A $1,000 5% annual coupon convertible bond is currently valued at $1,050. The discount rate is 5%. The conversion rate is 20. If the price of the common stock rises by $2, what is the amount of the
Change in the ﬂoor value of the bond?

Question

Quizplus · Accepted Answer

The floor value of a convertible bond is the greater of its straight bond value (just the bond component without the conversion option) or its conversion value (the value if the bond were converted into common stock at the current price).

We can calculate the straight bond value as:
Bond value = Annual coupon payment / Discount rate
Bond value = $50 / 0.05 = $1,000

We can calculate the conversion value as:
Conversion value = Conversion ratio x Current stock price
Conversion value = 20 x ($1,050 / 20) = $1,050

Because the current bond price is $1,050, which is greater than the straight bond value of $1,000, the floor value of the bond is $1,050. Therefore, the bond price will not change with a $2 increase in stock price, so the change in floor value is $0.

However, if the stock price had gone down instead of up, the floor value of the bond would have changed. In that case, the change in the floor value would be:
Change in floor value = (New conversion value or straight bond value - Current bond price)
Change in floor value = ($1,070 - $1,050) = $20

Therefore, the correct answer is choice C.

A $1,000 5% Annual Coupon Convertible Bond Is Currently Valued