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

Question

Quizplus · Accepted Answer

The floor value of a convertible bond is the greater of its straight bond value and its conversion value.

The straight bond value can be calculated as follows:

PV = coupon payment / (1 + discount rate) + coupon payment / (1 + discount rate)^2 + ... + coupon payment / (1 + discount rate)^n + par value / (1 + discount rate)^n

Where:
coupon payment = $1,000 x 5% = $50
discount rate = 5%
n = 10 years

PV = $50 / 1.05 + $50 / 1.05^2 + ... + $50 / 1.05^10 + $1,000 / 1.05^10
PV = $937.89

The conversion value can be calculated by multiplying the conversion ratio (40 shares) by the current stock price ($31.25):

Conversion value = conversion ratio x current stock price
Conversion value = 40 x $31.25
Conversion value = $1,250

Therefore, the floor value of the convertible bond is the greater of its straight bond value ($937.89) and its conversion value ($1,250), which is $1,250.

Hence, the correct answer is (C)

A Convertible Bond Pays Interest Annually at a Coupon Rate