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

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. What is the value of each bond's conversion option? What is the minimum value of the firm that will induce the bondholders to convert the bonds into stock on the day before maturity? Draw the payoff diagram for the convertible bondholders as a function of the firm value. Specify the slopes of the lines that you draw. 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. No. of shares on each bond conversion = 50 shares

Market Price of share = $25

Value of each bond's conversion option = No. of shares * Market Price per share

= 50*25 = $1250

b. Minimum Value of the firm that will induce the bondholders to convert the bonds into stock on the day before maturity = Value raised by the firm from bondholders by issue of bonds = $10 Million

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