Big Canyon Enterprises has bonds on the market making annual payments, with 14 years to maturity, a par value of $1,000, and a price of $967. At this price, the bonds yield 7.9 percent. What must the coupon rate be on the bonds

The coupon rate must be 7.50%

Explanation:

Use the following formula to calculate the coupon rate

Price of the bond = [ C x ( 1 - ( 1 + r )^-n ) / r ] + [ F / ( 1 + r )^n ]

Where

Price of the bond = $967

F = Face value = $1,000

r = Periodic interest rate = 7.9%

n = Numbers of periods = 14 years

C = Periodic coupon payment = ?

Placing values in the formula

$967 = [ C x ( 1 - ( 1 + 7.9% )^-14 ) / 7.9% ] + [ $1,000 / ( 1 + 7.9% )^14 ]

$967 = [ C x 8.29233891544 ] + $344.91

$967 - $344.91 = C x 8.29233891544

$622.09 = C x 8.29233891544

C = $622.09 / 8.29233891544

C = $75.02

Now caculate the coupon rate as follow

Coupon rate = C / F

Coupon rate = $75.02 / $1,000

Coupon rate = 0.07502

Coupon rate = 7.502%

Coupon rate = 7.50%