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(^212) Financial Management
point, (Y ñ X) money is transferred out of the cash account and into marketable securities.
The balance continues to fluctuate, falling to zero at t 2 , at which time X value of
marketable securities are sold and the proceeds transferred to the working balance.
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 did
the simple inventory mode. One of the important insight of the control limit model is
that, where cash flows are uncertain, the greater the variability the higher the minimum
balance.
Using Mathematical Models
Formal mathematical models such as those mentioned above are useful for increasing
our understanding of the cash management problem and providing insights and qualitative
guidance. The models tell us which factors are important and make the tradeoffs explicit.
We see, for example, that transaction costs play a central role. If transaction costs
were zero, the firm would require no working cash balance at all; it simply would sell
securities or borrow to pay every bill.
Are formal mathematical models also useful for quantitative applications? In practice,
the cash flow patterns of most firms are partly predictable and partly random. Neither
the inventory model nor the control limit model is strictly applicable. By combining the
insights from formal models with the techniques of cash budgeting and pro forma analysis,
many firms can arrive at reasonable answers by experience and experiment. In deciding
how far to go in analysing the problem, we must consider the cost of the analysis.
Except in the case of very large firms, quantitative solutions to the cash balance problem
using formal mathematical models are likely to be uneconomical. Often, the cost of
obtaining the necessary input data and operating the model exceeds the savings over
solutions that can be attained by experience and experiment. As always, we must keep
an eye on the cost of our analytical techniques as well as on the benefits.
Planning Cash Requirement
In most cases, to search for the optimal working cash balance probably overstates our
capabilities; we must be content to get reasonably close. Perhaps we should substitute
the word ìappropriateî for ìoptimal.î
The current account balance that the firm should maintain is the compensating balance
requirement, or the optimal working balance. Whichever is greater. Some firms,
especially those with seasonal sales patterns, may find that the appropriate working
balance varies somewhat over the year. As a firm grows, the appropriate working cash
balance also will grow, although probably not proportionally.
Once we have settled on the appropriate balance to be maintained in the current account,