Question

Problem 7-5 Coupon Rates [LO2] Gabriele Enterprises has bonds on the market making annual payments, with eight years to maturity, a par value of $1,000, and selling for $952. At this price, the bonds yield 6.1 percent. What must the coupon rate be on the bonds

Answer 1

Answer:

5.32%

Explanation:

The computation of the coupon rate on the bonds is shown below:

As we know that

Current price = Annual coupon × Present value of annuity factor(6.1%,8 ) + $1,000 × Present value of discounting factor(6.1%,8)

$952 = Annual coupon × 6.18529143 + $1,000 × 0.622697222

Annual coupon is

= ($952 - 622.697222) ÷ 6.18529143

= $53.24

Now

Coupon rate is

= Annual coupon ÷ Face value

= $53.24 ÷ $1,000

= 5.32%

Working notes:

1. Present value of annuity is

= Annuity × [1 - (1 + interest rate)^-time period] ÷ rate

= Annual coupon × [1 - (1.061)^-8] ÷ 0.061

= Annual coupon × 6.18529143

And,

2.Present value of discounting factor is

= $1,000 ÷ 1.061^8

= $1000 × 0.622697222