The optimal payment policy for a firm: cash sale versus credit sale

Abstract

Both cash and credit sale are common. Considering the upsides and downsides of these two payment policies, in this paper, we study how a firm should choose between them. In particular, based on the relationship between demand and the inventory level, four strategies are considered for the case of credit sale: only selling to high-quality buyers (S1); selling to high-quality buyers when demand is high and selling to both low- and high-quality buyers otherwise (S2); selling to both when the demand is moderate and selling only to high-quality buyers otherwise (S3); and selling to both when demand is low and selling only to high-quality buyers otherwise (S4). What we find is that credit sale strictly dominates cash sale except when the expected profit from selling to low-quality buyers is less than the salvage value and the demand coefficient of variation is extremely high. Further, under credit sale, two counterintuitive observations are obtained if the demand coefficient of variation is small. The first is that the analysis reveals that the firm may not serve the low-quality buyers despite that doing so offers profits, i.e., S3 is the most preferable strategy for the firm. The second is that the firm may also serve the low-quality buyers despite incurring a loss by doing so, i.e., S4 is the most attractive strategy. In addition, we demonstrate that when the credit sale is employed, the firm’s optimal expected profit decreases both in the proportion of high-quality buyers in the market and in the low-quality buyers’ payment probability when the demand coefficient of variation is significantly small, which is quite different from our conjecture. All of these results provide some distinct insights into the question of what the firm’s best payment policy is and how credit should be extended when credit sale is used.