Question

A 12-year bond has a 10% semiannual coupon and a face value of $1000. The bind has a nominal yield to maturity of 7%. The bond can be called in five years at a call price 1050. What is the bond's nominal yield to call?

Answer 1

Calculation of current price:

Face Value = $1,000

Annual Coupon Rate = 10.00%
Semiannual Coupon Rate = 5.00%
Semiannual Coupon = 5.00% * $1,000
Semiannual Coupon = $50

Time to Maturity = 12 years
Semiannual Period = 24

Annual YTM = 7.00%
Semiannual YTM = 3.50%

Current Price = $50 * PVIFA(3.50%, 24) + $1,000 * PVIF(3.50%, 24)
Current Price = $50 * (1 - (1/1.035)^24) / 0.035 + $1,000 * (1/1.035)^24
Current Price = $50 * 16.058368 + $1,000 * 0.437957
Current Price = $1,240.88

Calculation of yield to call:

Face Value = $1,000
Semiannual Coupon = $50
Call Value = $1,050

Time to Call = 5 years
Semiannual Period = 10

Let Semiannual YTC be i%

$1,240.88 = $50 * PVIFA(i%, 10) + $1,050 * PVIF(i%, 10)

Using financial calculator:
N = 10
PV = -1240.88
PMT = 50
FV = 1050

I = 2.667%

Semiannual YTC = 2.667%
Annual YTC = 2 * 2.667%
Annual YTC = 5.33%