Firms X and Y are identical in all respects except for capital structure. These firms operate in a tax-exempt haven where firms and individuals pay no taxes. Current data on the financial structure of the two firms is as follows:
Firm X:
1,000 shares outstanding, current market price of $10 per share 100 bonds outstanding with a current bond price of $100 per bond
Firm Y:
2,000 shares outstanding, current market price of $8 per share 50 bonds outstanding with a current bond price of $100 per bond The bonds in both firms are risk free and they are zero-coupon bonds that will pay the holder principal and interest one year from today. The risk-free interest rate is 10%. An individual investor can also borrow or lend from a bank at the 10% risk-free rate.
a) Construct an arbitrage portfolio that includes exactly 50 shares of stock in firm X. How large are the arbitrage profits from this portfolio? Hint: The arbitrage portfolio will consist of the bonds and stocks of both firm X and firm Y and will require short-selling some of these
securities.

 

b) Suppose that firm Y is planning on issuing $2,000 in new stock and using the proceeds to repurchase some of the existing bonds. Investor ABC currently owns 40 shares of stock in Firm Y and is concerned that the stock will offer a lower return after the financial restructuring because she (correctly) anticipates that the stock will be less risky with lower leverage. She wants to counteract the firm's financial restructuring so that her payoffs are exactly the same as before the restructuring. What financial transactions after the restructuring will enable her to replicate the original payoffs from her investment in Firm Y?
Hint: Consider the amount of cash flow Investor ABC receives before the change in capital structure if the firm's total cash flow is C, where C is unknown today and could be any
number. Choose financial transactions that Investor ABC needs to take in order to receive exactly the same amount of cash flow after the change in capital structure when total cash flow is C.