Cash Management and Marketable Securities^211
and uncertainty. In most firms, receipts and disbursements vary both over the month
and over the year. Over a month, receipts and disbursements for current operating
expenses are likely to show some variation, perhaps in a regular pattern. In seasonal
firm, the amounts also will vary over the year less frequent outlays. Such as those for
capital expenditure, taxes, and dividends, introduce still more variability. Some of this
variability may be predictable, but some probable is not. Let us examine these two
problems variability and uncertainty separately.
Variability
Suppose receipts and disbursements both vary and are not synchronised, but the variations
are completely predictable. Determining the appropriate working balance in the face of
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.
Uncertainty
Receipt and disbursements are very seldom completely predictable. If we go to the
opposite extreme and assume receipts and disbursements for 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 firmís
checking account, denoted by levels X and Y.
In the firmís working cash balance fluctuates randomly in response to random
inflows and outflows. At time t 1 , the balance reaches the upper control limit Y. At that