The document discusses two cash flow models: (1) The Baumol model treats cash as inventory and determines the optimal amount and timing of cash transactions in a predictable environment. (2) The Miller-Orr model seeks to overcome the Baumol model's limitations by accounting for unpredictable cash flows and establishing upper and lower cash limits. An example applies the Miller-Orr model to determine optimal cash levels for a company. Effective cash modeling can help large businesses and small businesses optimize their cash resources but businesses must balance modeling with actual cash flows.

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Cash Flow Part 12 – Cash Models
By Howard Fletcher
November 30, 2007
Modeling can also be useful in predicting the optimal amount of cash on hand to maximize cash
flow and minimize interest expense. The most common models are the Baumol cash model and
Miller-Orr cash model.
Baumol Model
Developed by William Baumol it is a derivative of the EOQ model. It is used to determine the
optimal amount of cash to hold in a predictable environment. It treats cash as inventory and
buying and selling investment transactions as ordering costs. The objective is to minimize the
fixed cost of buying and selling investment transactions and minimize the opportunity cost of
holding too much cash. Just like in EOQ Baumol is a two-step formula. Step one is to determine
the optimal transaction size. Step two is to determine the optimal number of transactions in a
period. Average cash holdings would be one half of the optimal transaction size.
Baumol formula is same as the EOQ formula except transaction cost is substituted for order cost
and interest cost is substituted for carry cost. The formula is:
Z = √2NF / i
Where:
Z = the zero point to which the cash balance returns (the EOQ)
N = the annual cash need (the usage rate, S)
F = the fixed cost of each cash-securities transaction (the order cost, O)
i = the annual interest rate on marketable securities
The Baumol model can be depicted by the graph on the following page. The amount of cash to
be held is that point where the combined cost of cash transactions and the opportunity cost of
holding cash are the least.

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As with the EOQ model, the average amount of cash to be held and the frequency of securities
transactions can be depicted in a graph as shown below. Should the company have an unexpected
need for cash it will have to sell securities to raise cash earlier than it anticipated. An example
shows how the formula works.
Example
A company has $5,000,000 per year in total cash disbursements. It costs $75 on average every
time securities are sold for cash. Calculate the Zero point, the number of transfers each year, the
frequency of transfers and the average cash holdings, if the current short term investment rate is
5%.
Zero point = Z = √2NF / I = √2 x 5,000,000 x 75 / .05 = √15,000,000 = $38,730 (max cash)
Number of transfers per year = N/Z = 5,000,000 / 38,730 = 129 transfers
Transfer frequency = 360/number of transfers = 360 / 129 = 2.8 days
Average cash balance = Z/2 = 38,730 / 2 = $19,365
In this case the company would replenish cash from securities approximately once every 3 days
with each transaction being $38,730.
Baumol represents a good first try to the cash holdings problem. It is easy to use and understand.
It is useful when cash in and out is constant and predictable. But it suffers from some
shortcomings. It relies on a constant cash flow which is unrealistic. It ignores the possibility of
accumulating excess cash. Transaction costs are not always fixed.
Miller-Orr Model
This model seeks to overcome the shortcomings of the Baumol model. It determines the optimal
amount of cash to hold in an unpredictable environment. It extends the Baumol model in that it
tracks both inflows and outflows of cash, allows inflows and outflows on an irregular and

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unpredictable basis and establishes two trigger points - the lower cash level at which securities
must be sold to replenish cash and the upper cash level at which surplus cash should be invested.
Miller-Orr is not concerned with the frequency of the securities transactions. It is trying to
determine the optimal time to buy or sell securities based on the amount of cash on hand. Miller-
Orr takes into consideration the fixed cost of securities transactions and assumes these costs are
the same when both buying and selling, the daily interest rate on marketable securities and the
variance of the daily net cash flows. The formula is:
Z = 3√3F∆2/4i +LCL
Where:
Z = Zero Point – the cash balance return point
F = Fixed cost of each securities transaction
i = Interest rate per day on marketable securities
∆2 = Statistical variability of the net daily cash flow
LCL = Lower cash limit (established by management)
The upper cash limit, or UCL, is established by the formula
UCL = 3Z – 2(LCL)
The average cash balance is established by the formula
(4Z – LCL) / 3
The Miller-Orr model can be depicted by the following graph:

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Example
A company has $5,000,000 per year in total cash disbursements. It costs $75 on average every
time securities are sold for cash. The cash manager estimates that the variance of change in the
daily cash flow balance is $200,000. He also establishes that the lower cash limit is $5,000.
Calculate the Zero point, the upper cash limit and the average cash balance if the current short
term investment rate is 5%.
Answer:
I = .05/365
= .000137
LCL = $5,000
Z = 3√3F∆2/4i + LCL
= 3√(3 x 75 x 2,000,000) / (4 x.000137) + 5,000
= 3√(8.21168E+15) + 5,000
= 20,175 + 5,000
= $25,175
UCL = 3Z – (2 x 5,000)
= 75,525 – 10,000
= $65,525
Average cash balance = (4Z – 5,000) / 3
= 95,700 / 3
= $31,900
The upper cash limit, or that point where the company buys securities with cash over and above
that amount, is $65,525. The lower cash limit set by management is $5,000 at which point the
company sells securities to raise cash. The average cash balance is $31,900.
Effective modeling is not essential to any company seeking optimal utilization of its cash
resources but it can help if used properly. It is particularly useful to large and rapidly growing
companies that have complex cash management requirements. It can also be useful to small
companies which are cash constrained. However business owners must be careful not to lose
touch with actual day to day cash flow challenges for the sake of modeling. One could model
oneself right out of business.
Howard Fletcher is the principal owner of Bayshore Management Partners. As an author, speaker,
consultant and mentor, Mr. Fletcher has helped many senior executives and business owners
reinvigorate their personal growth, increase their self-satisfaction, improve their quality of life and take
their businesses to new levels of success. Mr. Fletcher has been CEO of four companies, COO of three
others, consultant to others and the owner of a small manufacturing company. He has been a senior
executive of a major international corporation and non-executive director of numerous for-profit and not-
for-profit organizations. He is a founding partner of Stronghold Capital Partners, a private intermediary
based in Scottsdale, Arizona. Mr. Fletcher has lived, worked and traveled extensively overseas as a

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corporate finance professional and he is a keen observer of global political, economic and financial
trends. Mr. Fletcher has a Masters Degree in International Management and a Bachelors Degree in
Finance, both from the University of Southern California. He is also a graduate of the Stanford University
Executive Management Program. He is an Accredited Associate of the Institute for Independent Business
and he holds four active securities licenses.