The MillerOrr Model
Most firms don’t use their cash flows uniformly and
also cannot predict their daily cash inflows and outflows.
MilleOrr Model helps them by allowing daily cash
flow variation.
Under the model, the firm allows the cash balance to fluctuate
between the upper control limit and the lower control limit,
making a purchase and sale of marketable securities only
when one of these limits is reached. The assumption made
here is that the net cash flows are normally distributed
with a zero value of mean and a standard deviation. This
model provides two control limits – the upper control
limit and the lower control limit as well as a return point.
When the firm’s cash limit fluctuates at random and
touches the upper limit, the firm buys sufficient marketable
securities to come back to a normal level of cash balance
i.e. the return point. Similarly, when the firm’s cash
flows wander and touch the lower limit, it sells sufficient
marketable securities to bring the cash balance back to
the normal level i.e. the return point.
The lower limit is set by the firm based on its desired
minimum “safety stock” of cash in hand The firm
should also determine the following factors:
1. An interest rate for marketable securities, (i)
2. A fixed transaction cost for buying and selling marketable
securities, (c)
3. The standard deviation if its daily cash flows, (s)
The upper control limits and return path are than calculated
by the MillerOrr Model as follows:
Distance between the upper limits and lower limits is 3Z.
(Upper limit – Lower limit) = (3/4 C Transaction Cost
C Cash Flow Variance/Interest Rate) ^{1/3}
Z = (3/4 C cs2/i) ^{1/3}
If the transaction cost is higher or cash flows shows greater
fluctuations, than the upper limit and lower limit will
be far off from each other. As the interest rate increases,
the limits will come closer. There is an inverse relation
between the Z and the interest rate. The upper control limit
is three times above the lower control limits and the return
point lies between the upper and lower limits. Hence,
Upper Limit = Lower Limit + 3Z
Return Point = Lower Limit + Z
So, the firm holds the average cash balance equal to:
Average Cash Balance = Lower Limit + 4/3 Z
The MillerOrr Model is more realistic as it allows variation
in cash balance within the lower and upper limits. The lower
limit can be set according to the firm’s liquidity
requirement. To determine the standard deviation of net
cash flows the pasty data of the net cash flow behaviour
can be used. Managerial attention is needed only if the
cash balance deviates from the limits.
