Inventory and financial strategies of capital-constrained firms under limited joint liability financing

This paper studies the operations and financial decisions of two capital-constrained firms via a limited joint liability (LJL) financing scheme offered by a bank with a menu of loan terms including interest rate and leverage ratio/credit line. To explicitly assess the value of LJL financing, we assume that the firms either use LJL financing scheme or traditional individual financing scheme to finance their operations. Under LJL financing scheme, we construct a non-cooperative game model in which the two firms separately determine their own inventory decision to serve random demand, according to the prior joint liability agreement between the two firms and the bank. We prove that the non-cooperative game between the two firms under the LJL financing scheme is a supermodular, and thus establish the existence of equilibrium inventory decisions of the firms. We then characterize the optimal loan terms of the profit-seeking bank under the proposed two financing schemes. Our results show that the joint-liability mechanism of the LJL financing scheme always induces the firms to overinvest in their ordering decisions (relative to the case of the individual financing scheme), which reveals that the endogenous financial terms of the LJL financing scheme have a positive effect on the firms' operational decisions. Importantly, we provide conditions under which the loan terms of the proposed two financing schemes can be properly set by the bank to make the LJL financing scheme more beneficial to the bank and the two firms, and the bank offering this financing scheme can obtain two additional benefits-that is, a higher probability of recouping all the loans and a lower profit risk (i.e., the standard derivation of the bank's random total profit), compared to individual financing scheme. The research findings provide managerial insights for a profit-seeking bank on how to offer financial loans to capital-constrained firms and for those capital-constrained firms on how to cooperate with one another.