Sep 18, 2017

(RANDOM FINANCING). CONSIDER THE FIXED-INVESTMENT MODEL OF SECTION 3.2. WE KNOW THAT IF A ≥ A,…

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(random financing). Consider the fixed-investment model of Section 3.2. We know that if A ≥A, where

t is both optimal and feasible for the borrower to sign a contract in which the project is undertaken for certain. We also noted that for A < A, the borrower cannot convince investors to undertake the project with probability 1. With A > 0, the entrepreneur benefits from signing a “random financing contract,” though.

(i) Consider a contract in which the borrower invests Aˆ ∈ [0, A] of her own money, the project is financed with probability x, and the borrower receives Rb in the case of success and 0 otherwise. Write the investors’ breakeven condition.

(ii) Show that (provided the NPV, pHR − I, is positive) it is optimal for the borrower to invest

How does the probability that the project is undertaken vary with A?


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