Question

You can purchase a $1000 face value bond with 10 years to maturity for $980. The bond pays a semi-annual coupon. The market requires a return of 8%, compounded semi-annually on similar bonds. What is the coupon rate?

7.71%

8%

2%

3.85%

4%

Answer 1

Answer is 7.71%

Face Value = $1,000
Current Price = $980

Annual YTM = 8.00%
Semiannual YTM = 4.00%

Time to Maturity = 10 years
Semiannual Period = 20

Let Semiannual Coupon be $C

$980 = $C * PVIFA(4.00%, 20) + $1,000 * PVIF(4.00%, 20)
$980 = $C * (1 - (1/1.04)^20) / 0.04 + $1,000 / 1.04^20
$980 = $C * 13.590326 + $456.386946
$C * 13.590326 = $523.613054
$C = $38.53

Semiannual Coupon = $38.53

Annual Coupon = 2 * $38.53
Annual Coupon = $77.06

Coupon Rate = Annual Coupon / Face Value
Coupon Rate = $77.06 / $1,000
Coupon Rate = 0.07706 or 7.706% or 7.71%