Optimal Cash Models
A number of mathematical models have been formulated to help the financial manager in distributing a company's funds so that they render a maximum return to the company.
William Baumol Model
The model formulated by William Baumol can decide the optimum amount of cash for a company to conciliate under conditions of certainty. The objective is to minimize the sum of the fixed costs of transactions and the opportunity cost of accommodating cash balances that do not yield a return. This is similar to the EOQ model utilized in inventory management. The costs can be shown as follows, according to his model:
F (T/C) + I (C/2)
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Where:
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F
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Fixed costs of a transaction
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T
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Total cash anticipated for the specified time period
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I
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Interest rate on marketable securities
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C
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=
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Cash balance
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The optimal level of cash is decided using the following formula:
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Optimal level of cash = √(2FT / I)
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Miller-Orr Model
When the cash payments are not certain, Miller-Orr model can be utilized. This model directs upper and lower limits on cash balances. When the upper limit is attained, a transfer of cash to marketable securities is attained. When the lower limit is reached, a transfer from securities to cash is attained. As long as the cash balance stays within the limits, no transaction occurs. There are several factors in this model are fixed costs of a securities transaction referred as F, which is presumed to be the same for purchasing and selling, the daily interest rate on marketable securities known as I and variance of the daily net cash flows, comprised by σ2. This model presumes that the cash flows are random. The control limits in this model are d dollars as an upper limit and zero dollars at the lower r limit. When the cash balance attains the upper level, d less z dollars of securities are bought and the new balance becomes z dollars. When the cash balance equals zero, z dollars of securities are sold and the new balance again attains z. According to this model, the optimal cash balance z is computed as follows:
Z = 3√(3F σ2)/ 4I
The optimal value for d is computed as 3z.
Average cash balance (approx.) = (z + d)/3
Ogler's Model
This model states that the optimal cash management strategy can be decided through the use of a multiple linear programming model. It is a model that renders for integration of cash management with production and other aspects of the firm. The construction of this model comprises three sections mentioned below:
Selection of the particular planning horizon
Selection of the particular decision variables
Conceptualization of the cash management strategy.
This model utilizes one year planning horizon with twelve monthly periods because of its simpleness. It has 4 basic sets of decision variables which affect cash management of a firm and which must be comprised into the linear programming model of the firm.
These are
Payment schedule
Short-term financing
Sale and purchase of marketable securities
Cash balance.
The acquaintance of all the above models renders the financial managers an perceptibly into the normative framework as to how cash management should be carried on.
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