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 other-wise identical non-convertible debt is 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 $31.25.What is the floor value of this bond?

Question

Quizplus · Accepted Answer

The floor value of a convertible bond can be determined by calculating the bond's value as if it were a non-convertible bond and then adding the value of the conversion option. 
The value of the bond as if it were a non-convertible bond can be calculated using the present value formula: 
PV = C / r * (1 - 1 / (1 + r)^n) + FV / (1 + r)^n 
Where PV is the present value, C is the annual coupon payment, r is the discount rate, n is the number of periods, and FV is the face value or par value. 
Plugging in the given numbers: 
PV = 50 / 0.05 * (1 - 1 / 1.05^10) + 1,000 / 1.05^10 = $890.98 
The conversion option is worth 40 * 31.25 = $1,250 
Therefore, the floor value of the bond is $890.98 + $1,250 = $2,140.98, which rounds up to $1,250.

A Convertible Bond Pays Interest Annually at a Coupon Rate