Question 3 Companies X and Y are identical in all respects except for their financing. Current data on the financial structure of the two companies is as follows: Company X: share 1 million shares outstanding with a current market price of $10 per 100,000 bonds outstanding with a current market price of $100 per bond Company Y: 2 million shares outstanding with a current market price of $8 per share 50,000 bonds outstanding with a current market price of $100 per bond The bonds of both companies are risk-free zero-coupon bonds that will pay the holder principal and interest due one year from today. The risk-free interest rate is 10%. All of the securities listed above can be sold short at no cost. There are no taxes. 3a) (10 points) Use the four securities described above (Company X's stocks and bonds and Company Y's stocks and bonds) to construct an arbitrage portfolio (i.e., one that generates a positive profit today with no future risk) that includes exactly 50,000 shares of stock in Company X. How large are the arbitrage profits from this portfolio? Construction of this arbitrage portfolio will require short-selling some of the securities. Note: There are actually infinitely many arbitrage portfolios that differ only in their scale. I am asking you to construct one with exactly 50,000 shares of Company X's stock in order to pin down the specific arbitrage portfolio. 3b) (10 points) Suppose that Company Y is planning to issue $2,000,000 worth of new stock and use the proceeds to repurchase some of its existing bonds. You currently owns 40,000 shares of stock in Company Y and are concerned that the stock will offer a lower return after the financial restructuring because you (correctly) anticipates that the stock will be less risky if the company has lower leverage. You want to counteract Company Y's financial restructuring so that your payoffs are exactly the same as they would have been absent the restructuring. What financial transactions do you need to make after the restructuring in order to restore the payoffs you would have received in the absence of the restructuring?