Equilibrium Rate Analysis of Cash Conversion Systems: The Case of Corporate Subsidiaries

This chapter defines and studies a class of cash conversion systems in firms, consisting of a funds pool, a single-product Make-to-Stock inventory, and a receivables pool. The system implements a perpetual flow cycle where funds convert to product and back to funds. The equilibrium rate analysis (ERA) methodology is used to analyze the firm’s operational and financial performance metrics, including net profit rate, rate of return on investment, and cash conversion cycle statistics. Specifically, in this chapter, we model the case where the firm is a subsidiary of a financially stable parent corporation, and the subsidiary’s cash conversion system is capital-rationed. We model this system as a discrete-state continuous-time Markovian process, and compute its stochastic equilibrium distribution using analytic and numerical methods. These are used, in turn, to compute the aforesaid financial metrics in stochastic equilibrium. Finally, we present a methodology that uses these financial metrics to optimize the financial and operational design of the system, and specifically, the firm’s capital structure and the sizing of the inventory’s base stock level. Numerical results show that optimal designs for profit rate maximization and rate of return maximization can differ substantially, reflecting the differing interests of firm managers and investors.