Question

Interest rate risk and bond price changes Apex Corp. has two outstanding bond issues. One issue consists of 7% annual coupon bonds and the other issue consists of zero-coupon bonds. Both bonds have a $1,000 par value. For each bond, calculate the bond price and the percentage change in price when the required rate of return changes as described below.

a. Ten years to maturity and the required rate of return goes from 7% to 8%.
b. Twenty years to maturity and the required rate of return goes from 7% to 8%.
c. Ten years to maturity and the required rate of return goes from 7% to 6%.
d. Twenty years to maturity and the required rate of return goes from 7% to 6%.
e. Compare and contrast your answers for parts a through d and comment on your observations

Answer 1

Interest rate risk refers to the potential for changes in interest rates to affect the price of a bond. When interest rates rise, bond prices generally fall, and when interest rates fall, bond prices generally rise. The impact of interest rate changes on bond prices can be calculated using the bond price formula. The percentage change in price can be calculated using a formula that considers the new price and the old price.

Step-by-step explanation:

Interest rate risk refers to the potential for changes in interest rates to affect the price of a bond. When interest rates rise, bond prices generally fall, and when interest rates fall, bond prices generally rise. The impact of interest rate changes on bond prices can be calculated using the bond price formula.

a. For the 10-year, 7% annual coupon bond, when the required rate of return goes from 7% to 8%, the bond price decreases. The bond price can be calculated using the bond price formula: Bond Price = (Coupon Payment / Required Rate of Return) * (1 - (1 / (1 + Required Rate of Return)^Number of Periods)) + (Par Value / (1 + Required Rate of Return)^Number of Periods). The percentage change in price can be calculated using the formula: Percentage Change in Price = (New Price - Old Price) / Old Price * 100%.

b. For the 20-year, 7% annual coupon bond, when the required rate of return goes from 7% to 8%, the bond price decreases. The percentage change in price can be calculated using the same formula as in part a.

c. For the 10-year, 7% annual coupon bond, when the required rate of return goes from 7% to 6%, the bond price increases. The percentage change in price can be calculated using the same formula as in part a.

d. For the 20-year, 7% annual coupon bond, when the required rate of return goes from 7% to 6%, the bond price increases. The percentage change in price can be calculated using the same formula as in part a.

e. When comparing the answers for parts a through d, we can observe that for both the 10-year and 20-year bonds, a higher required rate of return leads to a lower bond price and a lower required rate of return leads to a higher bond price. This is consistent with the inverse relationship between interest rates and bond prices.