Question

A $1,000 par value bond is currently valued at $1,055. The bond pays interest semi-annually, has 10 years to maturity, and has a yield to maturity of 7.3 percent. The coupon rate is _____ percent and the current yield is _____ percent.

Answer 1

Par Value = $1,000
Current Value = $1,055

Time to Maturity = 10 years
Semiannual Period = 20

Annual YTM = 7.30%
Semiannual YTM = 3.65%

Let Semiannual Coupon be $C

$1,055 = $C * PVIFA(3.65%, 20) + $1,000 * PVIF(3.65%, 20)
$1,055 = $C * (1 - (1/1.0365)^20) / 0.0365 + $1,000 / 1.0365^20
$1,055 = $C * 14.021422 + $488.218095
$566.781905 = $C * 14.021422
$C = $40.42

Semiannual Coupon = $40.42

Annual Coupon = 2 * Semiannual Coupon
Annual Coupon = 2 * $40.42
Annual Coupon = $80.84

Coupon Rate = Annual Coupon / Par Value
Coupon Rate = $80.84 / $1,000
Coupon Rate = 0.0808 or 8.08%

Current Yield = Annual Coupon / Current Price
Current Yield = $80.84 / $1,055
Current Yield = 0.0766 or 7.66%

The coupon rate is 8.08 percent and the current yield is 7.66 percent.