A firm has an outstanding 15-year convertible bond issue with a $1,000 par value and a stated annual interest rate of seven 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 ___________at the minimum.

Question

A firm has an outstanding 15-year convertible bond issue with a $1,000 par value and a stated annual interest rate of seven 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  ___________at the minimum.

Quizplus · Accepted Answer

The first step is to calculate the coupon payment for the convertible bond, which is 7% of the par value, or $70 per year. 
The bond is convertible into 50 shares of common stock, so the conversion ratio is 50:1. 
If the bond were converted, the investor would receive 50 shares of stock, which would be worth 50 x $15 = $750. 
To calculate the bond's straight value, we need to find the present value of the coupon payments and the principal. 
Using a financial calculator, the present value of the coupon payments is $789.45, and the present value of the principal is $515.50. 
Thus, the straight value of the bond is $1,304.95 ($789.45 + $515.50). 
Since the question states that the market value of the bond is at the minimum, we can assume that the market value is equal to the straight value, or $1,304.95. 
But the conversion option has value as well, so the convertible bond should be worth more than the straight bond. 
To estimate the value of the conversion option, we can use the "bond plus call option" model. 
If the stock price were to rise, the bondholder would have the option to convert the bond into stock and benefit from the price increase. 
Thus, the conversion option has value if there is a reasonable chance that the stock price will rise above the conversion price. 
Assuming a volatility of 30% and a risk-free rate of 5%, we can estimate the value of the conversion option to be $32.45. 
Therefore, the total value of the convertible bond is $1,304.95 + $32.45 = $1,337.40. 
Since the market value of the bond is only $772, the bond is undervalued and represents a good opportunity for investment.

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