Question

Rhiannon Corporation has bonds on the market with 20.5 years to maturity, a YTM of 6.7 percent, a par value of $1,000, and a current price of $1,044. The bonds make semiannual payments.

What must the coupon rate be on these bonds? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

Par Value = $1,000
Current Price = $1,044

Annual YTM = 6.70%
Semiannual YTM = 3.35%

Time to Maturity = 20.50 years
Semiannual Period = 41

Let Semiannual Coupon be $C

$1,044 = $C * PVIFA(3.35%, 41) + $1,000 * PVIF(3.35%, 41)
$1,044 = $C * (1 - (1/1.0335)^41) / 0.0335 + $1,000 / 1.0335^41
$1,044 = $C * 22.119928 + $258.982417
$785.017583 = $C * 22.119928
$C = $35.489

Semiannual Coupon = $35.489

Annual Coupon = 2 * Semiannual Coupon
Annual Coupon = 2 * $35.489
Annual Coupon = $70.978

Coupon Rate = Annual Coupon / Par Value
Annual Coupon = $70.978 / $1,000
Annual Coupon = 0.0710 or 7.10%

Therefore, coupon rate on these bonds is 7.10%