Question

Gabriele Enterprises has bonds on the market making annual payments, with 13 years to maturity, a par value of $1,000, and selling for $950. At this price, the bonds yield 10 percent. What must the coupon rate be on the bonds?

Answer 1

The coupon rate is computed as shown below:

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

$ 950 = Coupon payment x [ [ (1 - 1 / (1 + 0.10)¹³ ] / 0.10 ] + $ 1,000 / 1.10¹³

$ 950 = Coupon payment x 7.103356203 + $ 289.6643797

Coupon payment = ($ 950 - $ 289.6643797) / 7.103356203

Coupon payment = $ 92.96107381

So, the coupon rate is computed as follows:

= Coupon payment / Par value

= $ 92.96107381 / $ 1,000

= 9.30% Approximately

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