A firm has applied for a loan with the goal to fund a risky project. The bank is considering whether to grant a loan to the firm. The bank knows that the firm may choose between two projects: A or B. The return of these two projects is described below.

A: Invest 40 and obtain 300 with probability 0.3 and 0 with probability 0.7.

B: Invest 40 and obtain 200 with probability 0.6 and 0 with probability 0.4. The choice, made by the firm, of which project to invest in is not verifiable by the bank. However, the outcome of the project (i.e., whether the firm obtains 300, 200 or 0) is verifiable. The bank is a monopolist in the lending market (that is, there is no other bank that can grant a loan to the firm) and the bank can guarantee to obtain 45 for lending 40 of its funds elsewhere. The firm does not have funds of its own to carry out the project, so that the firm gets a value of 0 if not funded by the bank. The firm operates with limited liability. A loan contract specifies that the firm will have to pay R in case the implemented project succeeds (that is, if the firms revenue is 200 or 300). Which is the profit-maximizing amount R that the bank should ask the firm to repay in case the implemented project succeeds? Which project will be implemented? Comment on its efficiency.

Note: To resolve indifferences, assume that the firm chooses Project B whenever it is payoff-indifferent between A and B; also, assume that whenever the firm is indifferent between carrying out a given project and not carrying out any project, the firm carries out the project.