Question

You own a bond with a coupon rate of 5 percent and a yield to call of 5.9 percent. The bond currently sells for $1,074. If the bond is callable in five years, what is the call premium of the bond? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

Face Value = $1,000
Current Price = $1,074

Annual Coupon Rate = 5.00%
Annual Coupon = 5.00% * $1,000
Annual Coupon = $50

Time to Call = 5 years
Annual YTC = 5.90%

Let Call Price be $C

$1,074 = $50 * PVIFA(5.90%, 5) + $C * PVIF(5.90%, 5)
$1,074 = $50 * (1 - (1/1.059)^5) / 0.059 + $C * (1/1.059)^5
$1,074 = $50 * 4.223848 + $C * 0.750793
$1,074 = $211.1924 + $C * 0.750793
$C * 0.750793 = $862.8076
$C = $1,149.20

Call Price = $1,149.20

Call Premium = Call Price - Face Value
Call Premium = $1,149.20 - $1,000
Call Premium = $149.20