A firm has an outstanding 15-year convertible bond issue with a $1,000 par value and a stated annual interest rate of 7 percent. The bond is convertible into 50 shares of common stock which has a current market price of $15. A straight bond could have been sold with a 10 percent stated interest rate. The market value of the bond is ________.
A) $750
B) $772 at the minimum
C) $1,250 at the minimum
D) $1,000

Question

Quizplus · Accepted Answer

To find the market value of the bond, we need to calculate the present value of its future cash flows, which consist of the annual interest payments and the value of the conversion option.

First, let's calculate the annual interest payment on the bond:

Annual interest payment = $1,000 x 7% = $70

Next, let's calculate the price of a straight bond with a 10% stated interest rate:

Price of straight bond = $70 / 0.10 = $700

This represents the value of the bond's fixed-income portion.

To calculate the value of the conversion option, we need to figure out how many shares the bondholder can receive if they choose to convert.

Conversion ratio = $1,000 par value / $15 per share = 66.67 shares

Since we can't have a fraction of a share, the bondholder can convert the bond into 66 shares, meaning they receive $990 worth of stock.

Now, we need to calculate the value of the conversion option:

Conversion option value = 66 shares x $15 per share = $990

Finally, we can calculate the market value of the bond:

Market value of bond = Present value of annual interest payments + Present value of conversion option 
= $70 x (1 - 1 / (1 + 10%)^15) / 0.10 + $990 / (1 + 10%)^15 
= $772 at the minimum

Therefore, the correct answer is B.

A Firm Has an Outstanding 15-Year Convertible Bond Issue with a $1,000