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# Callable and Convertible Bonds

Suppose that the yield curve on bonds that are free of the risk of default is flat at 5% per year. a 20 year default-free coupon bond (with annual coupons and \$1,000 face value) that becomes callable after 10 years is trading at par and has a coupon rate of 5.5%

Questions:

a) What is the implied value of the call provision?
b) A Safeco Corporation bond, which is otherwise identical to the callable 5.5% coupon bond just described, is also convertible into 10 shares of Safeco stock at any time up to the bond's maturity. if its yield to maturity is currently 3.5% per year, what is the implied value of the conversion feature?

#### Solution Preview

Suppose that the yield curve on bonds that are free of the risk of default is flat at 5% per year. a 20 year default-free coupon bond (with annual coupons and \$1,000 face value) that becomes callable after 10 years is trading at par and has a coupon rate of 5.5%

First, we calculate the value of the straight bond without any provisions
The difference between this value and the price of bonds with call provision or conversion feature is the implied value of call provision or implied value of conversion feature

Calculating Value of a bond
To calculate the price of the bond we need to calculate / read from tables the values of
PVIF= Present Value Interest Factor
PVIFA= Present Value Interest Factor for an Annuity
Value of bond= PVIF * Maturity value + PVIFA * interest payment per period

PVIFA( n, r%)= =[1-1/(1+r%)^n]/r%
PVIF( n, r%)= =1/(1+r%)^n

The yield to maturity ...

#### Solution Summary

Calculates
1) implied value of the call provision for a callable bond.
2) implied value of the conversion feature for a convertible bond.

\$2.19