## **Learning Outcomes**

After reading this article, you will be able to explain why firms hold cash, describe and distinguish the Baumol and Miller–Orr cash management models, and apply these models to calculate optimal cash transfer amounts or control limits. You will also understand the relevance of these models to exam questions on payables and short-term liquidity management for the ACCA FM exam.

## **ACCA Financial Management (FM) Syllabus**

For ACCA Financial Management (FM), you are required to understand how effective cash and payables management supports business liquidity and profitability. In particular, your knowledge should cover:

- The reasons businesses hold cash balances, including transaction, precautionary, and speculative motives
- Principles and calculations of cash management models, specifically the Baumol (economic order quantity) model and the Miller–Orr model
- Determining optimal cash transfer amounts and control limits under certainty and uncertainty
- The link between cash management and payables, short-term investments, and short-term borrowing decisions

## **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 motive for holding cash relates to taking advantage of unexpected investment opportunities?
   a) Transaction
   b) Precautionary
   c) Speculative
   d) Financing

2. When is the Baumol cash management model most appropriate?  
   a) Cash flows are steady and predictable  
   b) Cash flows are random and unpredictable  
   c) There is no transaction cost  
   d) Payables are all paid immediately

3. List two advantages of the Miller–Orr model compared to the Baumol model.

4. True or false? In the Miller–Orr model, cash is transferred to marketable securities only when the cash balance hits the lower control limit.

## **Introduction**

Efficient management of cash and payables is essential for balancing profitability and liquidity in any business. Cash that is not earning a return is a lost opportunity, but a shortage of cash can lead to missed payments and possible insolvency. This article explains why companies hold cash, and shows how the Baumol and Miller–Orr models can help determine when and how much cash to move between bank accounts and investments, supporting strong payables management.

> **Key Term: cash management**
> Cash management is the planning and control of an organisation’s cash position to ensure sufficient liquidity for payments while minimising idle balances.

## Reasons for Holding Cash

Businesses maintain cash balances for three main purposes:

- **Transaction motive:** to cover routine outflows such as payroll and supplier payments.
- **Precautionary motive:** as a buffer against unexpected expenses or delayed receipts.
- **Speculative motive:** to capitalise on unforeseen investment opportunities, such as purchasing goods at a discount.

> **Key Term: transaction cost**
> The transaction cost is the expense incurred when moving funds, such as brokerage fees or bank charges, associated with buying or selling short-term investments.
>
> **Key Term: opportunity cost**
> Opportunity cost is the potential return lost by holding cash in a non-interest-bearing account rather than investing it elsewhere.

## The Cash Management Problem

Holding too little cash risks being unable to pay bills on time. Holding too much results in lost interest or investment return. The objective is to keep enough cash to meet payments when due, while investing surpluses to earn a return. This is particularly important in payables management—timing payments efficiently can maintain supplier goodwill while optimising the use of cash.

## The Baumol Model

The Baumol cash management model applies the logic of inventory control (economic order quantity, EOQ) to cash. It is best suited where cash outflows are steady and predictable.

### Assumptions of the Baumol Model

- Cash usage is constant and known in advance.
- Transaction costs are fixed each time funds are transferred.
- Opportunity cost (the interest foregone on idle cash) is known.
- No buffer cash is held for emergencies.

When the current account runs low, cash is transferred from investments in fixed, optimal amounts.

> **Key Term: Baumol model**
> The Baumol model is a formula-based approach for determining the optimal size and timing of cash transfers between investment and current accounts, minimising the total cost of transactions and idle balances.

### The Baumol Formula

The optimal transfer amount, $ Q $, is calculated as:

$$
Q = \sqrt{\frac{2C_0 D}{C_H}}
$$

Where:

- $ C_0 $ = transaction (transfer) cost per transaction
- $ D $ = total cash needed over the period
- $ C_H $ = opportunity (holding) cost per unit of cash per period

### **Worked Example 1.1**

A company expects to have a steady monthly cash need of \$12,000. Each transfer from investments to current account costs \$45. The opportunity cost of holding cash is 6% per year.

**Required:** Calculate the optimal transfer amount and number of transfers per year.

> **Answer:**
>
> Annual cash need: \$12,000 × 12 = \$144,000
>
> $Q = \sqrt{\frac{2 \times 45 \times 144{,}000}{0.06 \times 144{,}000}}$
>
> $$
> C_H = 6\%
> $$
>
> of the average cash balance.
>
> Simplify: $Q = \sqrt{\frac{2 \times 45 \times 144{,}000}{0.06 \times 144{,}000}} = \sqrt{\frac{12{,}960}{8.64}} = \sqrt{1{,}500} \approx 38.73$, so $Q \approx$ \$38.73
>
> But this seems very low; let's recalculate:
>
> Actually, C_H should be 6% per year, so:
>
> $Q = \sqrt{\frac{2 \times 45 \times 144{,}000}{0.06}} = \sqrt{\frac{12{,}960{,}000}{0.06}} = \sqrt{216{,}000{,}000} \approx 14{,}697$, so $Q \approx$ \$14,697
>
> Number of transfers per year =
>
> $$
> 144,000 / 14,697 ≈ 10
> $$
>
> The company should make about 10 transfers per year of \$14,700 each.

