the limitations of contribution costing

5.4 Costs – Approaches to Costing

Learning Objective

Understand the two principal costing approaches – full (absorption) costing and contribution (marginal) costing – their definitions, profit‑measurement formulas, uses, limitations and how they are applied in managerial decision‑making (break‑even, CVP, product‑mix, etc.).

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1. Cost‑type refresher (5.4.1)

Before applying any costing method it is essential to classify costs correctly.

Cost type	Behaviour	Typical examples	Relevance to costing methods
Variable	Changes in total in direct proportion to output; unit cost remains constant within the relevant range.	Direct material, direct labour (hourly), variable factory overhead (e.g., power per machine hour).	Allocated to units in both full and contribution costing; forms the basis of the contribution margin.
Fixed	Total amount remains constant regardless of output (within the relevant range); unit cost varies with output.	Rent of factory premises, salaries of production supervisors, depreciation of plant, insurance.	Full costing: absorbed into unit cost. Contribution costing: treated as period cost (expensed in the period incurred).
Direct (or primary)	Can be traced directly to a single cost object (product, service, department).	Direct material, direct labour.	Always treated as variable in the standard syllabus, but may be fixed in special circumstances (e.g., a fixed‑rate labour contract).
Indirect (or secondary)	Cannot be traced to a single cost object without allocation.	Factory overheads (both variable and fixed), administration costs.	Full costing: allocated to units. Contribution costing: only the variable portion is allocated; the fixed portion is a period cost.

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2. Full (Absorption) Costing – 5.4.2

Definition

All manufacturing costs – both variable and fixed – are absorbed into the cost of each unit produced. The resulting figure is the full (or absorption) cost per unit.

Steps to calculate full cost per unit

1. Identify total manufacturing costs for the period:
   • Variable manufacturing costs (direct material, direct labour, variable overhead).
   • Fixed manufacturing overhead (e.g., rent, supervisor salaries, depreciation).
2. Choose an appropriate allocation base (normally the expected or normal capacity – e.g., units, machine‑hours, labour‑hours).
3. Calculate the fixed‑overhead absorption rate:
   Fixed OH rate per unit = Total Fixed Manufacturing OH ÷ Expected output (units)
4. Add the variable cost per unit to the fixed‑OH rate to obtain the full cost per unit.

Profit‑measurement formula (required by the syllabus)

Full‑cost profit = Sales – (Variable manufacturing + Fixed manufacturing + Fixed period costs)

where “Fixed period costs” are non‑production fixed costs such as administration and selling expenses.

Uses

• External financial reporting (IFRS/GAAP requirement).
• Pricing when a “full‑cost‑plus” approach is required.
• Long‑run product‑line profitability analysis.
• Budgeting – inventory valuation in the production and profit‑and‑loss budgets.

Limitations

1. Inventory distortion: Fixed overhead is tied up in closing stock; profit can rise when inventories increase and fall when they are drawn down.
2. Less useful for short‑run decisions: Fixed costs are treated as product costs even though they are sunk in the short term.
3. Allocation arbitrariness: The choice of allocation base may be subjective and can distort cost comparisons.
4. Assumes linear cost behaviour: Variable cost per unit is assumed constant, which may not hold in reality.

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3. Contribution (Marginal) Costing – 5.4.2

Definition

Costs are split into:

• Variable costs – change directly with output and are allocated to each unit.
• Fixed costs – remain constant in total over the relevant range and are treated as period expenses.

The central figure is the Contribution Margin (CM):

$$CM = \text{Sales} - \text{Variable Costs}$$

and the Contribution Margin Ratio (CMR):

$$CMR = \frac{CM}{\text{Sales}}$$

Profit‑measurement formula (syllabus requirement)

Contribution‑cost profit = Contribution – Fixed period costs

where “Contribution” = Sales – Variable costs (both manufacturing and, if relevant, variable selling & admin).

How to calculate contribution per unit

$$\text{CM per unit} = \text{Selling price per unit} - \text{Variable cost per unit}$$

Uses

• Short‑run pricing, special‑order and make‑or‑buy decisions.
• Product‑mix optimisation and “what‑if” scenarios.
• Cost‑Volume‑Profit (CVP) and break‑even analysis.
• Assessing the impact of sales‑volume changes when capacity is not a constraint.

Limitations

1. Ignores fixed‑cost behaviour at different output levels: Fixed costs may change when capacity is expanded or reduced.
2. Not acceptable for external reporting: Statutory accounts must use absorption costing.
3. Potential distortion in multi‑product environments: Shared fixed overheads are not allocated, which can mislead product‑profit comparisons.
4. Assumes constant variable cost per unit: Economies or diseconomies of scale can cause variable cost to vary.
5. Does not consider capacity constraints: The analysis often assumes unlimited capacity.
6. Limited for long‑term strategic planning: Capital expenditure and long‑term fixed costs are omitted.

