A convertible bond is selling for $993. It has 15 years to maturity, $1,000 face value, and pays 8% coupon interest payments annually. Similar straight bonds (non-convertible) are priced to yield 8.5%. The conversion ratio is 20. The stock is currently selling for $45. Calculate the convertible bond's option value.
A) $34.52
B) $93.00
C) $7.00
D) None of the above

Question

Quizplus · Accepted Answer

To calculate the convertible bond's option value, we need to compare its theoretical value to its actual market price.

First, let's calculate the straight bond's price: 
Coupon payment = $1,000 x 8% = $80 
Yield to maturity = 8.5% 
Using a financial calculator, we find that the price of the straight bond is $920.47.

Next, let's calculate the theoretical value of the convertible bond if it were a straight bond: 
Coupon payment = $1,000 x 8% = $80 
Yield to maturity = 8.5% 
Using a financial calculator, we find that the theoretical value of the convertible bond is $927.93.

The difference between the theoretical value and actual market price is the option value: 
Option value = $993 - $927.93 = $65.07

To calculate the conversion value, we need to multiply the conversion ratio by the current stock price: 
Conversion value = 20 x $45 = $900

Therefore, the total value of the convertible bond is: 
Convertible bond value = Option value + Conversion value 
Convertible bond value = $65.07 + $900 = $965.07

Since the face value of the bond is $1,000, the bond is selling at a discount. Therefore, the option value is positive, as expected.

The closest answer choice is A) $34.52, which is the correct option value calculated above.

A Convertible Bond Is Selling for $993