Question

A $1,300 face value corporate bond with a 7.10 percent coupon (paid semiannually) has 15 years left to maturity. It has had a credit rating of BB and a yield to maturity of 8.5 percent. The firm recently became more financially stable and the rating agency is upgrading the bonds to BBB. The new appropriate discount rate will be 7.4 percent. What will be the change in the bond’s price in dollars and percentage terms? (Round your answers to 3 decimal places. (e.g., 32.161))

a) Change in the bond’s price in dollars
b) Change in the bond’s price in percentage ___%

Answer 1

The bond's price change can be calculated by finding the present value before and after the change in discount rates after the rating upgrade, taking into account the coupon payments and face value.

Step-by-step explanation:

To determine the change in the bond's price in dollars and percentage, we must calculate the bond's price before and after the credit rating upgrade and its resulting new discount rate. Using the formula for present value of a bond, which includes the present values of all future coupon payments and the repayment of the face value, we can calculate this change.

The coupon payment for the bond is 7.10% of $1,300, paid semiannually, which is $1,300 x 0.071 / 2 = $46.15 per period. There are 30 periods left (15 years x 2), and the face value of the bond is $1,300. We will calculate the bond's price before the upgrade at the 8.5% yield to maturity (semiannual rate of 4.25%) and after the upgrade at the new 7.4% discount rate (semiannual rate of 3.7%).

With this information, we can proceed with the present value calculations for both scenarios and then calculate the difference in price between the two rates to answer the question.