Question

Ervin’s Enterprises has bonds on the market making annual payments, with 13 years to maturity, a par value of $1,000, and selling for $880. At this price, the bonds yield 11 percent. What must the coupon rate be on the bonds?

Answer 1

The coupon rate is computed as follows:

= Coupon payment / Par value

Coupon payment is computed as follows:

Bonds Price = Coupon payment x [ [ (1 - 1 / (1 + r)ⁿ ] / r ] + Par value / (1 + r)ⁿ

$ 880 = Coupon payment x [ [ (1 - 1 / (1 + 0.11)¹³ ] / 0.11 ] + $ 1,000 / 1.11¹³

$ 880 = Coupon payment x 6.749870404 + $ 257.5142555

Coupon payment = ($ 880 - $ 257.5142555) / 6.749870404

Coupon payment = $ 92.2218809

So, the coupon rate will be as follows:

= $ 92.2218809 / $ 1,000

= 9.22%

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