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Chapter 10

3.3 The Miller-Orr cash management model

The Miller-Orr model controls irregular movements of cash by the setting of upper
and lower control limits on cash balances.

It has the advantage of incorporating uncertainty in the cash outflows and inflows.

3 × transaction cost × variance of cash flows 1/3

Spread = 3 4
interest rate

(1) Lower limit – must be given by the question.

(2) Upper limit = lower limit + spread.

(3) Return point = lower limit +1/3 × spread.

This model is most useful when cash balances fluctuate up and down over time.

Question 5

Miller Orr model

The cash balance at ABC plc fluctuates over time with some months seeing a
large positive cash balance and others showing an overdraft. The company
wishes to control its cash more efficiently and take advantage of available short-
term investments when it has surplus cash. It wishes to maintain a minimum
cash balance of $10,000. The short-term investments earn interest at 0.04%
per day.

If the transaction cost of switching cash between the current account and the
company’s short-term investments is $15 and the variance of the company’s
cash flows is $6 million per day, use the Miller Orr model to calculate the
spread, the return point and the upper limit.

1/3
Spread = 3 × [0.75 × $15 × $6,000,000/0.0004] = $16,578

Return point = $10,000 + (1/3 × $16,578) = $15,526

Upper limit = $10,000 + $16,578 = $26,578

NB: remember that 0.04% expressed as a decimal is 0.0004

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