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Baumol Cash Model

In Cash Management, Baumol has a great contributions by giving some very useful models, one of them is his Cash Model which provides a formal approach for determining firm’s optimum cash balance under certainty. Cash management is similar to an inventory management problem which is very deliberately illustrated and considered under this Cash Model presented by Baumol. As such, the firm attempts to minimise the sum of the cost of holding cash (inventory of cash) and the cost of converting marketable securities to cash. This model of Cash is based on the assumption that the firm is able to forecast its cash need with certainty and all the cash payments related to form occur uniformly over a period of time. Another assumption is to holding the cash as to the opportunity cost is known and it does not change over time and the firm will incur the same transaction cost whenever it converts securities to cash.

Let us assume that the firm sells securities and starts with a cash balance of C dollars. As the firm spends cash, its cash balance decreases steadily and reaches to zero. The firm replenishes its cash balance to C rupees by selling marketable securities. This pattern continues over time. Since the cash balance decreases steadily, the average cash balance will be: C/2 this pattern is shown in.

The firm incurs a holding cost for keeping the cash balance, it is an opportunity cost; that is, the return foregone on the marketable securities. If the opportunity cost is k, then the firm’s holding cost for maintaining an average cash balance is as follows:

The firm incurs a transaction cost whenever it converts its marketable securities to cash. Total number of transactions during the year will be total fund requirement, divided by the cash balance, C, T/C. The per transaction cost is assumed to be constant. If per transaction cost is c, then the total transaction cost will be:

The optimum cash balance, C, is obtained when the total cost is minimum. The formula for the optimum cash balance is as follows:

Here, C stands for the optimum cash balance, c is the cost per transaction, T is the total cash needed during the year and k is the opportunity cost of holding cash balance. As there is increase in the per transaction cost and total funds required and decrease with the opportunity cost of the firm, the optimum cash balance will also increases with it.