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Problem: There are three dates (t=0, 1, 2). An entrepreneur has the following project. At t=0, an investment of $25 million is needed. At t=1, the investor decides to exert effort or not. If he does not exert effort, the entrepreneur enjoys a private benefit B>0. There is no private benefit for the entrepreneur if he exerts effort. At t=2 the project yields a cash-flow of $80 million with probability p and zero 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 p=0.7, 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. Suppose that the entrepreneur has no wealth and needs to borrow the money required for the investment.
Required:
Question 1: Find the face value of debt when the entrepreneur exerts effort. For what values of B does the entrepreneur exert effort? What is the entrepreneur's expected payoff in this case?
Question 2: Find the face value of debt in the case where the entrepreneur does not exert effort. What is the payoff of the entrepreneur in this case?
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