Question

5 Sunrise, Incorporated, is trying to determine its cost of debt. The firm has a debt issue outstanding with 23 years to maturity that is quoted at 96 percent of face value. The issue makes semiannual payments and has an embedded cost of 5 percent annually. 10 points a. What is the company's pretax cost of debt? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) b. If the tax rate is 21 percent, what is the aftertax cost of debt? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Print a. Pretax cost of debt % b. Aftertax cost of debt %

Answer 1

A simple two-year bond paying 8% interest will have a present value equal to its face value when discounted at the same rate. However, if interest rates rise to 11%, the present value of the bond's future cash flows decreases due to the higher discount rate. This shows the inverse relationship between bond value and interest rates.

Step-by-step explanation:

Considering a simple two-year bond with a face value of $3,000 and an interest rate of 8%, the bond will pay an annual interest payment of $240. If we calculate the present value of this bond using a discount rate equal to its interest rate, which is 8%, the present value will be equal to the face value because the bond is priced at par.

However, if interest rates rise and the new discount rate is 11%, the present value of the bond's future cash flows would be decreased. To find the new present value, each cash flow should be discounted back to their present value at the new higher rate of 11%. The formula for present value is PV = C / (1+r)^t, where C is the future cash flow, r is the discount rate, and t is the number of periods. Using this formula:

• The present value of the first $240 interest payment at 11% is $240 / (1+0.11) which is about $216.22.
• For the second year, considering both the final interest payment and the principal amount, the present value calculation would be $3,240 / (1+0.11)^2 which is about $2,630.63.
• The total present value of the bond when the discount rate is 11% is the sum of the present value of both payments which equals approximately $2,846.85.

The calculations demonstrate that an increase in market interest rates results in a lower present value of future payments from a bond.