Question

Big Canyon Enterprises has bonds on the market making annual payments, with 18 years to maturity, a par value of $1,000, and a price of $965. At this price, the bonds yield 7.7 percent.

What must the coupon rate be on the bonds? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

The coupon rate is computed as shown below:

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

$ 965 = Coupon payment x [ [ 1 - 1 / (1 + 0.077)¹⁸ ] / 0.077 ] + $ 1,000 / 1.077¹⁸

$ 965 = Coupon payment x 9.570157465 + $ 263.0978752

$ 965 - $ 263.0978752 = Coupon payment x 9.570157465

Coupon payments = $ 73.3427979

So, the coupon rate will be:

= Coupon payment / Par value

= $ 73.3427979 / $ 1,000

= 7.33% Approximately

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