What you'll learn
Cost accounting begins with a question financial accounting never asks: what does one unit of output actually cost? Answering it requires sorting costs in more than one way at once, because the useful classification depends on the decision being made. The same wage bill is a direct cost when you are costing a product, a variable cost when you are forecasting the effect of higher output, and a controllable cost when you are judging a supervisor's performance.
The two classifications that matter most are by behaviour — how a cost responds when activity changes — and by traceability — whether a cost can be identified with a specific cost unit. Behaviour drives every planning and decision-making technique in the rest of the module: break-even analysis, marginal costing, budgeting and relevant costing all rest on being able to split costs into fixed and variable.
By the end of this topic you should be able to classify a cost several ways, describe fixed, variable, semi-variable and stepped fixed behaviour, separate a semi-variable cost using the high-low method, and explain what the relevant range means and why it limits every one of these techniques.
Key terms and definitions
Cost unit — the unit of output whose cost is being measured: a crate of mangoes, a guest-night, a repaired vehicle.
Cost centre — a location, function or department to which costs are charged, such as the packing hall or the maintenance workshop.
Direct cost — a cost traceable in full to a cost unit: direct materials, direct labour, direct expenses. Their total is the prime cost.
Indirect cost (overhead) — a cost that cannot be traced to a single unit and must be shared out: factory rent, supervision, depreciation of machinery.
Fixed cost — a cost whose total does not change with activity within the relevant range.
Variable cost — a cost whose total changes in direct proportion to activity.
Semi-variable (mixed) cost — a cost with a fixed element and a variable element, such as a phone bill with a line rental plus call charges.
Stepped fixed cost — a cost fixed over a band of activity, then jumping to a new level: one supervisor per shift, one more shift needed.
Relevant range — the band of activity within which the assumed cost behaviour actually holds.
Core concepts
Behaviour: totals versus per unit
The single most common confusion in this topic is between a total and a per-unit figure, and it reverses for the two cost types.
A fixed cost is fixed in total and therefore falls per unit as output rises. Rent of $36,000 is $36 per unit at 1,000 units and $9 per unit at 4,000 units. This is where economies of scale come from.
A variable cost is constant per unit and therefore rises in total as output rises. Materials at $7 per unit cost $7,000 at 1,000 units and $28,000 at 4,000.
Whenever a question says a cost "increases", establish immediately whether it means in total or per unit. The two answers are usually both available as distractors.
Semi-variable and stepped fixed costs
A semi-variable cost contains both elements and must be split before it can be used in any planning technique. Electricity with a standing charge and a usage rate is the standard example; a vehicle with road tax and fuel is another.
A stepped fixed cost is fixed within a band and then jumps. A factory needs one supervisor for every 20 workers, so supervision is flat up to 20, flat again from 21 to 40, and higher at each threshold. Treating it as variable understates cost just below a step and overstates it just above.
Stepped costs are the practical reason the relevant range exists, and a question that gives a capacity limit is usually inviting you to notice one.
The high-low method
To split a semi-variable cost, take the highest and lowest activity levels observed and the total cost at each.
The variable cost per unit is the change in cost divided by the change in activity, because only the variable element moved. The fixed element is then whatever remains at either level once the variable portion is stripped out.
The method's weakness is that it uses only two observations, and if either is unrepresentative — a month with a breakdown, a month with overtime — the whole split is wrong. Say so if asked to evaluate it; regression using all observations is the more reliable alternative.
Other classifications worth knowing
Product versus period costs. Product costs attach to units and sit in inventory until sold; period costs are charged in full to the period. Misclassifying moves profit between years.
Controllable versus uncontrollable. A cost is controllable at the level of management that can influence it. Judging a departmental manager on an apportioned share of head office rent measures something they cannot change, which is why responsibility accounting separates the two.
Relevant versus irrelevant. For a specific decision, only future cash flows that differ between alternatives are relevant. A cost already incurred is sunk and never relevant — a point developed fully in the relevant costing topic.
Why the split matters downstream
It is worth being explicit about what the fixed/variable split is for, because the rest of the costing module is built on it and a student who treats this topic as vocabulary will struggle later.
Break-even analysis needs contribution per unit, which is selling price less variable cost per unit — impossible to compute without the split. Marginal costing values inventory at variable production cost only, and charges fixed overhead in full to the period. Budgeting needs to flex a budget to actual activity, which means knowing which costs move with output and which do not. Relevant costing asks which costs change between alternatives, and a fixed cost that will be incurred either way is usually irrelevant to the decision.
Each of those techniques inherits the weaknesses of the split it rests on. If the high-low method produced the fixed and variable figures from two unrepresentative months, every break-even calculation built on them carries the same error forward without showing it. That is a legitimate and well-rewarded criticism to raise whenever a question asks you to evaluate one of those techniques — the arithmetic may be flawless while the inputs are not.
The relevant range
Every statement about cost behaviour is conditional on the relevant range. Rent is fixed — until output requires a second building. Materials are $7 a unit — until volume earns a bulk discount or exhausts the cheap supplier.
This is the honest limitation to raise in an evaluation question. Break-even analysis and marginal costing both assume linear behaviour, and that assumption holds only across the band of activity where it was observed.
