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Value Tree has suffered a series of negative shocks and is now facing the following situation: (1) It has debt outstanding of par value $40 million which is due next year. (2) Next year, its assets have the following prospects: Good scenario Bad scenario Probability Asset value ($ million) 0.5 100 0.5 10 The 1-year risk-free interest rate is now at zero. (a) Determine the payoff to debt and equity holders next year in the two scenarios. What is the current value of Value Tree's debt and equity? (b) The firm now has a new project, which requires a new investment of $12 million and yields $30 million in the good state and -$10 million in the bad state next year. What is the NPV of this project? (e) Will the equity holders take on this project? How much will the value of the firm (debt plus equity) change if Value Tree announces the project? Explain your answers. Suppose two companies X and Z have exactly the same operating characteristics and their business risks are perfectly correlated (i.e., exactly the same cashflows). They differ only in the way they finance their operations. Both companies will be liquidated exactly one year from now and shareholders will receive a liquidating dividend at the end of the year. Company X is expected to pay a liquidating dividend of $55 million, but this is uncertain, so shareholders discount this dividend at a rate of 10%. Z has issued bond to finance its operations. Currently Z's securities are trading as follows: Bonds $10 million Shares $42 million The bonds are AAA rated and the expected return is the same as on the risk free asset which is 5%. (a) Suppose company X has 2,500,000 shares outstanding. What is the current share price of X? (b) What is the total valuation of company Z's assets today? (c) Show how you can set up an arbitrage portfolio in order to bene mispricing of companies X and Z relative to each other