Question

McConnell Corporation has bonds on the market with 12 years to maturity, a YTM of 11.0 percent, a par value of $1,000, and a current price of $1,246.50. The bonds make semiannual payments. What must the coupon rate be on these bonds?

Answer 1

Par Value = $1,000
Current Price = $1,246.50

Annual YTM = 11.00%
Semiannual YTM = 5.50%

Time to Maturity = 12 years
Semiannual Period = 24

Let Semiannual Coupon be $C

$1,246.50 = $C * PVIFA(5.50%, 24) + $1,000 * PVIF(5.50%, 24)
$1,246.50 = $C * (1 - (1/1.055)^24) / 0.055 + $1,000 / 1.055^24
$1,246.50 = $C * 13.15170 + $1,000 * 0.27666
$1,246.50 = $C * 13.15170 + $276.66
$969.84 = $C * 13.15170
$C = $73.74

Semiannual Coupon = $73.74

Annual Coupon = 2 * Semiannual Coupon
Annual Coupon = 2 * $73.74
Annual Coupon = $147.48

Coupon Rate = Annual Coupon / Par Value
Coupon Rate = $147.48 / $1,000
Coupon Rate = 0.1475 or 14.75%

So, coupon rate of these bonds is 14.75%