## Figure 20a2

Cash Balances for the Golden Socks Corporation

Ross et al.: Fundamentals I VII. Short-Term Financial I 20. Cash and Liquidity I I © The McGraw-Hill of Corporate Finance, Sixth Planning and Management Management Companies, 2002

Edition, Alternate Edition

698 PART SEVEN Short-Term Financial Planning and Management

In contrast, the opportunity costs of holding cash are very low if the firm holds very little cash. These costs increase as the cash holdings rise because the firm is giving up more and more in interest that could have been earned.

In Figure 20A.1, the sum of the costs is given by the total cost curve. As shown, the minimum total cost occurs where the two individual cost curves cross at Point C*. At this point, the opportunity costs and the trading costs are equal. This point represents the target cash balance, and it is the point the firm should try to find.

Figure 20A.1 is essentially the same as Figure 19.2 in the previous chapter. As we discuss next, however, we can now say more about the optimum investment in cash and the factors that influence it.

### The BAT Model

The Baumol-Allais-Tobin (BAT) model is a classic means of analyzing our cash management problem. We will show how this model can be used to actually establish the target cash balance. It is a straightforward model and very useful for illustrating the factors in cash management and, more generally, current asset management.

To develop the BAT model, suppose the Golden Socks Corporation starts off at Week 0 with a cash balance of C = \$1.2 million. Each week, outflows exceed inflows by \$600,000. As a result, the cash balance will drop to zero at the end of Week 2. The average cash balance will be the beginning balance (\$1.2 million) plus the ending balance (\$0) divided by 2, or (\$1.2 million + 0)/2 = \$600,000, over the two-week period. At the end of Week 2, Golden Socks replenishes its cash by depositing another \$1.2 million.

As we have described, the cash management strategy for Golden Socks is very simple and boils down to depositing \$1.2 million every two weeks. This policy is shown in Figure 20A.2. Notice how the cash balance declines by \$600,000 per week. Because the company brings the account up to \$1.2 million, the balance hits zero every two weeks. This results in the sawtooth pattern displayed in Figure 20A.2.

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