A 10% semiannual coupon convertible bond has 10 years to maturity.Market rates on similar non-convertible bonds are 8.5%.Each bond is convertible into 40 common shares.The shares are currently trading at $30.What is the floor value of the bond?

Question

Quizplus · Accepted Answer

To find the floor value of the bond, we need to calculate the value of the bond if it were a non-convertible bond (i.e., if it did not have the option to convert into shares).

First, we calculate the present value of the semiannual coupon payments:
Coupon payment = 10% * $1,000 / 2 = $50
Discount rate = 8.5% / 2 = 4.25%
Number of periods = 2 * 10 = 20
Using the formula for the present value of an ordinary annuity, we get:
PV of coupon payments = $50 * (1 - 1 / (1 + 4.25%)^20) / (4.25%) = $645.10

Next, we calculate the present value of the bond's face value:
Face value = $1,000
Discount rate = 8.5% / 2 = 4.25%
Number of periods = 2 * 10 = 20
Using the formula for the present value of a single amount, we get:
PV of face value = $1,000 / (1 + 4.25%)^20 = $376.89

Therefore, the value of the non-convertible bond is:
Value of bond = PV of coupon payments + PV of face value
Value of bond = $645.10 + $376.89 = $1,021.99

Since the convertible bond has the option to convert into 40 shares, its minimum value would be the greater of its value as a non-convertible bond ($1,021.99) and the value of 40 shares at the current market price of $30 per share ($1,200). Therefore, the floor value of the bond is $1,200. Choice C is the correct answer.

A 10% Semiannual Coupon Convertible Bond Has 10 Years to Maturity.Market