The Miller-Orr Model The Baumol Model assumes that cash is used uniformly throughout the

The Miller-Orr Model The Baumol Model assumes that cash is used uniformly throughout the

period. The Miller-Orr Model recognizes that cash flows vary through- out the period in an unpredictable manner. 3

To see how the Miller-Orr model takes account of changes in the need for cash, consider the three key levels of inventory:

■ the lower limit, below which inventory does not fall ■ the return point, the level of inventory that is the target if either the

lower or upper limit is reached ■ the upper limit, above which inventory does not rise

The lower limit is really a safety stock of cash—the cash on hand must never fall below this level. We need to apply experience and judgment in determining the lower level.

Based on (a) how much needs are expected to vary each day, (b) the cost of a transaction, and (c) the opportunity cost of cash expressed on

a daily basis, this model tells us:

1. The level of cash at which a new cash infusion is needed. This level is referred to as the return point (not to be confused with the level of safety stock). Levels of cash below the safety stock cannot be tolerated; levels below the return point are tolerated—until they hit the safety stock level, of course.

2. The upper limit of cash. The amount of cash that would exceed this limit is invested in marketable securities.

3 Merton H. Miller and Daniel Orr, “A Model of the Demand for Money by Firms,” Quarterly Journal of Economics (July 1966) pp. 413–435.

MANAGING WORKING CAPITAL

The return point and the upper limit are determined by the model as the levels necessary to minimize costs of cash, considering (a) daily swings in cash needs, (b) the transactions cost, and (c) the opportunity cost of cash.

The Miller-Orr model provides us with a few decision rules: ■ Our cash balance can be any level between the upper and lower limit.

■ There is a cash balance (the return point) that we aim for if our cash balance exceeds the upper limit or if our cash balance is below the lower limit:

If our cash balance exceeds the upper limit, any cash in excess of the return point is invested in marketable securities. If our cash balance is below the lower limit, any deficiency up to the return point is made up by selling marketable securities or borrowing.

The return point is a function of: ■ the lower limit

■ the cost per transactions ■ the opportunity cost of holding cash (per day) ■ the variability of daily cash flows, which we measure as the variance of

daily cash flows and is determined mathematically as follows:

Return point

(19-1) = Lower limit + --------------------------------------------------------------------------------------------------------------------------------------------------- ( 0.75 Cost per transcation ) Variance of daily cash flows ( ) Opportunity cost per day

In this equation, we see that: ■ The higher the safety stock (the lower limit), the higher the return point.

■ The higher the cost of making a transaction, the higher the return point. ■ The greater the variability of cash flows, the higher the return point. ■ The greater the holding cost of cash, the lower the return point.

The upper limit is the sum of the lower limit and three times the right- most term of the return point equation:

Upper limit = Lower limit 3 ( 0.75 Cost per transcation ) Variance of daily cash flows ( )

(19-2)

+ 3 --------------------------------------------------------------------------------------------------------------------------------------------------- Opportunity cost per day

Management of Cash and Marketable Securities

To see how this model works, suppose we estimate the following items: Opportunity cost per day

Variance of daily cash flows = $20,000 Cost per transaction

Lower limit

Then:

Lower limit = $10,000

Return point = $10,000 + --------------------------------------------------------- ( 0.75 $200 ) $20,000 ( ) = $13,107

0.0001 Upper limit = $10,000 + ( 3 $3,107 ) = $19,321 What we have just determined using the Miller-Orr model is that

the cash balance is allowed to fluctuate between $13,107 and $19,321. If the cash balance exceeds $19,321, we invest the difference between the cash balance and the return point, restoring the cash balance to the return point. If the cash balance is below the lower limit, marketable securities are sold to bring the cash balance to the return point. Each time the cash balance is outside either the lower or the upper limit, we bounce back to the return point.

This “bouncing” is illustrated in Exhibit 19.4. In part (a) of this fig- ure, the cash flow per day is graphed against time—sometimes cash flows in, sometimes cash flows out. In part (b) this figure, the cash bal- ance is plotted for each day using the Miller-Orr model. Each time the balance is hits $10,000, it bounces back to $13,107 and each time the balance is hits $19,321, it bounces back to $13,107.