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The Miller-Orr Model

Most firms don’t use their cash flows uniformly and also cannot predict their daily cash inflows and outflows. Mille-Orr Model helps them by allowing daily cash flow variation.

Under the model, the firm allows the cash balance to fluctuate between the upper control limit and the lower control limit, making a purchase and sale of marketable securities only when one of these limits is reached. The assumption made here is that the net cash flows are normally distributed with a zero value of mean and a standard deviation. This model provides two control limits – the upper control limit and the lower control limit as well as a return point. When the firm’s cash limit fluctuates at random and touches the upper limit, the firm buys sufficient marketable securities to come back to a normal level of cash balance i.e. the return point. Similarly, when the firm’s cash flows wander and touch the lower limit, it sells sufficient marketable securities to bring the cash balance back to the normal level i.e. the return point.

The lower limit is set by the firm based on its desired minimum “safety stock” of cash in hand The firm should also determine the following factors:
1. An interest rate for marketable securities, (i)
2. A fixed transaction cost for buying and selling marketable securities, (c)
3. The standard deviation if its daily cash flows, (s)

The upper control limits and return path are than calculated by the Miller-Orr Model as follows:
Distance between the upper limits and lower limits is 3Z.

(Upper limit – Lower limit) = (3/4 C Transaction Cost C Cash Flow Variance/Interest Rate) 1/3

Z = (3/4 C cs2/i) 1/3

If the transaction cost is higher or cash flows shows greater fluctuations, than the upper limit and lower limit will be far off from each other. As the interest rate increases, the limits will come closer. There is an inverse relation between the Z and the interest rate. The upper control limit is three times above the lower control limits and the return point lies between the upper and lower limits. Hence,
Upper Limit = Lower Limit + 3Z
Return Point = Lower Limit + Z

So, the firm holds the average cash balance equal to:
Average Cash Balance = Lower Limit + 4/3 Z

The Miller-Orr Model is more realistic as it allows variation in cash balance within the lower and upper limits. The lower limit can be set according to the firm’s liquidity requirement. To determine the standard deviation of net cash flows the pasty data of the net cash flow behaviour can be used. Managerial attention is needed only if the cash balance deviates from the limits.


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