## **Learning Outcomes**

After reading this article, you will be able to explain the rationale for holding cash, identify the motives for cash balances, and describe the limitations of simple cash management approaches. You will learn to apply and critically evaluate the Baumol and Miller-Orr models for determining optimal cash balances under different cash flow patterns. By the end, you should be able to calculate optimal transfer amounts, set control limits for cash balances, and recognise key exam pitfalls for these models.

## **ACCA Advanced Financial Management (AFM) Syllabus**

For ACCA Advanced Financial Management (AFM), you are required to understand how organisations manage liquidity and determine optimal cash balances. This includes the application of analytical cash management models. In particular, you should focus on:

- The role of cash and liquidity management within working capital policy
- The motives for holding cash and the risks of inadequate liquidity
- Methods for managing cash balances, including cash flow forecasting and target balances
- Application, strengths, and limitations of the Baumol and Miller-Orr models for cash management
- Calculation of optimal cash transfers and control limits under varying cash flow conditions

## **Test Your Knowledge**

_Attempt these questions before reading this article. If you find some difficult or cannot remember the answers, remember to look more closely at that area during your revision._

1. Which of the following is a key assumption of the Baumol cash management model?
   a) Cash inflows and outflows are unpredictable.  
   b) Cash movements occur at a constant, predictable rate.  
   c) Interest rates vary daily.  
   d) The company does not incur transaction costs.

2. The main innovation of the Miller-Orr model compared to the Baumol model is:
   a) Allowing for fluctuating interest rates.  
   b) Accounting for unpredictable daily net cash flows.  
   c) Eliminating all transaction costs.  
   d) Ignoring the cost of running out of cash.

3. True or false? The Baumol model is best suited for organisations with highly variable daily cash movements.

4. Outline the three key motives for holding cash in a business context.

5. When using the Miller-Orr model, what action should be taken if the cash balance reaches the lower control limit?

## **Introduction**

All organisations must ensure they maintain sufficient cash to meet payment obligations while minimising idle balances that earn little or no return. Effective cash management balances liquidity and profitability objectives, requiring practical tools to help set target cash levels and timing of transfers between cash and marketable securities. The Baumol and Miller-Orr models are key analytical techniques for managing cash flows, each designed for specific operating environments.

> **Key Term: liquidity management**
> The process of planning and monitoring cash inflows and outflows to ensure a business can meet its financial obligations as they fall due, without holding excessive idle resources.

## **THE MOTIVES FOR HOLDING CASH**

The decision to hold cash is influenced by three main motives:

> **Key Term: transaction motive**
> The need to hold cash to cover regular, predictable business payments arising from day-to-day operations (e.g., payroll, suppliers).
>
> **Key Term: precautionary motive**
> The need to hold cash as a buffer against unexpected expenses or fluctuations in receipts and payments.
>
> **Key Term: speculative motive**
> The holding of cash to take advantage of unexpected business opportunities, such as purchasing inventories at a discount.

Efficient cash management involves deciding the right amount to hold for each motive, thereby avoiding both liquidity shortfalls and excessive opportunity costs.

## **CASH MANAGEMENT MODELS: OVERVIEW**

Traditional approaches to cash management relied heavily on subjective judgement or arbitrary target balances. Analytical models, such as Baumol and Miller-Orr, provide a more structured way to decide when and how much cash to transfer between operating accounts and interest-earning investments.

### **Limitations of Simple Approaches**

- Often ignore the cost/benefit trade-off between holding cash and earning interest.
- Do not account for the pattern or variability of cash movements.
- Can result in unnecessary bank charges or missed opportunities.

## **THE BAUMOL CASH MANAGEMENT MODEL**

The Baumol model applies inventory management logic (specifically, the Economic Order Quantity approach) to cash balances. It aims to determine the most cost-effective transfer size between cash and marketable securities when outflows occur at a steady predictable rate and inflows are infrequent and large.

> **Key Term: Baumol cash model**
> An analytical tool for determining the optimal amount and timing of cash transfers, assuming predictable and constant rates of cash outflows and known transaction and opportunity costs.

### **Assumptions of the Baumol Model**

- Cash outflows occur at a steady, known rate.
- Cash inflows are periodic and predictable.
- Each transfer between cash and investments incurs a fixed transaction cost.
- There is a known opportunity cost for holding cash (the lost interest on investments).

The objective is to minimise total costs, comprising transaction costs for converting securities to cash and the opportunity cost of holding cash.

### **Baumol Formula**

The optimal cash transfer amount, $ C^\* $, is given by:

$$ C^\* = \sqrt{\frac{2 b T}{i}} $$

Where:

- $ b $ = fixed transaction cost per transfer
- $ T $ = total cash requirement over the period
- $ i $ = opportunity cost (interest rate) per period

### **Worked Example 1.1**

A company expects payments of \$1,800,000 evenly spread over the year. Each transfer from investments to the cash account costs \$75. The annual opportunity cost of holding cash is 5%. What is the optimal transfer size and how many transfers should be made per year?

> **Answer:**
>
> $ C^\* = \sqrt{\frac{2 \times 75 \times 1,800,000}{0.05}} = \sqrt{\frac{270,000}{0.05}} = \sqrt{5,400,000} = \$2,323.79 $
>
> However, since annual payments are spread evenly, the formula should read:
>
> $ C^\* = \sqrt{\frac{2 \times 75 \times 1,800,000}{0.05}} = \sqrt{5,400,000} \approx \$2,323.79 $
>
> The number of transfers per year = \$1,800,000 / \$2,323.79 ≈ 775.
>
> Every transfer of approximately \$2,324 minimises total cost.

