Question

Fidelity Music Inc. has an older high yield bond (i.e. junk bond) issue and more recent investment grade bond issue. Fidelity's high yield 13% coupon bonds have a YTM of 16% and will mature i 10 years. The investment grade bonds have a 8% YTM, mature in 22 years, and pay a 5% annual coupon. As a bond investor you would like to evaluate the bond price sensitivity to underlying interest rate fluctuations for both Fidelity Music bond issues.

a. What is the current price of both bonds?
b. What will be the percentage change in bond price for both bonds if the underlying interest rates increase by 2% ?
Which bond has more price sensitivity to interest rate risk?
c. Alteratively, what will be the percentage change in bond price for both bonds if the underlying interest rates decrease by 2%? Which bond has more price sensitivity to interest rate risk?
d. What conclusions do you draw from comparing your answers to parts b and c?
e. Would your answers to parts b through a change if both bonds matured in 13 years and paid a 12% annual coupon and, if so, how?

Answer 1

The current price of the high yield bond is $850.03 and the current price of the investment grade bond is $1,286.26. The high yield bond has more price sensitivity to interest rate risk when interest rates increase, while the investment grade bond has more price sensitivity when interest rates decrease. Comparing the answers to parts b and c, the high yield bond is more responsive to changes in interest rates. If both bonds matured in 13 years and paid a 12% annual coupon, the current prices and percentage changes in bond price would be different.

Step-by-step explanation:

To calculate the current price of the high yield bond, we need to find the present value of the bond's future cash flows. Since it has a 13% coupon rate and a YTM of 16%, we can use the formula for the present value of an annuity to calculate the present value of the bond's coupon payments, and then add the present value of the bond's face value. The current price of the high yield bond is $850.03.

Similarly, to calculate the current price of the investment grade bond, we need to find the present value of its future cash flows. Since it has a 8% coupon rate and a YTM of 5%, which is lower than the coupon rate, the present value of the coupon payments is equal to the coupon rate multiplied by the face value. We also need to add the present value of the face value. The current price of the investment grade bond is $1,286.26.

If the underlying interest rates increase by 2%, we can calculate the new bond prices using the same approach. The percentage change in bond price for the high yield bond is -19.01% and for the investment grade bond is -26.16%. Therefore, the investment grade bond has more price sensitivity to interest rate risk.

If the underlying interest rates decrease by 2%, the percentage change in bond price for the high yield bond is 23.81% and for the investment grade bond is 22.93%. In this case, the high yield bond has more price sensitivity to interest rate risk.

Comparing the answers to parts b and c, we can conclude that the high yield bond is more responsive to changes in interest rates. It experiences larger changes in price for the same magnitude of interest rate change.

If both bonds matured in 13 years and paid a 12% annual coupon, the current price of the high yield bond would be $913.73 and the current price of the investment grade bond would be $1,206.94. The percentage change in bond price for the high yield bond if the interest rates increase by 2% would be -6.67%, and for the investment grade bond would be -11.76%. If the interest rates decrease by 2%, the percentage change in bond price for the high yield bond would be 11.17%, and for the investment grade bond would be 11.64%.