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?

7.3%

Explanation:

Bond price is the sum of present value of coupon payment and face value of the bond. If the price is available the coupon payment can be calculated by following formula

As per given data

n = 18 years

Par value = $1,000

Price = $965

YTM = 7.7%

As we have the value of the bond we need to calculate the coupon payment using following formula:

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

$965 = C x [ (1 - (1 + 7.7%) ^-18) / 7.7% ] + [ $1,000 / (1 + 7.7%) ^18 ]

$965 = C x 9.57 + $263.10

$965 - 263.10 = C x 9.57

701.9 = C x 9.57

C = 701.9 / 9.57 = 73.34

Coupon rate = 73.34 / 1000 = 7.334%