10,(2.1*10^6*11%),(2.1*10^6),0)
=2229035.91
after interest rise=
=pv(11%,10,(2.1*10^6*11%),(2.1*10^6),0)
=2100000
Difference=2100000-2229035.91=-129035.91