Question

You own a bond with a coupon rate of 6.4 percent and a yield to call of 7.3 percent. The bond currently sells for $1,087. If the bond is callable in five years, what is the call premium of the bond?

Answer 1

Face Value = $1,000
Current Price = $1,087

Annual Coupon Rate = 6.40%
Annual Coupon = 6.40% * $1,000
Annual Coupon = $64

Time to Call = 5 years
Annual YTC = 7.30%

Let Call Price be $C

$1,087 = $64 * PVIFA(7.30%, 5) + $C * PVIF(7.30%, 5)
$1,087 = $64 * (1 - (1/1.073)^5) / 0.073 + $C * (1/1.073)^5
$1,087 = $260.3182 + $C * 0.703075
$C * 0.703075 = $826.6818
$C = $1,175.81

Call Price = $1,175.81

Call Premium = Call Price - Face Value
Call Premium = $1,175.81 - $1,000.00
Call Premium = $175.81