Berkovitch, Elazar and Stuart I. Greenbaum, "The Loan Commitment as an Optimal Financing Contract", Journal of Financial and Quantitative Analysis, Vol. 26, No. 1, (March 1991), pp. 83-95.

Abstract: This paper provides an imperfect information explanation for the existence of bank loan commitments when both the bank and the potential borrower are risk neutral. The borrower is assumed to have access to a two-stage investment project wherein the investment requirement is revealed to the borrower, but not to the bank, at the beginning of the second stage. If the investor borrows at the beginning of the first stage, the realization at the beginning of the second stage might prompt a default in a situation where the project yields positive net present value. The reason is that the borrower does not regard the first-stage investment as a sunk cost. We show that a two-stage contract resembling a loan commitment can solve this under-investment problem.