Question

Aurora Hops, Inc. has a bond outstanding that has a $1,000 par value and a market price of $770.60. The bond has 10 years remaining to maturity. Assuming an annual market interest rate of 12% and that the bond pays interest semiannually, calculate the ANNUAL coupon rate on the bond. (Round to nearest DOLLAR for your payment and round to the nearest whole percentage for the rate).

Answer 1

Face Value = $1,000
Current Price = $770.60

Annual Market Interest Rate = 12%
Semiannual Market Interest Rate = 6%

Time to Maturity = 10 years
Semiannual Period to Maturity = 20

Let Semiannual Coupon be $x

$770.60 = $x * PVIFA(6%, 20) + $1,000 * PVIF(6%, 20)
$770.60 = $x * (1 - (1/1.06)^20) / 0.06 + $1,000 / 1.06^20
$770.60 = $x * 11.46992 + $311.80473
$x * 11.46992 = $458.79527
$x = $40

Semiannual Coupon = $40
Semiannual Coupon Rate = $40 / $1,000
Semiannual Coupon Rate = 4%
Annual Coupon Rate = 2 * 4%
Annual Coupon Rate = 8%