Question

4. [14 Points] You have been hired to value a new 20-year convertible bond. The bond has a coupon rate of 3%, payable semiannually, and its face value if $1,000. The conversion price is $50, and the stock currently sells for $38. a. What is the minimum value of the bond? Comparable nonconvertible bonds are priced to yield 4% b. What is the conversion premium for this bond?

Answer 1

a.

A Convertible bond, at lowest, trade at the higher of either conversion value or straight value.

First, we have to calculate the price of the bond.

Semi annual payments of $15(1.5% of $1000) for 20 years.Yield is given as 4%

Formula to calculate the price is C*((1-(1+i)^-n)/i), where C=coupon payments, i=yield, n=number of payments.

On substituting, Price = 296.891.

So, Straight value = $296.891

Now calculating Conversion value,

Conversion value=stock price*(par/conversion price)=38*(1000/50)=760.

So, the minimum value if the bond=$760.

b.

Conversion premium for the bond is the difference between current market price of the stock and conversion price

current ratiomarket price is $38 and conversion price is $50. So, the conversion premium of the bond is $12.