Coupon: 0% Conversion Ratio: 285 shares per $10,000 principal amount Call Date: 1 July 2012 Maturity: 1 July 2019 A firm issues the convertible debt shown above. The price of stock in this company on 1 July 2012 is $36.00. What is the minimum call price that would make a bondholder prefer to accept the call rather than convert?

Question

Quizplus · Accepted Answer

To determine the minimum call price that would make a bondholder prefer to accept the call rather than convert, we need to compare the value of the bond if it is called versus the value of the bond if it is converted. 
If the bond is called, the bondholder will receive the call price, which we need to determine. If the bond is converted, the bondholder will receive a certain number of shares determined by the conversion ratio. 
To determine the number of shares that the bondholder would receive upon conversion, we divide the principal amount of $10,000 by the conversion price, which is the stock price on the conversion date divided by the conversion ratio. 
Conversion Price = Stock Price / Conversion Ratio 
Conversion Ratio = 1 / Conversion Price 
On the call date, the stock price is $36.00, and the conversion ratio is 285 shares per $10,000 principal amount. Therefore, the conversion price is: 
Conversion Price = $36.00 / 285 = $0.1263 per share 
Conversion Ratio = 1 / $0.1263 = 7.917 shares per dollar of principal 
If the bond is converted, the bondholder would receive: 
Conversion Value = Conversion Ratio * Stock Price 
Conversion Value = 7.917 * $36.00 
Conversion Value = $284.95 per $10,000 principal amount 
If the bond is called, the bondholder would receive the call price. Let's denote the call price as X. 
Call Value = X / principal amount 
For the bondholder to prefer the call option over the conversion option, the call price must be greater than the conversion value. 
X / $10,000 > $284.95 / $10,000 
X > $2,849.50 
Therefore, the minimum call price that would make a bondholder prefer to accept the call rather than convert is $2,849.50, which is par plus 2.6%. 
The correct answer is C.

Coupon: 0% Conversion Ratio: 285 Shares Per $10,000 Principal Amount