the nature of the technique of contribution costing

5.4 Costs – Approaches to Costing

Objective

To understand the nature, purpose and limitations of the contribution costing technique (also called marginal or variable costing) and to be able to apply it to short‑run managerial decisions such as pricing, product‑mix and make‑or‑buy.

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1. Why Accurate Cost Information Is Essential

• Cost data form the basis for:
  • Setting selling prices
  • Choosing the optimal product‑mix
  • Deciding whether to make a component in‑house or buy it externally
• Incorrect or incomplete cost information can lead to:
  • Wrong pricing decisions (under‑ or over‑pricing)
  • Mis‑allocation of resources between products or departments
  • Inaccurate break‑even analysis and profit forecasts
• Therefore managers must obtain reliable, up‑to‑date information on the nature and behaviour of each cost element.

1.1 Cost Classification

Classification	Definition	Typical Examples	Behaviour in the short‑run
Variable	Changes in direct proportion to output	Direct materials, hourly labour, power per unit	Increases or decreases exactly with the level of activity
Fixed	Remains constant in total regardless of output (within the relevant range)	Rent, salaried staff, depreciation, insurance	Unchanged in total; per‑unit cost falls as output rises
Direct	Can be traced directly to a single product, service or department	Raw material for Product A, machine‑hour cost for a specific line	Usually variable, but can be fixed (e.g., a fixed‑rate supervisor assigned to one product)
Indirect	Cannot be traced to a single cost object without allocation	Factory supervision, utilities for the whole plant	Often fixed, but may contain a variable component
Semi‑variable (mixed)	Contains both a fixed component and a variable component	Telephone bill = £30 fixed + £0.10 per minute; maintenance contract = £5 000 fixed + £2 per machine‑hour	Partly fixed, partly variable – the variable part behaves like a variable cost

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2. Approaches to Costing

2.1 Full (Absorption) Costing

• All manufacturing costs – both variable and fixed – are allocated to units of product.
• Used for external financial reporting (IFRS/GAAP require absorption costing) and for long‑run strategic planning.
• Profit is measured as gross profit (sales – cost of goods sold).

2.2 Contribution (Marginal) Costing

• Only variable manufacturing costs are assigned to units; fixed manufacturing costs are treated as period costs.
• Focuses on the contribution each unit makes toward covering fixed costs and generating profit.
• Primarily a short‑run decision‑making tool.

2.3 Comparison – Full vs. Contribution Costing

Aspect	Full (Absorption) Costing	Contribution (Marginal) Costing
Cost allocation	Variable + fixed manufacturing costs absorbed into product cost	Only variable manufacturing costs absorbed; fixed manufacturing costs are period costs
Profit measure	Gross profit (sales – cost of goods sold)	Contribution margin (sales – variable costs) – fixed costs = net profit
Inventory valuation	Variable + fixed manufacturing costs	Variable manufacturing costs only
Decision‑making focus	Long‑run, full‑cost recovery	Short‑run, marginal analysis
Effect of production volume on profit	Profit can change with inventory levels because fixed overhead is spread over units produced	Profit changes only with changes in contribution; fixed costs stay unchanged
External reporting	Required under IFRS/GAAP	Not acceptable for external financial statements

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3. Core Concepts of Contribution Costing

3.1 Contribution

Contribution = Sales Revenue – Variable Costs

3.2 Contribution per Unit

Contribution per unit = Selling price per unit – Variable cost per unit

3.3 Contribution Margin Ratio (CMR)

CMR = (Contribution ÷ Sales Revenue) × 100 %

3.4 Total Contribution

Total Contribution = Σ (Contribution per unit × Quantity sold) for each product or department.

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4. Using Contribution for Decision‑Making (Syllabus 5.4.2)

1. Break‑Even Analysis – Finds the sales level where total contribution equals total fixed costs.
2. Pricing Decisions – Shows how a change in price affects contribution and profit.
3. Product‑Mix Decisions – Selects the combination of products that maximises total contribution, subject to capacity constraints.
4. Make‑or‑Buy Decisions – Compares contribution from in‑house production with the cost of purchasing externally.
5. Special‑Order Decisions – Determines whether a one‑off order (often at a reduced price) adds to profit.
6. Short‑Run Profit Planning – Forecasts profit changes when sales volume varies within the relevant range.

