## **Learning Outcomes**

After reading this article, you will be able to identify types of cost behaviour, separate fixed and variable components using the high–low method, and construct linear equations for forecasting costs. You will also understand key assumptions of the approach, handle unusual cases such as stepped or changing costs, and evaluate the strengths and limitations of high–low analysis for ACCA exam questions.

## **ACCA Management Accounting (MA) Syllabus**

For ACCA Management Accounting (MA), you are required to understand the analysis of cost behaviour and its use for estimating and forecasting in budgeting and management accounting. In particular, you must be able to:

- Identify and classify costs as variable, fixed, semi-variable, or stepped fixed costs using examples and data
- Use the high–low method to separate fixed and variable cost elements, including when costs are semi-variable or stepped
- Construct and use linear cost equations for forecasting future costs
- Recognise the assumptions and limitations of the high–low method
- Interpret cost behaviour and cost separation from tables, graphs, and scenario data
- Apply high–low analysis for budgeting, planning, and control

## **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. What two main types of cost behaviour does the high–low method aim to separate in semi-variable cost data?
2. If the total cost at 200 units is \$4,000 and at 400 units is \$6,500, what is the variable cost per unit using the high–low method?
3. Describe one main limitation of the high–low method when forecasting costs for volume levels outside the observed range.
4. How does the cost equation $y = a + bx$ relate to cost separation? What does each parameter represent?
5. Why is it important to identify stepped fixed costs separately from standard fixed costs in cost forecasting?

## **Introduction**

Cost forecasting is a key management accounting activity, enabling budgeting and operational decision-making. In practice, many costs do not behave purely as fixed or variable but instead are a mixture—called semi-variable (or mixed) costs. The ability to separate these components is fundamental for producing accurate forecasts as business activity changes.

The high–low method is a practical cost separation technique, allowing you to derive approximate fixed and variable cost elements from limited historical data. This is especially useful when detailed records or regression analysis tools are unavailable. The approach assumes a linear cost relationship and is widely used in the early stages of budgeting or for rapid analysis.

> **Key Term: cost behaviour**
> The way in which a cost changes in response to changes in business activity or production volume.

## **COST CLASSIFICATION AND BEHAVIOUR**

Understanding how costs react as output changes is essential for planning and control. Costs are typically classified as follows:

- **Variable costs**: Increase or decrease directly with activity (e.g., direct materials).
- **Fixed costs**: Remain unchanged over a relevant range, irrespective of output (e.g., rent).
- **Semi-variable costs**: Contain both fixed and variable elements (e.g., electricity bills with a standing charge plus cost per unit used).
- **Stepped fixed costs**: Are constant within certain activity levels but jump up when output moves to a new band (e.g., supervisor wages where an additional shift requires hiring another supervisor).

> **Key Term: semi-variable cost**
> A cost containing both fixed and variable components, changing partly with output but with a baseline that is incurred even at zero activity.
>
> **Key Term: stepped fixed cost**
> A fixed cost that increases in discrete steps as activity crosses specified thresholds but remains constant within each band.

### Recognising cost patterns

Financial information and graphical data (such as line graphs or scatter plots) can be used to distinguish cost types. It's important to correctly identify them before cost estimation and forecasting.

## **THE HIGH–LOW METHOD**

The high–low method is a straightforward analytical technique to separate fixed and variable components from cost data that varies with activity. Its attractiveness lies in its simplicity and minimal data requirement.

### How the high–low method works

1. **Identify the highest and lowest activity levels** (not costs—activity comes first).
2. **Calculate the variable cost per unit** as follows:

   $$
   \text{Variable cost per unit} = \frac{\text{Total cost at high activity} - \text{Total cost at low activity}}{\text{High activity units} - \text{Low activity units}}
   $$

3. **Determine total fixed cost** by substituting either the high or low pair into:

   $$
   \text{Fixed cost} = \text{Total cost at activity} - (\text{Variable cost per unit} \times \text{Activity units})
   $$

4. **Formulate the linear cost equation** for forecasting:

   $$
   y = a + bx
   $$

   Where:
   - $y$ = total cost,
   - $a$ = total fixed cost,
   - $b$ = variable cost per unit,
   - $x$ = number of units (or activity measure).

> **Key Term: high–low method**
> A method that estimates variable and fixed cost components using the highest and lowest activity data points.

### **Worked Example 1.1**

**A firm records the following data:**

- At 1,000 units: Total cost = \$18,000
- At 2,000 units: Total cost = \$25,000

**Required: Estimate the variable and fixed costs using the high–low method.**

> **Answer:**  
> Variable cost per unit = (\$25,000 − \$18,000) / (2,000 − 1,000) = \$7 per unit  
> Fixed cost = \$18,000 − (1,000 × \$7) = \$11,000  
> Cost equation: $y = \$11,000 + \$7x$

## **STEPPED FIXED COSTS AND SEMI-VARIABLE COSTS**

When working with costs that do not behave purely as fixed or variable, adjustments may be necessary:

- **Stepped fixed costs**: Within a certain output range, fixed costs are stable but then jump when a higher threshold is passed.
- **Semi-variable costs**: High–low works as long as variable cost per unit and fixed cost remain constant within the examined range.

