Question

19, Interest Rate Risk The Faulk Corp. has a 7 percent coupon bond outstanding. The Yoo Company has an 11 percent bond outstanding. Both bonds have 12 years to maturity, make semiannual payments, and have a YTM of 9 percent. If interest rates suddenly rise by 2 percent, what is the percentage change in the price of these bonds? What if interest rates suddenly fall by 2 percent instead? What does this problem tell you about the interest rate risk of lower coupon bonds?

Answer 1

1.

Old Price of Faulk's bonds=7%*1000/9%*(1-1/1.045^24)+1000/1.045^24=855.045

New Price of Faulk's bonds=7%*1000/11%*(1-1/1.055^24)+1000/1.055^24=736.96

%change=-13.81%

Old Price of Yoo's bonds=11%*1000/9%*(1-1/1.045^24)+1000/1.045^24=1144.95

New Price of Yoo's bonds=11%*1000/11%*(1-1/1.055^24)+1000/1.055^24=1000

%change=1000/1144.95-1=-12.66%

2.

New Price of Faulk's bonds=7%*1000/7%*(1-1/1.035^24)+1000/1.035^24=1000

%change=1000/855.045-1=16.95%

New Price of Yoo's bonds=11%*1000/7%*(1-1/1.035^24)+1000/1.035^24=1321.17

%change=1321.17/1144.95-1=15.39%

3.

Lower coupon bonds have higher duration and hence higher interest rate risk