A convertible bond pays interest annually at a coupon rate of 5% 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%. 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

The floor value of the bond is the greater of the value of the bond as a straight bond or the value of the bond if it were converted into shares and sold.

Value of straight bond = PV of cash flows
= (coupon rate x par value) / discount rate * (1 - 1 / (1 + discount rate)^n) + par value / (1 + discount rate)^n
= (0.05 x 1000) / 0.065 * (1 - 1 / 1.065^10) + 1000 / 1.065^10
= $754.51

Value of converted shares = Conversion ratio x market price per share 
= 40 x $20 
= $800.00

Since the value of the straight bond is less than the value of the converted shares, the floor value of the bond is $800.00, which is answer choice B.

A Convertible Bond Pays Interest Annually at a Coupon Rate