Question 1
An entrepreneur has to finance a project of fixed size I. The entrepreneur has “cash-on-hand” A, where A < I. To implement the project, the entrepreneur (that is, the borrower) must borrow I −A from lenders. If undertaken, the project either succeeds, in which case it yields a return R > 0, or fails, in which case it delivers a zero return. The probability of success depends on the effort exerted by the borrower: if the borrower exerts effort, the probability of success is equal to pH; if the borrower exerts no effort, the probability of success is equal to pL, where ∆p = pH −pL > 0. If the borrower exerts no effort, he also obtains a private benefit B > 0, while there is no private benefit when the borrower exerts effort. Define as Rb the amount of profit going to the borrower, and as Rl the amount of profit going to the lenders in case of success, where R = Rb + Rl. All the players are risk neutral. Lenders behave competitively, and both borrower and lenders receive zero if the project fails.
(a) Write down the Net Present Value (NPV ) of the project when the borrower exerts i) effort and ii) no effort. (10% of the marks)
(b) Let us assume that NPV is positive only when the borrower exerts effort. Write down the “break-even constraint” for the lenders (IRl) assuming that the borrower exerts effort. (10% of the marks)
(c) Write down the borrower’s “Incentive Compatibility Constraint” (ICb) and derive the minimum level of Rb such that the borrower exerts effort. (10% of the marks)
(d) In this moral hazard framework, is there any relationship between the borrower’s cashon-hand (A) and the probability that the borrower obtains a loan from the lenders? Explain your answer. (20% of the marks)
(e) Suppose now that there are two variants, “A” and “B”, of the project, which differ only with respect to “riskiness”. We denote each variant by adding a superscript – either A or B – to our parameters. For instance, pAH denotes the probability of success under variant A, when the borrower exerts effort; likewise, RA is the return in case of success under variant A. In particular, we assume that:
pAHRA = pBHRB, with pAH > pBH,
so that project “B” is “riskier”. The investment cost (I) is the same for both variants. The return in case of failure is zero for both variants. Furthermore,
pAH −pAL = pBH −pBL.
Which variant is less prone to credit rationing? Explain. (50% of the marks)
BEEM117 2