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AB Builders, Inc., has 24-year bonds outstanding with a par value of $2,000 and a quoted...

AB Builders, Inc., has 24-year bonds outstanding with a par value of $2,000 and a quoted price of 98.145. The bonds pay interest semiannually and have a yield to maturity of 6.86 percent. What is the coupon rate?

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Answer #1

Number of periods = 24 * 2 = 48

Price = (98.145 / 100) * 2000 = 1,962.9

Semi annual rate = 6.86% / 2 = 3.43%

Price = Coupon * [1 - 1 / (1 + r)^n] / r + FV / (1 + r)^n

1,962.9 = Coupon * [1 - 1 / (1 + 0.0343)^48] / 0.0343 + 2000 / (1 + 0.0343)^48

1,962.9 = Coupon * [1 - 0.198138] / 0.0343 + 396.275124

1,962.9 = Coupon * 23.377914 + 396.275124

Coupon = 67.01

Annual coupon = 67.01 * 2 = 134.02

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

Coupon rate = (134.02 / 1000) * 100

Coupon rate = 13.40%

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