## Limitations of the Baumol Model

- It assumes cash flows are perfectly predictable, which is rare in reality.
- No cash buffer is provided for unexpected expenses.
- Not suitable when cash inflows/outflows are erratic.

### **Revision Tip**

Review the Baumol model only when the question states that cash usage is steady and transaction/holding costs are easy to identify.

## The Miller–Orr Model

The Miller–Orr model is suitable when cash flows are variable and less predictable. Instead of a fixed transfer schedule, it sets upper and lower control limits for cash balances and a “return point.”

> **Key Term: Miller–Orr model**
> The Miller–Orr model sets upper and lower cash balance limits and a target return point, triggering transfers between cash and marketable securities only when extremes are reached, allowing random cash flows between limits.

### How the Miller–Orr Model Works

- **Lower limit:** Set by management based on minimum acceptable cash.
- **Upper limit:** Calculated by the model. When exceeded, transfer the excess cash into investments.
- **Return point:** The balance to which cash should be restored after a transfer.

When the cash balance falls to the lower limit, funds are transferred from investments to cash up to the return point. When the balance rises to the upper limit, cash is invested down to the return point.

### Miller–Orr Model Calculations

Given:

- Transaction cost per transfer ($C_0$)
- Variance of daily cash flows ($ \sigma^{2} $)
- Daily interest rate ($r$)

The spread is:

$$
\text{Spread} = 3 \left[ \frac{3}{4} \times \frac{C_0 \times \sigma^2}{r} \right]^{1/3}
$$

Upper limit = lower limit + spread

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

> **Key Term: variance of cash flows**
> Variance of cash flows is a measure of the daily or periodic unpredictability in cash receipts and payments, needed to set Miller–Orr model limits.

### **Worked Example 1.2**

A company sets its minimum cash balance at \$10,000. Transaction cost per transfer is \$40. Variance of daily cash flows is \$900,000. The daily interest rate is 0.02%.

**Required:** Calculate the spread, upper limit, and return point.

> **Answer:**
>
> Spread =
>
> $$
> 3 \left[ \frac{3}{4} × \frac{40 × 900,000}{0.0002} \right]^{1/3}
> $$
>
> Calculate inside the brackets:
>
> $$ 3/4 × 40 × 900,000 = 27,000,000 $$
>
> $$ 27,000,000 / 0.0002 = 135,000,000,000 $$
>
> $$ \left(135,000,000,000\right)^{1/3} ≈ 5103 $$
>
> Spread = $ 3 × 5103 ≈ \$15,309 $
>
> Upper limit = \$10,000 + \$15,309 = \$25,309
>
> Return point = \$10,000 + \$15,309 / 3 ≈ \$15,103

## Miller–Orr vs Baumol: Key Differences

- **Baumol:** Use when cash flows are steady and predictable.
- **Miller–Orr:** Use when cash flows are random or erratic.

### **Exam Warning**

Do not use the Baumol model if the question mentions unpredictable or highly variable cash flows. For irregular patterns, state the Miller–Orr model is more suitable.

## Relevance to Payables Management

Well-managed cash optimises timing of payments to suppliers (payables), avoiding unnecessary overdraft interest and maintaining supplier goodwill. Applying these models ensures the business can pay suppliers promptly when required, without holding excessive idle cash.

## **Summary**

Effective cash and payables management requires balancing liquidity and profitability. Use the Baumol model to plan transfers when outflows are predictable, and the Miller–Orr model when cash flows are random. Both models support timely payables management and help minimise finance costs.

## **Key Point Checklist**

_This article has covered the following key knowledge points:_

- The main motives for holding cash in business operations
- The structure and assumptions of the Baumol cash management model
- Calculation of optimal cash transfer amounts under Baumol
- The purpose and mechanics of the Miller–Orr model for uncertain cash flows
- Calculation of spread, limits, and return point under Miller–Orr
- Application of cash management techniques to payables management

## **Key Terms and Concepts**

- cash management
- transaction cost
- opportunity cost
- Baumol model
- Miller–Orr model
- variance of cash flows


Cash and payables management - Baumol and Miller–Orr models