Question

McConnell Corporation has bonds on the market with 18 years to maturity, a YTM of 11.0 percent, a par value of $1,000, and a current price of $1,266.50. The bonds make semiannual payments. What must the coupon rate be on these bonds?

Answer 1

Face Value = $1,000
Current Price = $1,266.50

Annual YTM = 11.00%
Semiannual YTM = 5.50%

Time to Maturity = 18 years
Semiannual Period = 36

Let Semiannual Coupon be $C

$1,266.50 = $C * PVIFA(5.50%, 36) + $1,000 * PVIF(5.50%, 36)
$1,266.50 = $C * (1 - (1/1.0550)^36) / 0.0550 + $1,000 / 1.0550^36
$1,266.50 = $C * 15.53607 + $145.51624
$1,120.98376 = $C * 15.53607
$C = $72.15

Semiannual Coupon = $72.15
Annual Coupon = 2 * $72.15
Annual Coupon = $144.30

Coupon Rate = Annual Coupon / Face Value
Coupon Rate = $144.30 / $1,000
Coupon Rate = 0.1443 or 14.43%