Kiss the Sky Enterprises has bonds on the market making annu

Kiss the Sky Enterprises has bonds on the market making annual payments, with 6 years to maturity, and selling for $900. At this price, the bonds yield 10.0 percent. What must the coupon rate be on the bonds?

Solution

Face Value = $1,000
Current Price = $900
Time to Maturity = 6 years
Annual Yield = 10.0%

Let annual coupon be $x

$900 = $x * PVIFA(10%, 6) + $1,000 * PVIF(10%, 6)
$900 = $x * (1 - (1/1.10)^6) / 0.10 + $1,000 / 1.10^6
$900 = $x * 4.35526 + $564.47
$335.53 = $x * 4.35526
$x = $77.0

Annual Coupon = $77.0

Annual Coupon Rate = Annual Coupon / Face Value
Annual Coupon Rate = $77.0 / $1,000
Annual Coupon Rate = 7.70%