Question

Compute the Yield to Call (YTC) of a 9% coupon bond, with a $1,000 face value maturing 20 years from now, but callable in 10 years with a call price of $1,300. Assume the market price of the bond to be $750 and that the coupons are:

a)   paid annually.

b)   paid semi-annually.

Answer 1

Answer a.

Par Value = $1,000

Annual Coupon Rate = 9.00%
Annual Coupon = 9.00%*$1,000 = $90

Call Price = $1,300
Current Price = $750
Time to Call = 10 years

Let Annual YTC be i%

$750 = $90 * PVIFA(i%, 10) + $1,300 * PVIF(i%, 10)

Using financial calculator:
N = 10
PV = -750
PMT = 90
FV = 1300
I = 15.52%

Annual YTC = 15.52%

Answer b.

Par Value = $1,000

Annual Coupon Rate = 9.00%
Semiannual Coupon Rate = 4.50%
Semiannual Coupon = 4.50%*$1,000 = $45

Call Price = $1,300
Current Price = $750
Time to Call = 10 years
Semiannual Period to Call = 20

Let Semiannual YTC be i%

$750 = $45 * PVIFA(i%, 20) + $1,300 * PVIF(i%, 20)

Using financial calculator:
N = 20
PV = -750
PMT = 45
FV = 1300
I = 7.66%

Semiannual YTC = 7.66%
Annual YTC = 2 * 7.66%
Annual YTC = 15.32%