# Classification of Cost by Behaviour

This classification looks at how cost responds to changes in the level of activity (units produced / sold). It is critical for break-even analysis, marginal costing, and decision-making.

## The Three Behavioural Categories

### 1. Variable Cost

Total cost changes in direct proportion to the level of output.
Per-unit cost remains constant.
Examples: raw material consumed per unit, piece-rate wages, power consumed per machine hour.

### 2. Fixed Cost

Total cost remains constant within the relevant range, irrespective of output.
Per-unit cost decreases as output increases (spread over more units).
Examples: factory rent, depreciation (straight-line), salary of permanent staff.

### 3. Semi-Variable Cost (Mixed Cost)

A combination of fixed + variable components.
Has a fixed minimum charge plus a variable element that rises with usage.
Examples: telephone bill (rental + call charges), electricity (fixed demand charge + units consumed), machine set-up cost.

## Behaviour Summary Table

Type	Total Cost	Per-unit Cost
Variable	Increases proportionately	Constant
Fixed	Constant	Decreases
Semi-Variable	Increases (but not proportionately)	Decreases (irregularly)

## Decision Tree — How to Identify the Type

```

Does total cost increase when output rises?

│

├── NO → FIXED COST

│

└── YES → Does it rise in the SAME proportion?

│

├── YES → PURE VARIABLE COST

│

└── NO → SEMI-VARIABLE COST

```

## Bifurcating Semi-Variable Cost — High-Low Method

When given cost data at two different activity levels, split semi-variable cost into its fixed and variable components:

$$\text{Variable cost per unit} = \frac{\text{Difference in Total Cost}}{\text{Difference in Units}}$$

$$\text{Total Fixed Cost} = \text{Total Cost} - (\text{Variable cost per unit} \times \text{No. of Units})$$

> The fixed component can be verified using either the high or the low data point — both should give the same answer.

## Why This Matters

Marginal costing uses only variable cost.
Break-even analysis needs fixed and variable cost separately.
Flexible budgets are built on this classification.

Worked example

### Example 1

Example 1 — Behavioural movement

A factory's rent is ₹60,000 per month. Direct material cost is ₹20 per unit.

Compute total and per-unit cost at output of (a) 1,000 units (b) 2,000 units.

Output	Total Rent	Rent/Unit	Total Material	Material/Unit
1,000	60,000	60	20,000	20
2,000	60,000	30	40,000	20

Observation: Rent is fixed — total unchanged, per-unit falls. Material is variable — total rises proportionately, per-unit constant.

### Example 2

Example 2 — Bifurcating semi-variable cost (High-Low method)

The following data is given:

Output (units)	Total Maintenance Cost (₹)
4,000	50,000
7,000	65,000

Separate fixed and variable elements.

Step 1 — Variable cost per unit

$$\text{VC/unit} = \frac{65{,}000 - 50{,}000}{7{,}000 - 4{,}000} = \frac{15{,}000}{3{,}000} = ₹5 \text{ per unit}$$

Step 2 — Fixed cost (using the 7,000-unit level)

$$\text{FC} = 65{,}000 - (5 \times 7{,}000) = 65{,}000 - 35{,}000 = ₹30{,}000$$

Verification at 4,000 units: 30,000 + (5 × 4,000) = 30,000 + 20,000 = ₹50,000 ✓

Cost equation: Total Cost = ₹30,000 + ₹5 × Units

⚠️ Common exam mistakes

Saying 'fixed cost per unit is fixed' — total fixed cost is fixed; per-unit fixed cost FALLS as output rises.
Saying 'variable cost per unit changes' — total variable cost changes; per-unit variable cost stays CONSTANT.
Applying the high-low formula to non-adjacent or unreliable data points without checking whether either extreme is abnormal.
Forgetting to verify the fixed cost using both data points — small calculation errors slip in unnoticed.
Treating stepped fixed costs (e.g., extra supervisor at every 1,000 units) as purely variable — they are fixed within each step.

Reference:

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Classification of Cost by Behaviour / Variability (Fixed, Variable, Semi-Variable)

Worked example

⚠️ Common exam mistakes