4.1 Break‑Even Point (BEP)

• Units: BEP (units) = Total Fixed Costs ÷ Contribution per unit
• Value (sales £): BEP (value) = Total Fixed Costs ÷ Contribution Margin Ratio

4.2 Contribution‑Based Product‑Mix Example

Factory capacity: 12 000 units per month; two products are available.

Product	Selling price	Variable cost	Contribution per unit	Machine‑hours per unit
A	£30	£18	£12	0.5 h
B	£25	£15	£10	0.3 h

Available machine‑hours = 6 000 h.

Contribution per machine‑hour:

• Product A: £12 ÷ 0.5 h = £24 per hour
• Product B: £10 ÷ 0.3 h = £33.33 per hour

Because Product B yields a higher contribution per limited resource, allocate capacity to B first, then use any remaining hours for A. This demonstrates how contribution guides product‑mix decisions.

4.3 Make‑or‑Buy Decision Example

Component X – internal vs external:

• Internal variable cost per unit: £4
• Fixed overhead attributable to the component: £30 000 (period cost, unchanged if bought)
• External purchase price: £5 per unit
• Expected volume: 10 000 units

Contribution if made internally:

 ( Selling price – £4 ) × 10 000 – £30 000

Contribution if bought:

 ( Selling price – £5 ) × 10 000  (no fixed cost)

Compare the two contributions; the option with the higher contribution is preferred.

4.4 Special‑Order Decision Example

A customer offers to buy 2 000 units of Product C at £22 each. Normal selling price = £30; variable cost = £15; fixed costs = £80 000.

• Contribution from the order = ( £22 – £15 ) × 2 000 = £14 000
• Since the fixed cost of £80 000 is already incurred, the order adds £14 000 to profit, provided there is sufficient unused capacity.

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5. Advantages and Disadvantages (Syllabus 5.4.3)

5.1 Advantages

• Shows clearly the relationship between sales, variable costs and profit.
• Simple to calculate – useful for quick, short‑run decisions.
• Facilitates break‑even and cost‑volume‑profit (CVP) analysis.
• Highlights the effect of changes in sales volume or product mix on profitability.
• Helps identify the most profitable use of limited resources (e.g., machine time, labour).

5.2 Disadvantages

• Ignores the allocation of fixed manufacturing overhead to inventory, which can give a distorted view of product cost for long‑term planning.
• Not acceptable for external financial statements under IFRS/GAAP (which require absorption costing).
• Assumes costs are either strictly variable or strictly fixed; many real‑world costs are semi‑variable or step‑fixed.
• Can lead to inappropriate long‑run pricing if fixed costs are overlooked.

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6. Full Example Calculation

Data for Product X

• Selling price per unit: £120
• Variable cost per unit: £70
• Total fixed costs: £150 000

1. Contribution per unit = £120 – £70 = £50
2. Contribution margin ratio = (£50 ÷ £120) × 100 % = 41.67 %
3. Break‑even point (units) = £150 000 ÷ £50 = 3 000 units
4. Break‑even point (value) = £150 000 ÷ 0.4167 ≈ £360 000 sales

Interpretation

At 3 000 units the business covers all its fixed costs. Every unit sold beyond this point contributes £50 to profit.

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7. Suggested Diagram for Revision

Draw a graph with:

• X‑axis: Quantity of units
• Y‑axis: £ (costs / revenue)
• Three lines:
  1. Total Fixed Cost – horizontal line.
  2. Total Variable Cost – starts at the origin; slope = variable cost per unit.
  3. Total Revenue – starts at the origin; slope = selling price per unit.
• The intersection of Total Revenue and Total Cost (Fixed + Variable) marks the break‑even point.

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8. Summary

Contribution costing separates costs into variable and fixed components, allowing managers to calculate the contribution each product makes toward covering fixed costs and generating profit. It is a powerful short‑run tool for break‑even analysis, pricing, product‑mix, make‑or‑buy and special‑order decisions. While its simplicity and focus on marginal information are clear strengths, the method must be used alongside full (absorption) costing for external reporting and long‑term strategic planning.