There are three dates, t = 0, 1, 2. An entrepreneur has the following project. At t = 0, an investment of $90 million is needed. At t = 1, the entrepreneur decides whether to exert effort or not. If she does not exert effort, the entrepreneur enjoys a private benefit of X in millions of $. There is no private benefit for the entrepreneur if she exerts effort. At t = 2 the project yields a cash flow of $130 million with probability p and $60 million with probability (1 p). The probability p of success of the project depends on whether the entrepreneur has exerted effort. If the entrepreneur exerts effort then p = 0.8, but if the entrepreneur does not exert effort then p = 0.4. All agents are risk-neutral and the risk-free rate is assumed to be zero. There are no taxes. Suppose that the entrepreneur has no wealth and needs to raise equity from an investor to finance the investment.

1. Is the investor willing to invest in the project if the entrepreneur does not exert effort? Explain your result. [2 marks]
2. Find the maximum value of the private benefit X for which the investor is willing to invest in the project if the entrepreneur does exert effort. Explain and discuss your results. [8 marks]

Now assume that the private benefit is $12 million and that the entrepreneur can also raise debt with a face value of $F million.

3. Can the entrepreneur finance the project solely with debt? What are the payoffs to the debt-holder and to the entrepreneur in this case? Explain and discuss your results. [8 marks]
4. Can the entrepreneur finance the project with a combination of risk-free debt and new equity? Specifically, assume that the entrepreneur raises debt with a face value X < $60 million and finances the remainder of the investment with equity. What minimum level of risk-free debt must be raised for the investment to go ahead? Discuss your results. [7 marks]