Rogue Outfitters Inc. has outstanding $1,000 face value that make semiannual payments, and have 10 years remaining to maturity. If the current price for these bonds is $938.57, and the yield to maturity is 4.78%, what is the coupon rate of these bonds?

The coupon rate of these bonds is 4%

Explanation:

The coupon rate is the interest rate written on the face of the bond and the interest payment is made on this rate.

Use the following formula to calculate the coupon rate of the bond

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

Where

F = Face value =  $1,000

Price of the bond = $938.57

r = Yield to maturity = 4.78% x 6/12 = 2.39%

n = Numbers of periods =  10 years x 12/6 = 20 periods

C = Periodic coupon payment =  ?

Placing values in the formula

$938.57 = [ C x ( 1 - ( 1 + 2.39% )^-20 ) / 2.39% ] + [ $1,000 / ( 1 + 2.39% )^20 ]

$938.57 = [ C x 15.75237625 ] + $623.52

C x 15.75237625 = $938.57 - $623.52

C x 15.75237625 = $315.05

C = $315.05 / 15.75237625

C = $20 semiannually

C = $20 x 12/6 = $40 annually

Coupon rate = Coupon Payment / Face value = $40 / $1,000 = 0.04 = 4%