Question

An investor has two bonds in his portfolio that have a face value of $1,000 and pay a 10% annual coupon. Bond L matures in 17 years, while Bond S matures in 1 year.

a. What will the value of the Bond L be if the going interest rate is 7%, 8%, and 11%? Assume that only one more interest payment is to be made on Bond S at its maturity and that 17 more payments are to be made on Bond L. Round your answers to the nearest cent.

  7% 8% 11%

Bond L $ $ $

Bond S $ $ $

b.   Why does the longer-term bond’s price vary more than the price of the shorter-term bond when interest rates change? The change in price due to a change in the required rate of return decreases as a bond's maturity increases. Long-term bonds have lower interest rate risk than do short-term bonds. Long-term bonds have lower reinvestment rate risk than do short-term bonds. The change in price due to a change in the required rate of return increases as a bond's maturity decreases. Long-term bonds have greater interest rate risk than do short-term bonds.

Answer 1

Price of Bond L

a. par value of Bond A =1000
Coupon = 10%*1000 = 100
Number of Periods =17

PV of Bond at 7% YTM = 100*(1-(1+7%)^-17)/7%+1000/(1+7%)^17=1292.90
PV of Bond at 8% YTM =100*(1-(1+8%)^-17)/8%+1000/(1+8%)^17=1182.43
PV of Bond at 11% YTM =100*(1-(1+11%)^-17)/11%+1000/(1+11%)^17=924.51

b. par value of Bond S =1000
Coupon = 10%*1000 = 100
Number of Periods =1

PV of Bond at 7% YTM = 100*(1-(1+7%)^-1)/7%+1000/(1+7%)^1=1028.04
PV of Bond at 8% YTM =100*(1-(1+8%)^-1)/8%+1000/(1+8%)^1=1018.52
PV of Bond at 11% YTM =100*(1-(1+11%)^-1)/11%+1000/(1+11%)^1=990.99

b.  Long-term bonds have greater interest rate risk than do short-term bonds.