Question

You have been hired to value a new 20-year callable, convertible bond. The bond has a 5 percent coupon, payable semi-annually, and its face value is $1,000. The conversion price is $55, and the stock currently sells for $45.

  

What is the minimum value of the bond? Comparable nonconvertible bonds are priced to yield 6 percent.

   

What is the conversion premium for this bond?

   

Answer 1

The minimum value is computed as shown below:

The coupon payment is computed as follows:

= 5% / 2 x $ 1,000 (Since the payments are semi annually, hence divided by 2)

= $ 25

The YTM will be as follows:

= 6% / 2 (Since the payments are semi annually, hence divided by 2)

= 3% or 0.03

N will be as follows:

= 20 x 2 (Since the payments are semi annually, hence multiplied by 2)

= 40

So, the price of the bond is computed as follows:

Bonds Price = Coupon payment x [ [ (1 - 1 / (1 + r)ⁿ ] / r ] + Par value / (1 + r)ⁿ

= $ 25 x [ [ (1 - 1 / (1 + 0.03)⁴⁰ ] / 0.03 ] + $ 1,000 / 1.03⁴⁰

= $ 25 x 23.11477197 + $ 306.5568408

= $ 884.43 Approximately

b. The conversion premium is computed as shown below:

= (Conversion price - current price) / current price

= ($ 55 - $ 45) / $ 45

= 22.22% Approximately

Feel free to ask in case of any query relating to this question