Question

Rhiannon Corporation has bonds on the market with 16.5 years to maturity, a YTM of 7.7 percent, a par value of $1,000, and a current price of $1,065. The bonds make semiannual payments. What must the coupon rate be on these bonds? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) What is the coupon rate?

Answer 1

Number of periods = 16.5 * 2 = 33

Rate = 7.7% / 2 = 3.85%

price = Semi annual coupon * [1 - 1 / (1 +r)ⁿ] / r + FV / (1 + r)ⁿ

1,065 = Semi annual coupon * [1 - 1 / (1 + 0.0385)³³] / 0.0385 + 1000 / (1 + 0.0385)³³

1,065 = Semi annual coupon * [1 - 0.287465] / 0.0385 + 287.465328

1,065 = Semi annual coupon * 18.507403 + 287.465328

Semi annual coupon = 42.0121

Annual coupon = 42.0121 * 2 = 84.0242

Coupon rate = (Annual coupon / face value) * 100

Coupon rate = (84.0242 / 1000) * 100

Coupon rate = 8.40%