Question

O'Brien Ltd.'s outstanding bonds have a $1,000 par value, and they mature in 20 years. Their nominal yield to maturity is 8.50%, they pay interest semiannually, and they sell at a price of $825. What is the bond's nominal (annual) coupon interest rate? Enter your answer rounded to two decimal places. Do not enter % in the answer box. For example, if your answer is 0.12345 or 12.345% then enter as 12.35 in the answer box.

Answer 1

Number of periods = 20 * 2 = 40

Rate = 8.5% / 2 = 4.25%

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

825 = Semi annual coupon * [1 - 1 / (1 + 0.0425)⁴⁰] / 0.0425 + 1000 / (1 + 0.0425)⁴⁰

825 = Semi annual coupon * [1 - 0.189216] / 0.0425 + 189.215824

825 = Semi annual coupon * 19.077271 + 189.215824

Semi annual coupon = 33.3268

Annual coupon = 33.3268 * 2 = 66.6536

nominal (annual) coupon interest rate = (Annual coupon / face value) * 100

nominal (annual) coupon interest rate = (66.6536 / 1000) * 100

nominal (annual) coupon interest rate = 6.67%