A 10% corporate bond with a face value of $10,000 was issued in May of 2006. At issue, the bond had 25 years to maturity and 10 years of call protection (first call at 104% of par). In May of 2016 (at the expiration of call protection) similar bonds trade to yield 8%. Compute the gain or loss per bond (expressed in PV terms) if the bonds are called immediately after their call protection has expired. Also, compute the Yield-to-Call as of May 2006 assuming the bond gets called at the expiration of its call protection. Hint: Do NOT use your calculator’s bond function.
We need to calculate the price of the bond after 10 years .
Here lets assume that the interest payments are made annually
Price of the bond = Principal / ( 1+ytm)^n + interest (PVAF , YTM , N)
Here ytm is 8% as similar bonds trade in the market at 8%
n= no of periods
Price of the bond after 10 years = 10000 /( 1 + .08)^15 + 1000 ( PVAF, 8%, 15)
= 10000 / 3.1722 + 1000 *8.5595
=3152.39 + 8559.50
= $11,711.89
Call price = 104% of par
= 10,400
Profit on the bond = Price of the bond after 10 years - call price
= 11711.89 - 10400 = $1311.89
The issuer will make profit of $1311.89 per bond if bond is called.
Yield to call = [C + ( FP -CP ) /N ] / (FP + CP ) / N
C= COUPON
FP = Face value of the bond
CP= Call price of bond
N = Number of years to call
Yield to call =[1000 +(10000 - 10400)/10 ] / ( 10000 + 10400 ) / 2
=(1000 - 40 ) / 20400 / 2
= 960 / 10200
= 9.41%
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