Question

Big Canyon Enterprises has bonds on the market making annual payments, with 17 years to maturity, a par value of $1,000, and a price of $961. At this price, the bonds yield 8.6 percent. What must the coupon rate be on the bonds

Answer 1

The coupon rate is 10.96%

Step-by-step explanation:

We must firstly find the bonds coupon in order to calculate the coupon rate of the bond, which is the interest that is received by a bondholder every period as interest which in this case is to be calculated be using the future value annuity formula : Pv = C[(1-(1+i)^-n)/i]

where Pv is the Present value of the bond $961

C is the coupon payment value every year.

i is the interest rate of the bond which is 8.6%

n is the number of years the bond takes to mature which is 17 years.

now we substitute the above values to the above mentioned formula to find the coupon value of the bond C;

$961 = C[(1-(1+8.6%)^-17)/8.6%]

$961/[(1-(1+8.6%)^-17)/8.6%] = C

C = $109.61 is the coupon value or interest payment every year

now to find the coupon rate we will say the coupon value/par value of bond x 100

$109.61/$1000 x 100 = Coupon Rate

Coupon Rate = 10.96%

We use the present value annuity formula as we are given the Present value of the annuity and the yield to maturity at this price.