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4. Break‑Even and CVP Analysis (using contribution costing)

Key formulas

Formula	Explanation
Contribution Margin per unit (CMu)	Selling price per unit – Variable cost per unit
Contribution Margin Ratio (CMR)	CMu ÷ Selling price per unit
Break‑Even Point (units)	Total Fixed Costs ÷ CMu
Break‑Even Point (sales £)	Total Fixed Costs ÷ CMR
Target‑Profit Sales (units)	(Fixed Costs + Desired Profit) ÷ CMu
Margin of Safety (%)	(Actual Sales – BEP) ÷ Actual Sales × 100

Numerical example

Item	Amount (£)
Selling price per unit	20
Variable cost per unit	12
Contribution margin per unit (CMu)	8
Total fixed costs (per period)	120 000

Break‑Even (units) = 120 000 ÷ 8 = 15 000 units

Break‑Even (sales £) = 120 000 ÷ (8 / 20) = 120 000 ÷ 0.40 = £300 000

CMR = 8 ÷ 20 = 0.40 → 40 % of each sales pound contributes to covering fixed costs and profit.

Using CVP for decision‑making

• Price change → recalculate CMR → new BEP.
• Introduce a new product → add its CM to total contribution and re‑evaluate fixed‑cost coverage.
• Target profit → compute required sales using the “Target‑Profit Sales” formula.

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5. Comparison of Full and Contribution Costing

Aspect	Full (Absorption) Costing	Contribution (Marginal) Costing
Cost allocation	All manufacturing costs (variable + fixed) are absorbed into unit cost.	Only variable manufacturing costs are absorbed; fixed manufacturing costs are period expenses.
Profit measurement formula	Profit = Sales – (Variable + Fixed manufacturing + Fixed period costs)	Profit = Contribution – Fixed period costs
Primary use	External reporting, long‑run pricing, budgeting, product‑line profitability.	Short‑run decisions, CVP/break‑even, special orders, make‑or‑buy.
Effect of inventory changes	Profit is affected because fixed overhead is tied up in inventory.	Profit is unaffected; fixed costs are expensed in the period incurred.
Regulatory status	Required by IFRS/GAAP for statutory accounts.	Not permitted for external financial statements.
Key limitation	Profit distortion when stock levels fluctuate.	Ignores fixed‑cost behaviour and capacity constraints.

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6. Decision‑Making Framework – When to Use Which Method

Use the checklist below to select the appropriate costing approach for a given decision.

1. Purpose of the decision
   • Short‑run (pricing, special order, make‑or‑buy, product‑mix) → Contribution costing
   • Long‑run (product‑line profitability, investment appraisal, external reporting) → Full costing
2. Regulatory requirement
   • Statutory accounts, tax returns, shareholder reporting → Full costing
   • Internal management analysis only → either method, based on other criteria
3. Inventory considerations
   • Significant expected changes in stock levels → Full costing (to reflect inventory valuation)
   • Stable inventory or a single‑period analysis → Contribution costing
4. Capacity constraints
   • If capacity is limited or a bottleneck exists, supplement contribution analysis with a capacity check (e.g., contribution per limiting factor).
5. Fixed‑cost behaviour
   • When fixed costs are likely to vary with output (e.g., new plant, overtime premiums) → use full costing for a realistic picture.

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7. Links to Other Syllabus Topics

• 5.5 Budgets: Full costing determines the value of closing stock in the production budget, influencing cash‑flow forecasts.
• 5.3 Cash‑flow forecasting: Contribution analysis highlights cash‑generating capacity (variable costs are usually cash costs), while full costing shows the cash impact of inventory investment.
• 5.6 Pricing strategies: Cost‑plus pricing uses full cost; marginal‑cost pricing uses contribution costing.

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8. Quick Reference – Key Formulas

Formula	Explanation
Contribution Margin (CM)	Sales – Variable Costs
CM per unit	Selling price per unit – Variable cost per unit
Contribution Margin Ratio (CMR)	CM ÷ Sales (or CM per unit ÷ Price per unit)
Break‑Even (units)	Total Fixed Costs ÷ CM per unit
Break‑Even (sales £)	Total Fixed Costs ÷ CMR
Target‑Profit Sales (units)	(Fixed Costs + Desired Profit) ÷ CM per unit
Margin of Safety (%)	(Actual Sales – BEP) ÷ Actual Sales × 100
Full‑cost profit	Sales – (Variable + Fixed manufacturing + Fixed period costs)
Contribution‑cost profit	Contribution – Fixed period costs

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9. Suggested Diagram (for classroom use)

Flowchart contrasting the two costing paths.

1. Start with total production cost.
2. Separate into variable and fixed components.
3. Full‑costing path: Allocate both variable and fixed to each unit → calculate full cost per unit → add desired profit margin → price.
4. Contribution‑costing path: Allocate only variable to each unit → obtain contribution per unit → subtract total fixed period costs → profit.
5. Decision point: Is the decision short‑run or long‑run? → Choose the appropriate path.

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Key Take‑aways

• Both costing methods are required tools; neither can replace the other.
• Use contribution costing for short‑run, volume‑sensitive decisions and CVP analysis.
• Use full costing for external reporting, budgeting, and long‑run strategic decisions.
• Always verify the underlying assumptions (fixed‑cost behaviour, capacity, inventory changes) before relying on a single method.