The Miller-Orr model
The fairly simple Baumol model is designed for averaged, stable cash outlays, which does not always correspond to reality. Naturally, this approach is acceptable for certain companies. However, much more often, cash outlays and receipts are random variables. This circumstance is taken into account in the Miller-Orr model. The main feature of this model is the account of instability of cash flows in the company and decision-making depending on the degree of their deviation from the established boundaries.
The main idea of the model is to establish, in addition to the normative balance of funds (), also its upper () and lower ) of the boundaries within which fluctuations in the money balance are allowed (Figure 7.8).
Fig. 7.8. Varying the cash balance
The amount of money in the model under review is adjusted only in case of exceeding the established limits. So, if the level of cash reaches the upper limit, then the amount () is withdrawn, which is then invested in short-term securities. If the level of funds is lowered to the lower limit, then the company's securities are sold for an amount (), which increases the money balance to the standard level. The implementation of the model is carried out according to the following algorithm.
1. The minimum amount of money resources () is established, which it is expedient to keep on the company's current account. It is determined expertly based on an acceptable level of losses due to a shortage of cash; this in turn depends on the availability of loans and the likelihood of a shortage of cash.
2. According to statistical data, the variance () of the net daily cash flow (the difference between the daily inflow and outflow of funds) is calculated.
3. The expenses () for the storage of funds on the settlement account (daily income rate for short-term securities) and expenses () are determined by mutual transformation of cash and securities. This value is assumed constant; an analogue of this type of expenditure is the commission established on a particular stock market.
4. The range of variation of the balance of cash on the settlement account is calculated:
5. The upper limit of money on the settlement account is calculated;
6. The normative level of the cash balance on the settlement account is determined, to which it is necessary to return if the actual balance falls outside the interval (, ):
7. There is an average balance of cash:
Example. Suppose that for a conditional company, it is necessary to justify the cash management policy in the settlement account for the following initial data: the minimum cash reserve on the current account is $ 4,000; costs for converting securities - $ 150; annual interest rate - 15%; the average square deviation of the net daily cash flow is $ 1,000.
1. Calculation of the indicator .
2. Calculation of the range of variation:
Thus, the balance of cash on the company's current account should vary in the range (4000-23821) dollars; when you exceed the limits of the interval, you must restore funds on your current account in the amount of $ 10607.
Fig. 7.9. The concept of the Stone model
As in the Miller-Orr model, in the Stone model, is the normative, target account balance that the company seeks to reach, and and - respectively, the upper and lower limits of its oscillations. In addition to these parameters, the Stone model has internal control limits () and (). Unlike the Miller-Orr model, where immediate adjustments are made when control limits are reached, this does not always happen in the Stone model.
Assume that the balance of funds on the account reached the external limit (point A in Figure 7.9) at the time L Instead of automatically converting ($ img src="images/image997.jpg">) from cash to securities, the financial manager makes a forecast for the next few days (). If the expected balance of funds at the time () remains above a certain limit (), for example, its size corresponds to the point In, then () dollars will be converted into securities. If the forecast shows that at the moment () the amount of money balance will correspond to the point C, the company will not buy valuable paper. Similar reasoning is also true for the lower limit.
Thus, the main feature of the Stone model is that the company's actions in each current moment are determined by the result of the forecast for the near future. In particular, reaching the upper limit may not cause an immediate conversion of cash into securities, if, for example, relatively high cash outlays are expected in the coming days. Thus, the number of conversion operations is minimized and, consequently, the company's costs are reduced.
In the practical use of the Stone model, the values , and can be determined using the Miller-Orr model, and the values x and are established on the basis of practical experience. A significant advantage of this model is the ability to take into account the so-called seasonal fluctuations, as the financial manager, when making a prediction, evaluates the features of production at specific time periods.
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