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Question 1 An entrepreneur has to finance a project of fixed size I. The entrepreneur has "cash-on-hand" A, where A 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 Pu; if the borrower exerts no effort, the probability of success is equal to P, where Ap = PA - 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 Ro the amount of profit going to the borrower, and as R the amount of profit going to the lenders in case of success, where R = R + R. 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 (IR) assuming that the borrower exerts effort. (10% of the marks) (c) Write down the borrower's "Incentive Compatibility Constraint (IC) and derive the minimum level of R, such that the borrower exerts effort. (10% of the marks) (d) In this moral hazard framework, is there any relationship between the borrower's cash- on-hand (A) and the probability that the borrower obtains a loan from the lenders? Explain your answer. (10% of the marks) (e) Suppose the borrower is thinking of issuing new securities (after having secured a first loan equal to I - A) to deepen the investment" and increase uniformly - that is, independently of the effort exerted - the probability of success by a factor 7 > 0, with T 0. Suppose the new investment is inefficient, that is, the expected increase in profit TR is smaller than J. In this moral hazard framework, should the initial lenders (those who lent I - A) be worried about the issuing of new securities? Explain. (30% of the marks). (e) Suppose the borrower is thinking of issuing new securities (after having secured a first loan equal to 1 - A) to "deepen the investment" and increase uniformly - that is, independently of the effort exerted - the probability of success by a factor 1 > 0, with T 0. Suppose the new investment is inefficient, that is, the expected increase in profit TR is smaller than J. In this moral hazard framework, should the initial lenders (those who lent I - A) be worried about the issuing of new securities? Explain. (30% of the marks). - (f) Let us continue with the framework introduced in point (e). Suppose T = PH - PL. Should the initial lenders (those who lent I - A) be worried about the issuing of new securities? Explain. (30% of the marks). Question 1 An entrepreneur has to finance a project of fixed size I. The entrepreneur has "cash-on-hand" A, where A 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 Pu; if the borrower exerts no effort, the probability of success is equal to P, where Ap = PA - 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 Ro the amount of profit going to the borrower, and as R the amount of profit going to the lenders in case of success, where R = R + R. 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 (IR) assuming that the borrower exerts effort. (10% of the marks) (c) Write down the borrower's "Incentive Compatibility Constraint (IC) and derive the minimum level of R, such that the borrower exerts effort. (10% of the marks) (d) In this moral hazard framework, is there any relationship between the borrower's cash- on-hand (A) and the probability that the borrower obtains a loan from the lenders? Explain your answer. (10% of the marks) (e) Suppose the borrower is thinking of issuing new securities (after having secured a first loan equal to I - A) to deepen the investment" and increase uniformly - that is, independently of the effort exerted - the probability of success by a factor 7 > 0, with T 0. Suppose the new investment is inefficient, that is, the expected increase in profit TR is smaller than J. In this moral hazard framework, should the initial lenders (those who lent I - A) be worried about the issuing of new securities? Explain. (30% of the marks). (e) Suppose the borrower is thinking of issuing new securities (after having secured a first loan equal to 1 - A) to "deepen the investment" and increase uniformly - that is, independently of the effort exerted - the probability of success by a factor 1 > 0, with T 0. Suppose the new investment is inefficient, that is, the expected increase in profit TR is smaller than J. In this moral hazard framework, should the initial lenders (those who lent I - A) be worried about the issuing of new securities? Explain. (30% of the marks). - (f) Let us continue with the framework introduced in point (e). Suppose T = PH - PL. Should the initial lenders (those who lent I - A) be worried about the issuing of new securities? Explain. (30% of the marks)