Question 2 Your firm wants to issue more equity but finds it costly to do so because of investment banking fees and the

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Question 2
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 firm
decides to issue convertible bonds because it believes that the
stock price will significantly appreciate in the future, implying a
high likelihood of conversion. That is, the firm plans to
indirectly issue equity by raising capital through the convertible
bond market.
Your firm raises capital by selling convertible bonds at $1,350 per
bond. Each bond has a face value of $1,000, an annual coupon rate
of 4 percent, and an 8 year maturity. The bonds can be exchanged at
any time for 50 shares. The expected return on historical straight
debt in your firm has been 6 percent per year. There is currently
no other debt outstanding.
a) What is the value of the conversion option for each convertible
bond?
b) What is the minimum stock price that will induce the bondholders
to convert their bonds into stock on the day before
maturity?
c) There are 1.0M shares outstanding and 5,000 convertible bonds
outstanding. What is the minimum value of the firm that will induce
the bondholders to convert their bonds into stock on the day before
maturity?