Page 101 - DCOM505_WORKING_CAPITAL_MANAGEMENT

Working Capital Management

Notes non-synchronous but predictable cash flows is a problem of minimising total costs. If we set the
balance too low, we incur high transaction costs; one might say we make too many trips to the
bank. If we set the balance too high, we lose too much interest on marketable securities.
The determination of the optimal working balance under conditions of certainty can be viewed
as an inventory problem in which we balance the costs of too little cash (transaction costs)
against the costs of too much cash (opportunity costs). If the cash shortage becomes severe
enough, we may begin to forego cash discounts on purchases, adding another element of
opportunity cost.
Formal models of the cash balance problem have been developed using inventory theory.
Inputs to such a model are the total net cash outflow over the period of time in question, the
transaction costs of replenishing the cash balance by selling securities or borrowing, and the
interest rate that can be earned on securities. The answer given by the model tells us how often
and in what amounts funds should be transferred to the checking account from other sources.

6.3.2 Uncertainty

Receipts and disbursements are very seldom completely predictable. If we go to the opposite
extreme and assume receipts and disbursements, or the difference between them, to be completely
random, a different kind of model can be developed using the technique of control theory. In
addition to information on transaction costs and interest rates on securities, we need a measure
of the variability of net cash flows. Using these data, we can determine the optimal maximum
and minimum balances in the firm’s checking account, denoted by levels X and Y in Figure 6.4
In Figure 6.4, the firm’s working cash balance fluctuates randomly in response to random
inflows and outflows. At time t, the balance reaches the lower control limit Y. At that point,
(Y – b) value of marketable securities is sold and the proceeds transferred to the working
balance. Such a transaction brings the firm’s working cash balance to the return point (R). The
balance continues to fluctuate, gradually rising to the maximum level X at t + 3. At this point,
(X – a) amount of cash is invested in marketable securities and the firm’s working cash balance
comes down to the level of return point (R) again. The control limit model thus gives an answer
in terms of maximum and minimum balances and provides a decision rule, rather than a fixed
schedule of transfers as done in the simple inventory model. One of the important insights of the
control limit model is that, where cash flows are uncertain, the greater the variability the higher
the minimum balance (X in Figure 6.4).

Figure 6.4: Control Limits Approach to Determine the Working Cash Balance

Working Cash Balance (in `)

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