A firm has an outstanding 15-year convertible bond issue with a $1,000 par value and a stated annual interest rate of 7 percent. The bond is convertible into 50 shares of common stock which has a current market price of $15. A straight bond could have been sold with a 10 percent stated interest rate. The market value of the bond is
A) $750.
B) $771 at the minimum.
C) $1,250 at the minimum.
D) $1,000.

Question

Quizplus · Accepted Answer

To calculate the market value of the convertible bond, we need to consider two scenarios:

1) If the bond is not converted to equity, it will pay a fixed interest rate of 7% per annum for 15 years. The present value of this cash flow can be calculated using the formula for the present value of an annuity:

PV = C x ((1 - (1 + r)^-n) / r)

where PV is the present value, C is the annual coupon payment, r is the discount rate, and n is the number of periods.

Using the values given in the question, we get:

PV = 70 x ((1 - (1 + 0.10)^-15) / 0.10)

PV = $624.92

2) If the bond is converted to equity, the holder will receive 50 shares of common stock. The current market price of one share is $15, so the value of 50 shares is 50 x $15 = $750.

The higher of these two values is the market value of the convertible bond. Hence, the minimum market value of the bond is $750, which is option B.

A Firm Has an Outstanding 15-Year Convertible Bond Issue with a $1,000