A Model for Optimal Utilization of a Firm's Line of Credit

Constant pressure to increase return on assets has firms seeking ways to reduce their working capital costs. In the cash management area, firms are employing more sophisticated collection and disbursement systems. Cash management systems today efficiently speed up collections and, at the end of the day, sweep excess balances into money market accounts. Cash managers focus on finding the optimal cash−short-term investment mix. We can view cash as a raw material. Accordingly, the cash manager and the production manager face similar challenges. The production manager is responsible for maintaining appropriate levels of raw materials, work-inprogress, and inventories. Similarly, the cash manager is responsible for maintaining optimal cash balances. Maintaining appropriate cash balances or inventory levels involves managing flows. As long as the cash manager has sources of credit (access to cash), the firm can cover operating costs while maintaining minimal cash balances. Likewise, the production manager who is able to purchase materials on an as needed basis can minimize the firm’s inventory levels. Inefficient use of cash and materials ultimately reduces the firm’s profitability. Inadequate levels of cash can preclude a firm from meeting its financial obligations as they become due, while material shortages can prevent meeting production schedules. Excess levels of cash and inventories tie up capital and reduce the firm’s return on assets. Short-term assets such as cash and inventories represent investments a firm must make in order to support its operations. As Beranek [2] notes, companies have short-term assets only because they face uncertainties related to their operations. For example, a firm could incur substantial costs if the labor force of a vendor supplying a critical part suddenly went on strike. An inventory of the critical part enables the firm to continue operating while it seeks an alternate supplier or waits out the strike. Similarly, a firm may hold a cash reserve to meet unanticipated demand for cash. Since cash is an unproductive asset, cash reserves are often held in the form of highly liquid short-term investments. Baumol [3] recognized the similarities between cash and inventory management. He extended the economic order quantity (EOQ) model to examine its implications to cash management. The Baumol model assumes the cash manager invests excess funds in interest bearing securities and liquidates them to meet the firm’s demand for cash. As investment returns increase, the opportunity cost of holding cash increases and the cash manager decreases cash balances. As transaction costs (cost of liquidating short-term investments) increase, the cash manager decreases the number of times he liquidates securities, leading to higher cash balances. Managing the cash short-term investments mix involves determining the optimal frequency for replenishing cash and the amount of securities to liquidate. Liquidating short-term investments is costly. Costs include the brokerage fees, delivery costs (such as the cost of a bonded courier), telephone charges, the opportunity cost of redirected managerial effort, and possibly, a liquidity discount on the securities the firm sells. A liquidity discount is the difference between a dealers quote and the price the firm would receive if it could wait for a buyer willing to pay full market value. Along with Baumol, Miller and Orr [6], and Stone [11] developed models for managing cash and short-term investments. The major limitations of cash management models are in their underlying assumptions. The Baumol model requires that cash outflows are certain and constant. The Miller-Orr model assumes that a firm’s net cash flows are normally distributed with a zero mean and a constant standard deviation. The Stone model is similar to the Miller-Orr Model except it assumes the firm has some knowledge of its demand for cash. Mullins and