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 $955. At this price, the bonds yield 9.2 percent. What must the coupon rate be on the bonds?

Answer 1

Answer:

The correct answer is 8.679%.

Explanation:

According to the scenario, the given data are as follows:

Face value (F) = $1,000

Bond value (B)= $955

Time (t) = 18 years

Yield (r) = 9.2%

First we calculate the coupon payment:

Let coupon payment = C

then,

B = C × $\frac{1 - \frac{1}{(1+r)^{t} } }{r} + \frac{F}{(1+r)^{t} }$

By putting the value, we get

$955 = C× $\frac{1 - \frac{1}{(1+0.092)^{18} } }{0.092} + \frac{1000}{(1+0.092)^{18} }$

$955 = C × 8.64 + 205.11

C = 86.79

So, Coupon Rate = Coupon Payment ÷ Face value

= 86.79 ÷ 1000

= 0.08679

= 8.679%