Factoring policy with constant demand and limited capital

Abstract

AbstractThe convention of selling on credit (to customers) results in mass accumulation of accounts receivable (AR) on the balance sheet of firms. However, capital‐constrained firms do not have enough capital to invest in AR and cover the production cost incurred during the credit period. To finance future business, a capital‐constrained firm can employ factoring—a financing scheme wherein firms sell AR to a financial institution (called a factor) at a discount—to advance cash from AR. By formulating a time‐continuous model with constant demand over an infinite horizon, we study the factoring policy of firms in two practice‐based discounting schemes: automatic discounting and manual discounting. In the automatic discounting scheme, AR should be discounted at the same age, whereas this requirement is relaxed in the manual discounting scheme and how long in advance to discount the AR is contingent over time. In both discounting schemes, the firm needs to choose the timing of discounting in order to reach a capital‐unconstrained state as soon as possible. In the automatic discounting scheme, we approximate the firm's objective function with a quasi‐convex function whose error is demonstrated to be small. Based on this approximation, the firm's optimal decision and the factor's profit can be calculated more easily. When manual discounting is adopted, the firm should meet all the demand by exploiting factoring if the profit margin under immediate discounting is nonnegative. Given the same factoring discount rate, manual discounting is always more attractive to the firm than automatic discounting. However, the preference of the factor over the two discounting schemes depends on the factoring discount rate.