Question

# You have been hired to value a new 20-year callable, convertible bond. The bond has a...

 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?

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

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