### Dealing with stepped costs

If cost data suggests a change in fixed cost partway through, the high–low method should be applied using data from within the same step. When the required output falls within a different band, adjust the fixed cost accordingly.

### **Worked Example 1.2**

**A delivery company incurs the following transport costs:**

- 100 trips: \$5,200
- 180 trips: \$6,800

Fixed costs rise by \$900 once activity exceeds 150 trips (extra vehicle hired).

**Required: Estimate total cost at 170 trips.**

> **Answer:**
> Use high–low within the >150 trip band (i.e., 180 and 100, but adjust for step):  
> Variable cost per trip = (\$6,800 − [\$5,200 + \$900]) / (180 − 100) = (\$6,800 − \$6,100)/80 = \$8.75/trip  
> Fixed cost above 150 trips = \$5,200 + \$900 − (100 × \$8.75) = \$1,325  
> Estimated cost at 170 trips:  
> \$1,325 (fixed) + (170 × \$8.75) = \$2,822.50

## **FORECASTING AND COST EQUATIONS**

Once fixed and variable elements have been separated, forecasts can be produced for any realistic output level using the cost equation:

$$
y = a + bx
$$

Where:

- $y$ = total estimated cost,
- $a$ = total fixed cost,
- $b$ = variable cost per unit,
- $x$ = activity level.

### **Worked Example 1.3**

**Given: Cost equation $y = 4,000 + 12x$. Estimate total cost if output rises to 500 units.**

> **Answer:** $y = 4,000 + (12 × 500) = 4,000 + 6,000 = \$10,000

## **ASSUMPTIONS AND LIMITATIONS OF THE HIGH–LOW METHOD**

The high–low method relies on several assumptions that may not hold in all situations:

- **Linearity**: Assumes cost behaviour follows a straight line across the relevant range.
- **Consistent behaviour**: Assumes no changes in cost per unit or fixed cost across the span between high and low activities.
- **Limited data usage**: Only the highest and lowest data points are used; intermediate data, which might reflect normal rather than exceptional operations, is excluded.

### **Exam Warning**

> The high–low method can produce misleading forecasts if the high or low point is an abnormal value (e.g., includes one-off costs or errors). Always check for consistency in cost behaviour, and justify the choice of points if unusual.

### **Revision Tip**

> In exams, always show workings and label your equations. Clearly state variable cost, fixed cost, and the final cost equation used.

## **SPECIAL CASES: CHANGES IN COST STRUCTURE**

Occasionally, variable costs per unit may change once output exceeds a threshold, or a bulk discount applies. For these, match your high–low calculation to periods with the same cost structure.

### **Worked Example 1.4**

**Output up to 2,000 units:**

- At 1,000 units: \$6,000
- At 1,800 units: \$9,000

**For output above 2,000 units:**

- At 2,200 units: \$10,400
- At 3,000 units: \$13,600

**Required: Calculate variable cost per unit above 2,000 units.**

> **Answer:**
> Variable cost per unit above 2,000 units = (\$13,600 − \$10,400) / (3,000 − 2,200) = \$3,200 / 800 = \$4 per unit

## **ADVANTAGES AND LIMITATIONS OF THE HIGH–LOW METHOD**

### Advantages

- Simple and quick with minimal data.
- Useful for initial budgeting and rapid cost separation.
- No advanced statistical tools needed.

### Limitations

- Sensitive to unusual data at high or low levels (outliers).
- Ignores all other data points, which might lead to inaccuracy.
- Assumes no significant non-linearity, discounts, or multiple steps within the data range.
- May not be suitable for highly volatile or non-linear cost behaviour.

## **Summary**

The high–low method provides a practical tool for separating semi-variable costs into fixed and variable elements, key for forecasting and budgeting. By constructing a linear cost equation, you can estimate costs at different activity levels. However, awareness of stepped costs, changes in variable cost per unit, and the method's assumptions is essential to avoid errors. Always check for outliers and document your calculations.

## **Key Point Checklist**

_This article has covered the following key knowledge points:_

- Distinguish between fixed, variable, semi-variable, and stepped fixed costs
- Apply the high–low method to estimate fixed and variable cost elements
- Construct linear cost equations for forecasting
- Handle adjustments for stepped and changing variable costs
- State and evaluate assumptions and limitations of the high–low method

## **Key Terms and Concepts**

- cost behaviour
- semi-variable cost
- stepped fixed cost
- high–low method

Cost estimation and forecasting - High–low method and cost separation