ACCA FM Syllabus C. Working Capital Management - Miller-Orr Model - Notes ^{4 / 4}

The model works in terms of upper and lower control limits, and a target cash balance.

As long as the cash balance remains within the control limits the firm will make no transaction.

To use the Miller-Orr model, the manager must do 4 things

1. Set the lower control limits for the cash balance. 

   This lower limit can be related to a minimum safety margin decided by management

2. Estimate Standard deviation of daily cash flows

3. Determine Interest Rate

4. Estimate the trading costs of buying and selling marketable securities.

When the firm’s cash 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

Spread

Then the spread is calculated upper and then the upper limit and return point comes from this.

• Spread = 3(3/4 x Transaction cost x Cashflow variance / interest rate) power of 1/3

The return point

• Lower Limit + 1/3 x spread

Illustration

If a company must maintain a minimum cash balance of £8,000, and the variance of its daily cash flows is £4m (ie std deviation £2,000). The cost of buying/ selling securities is £50 & the daily interest rate is 0.025%.

• Required: Calculate the spread, the upper limit (max amount of cash needed) & the return point (target level)

Solution

Lower limit = 8,000 (per question)
Spread = 3(3/4 x 50 x 4,000,000 / 0.00025) power of 1/3 = 25,303
Upper limit = 8,000 + 25,303 = 33,303
Return point = 8,000 + (1/3 x 25,303) = 16,434

• NOTE
  The cashflow variance is DAILY. Also the standard deviation is the square root of the variance. 

  Therefore if given the standard deviation then you need to square it before putting it into the equation.

  The interest rate is also a daily one. A quick (if oversimplified way) of reaching this simply to divide the annual rate by 365)

Benefits

1. Allows for net cash flows occurring in a random fashion.

2. Transfers can take place at any time and are instantaneous with a fixed transfer cost.

3. Produces control limits which can be used as basis for balance management.

Limitations

1. May prove difficult to calculate.

2. Monitoring needs to be continuous for the organisation to benefit.

Baumol Model - Deterministic model

• Future cash requirements and disbursements are known with perfect certainty

Miller-Orr Model - Stochastic model

• Daily cash flows vary according to a normal probability distribution with known variance