Computation of Optimum Cash Balance

Principle & Practice of Management

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Computation of Optimum Cash Balance

A firm has to maintain sufficient liquidity by managing minimum cash balance. Firm needed cash to pay suppliers of raw materials, pay salaries and other expenses as well as paying interest, tax and dividends. Sufficient liquidity means the availability of cash to pay the firm obligations in time. Generally, the minimum cash balance is equal to the cash needed for transaction plus safety cash that can be maintained based on firm’s past experience. Maintenance of cash balance provides sufficient liquidity but involve opportunity cost (loss of interest), whereas less cash balance maintenance weakens liquidity and involves profitability. A firm has to maintain optimum cash balance. Optimal cash balance is that cash balance where the firm’s opportunity cost equals to transaction cost and the total cost are minimum. Then how to determine optimum cash balance?
Optimum cash balance can be determined by a number of mathematical models. But here the most important two models are discussed. They are:
1. Baumol Model (Inventory Model)
2. Miller and Orr Model (Statistical Model)

Baumol Model

This model was developed by Baumol. This model is suitable only when the cost flows are predictable (under certainty). It considers optimum cash balance similar to the economic order quantity, since it is based on EOQ Concept and also in both the cases there is trade off between cost of borrowing (sale of securities cost) and opportunity the cost. The point where the total cost is minimum. Figure 13.1 shows Baumol model.
Assumptions: Baumol model is based on the following:
1. The firm knows its cash needs with certainty.
2. The cash payments (disbursement) of the firm occur uniformly over a period of time and is known with certainty.
3. The opportunity cost of holding cash is known and it remains stable over time.
4. The transaction cost is known and remains stable.

Optimum Cash Balance

Miller and Orr Model

The Miller and Orr model is in fact an attempt to make Baumol model more elastic with regards to the pattern of periodic changes in cash balances. Baumol’s model is based on the assumption that uniform and certain level of cash balances. But in practice firms do not use uniform cash balances nor are they able to predict daily cash inflows and outflows. The Miller Orr Model overcomes the limitations of Baumol model. It’s augmented on the Baumol Model and came out of a statistical model. That is useful for the firms with uncertain cash flows. The Miller and Orr model provides two control limits—the upper control limit and the lower control limit along with a return point. The following Figure 13.2 shows the two control limits and return point.
According to this model, cash balance fluctuates between LCL and UCL. Whenever, cash balance touches UCL then the firm purchases sufficient (UCL – RP) marketable securities to take bank cash balance to return point. On the other hand when the firm touches the lower control limit, it will sell the marketable securities to the extent of (RP – LCL), take back cash balance to return point.
The cash balance at the lower control limit (LCL) is set by the firm as per requirement of maintaining minimum cash balance. The cash balances at upper control limit (UCL) and record points will be determined on the basis of the transaction cost (C), the interest rate (O) and standard deviation () of net cash flows.