5.4 Costs – Approaches to Costing
Objective
To understand the difference between contribution and profit, to compare the two costing approaches required by the Cambridge 9609 syllabus – full (absorption) costing and contribution (variable) costing – and to apply them in break‑even analysis and decision‑making.
1. Cost behaviour – a quick recap
- Variable costs: change in direct proportion to the level of activity (e.g., direct material, direct labour, variable overheads).
- Fixed costs: remain constant in total regardless of output (e.g., rent, salaried staff, fixed factory overheads).
- Semi‑variable (mixed) costs: contain a fixed component plus a variable component (e.g., a telephone bill = £30 fixed + £0.10 per call).
In costing they are split into a fixed part (treated as a period cost) and a variable part (treated as a unit cost).
2. Contribution (Variable) Costing
Definition
Calculates the amount of sales revenue that remains after **all variable costs** (including the variable part of semi‑variable costs) have been deducted.
Key formulas
\[
\text{Contribution (C)} = \text{Sales Revenue (S)} - \text{Variable Costs (VC)}
\]
\[
\text{Contribution per unit (C_u)} = \text{Selling price per unit} - \text{Variable cost per unit}
\]
\[
\text{Contribution‑margin ratio (CMR)} = \frac{\text{Contribution}}{\text{Sales Revenue}} \times 100\%
\]
Interpretation of CMR
- Shows the percentage of each sales pound that contributes to covering fixed costs and generating profit.
- A higher CMR indicates a more “efficient” product or sales mix.
Treatment of fixed costs
- All fixed costs (including the fixed portion of semi‑variable costs) are treated as **period expenses** and are not allocated to individual units.
- They are deducted from total contribution to arrive at profit.
When to use contribution costing
- Pricing decisions – ensuring the selling price exceeds the variable cost.
- Product‑mix analysis – ranking products by contribution per unit or contribution‑margin ratio.
- Make‑or‑buy decisions – compare contribution from in‑house production with the cost of purchasing.
- Special‑order evaluation – assess whether the extra contribution covers any incremental costs.
- Short‑term budgeting and performance measurement.
Limitations
- Ignores the allocation of fixed production overheads, which can distort product profitability when overheads are high.
- Not acceptable for external financial reporting – statutory accounts require full (absorption) costing.
- Can give misleading signals for long‑term decisions because capacity‑related fixed costs are omitted.
- Inventory is valued at variable cost only, potentially understating the balance‑sheet value of stock.
3. Full (Absorption) Costing
Definition
All manufacturing costs – both variable **and** fixed – are allocated to each unit of product. The resulting unit cost is called the **full (absorbed) cost**.
Allocation of fixed production overheads
Fixed overheads are spread over the units produced using a chosen allocation base, for example:
| Possible allocation base | Typical use |
|---|
| Machine‑hours | When overheads are driven mainly by equipment utilisation. |
| Labour‑hours | When labour time is the dominant cost driver. |
| Number of units produced | When overheads are relatively insensitive to activity levels. |
Key formula (per unit)
\[
\text{Full cost per unit} = \text{Variable cost per unit} + \frac{\text{Total fixed production overhead}}{\text{Allocation base total}} \times \text{Base per unit}
\]
Uses of full costing
- Preparation of statutory (external) accounts – required by accounting standards.
- Inventory valuation – stock is shown on the balance sheet at full cost (variable + allocated fixed).
- Long‑term profitability analysis and budgeting where fixed overheads form a significant part of total cost.
- Assessing the impact of changes in inventory levels on reported profit.
Limitations
- Less useful for short‑term decisions because fixed overheads are “hidden” in the unit cost.
- Can encourage over‑production: producing more units spreads fixed overhead over a larger base, inflating reported profit even though cash flow is unchanged.
- May mask the true profitability of individual products if a single overhead rate is applied to dissimilar items.
4. Contribution vs. Profit
- Contribution = Sales – Variable Costs (including the variable part of semi‑variable costs).
- Profit = Contribution – Fixed Costs (both fixed production overheads and fixed period costs).
Formulas
\[
\text{Profit (P)} = \text{Sales Revenue} - \text{Variable Costs} - \text{Fixed Costs}
\]
\[
\text{Profit} = \text{Contribution} - \text{Fixed Costs}
\]
5. Break‑Even Analysis (Applicable to Both Costing Methods)
The break‑even point (BEP) is the level of activity at which total contribution exactly equals total fixed costs, so that profit is zero.
