Question

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.

Answer 1

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%