### **Exam Warning (Baumol Model)**

> In exam questions, always check units. Ensure that the opportunity cost (interest) and other figures are expressed on the same time basis—e.g., all per annum or all per month. Using inconsistent periods will lead to incorrect results.

### **Applying the Baumol Model in Practice**

- Useful for large, predictable cash outflows (e.g., regular payroll or predictable supplier payments).
- Not suitable for businesses where cash flows fluctuate unpredictably on a day-to-day basis.

## **THE MILLER-ORR CASH MANAGEMENT MODEL**

In reality, cash movements are often volatile and unpredictable. The Miller-Orr model addresses this by setting upper and lower control limits around a target cash balance, triggering transfers only when these limits are reached.

> **Key Term: Miller-Orr cash model**
> A model that helps businesses manage cash balances under uncertain and fluctuating daily cash flows, by establishing control limits and an optimal return point for cash levels.

### **How Miller-Orr Works**

- Management sets a lower cash limit (can be zero or a minimum safe level).
- The model calculates the upper control limit and a target (return) cash balance.
- Daily net cash balances are monitored:
  - If the upper limit is exceeded: invest surplus cash to bring the balance back down to the return point.
  - If the lower limit is reached: transfer in cash to restore the balance up to the return point.
  - If the cash balance is within limits: take no action.

### **Key Variables**

- Fixed transaction cost per transfer (b)
- Variance of daily net cash flows ($ \sigma^2 $)
- Opportunity cost of holding cash (i)
- Lower limit (L), usually set by management

### **Formulas**

#### Target return point (Z)

$$
Z = L + \left[ \frac{3b\sigma^2}{4i} \right]^{1/3}
$$

#### Upper limit (H)

$$
H = 3Z - 2L
$$

Where:

- $ L $ = lower limit (minimum cash balance)
- $ b $ = fixed transaction cost per transfer
- $ \sigma^2 $ = variance of daily net cash movements
- $ i $ = daily opportunity cost (expressed per day)

### **Worked Example 1.2**

Rex Ltd observes a standard deviation of \$6,000 for daily net cash flows. Daily opportunity interest is 0.01%. Each securities transaction costs \$20. If the minimum cash balance set is \$18,000, calculate the return point and upper control limit. Use variance as the square of the daily standard deviation.

> **Answer:**
>
> Variance = (\$6,000)^2 = \$36,000,000
>
> Opportunity cost per day = 0.0001 (0.01%)
>
> $$ Z = 18,000 + \left[ \frac{3 \times 20 \times 36,000,000}{4 \times 0.0001} \right]^{1/3} $$
>
> $$ = 18,000 + \left[ \frac{2,160,000,000}{0.0004} \right]^{1/3} $$
>
> $$ = 18,000 + (5,400,000,000,000)^{1/3} $$
>
> $$ = 18,000 + 1,766,216 \approx 1,784,216 $$
>
> (In practice, the cube root is about 1,766, so total = \$18,000 + \$1,766 = \$19,766)
>
> Upper limit = $3Z - 2L = 3 \times 19,766 - 2 \times 18,000 = 59,298 - 36,000 = \$23,298$
>
> When cash hits \$23,298: invest enough to bring balance back to \$19,766. When it hits \$18,000: transfer in to bring to \$19,766.

### **Advantages of Miller-Orr**

- Adapts to random, fluctuating cash flows.
- Reduces unnecessary transactions by only moving cash when limits are breached.
- Can be adjusted easily as cash flow variability changes.

### **Exam Warning (Miller-Orr)**

> The Miller-Orr model requires the variance of DAILY net cash flows. Double-check time periods and convert annual or monthly variance if needed.

## **MODEL SELECTION AND LIMITATIONS**

| Model      | Suitable For                              | Key Limitation            |
| ---------- | ----------------------------------------- | ------------------------- |
| Baumol     | Stable, predictable cash movements        | Can't handle random flows |
| Miller-Orr | High volatility, unpredictable cash flows | Requires data on variance |

### **Revision Tip**

> Learn the Baumol and Miller-Orr formulas by heart, as they regularly feature in ACCA AFM calculations. Always clarify which model fits the scenario.

## **Summary**

Effective cash and liquidity management requires tools that balance transaction costs and the opportunity cost of holding cash. The Baumol model provides an optimal transfer size for predictable cash flows, while the Miller-Orr model manages balances under uncertainty using control limits and a return point. Select the model matching the pattern of cash flows and always confirm assumptions before use.

## **Key Point Checklist**

_This article has covered the following key knowledge points:_

- Explain the motives for holding cash and the risks of inadequate liquidity
- Identify when to use the Baumol or Miller-Orr cash models
- Apply the Baumol model to determine optimal cash transfer sizes under steady outflows
- Apply the Miller-Orr model to set control limits for random cash balances
- Calculate transaction amounts and limits using given formulae
- Recognise the main assumptions and limitations of each approach

## **Key Terms and Concepts**

- liquidity management
- transaction motive
- precautionary motive
- speculative motive
- Baumol cash model
- Miller-Orr cash model

Cash and liquidity management - Baumol and Miller-Orr cash models