A bank is considering whether to grant a loan to a firm that has applied for a loan to fund a project. The bank knows that the firm may choose between two projects: A or B, as described below.

A: Invest 50 and obtain 250 with probability 0.25 and 0 otherwise.

B: Invest 50 and obtain 200 with probability 0.5 and 0 otherwise.

The choice of projects by the firm is not verifiable but, once implemented, the outcome of the project (i.e., whether the firm obtains 250, 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). The bank can get a 5% return for its funds by lending these elsewhere. The firm does not have funds of its own to carry out the project, so that the firm would get a value of 0 if not funded by the bank. The firm operates with limited liability. Finally, assume that the firm would choose Project B whenever it is payoff-indifferent between A and B. To maximize its profit, which amount R should the bank ask the firm to repay in case the implemented project succeeds?