## Figure 20a2

Cash Balances for the Golden Socks Corporation

Ross et al.: Fundamentals of Corporate Finance, Sixth Edition, Alternate Edition

VII. Short-Term Financial Planning and Management

20. Cash and Liquidity Management

### CHAPTER 20 Cash and Liquidity Management

Implicitly, we assume that the net cash outflow is the same every day and that it is known with certainty. These two assumptions make the model easy to handle. We will indicate in the next section what happens when they do not hold.

If C were set higher, say, at \$2.4 million, cash would last four weeks before the firm would have to sell marketable securities, but the firm's average cash balance would increase to \$1.2 million (from \$600,000). If C were set at \$600,000, cash would run out in one week, and the firm would have to replenish cash more frequently, but the average cash balance would fall from \$600,000 to \$300,000.

Because transactions costs (for example, the brokerage costs of selling marketable securities) must be incurred whenever cash is replenished, establishing large initial balances will lower the trading costs connected with cash management. However, the larger the average cash balance, the greater is the opportunity cost (the return that could have been earned on marketable securities).

To determine the optimal strategy, Golden Socks needs to know the following three things:

F = The fixed cost of making a securities trade to replenish cash.

T = The total amount of new cash needed for transactions purposes over the relevant planning period, say, one year.

R = The opportunity cost of holding cash. This is the interest rate on marketable securities.

With this information, Golden Socks can determine the total costs of any particular cash balance policy. It can then determine the optimal cash balance policy.

The Opportunity Costs To determine the opportunity costs of holding cash, we have to find out how much interest is forgone. Golden Socks has, on average, C/2 in cash. This amount could be earning interest at rate R. So the total dollar opportunity costs of cash balances are equal to the average cash balance multiplied by the interest rate:

For example, the opportunity costs of various alternatives are given here assuming that the interest rate is 10 percent:

 Initial Cash Balance Average Cash Balance Opportunity Cost (R = .10)

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