Worked examples
Example 1 — Classifying one cost several ways (4 marks)
A bottling plant pays machine operators an hourly wage.
By traceability: direct labour, since the hours are traceable to the crates produced. By behaviour: variable, since total wages rise with the hours worked. By product/period: a product cost, attaching to units and sitting in inventory until sold. By controllability: controllable by the production supervisor, who sets the hours.
The point is that no single classification is the right one. The question decides which applies.
Example 2 — Fixed cost per unit (4 marks)
Factory rent is $36,000 a year.
At 1,000 units: $36,000 ÷ 1,000 = $36.00 per unit. At 4,000 units: $36,000 ÷ 4,000 = $9.00 per unit. At 8,000 units: $36,000 ÷ 8,000 = $4.50 per unit.
The total never moved. Spreading the same fixed cost over more units is the whole of the economies-of-scale argument at this level.
Example 3 — The high-low method (6 marks)
Maintenance costs were observed at two activity levels: 8,000 machine hours cost $92,000, and 3,000 machine hours cost $57,000.
Change in cost = $92,000 − $57,000 = $35,000. Change in activity = 8,000 − 3,000 = 5,000 hours. Variable cost per hour = $35,000 ÷ 5,000 = $7.00.
Fixed element, using the high point: $92,000 − (8,000 × $7.00) = $92,000 − $56,000 = $36,000.
Check at the low point: $36,000 + (3,000 × $7.00) = $36,000 + $21,000 = $57,000. It agrees, so the split is arithmetically sound.
The cost equation is therefore total cost = $36,000 + $7.00 per machine hour. Always perform that check at the other point — it costs one line and catches a reversed subtraction.
Example 4 — Predicting a cost, and its limit (5 marks)
Using the equation above, forecast maintenance at 6,500 hours.
Total cost = $36,000 + (6,500 × $7.00) = $36,000 + $45,500 = $81,500.
Now forecast at 14,000 hours: $36,000 + (14,000 × $7.00) = $134,000.
The second figure is far less reliable. Observations ran from 3,000 to 8,000 hours, so 14,000 lies well outside the relevant range — a second shift, additional supervision or a machine replacement could all change the fixed element entirely. State that limitation rather than presenting both forecasts with equal confidence; it is where the analysis marks sit.
Common mistakes and how to avoid them
Saying a fixed cost is fixed per unit. It is fixed in total and falls per unit as output rises.
Saying a variable cost rises per unit. It is constant per unit and rises in total.
Assuming direct means variable. They are different classifications. A supervisor's salary dedicated to one product line is direct but fixed.
Using two unrepresentative points in the high-low method. A breakdown month or an overtime month distorts the entire split.
Forgetting to check the split at the second point. One line of arithmetic catches a reversed subtraction.
Extrapolating far outside the observed range. Behaviour holds only within the relevant range, and stepped fixed costs lie in wait beyond it.
Treating a stepped fixed cost as variable. It understates cost just below a step and overstates it just above.
How this links to your Internal Assessment
If your Internal Assessment covers a business that makes or processes anything, classifying its costs is the natural analytical section, and the classification itself is a finding. Many small businesses treat every cost as a lump, which makes it impossible to know whether an extra order is worth taking.
Collect actual cost data at two or more activity levels and apply the high-low method to a genuine semi-variable cost — electricity and vehicle running costs are usually obtainable. Then state the cost equation you derived and the range over which you would trust it.
Say honestly how many observations you had. A split based on two months is a demonstration of the technique rather than a reliable model, and acknowledging that is stronger than presenting it as settled. If you can obtain six or twelve months, note that a line of best fit through all of them would be more reliable than the two extremes.
Exam technique for cost classification and behaviour
Questions divide between classification, which is quick, and high-low calculations, which carry more marks. Both reward layout.
For high-low, set the two points out in a small table with activity and cost columns before subtracting. Most errors here are subtraction the wrong way round, and a table makes that visible. Label the variable rate with its unit — per machine hour, per unit, per guest-night.
State the cost equation explicitly once you have derived it. Mark schemes frequently award a mark for the equation itself, separate from the fixed and variable figures.
Command words behave predictably. Classify wants the category and nothing more. Distinguish between a fixed and a stepped fixed cost wants the contrast made explicit. Calculate the fixed element wants the working. Explain why the high-low method may be unreliable wants the two-observation weakness with a reason. Assess its suitability wants both sides and a conclusion.
If a question gives three or more activity levels, use only the highest and lowest — that is what the method is, and using a middle pair earns nothing.
Quick revision summary
- Classify by behaviour, traceability, product/period, controllability and relevance — the decision determines which applies.
- Fixed: constant in total, falls per unit as output rises.
- Variable: constant per unit, rises in total as output rises.
- Semi-variable: has both elements and must be split before use.
- Stepped fixed: flat within a band, then jumps at a threshold.
- Direct costs total to prime cost; indirect costs are overheads and must be shared out.
- High-low: variable rate = change in cost ÷ change in activity; fixed = total cost less the variable portion at either point.
- Always check the split at the second observation.
- The high-low method uses only two points, so an unrepresentative observation wrecks it.
- Every behaviour assumption holds only within the relevant range — say so when forecasting beyond it.