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 $75, and the stock currently sells for $55.

  

What is the minimum value of the bond? Comparable nonconvertible bonds are priced to yield 11 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:

= 11% / 2 (Since the payments are semi annually, hence divided by 2)

= 5.50% or 0.055

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 + 0.055)⁴⁰ ] / 0.055 ] + $ 1,000 / 1.055⁴⁰

= $ 25 x 16.04612469 + $ 117.4631423

= $ 518.62 Approximately

b. The conversion premium is computed as shown below:

= (Conversion price - current price) / current price

= ($ 75 - $ 55) / $ 55

= 36.36% Approximately

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