XYZ is a firm that can be of two possible "types": good or bad. If XYZ is of the good type, its assets in place generate risk-free cash flows of 20m starting next year in perpetuity. If XYZ is of the bad type, its assets in place generate risk-free cash flows of 10m starting next year in perpetuity. The discount rate for all cash flows is 10%. Today, XYZ (regardless of type) has access to a new investment project that is commonly known and understood by all: by investing 25M today, XYZ receives 33M for sure in one year. XYZ currently has 1 million shares outstanding and zero debt. XYZ's managers want to maximize the value of existing shareholders' equity. (a) (6 marks) If XYZ has access to frictionless financial markets, should it undertake the new investment project? Explain. (b) (6 marks) Suppose that everyone knows that XYZ is of the good type. What is the price of one share of XYZ assuming that XYZ will not undertake the new investment? What is the price of one share of XYZ assuming that XYZ will issue debt to undertake the new investment? What is the price of one share of XYZ assuming that XYZ will issue equity to undertake the new investment? How many new shares will XYZ need to issue if it wanted to finance the new investment fully with equity? (c) (6 marks) Suppose now that XYZ's managers know that XYZ is of the good type, but outside investors believe that XYZ is good with probability and bad with probability 12. Will XYZ undertake the new investment opportunity if it needs to finance the investment fully with equity? Will XYZ undertake the new investment opportunity if it needs to finance the investment fully with debt? Carefully explain your answer. (d) (4 marks) Continue to assume that XYZ's managers know that XYZ is of the good type, and now also assume that, in one year from now, outside investors will learn XYZ's type. For some exogenous reason, XYZ cannot issue straight debt. However, today it can issue one-year maturity convertible bonds. Suppose that XYZ decides to raise 25M through risk-free convertible bonds and use the proceeds to undertake the new investment. Convertible holders may choose to surrender all convertible bonds in exchange for z million shares. The convertible bond is callable (by XYZ) at its face value. What is the minimum value of z such that XYZ can force conversion by calling the bond, after outside investors learn XYZ's type? What are the payoffs to the XYZ's equity holders if they issue such a convertible bond and invest in the project? Explain your answer carefully. (e) (3 marks) Suppose the market believes that if XYZ is of the good type it issues the convertible bond you computed in part (d). What would the share price of XYZ be in part (d) immediately following the issuance of convertible bonds? You can assume that, all else equal, XYZ's managers prefer to keep stock prices high for as long as possible.