Question

Gabriele Enterprises has bonds on the market making annual payments, with 20 years to maturity, a par value of $1,000, and selling for $810. At this price, the bonds yield 8.1 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

$ 810 = Coupon payment x [ [ (1 - 1 / (1 + 0.081)²⁰ ] / 0.081 ] + $ 1,000 / 1.081²⁰

$ 810 = Coupon payment x 9.745512851 + $ 210.6134591

Coupon payment = ($ 810 - $ 210.6134591) / 9.745512851

Coupon payment = $ 61.50384799

So, the coupon rate will be as follows:

= $ 61.50384799 / $ 1,000

= 6.15% Approximately

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