Sep 19, 2017

(BORROWER-FRIENDLY BANKRUPTCY COURT). CONSIDER THE TIMING DESCRIBED IN FIGURE 4.7. THE PROJECT,…

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(borrower-friendly bankruptcy court). Consider the timing described in Figure 4.7. The project, if financed, yields random and verifi- able short-term profit r ∈ [0, r ] (with a continuous density and ex ante mean E[r ]). After r is realized and cashed in, the firm either liquidates (sells its assets), yielding some known liquidation value L > 0, or continues. Note that (the random) r and (the deterministic) L are not subject to moral hazard. If the

firm continues, its prospects improve with r (so r is “good news” about the future). Namely, the probability of success is pH(r ) if the entrepreneur works between dates 1 and 2 and pL(r ) if the entrepreneur shirks. Assume that, and

is independent of r (so shirking reduces the probability of success by a fixed amount independent of prospects). As usual, one will want to induce the entrepreneur to work if continuation obtains. It is convenient to use the notation

Investors are competitive and demand an expected rate of return equal to 0. Assume

(i) Argue informally that, in the optimal contract for the borrower, the short-term profit and the liquidation value (if the firm is liquidated) ought to be given to investors. Argue that, in the case of continuation, Rb = B/∆p. (If you are unable to show why, take this fact for granted in the rest of the question.) Interpret conditions (1) and (2). (ii) Write the borrower’s optimization program. Assume (without loss of generality) that the firm continues if and only if r  r ∗ for some r ∗ ∈ (0,r). Exhibit the equation defining r ∗. (iii) Argue that this optimal contract can be implemented using, inter alia, a short-term debt

contract at level d = r. Interpret “liquidation” as a “bankruptcy.” How does short-term debt vary with the borrower’s initial equity? Explain. (iv) Suppose that, when the decision to liquidate is taken, the firm must go to a bankruptcy court. The judge mechanically splits the bankruptcy proceeds L equally between investors and the borrower. Define rˆ by

(where r is the value found in question (ii)). Show that the borrower-friendly court actually prevents the borrower from having access to financing. (Note: a diagram may help.) (v) Continuing on question (iv), show that when

the borrower-friendly court either prevents financing or increases the probability of bankruptcy, and in all cases hurts the borrower and not the lenders.


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