Consider a firm that needs $350 to invest in a project that will yield a single cash flow one period hence. The firm knows the probability distribution of this cash flow, but no one else does. As a banker you only know that the firm is either low risk (L) or high risk (H). If it is L, then it will yield $500 with probability 0.8 and nothing with probability 0.2 one period hence. If it is H, it will yield $1500 with probability 0.6 and nothing with probability 0.4 one period hence. The firm itself knows whether it is H or L.
Assume that both the principal and interest repayments on any debt are tax deductible. The corporate tax rate applicable to this firm is 0.2. There is no equity capital on the firm’s books at present, but it would raise equity as needed. The firm is locked into being either L or H, but as a banker you cannot tell which type it is.
Assume everybody is risk neutral and that the discount rate (and the bank’s cost of funds) is zero. Also, your bank is competitive (it prices loans to earn zero expected profit).
Construct a scheme consisting of two different loan contracts (one requiring the borrower to finance the project partly with equity capital and the other requiring no equity) such that the firm will truthfully reveal its private information by its choice of loan contract.