Question

1. University has bonds on the market making annual payments, with eight years to maturity, a par value of $1,000, and selling for $948. At this price, the bonds yield 5.9 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

$ 948 = Coupon payment x [ [ (1 - 1 / (1 + 0.059)⁸ ] / 0.059 ] + $ 1,000 / 1.059⁸

$ 948 = Coupon payment x 6.234445345 + $ 632.1677246

Coupon payment = ($ 948 - $ 632.1677246) / 6.234445345

Coupon payment = $ 50.65924198

So, the coupon rate will be as follows:

= Coupon payment / Par value

= $ 50.65924198 / $ 1,000

= 5.07% Approximately

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