An entrepreneur has to finance a project of fixed size I. The entrepreneur has no cash-onhand (A = 0). To implement the project, the entrepreneur must borrow I 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 entrepreneur (borrower) can be one of two types. A good borrower has a probability of success equal to p. A bad borrower has a probability of success equal to q, where p > q. Define as Rb the borrowers level of compensation when the project is financed and succeeds. All the players are risk neutral and there is limited liability for the borrower. Lenders behave competitively, and both borrower and lenders receive zero if the project fails. Assume pR > I > qR.

(a) Suppose first that lenders have complete knowledge of the borrowers type. Write down the lenders break-even constraint when the borrower is (i) good or (ii) bad.

(b) What is the highest level of compensation each type of borrower can obtain? Do both types of borrower obtain financing?

(c) Suppose now that lenders cannot observe the borrowers type. Lenders believe the borrower is good with probability , and bad with probability 1 . Comment on the effect of asymmetric information on (i) the availability of credit to both types of borrower, and (ii) if a loan is granted, on the compensation the two types of borrower obtain from undertaking the project.

(d) Suppose now that the entrepreneur already owns a project that, without further investment, will succeed with either probability p (if good) or probability q (if bad). In case of success, the project yields a return R. The project yields a zero return otherwise. Lenders believe the project is good with probability , and bad with probability 1 . We define m = p + (1 )q. We assume the entrepreneur owns all shares. If the entrepreneur were to put some of the shares on the market and if the true probability of success is q, are the assets in place over-valued or under-valued? Explain your answer.

(e) Let us continue with the framework in part (d). At a cost J, the entrepreneuer can finance a new project which increases the overall probability of success by an amount > 0. More specifically, if the new project is financed, the probability of success is either p + (if the initial project was good) or q + (if the initial project was bad). If the new project is not financed, the probability of success is either p (if the initial project was good) or q (if the initial project was bad). BEEM117 5 TURN OVER We assume: R > J. The entrepreneur has no cash-on-hand; thus, the new investment must be financed by issuing new shares. Write down the lenders break-even constraint in a separating equilibrium in which only the entrepreneur with a bad project issue shares.

(f) What is the good entrepreneurs utility from issuing shares in this separating equilibrium? What is her utility from not issuing shares?

(g) In this separating equilibrium, does the value of shares vary as the entrepreneur announces the issue of new equity? Explain your answer.