Question

26. The current price of a 20-year, $1,000 par value bond is $1,158.91. Interest on this bond is paid every six months, and the current yield to maturity on this bond 13.4 percent. Given these facts, what is the annual coupon rate on this bond?

Answer 1

Bond's Market Value = PV of Coupon Payment + PV of Maturity Value

Bond's Market Value = [Periodic Coupon Payment * {(1 - (1 + r)^-n) / r}] + [Face Value / (1 + r)^n]

$1,158.91 = [PMT * {(1 - (1 + 0.134/2)^-(20*2)) / (0.134/2)}] + [$1,000 / {1 + (0.134/2)}^(20*2)]

$1,158.91 = [PMT * {0.9253 / 0.067}] + [$1,000 / 13.3837]

$1,158.91 = [PMT * 13.8102] + $74.72

$1,158.91 - $74.72 = PMT * 13.8102

PMT = $1,084.19 / 13.8102 = $78.51

Annual Coupon Payment = PMT * No. of compounding periods in a year = $78.51 * 2 = $157.01

Coupon Rate = Annual Coupon Payment / Face Value = $157.01 / $1,000 = 0.1570, or 15.70%