Question

A 13-year bond with a 7.5 percent semiannual coupon and a $1,000 face value has a nominal yield to maturity of 8 percent. The bond currently sells for $960.04. The bond, which may be called after 2 years, has a nominal yield to call of 13.24% percent. What is the bond’s call price?

Group of answer choices $1,065 $1,045 $1,075 $1,035 $1,055

Answer 1

Answer is $1,075

Face Value = $1,000
Current Price = $960.04

Annual Coupon Rate = 7.50%
Semiannual Coupon Rate = 3.75%
Semiannual Coupon = 3.75% * $1,000
Semiannual Coupon = $37.50

Time to Call = 2 years
Semiannual Period = 4

Annual YTC = 13.24%
Semiannual YTC = 6.62%

Let Call Price be $x

$960.04 = $37.50 * PVIFA(6.62%, 4) + $x * PVIF(6.62%, 4)
$960.04 = $37.50 * (1 - (1/1.0662)^4) / 0.0662 + $x * (1/1.0662)^4
$960.04 = $37.50 * 3.416473 + $x * 0.773830
$960.04 = $128.1177375 + $x * 0.773830
$x * 0.773830 = $831.9222625
$x = $1,075

Call Price = $1,075