Your firm wants to issue more equity but finds it costly to do so because of inv

ID: 2715674 • Letter: Y

Question

Your firm wants to issue more equity but finds it costly to do so because of investment banking fees and the adverse selection problem associated with equity issuances. Given this, you decide to issue convertible bonds because you believe that the stock price will significantly appreciate in the future, implying a high likelihood of conversion. That is, you plan to issue equity indirectly by raising money via the convertible bond market.

Specifically, you raise $10M by selling convertible bonds at $1,250 per bond. Each bond has a face value of $1,000, a coupon rate of 4 percent, and a 5 year maturity. The bonds can be exchanged at any time for 50 shares. The expected return on straight debt issued in the past by your firm is 5 percent. Your firm currently has 1.2M shares outstanding priced at $25 per share. There is currently no other debt outstanding.
a) What is the value of each bond’s conversion option? (Hint: first find the value of the straight bond component of the convertible bond.)
b) What is the minimum value of the firm that will induce the bondholders to convert the bonds into stock on the day before maturity?
c) Draw the payoff diagram for the convertible bondholders as a function of the firm value. Specify the slopes of the lines that you draw.
d) Draw the payoff diagram for the current shareholders as a function of firm value. Specify the slopes of the lines that you draw.

Explanation / Answer

(a) Conversion Value of bond = No. of shares recievable on conversion of a bond * MPS

= 50*25 = 1250

Straight bond value = P.V of future interest + present value of redeemable value

= ($1000*4%)*4.3295 + 0.7835*$1000

= $956.68

Value of conversion option = Value of convertible bond - straight bond value

= $1250 - $956.68

= $293.32

(b) In order to determine the minimum value of the firm that will induce the bond holders to convert the bonds into stocks we have to determine Conversion parity price per stock.

Conversion parity price per stock = Value of convertible bond/No. of stocks recievable against one bond

=1250/50

= $25

Therefore value of the firm will be (25*1200000) = $30M