A corporate bond with a 5 percent coupon has 10 years left to maturity. It has had a credit rating of BBB and a yield to maturity of 8.0 percent. The firm has recently gotten into some trouble and the rating agency is downgrading the bonds to BB. The new appropriate discount rate will be 9 percent. What will be the change in the bond's price in dollars? Assume interest payments are paid semiannually and par value is $1,000.

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Quizplus · Accepted Answer

The bond's price change due to the increase in the discount rate (yield to maturity) from 8% to 9% can be calculated by finding the difference in the present value of the bond's cash flows (interest payments and principal repayment) before and after the change in the discount rate. Initially, the bond's semiannual coupon payment is 5% of $1,000 divided by 2, which is $25. The discount rates for the calculations are 4% per half-year (8% annual rate divided by 2) before the downgrade and 4.5% per half-year (9% annual rate divided by 2) after the downgrade. Using the present value formula for an annuity (for the coupon payments) and the present value formula for a single sum (for the principal repayment), we calculate the bond's price before and after the downgrade and find the difference. The calculation shows a decrease in the bond's price, which matches the option indicating a decrease of $56.31.

A Corporate Bond with a 5 Percent Coupon Has 10