The baumol model of cash management provides a formal approach for determining firm’s optimum cash balance under certainty. It considers cash management similar to an inventory management problem. 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.

The Baumol’s model makes the following assumption

1. The firm is able to forecast its cash need with certainty.
2. The firm’s cash payments occur uniformly over a period of time.
3. The opportunity cost of holding cash is known and it does not change over time.
4. 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 dollars 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:

Holding cost = k (C /2)

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:

Transaction cost = c (T / C)

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

C =  cT/k

Where C is 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. The optimum cash balance will increase with increase in the per transaction cost and total funds required and decrease with the opportunity cost.

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