Formula (units)
\[
\text{BEP (units)} = \frac{\text{Total Fixed Costs (FC)}}{\text{Contribution per unit (C_u)}}
\]
Interpretation
- Sales < BEP → loss.
- Sales = BEP → zero profit.
- Sales > BEP → profit (the excess units each generate C_u of profit).
Key point
Break‑even is **identical under both costing methods** because it is based on contribution. The difference appears only when inventory levels change – under absorption costing part of the fixed overhead is deferred in inventory, affecting the profit shown on the income statement.
6. Numerical Examples
6.1 Basic example (contribution, profit and BEP)
- Selling price per unit = £50
- Variable cost per unit = £30
- Contribution per unit = £20
- Total fixed costs = £120 000
- Expected sales = 10 000 units
| Item | Amount |
|---|
| Sales revenue | 10 000 × £50 = £500 000 |
| Total variable costs | 10 000 × £30 = £300 000 |
| Total contribution | £500 000 – £300 000 = £200 000 |
| Profit (variable costing) | £200 000 – £120 000 = £80 000 |
| Break‑even units | £120 000 ÷ £20 = 6 000 units |
6.2 Inventory‑level example – effect of production ≠ sales
Assume the same cost data, but the company **produces 12 000 units** and **sells only 10 000 units**. Fixed production overhead = £120 000 (allocated on a machine‑hour basis, 1 hour per unit).
| Costing method | Profit shown |
|---|
| Variable (contribution) costing |
- Sales revenue = £500 000
- Variable costs = £300 000
- Contribution = £200 000
- Fixed costs (all £120 000) are expensed in the period
- Profit = £80 000
|
| Absorption (full) costing |
- Full cost per unit = £30 (variable) + (£120 000 ÷ 12 000) = £40
- Cost of goods sold (COGS) = 10 000 × £40 = £400 000
- Closing inventory = 2 000 × £40 = £80 000 (still on the balance sheet)
- Sales revenue = £500 000
- Profit = £500 000 – £400 000 = £100 000
Note: £20 000 of the fixed overhead (£120 000 × 2 000/12 000) is deferred in inventory, so profit appears higher under absorption costing.
|
This example demonstrates why the two methods can give different profit figures when production and sales quantities differ.
7. Comparison of the Two Costing Approaches
| Aspect |
Contribution (Variable) Costing |
Full (Absorption) Costing |
| Definition |
Sales revenue minus **all variable costs** (including variable part of semi‑variable costs). |
All manufacturing costs (variable + fixed) allocated to each unit using an allocation base. |
| Fixed‑cost treatment |
Period expense – deducted after contribution. |
Allocated to units; part may be deferred in inventory. |
| Primary purpose |
Short‑term decision‑making (pricing, product‑mix, make‑or‑buy, special orders). |
External financial reporting, inventory valuation, long‑term budgeting. |
| Break‑even analysis |
Based directly on contribution (C ÷ FC). |
Same BEP as variable costing; profit shown differs when inventory changes. |
| Key limitation |
Ignores fixed overhead allocation; not GAAP‑compliant. |
Can mask product profitability and may encourage over‑production. |
| Allocation of fixed overheads |
Not allocated. |
Spread over units using a chosen base (machine‑hours, labour‑hours, units produced, etc.). |
| Effect of inventory changes on profit |
None – fixed costs are expensed in the period. |
Profit rises when production > sales (fixed overhead deferred) and falls when sales > production (fixed overhead released). |
8. Quick Revision Checklist
- Contribution = Sales – Variable Costs (incl. variable part of semi‑variable costs).
- Profit = Contribution – Fixed Costs.
- Contribution‑margin ratio = (Contribution ÷ Sales) × 100 % – tells you the % of each sales pound that covers fixed costs.
- Break‑even (units) = Fixed Costs ÷ Contribution per unit. The BEP is the same under both methods.
- Variable costing: fixed costs are period expenses; useful for short‑term decisions.
- Absorption costing: fixed production overheads are allocated to units; required for statutory accounts and inventory valuation.
- When production ≠ sales, profit differs between the two methods because absorption costing defers part of fixed overhead in inventory.
- Know at least one allocation base for fixed overheads (e.g., machine‑hours).
- Remember semi‑variable costs are split into a fixed component (treated as period cost) and a variable component (included in unit cost).
- Use contribution data for pricing, product‑mix, make‑or‑buy, and special‑order decisions; use absorption data for external reporting and long‑term budgeting.