Sep 19, 2017

OPTIMAL SALE POLICY). CONSIDER THE TIMING IN FIGURE 4.8. THE PROBABILITY OF SUCCESS S IS NOT…

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(optimal sale policy). Consider the timing in Figure 4.8. The probability of success s is not known initially and is learned publicly after the investment is sunk. If the assets are not sold, the probability of success is s if the entrepreneur works and s − ∆p if she shirks (in which case she gets private benefit B). Assume that the (state-contingent) decision to sell the firm to an acquirer can be contracted upon ex ante. It is optimal to keep the entrepreneur (not sell) if and only if s ≥ s for some threshold s∗. (Assume in the following that s has a wide enough support and that there are no corner solutions. Further assume that, conditional on not liquidating, it is optimal to induce the entrepreneur to exert effort. If you want to show off, you may derive a sufficient condition for this to be the case.) As is usual, everyone is risk neutral, the entrepreneur is protected by limited liability, and the market rate of interest is 0. (i) Suppose that the entrepreneur’s reward in the case of success (and, of course, continuation) is

Rb = B/∆p. Assuming that the financing constraint is binding, write the NPV and the investors’ breakeven constraint and show that for some µ > 0. Explain the economic tradeoff. (ii) Endogenize Rb(s) assuming that effort is to be encouraged and show that indeed Rb(s) = B/∆p for all s. What is the intuition for this “minimum incentive result”? (iii) Suppose now that s can take only two values, s1 and s2, with s2 > s1 and Introduce a first-stage moral hazard (just after the investment is sunk). The entrepreneur chooses between taking a private benefit B0, in which case s = s1 for certain, and taking no private benefit, in which case s = s2 for certain. Assume that financing is infeasible if the contract induces the entrepreneur to misbehave at either stage. What is the optimal contract? Is financing feasible? Discuss the issue of contract renegotiation

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