A convertible bond pays interest annually at a coupon rate of 5 percent on a par value of $1,000.The bond has 10 years maturity remaining and the discount rate on otherwise identical non-convertible debt is 6.5 percent.The bond is convertible into shares of common stock at a conversion price of $25 per share (i.e.the bond is exchangeable for 40 shares).Today's closing stock price was $20.What is the floor value of this bond?

Question

Quizplus · Accepted Answer

To calculate the floor value of a convertible bond, we need to compare it to a non-convertible bond with the same terms and choose the lower value as the floor.

Using the formula for the price of a bond with annual coupon payments:

P = C / r * (1 - 1 / (1 + r)^n) + M / (1 + r)^n

Where: 
P = Price of the bond 
C = Annual coupon payment 
r = Discount rate 
n = Number of years to maturity 
M = Par value

For the convertible bond:

C = $1,000 * 5% = $50 
r = 6.5% 
n = 10 
M = $1,000

Using the above formula, we get:

P(convertible) = $50 / 6.5% * (1 - 1 / 1.065^10) + $1,000 / 1.065^10 
P(convertible) = $802.86

To calculate the value of the bond if it were pure debt (i.e., non-convertible), we would use the same formula, but with the discount rate of 6.5% instead of the conversion option.

P(non-convertible) = $50 / 6.5% * (1 - 1 / 1.065^10) + $1,000 / 1.065^10 
P(non-convertible) = $892.17

Therefore, the floor value of the convertible bond is $802.86.

A Convertible Bond Pays Interest Annually at a Coupon Rate