Cash Conversion Systems in Corporate Subsidiaries

This paper models a cash conversion system in a subsidiary of a parent company where there is an active internal capital market, but otherwise the subsidiary has no access to additional external funds. The cash conversion system consists of a treasury, a single-product make-to-stock inventory, and a receivables pool. It implements a perpetual flow cycle, where funds convert to product and back to funds. The system is stationary, and revenues and costs flow directly to the parent company. The parent company aims to maximize equilibrium (long-run) financial metrics in terms of net profit rate and rate of return. To this end, we model this system as a discrete-state continuous-time Markov process and compute its equilibrium state distribution using analytic and numerical methods. These are then used to derive statistics of the equilibrium cash conversion cycle and define equilibrium financial rate metrics and cumulative counterparts that incorporate the time value of money. We further optimize the financial and operational designs of the system and, specifically, the internal capital allocation and inventory base stock level. Finally, noting the potential for friction in the parent–subsidiary relationship, we study numerically the impact of moral hazard and internal capital market inefficiency on optimal designs.