Notes · AccountingUK · A-Levels

Marginal costing

Marginal costing analyses how costs behave and uses contribution to inform short-term decisions. This chapter covers cost behaviour and contribution, break-even analysis and the margin of safety, cost-volume-profit and target-profit calculations, and the use of contribution in decisions such as special orders, make-or-buy and the best use of a limiting factor - pairing every calculation with its interpretation and its assumptions.

4 sections~19 min reading time3 competenciesLevel Standard 1 · Advanced 3

T·131313 / 18

Exam profile

AO1 · Understand cost behaviour, contribution, break-even and the margin of safetyAO2 · Calculate contribution, break-even, margin of safety, target-profit output and the best use of a limiting factorAO3 · Analyse and evaluate marginal-costing decisions, including qualitative factors and the assumptions of break-even

Operators:calculateprepareexplainanalyseevaluaterecommendassess

basic level

AS-Level expects contribution, break-even and the margin of safety.

higher level

The full A-Level adds cost-volume-profit and target profit, limiting-factor and special-order decisions, and evaluation of the assumptions of marginal costing.

Depth

Text

Contents · 4 sections

Marginal costing

Cost behaviour and contribution#

StandardAQA 7127 3.10

Classification of costs

Fig. 1Costs are classified by behaviour (fixed, variable, semi-variable) and by traceability (direct, indirect) - marginal costing needs the fixed/variable split.

Marginal costing begins with how costs behave as output changes. Fixed costs do not change with the level of output over the relevant range - rent, salaries, insurance - and must be paid even at zero output; they are fixed in total but fall per unit as output rises (spread over more units). Variable costs change directly with output - raw materials, piece-rate wages, packaging - so they are constant per unit but rise in total as output rises. Many real costs are semi-variable, having a fixed element and a variable element (a standing charge plus a usage charge), and these must be split into their fixed and variable parts before marginal-costing techniques can be applied. Costs are also classified by traceability into direct costs (traceable to a unit) and indirect costs or overheads (not directly traceable).

Contribution is the central concept of marginal costing and one of the most useful ideas in the whole subject. Contribution per unit is the selling price less the variable cost per unit - the amount each unit sold contributes towards covering fixed costs and, once those are covered, towards profit. Total contribution is the contribution per unit multiplied by the units sold, or equivalently total revenue less total variable costs. The power of contribution is that it separates the costs that vary with each sale (variable) from the fixed overheads, which lets a firm answer decisive questions: how many units must we sell to cover our fixed costs, and how much does each extra sale add to profit?

Contribution leads directly to profit through a simple and powerful relationship: total profit equals total contribution minus fixed costs. This reformulation is far more useful for decision-making than 'revenue minus total cost', because it isolates the effect of selling one more or one fewer unit. Once fixed costs are covered, every additional unit's contribution is pure profit; below that point, each unit's contribution is reducing the loss. Thinking in terms of contribution rather than full cost per unit is what allows a manager to make correct short-term decisions - accepting extra business at a price above variable cost even if it is below full cost, because it still adds to the fixed costs already being paid.

The contribution-to-sales (C/S) ratio, also called the profit-volume ratio, expresses contribution as a proportion of sales revenue - contribution per unit divided by selling price, or total contribution divided by revenue. It is useful because it stays constant as long as selling prices and variable costs per unit are unchanged, so it can be applied to revenue directly: break-even revenue, for example, is fixed costs divided by the C/S ratio. If a product sells for £50 with a variable cost of £35, contribution is £15 and the C/S ratio is 15/50 = 0.30, meaning 30 pence of every sales pound contributes to fixed costs and profit. These building blocks - cost behaviour, contribution and the C/S ratio - underpin everything that follows.

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

Contribution per unit

The amount each unit contributes to fixed costs and then profit - the key to break-even and short-term decisions.

\text{Profit} = \text{Total contribution} - \text{Fixed costs}

Profit via contribution

Once total contribution exceeds fixed costs, the surplus is profit. More useful for decisions than revenue minus total cost.

\text{C/S ratio} = \frac{\text{Contribution per unit}}{\text{Selling price}}

Contribution-to-sales ratio

Contribution as a proportion of sales. Constant while price and unit variable cost hold. Here 15/50 = 0.30.

Worked example

Contribution and profit

A product sells for £50, with a variable cost of £35 per unit and fixed costs of £45,000. If 4,000 units are sold, calculate the contribution per unit, the C/S ratio, total contribution and profit.

Contribution per unit and C/S ratio
Contribution per unit = £50 - £35 = £15. C/S ratio = £15 / £50 = 0.30 (30%).
Total contribution
Total contribution = £15 x 4,000 = £60,000 (equivalently revenue £200,000 less variable costs £140,000).
Profit
Profit = total contribution - fixed costs = £60,000 - £45,000 = £15,000.

Result: Contribution is £15 per unit (C/S ratio 0.30); on 4,000 units total contribution is £60,000, giving a profit of £15,000 after fixed costs of £45,000.

Typical mistakes

Confusing contribution (price minus variable cost) with profit (which also deducts fixed costs).
Treating a fixed cost as changing per unit in total, or forgetting to split semi-variable costs.

Active revision

A product sells for £50 with variable costs of £35. Calculate the contribution per unit and the C/S ratio, and the total contribution and profit if 4,000 are sold and fixed costs are £45,000.

Active recall

Recall the key points — then reveal.

Sources: AQA A-level Accounting 7127 specification (AQA)

Break-even analysis and the margin of safety#

AdvancedAQA 7127 3.10

Break-even chart

Fig. 2The total revenue and total cost lines cross at the break-even point of 3,000 units (£150,000). Left of it is a loss, right of it a profit; the margin of safety is the gap to the actual output.

Break-even analysis finds the level of output and sales at which a business exactly covers its costs, making neither profit nor loss. At the break-even point total revenue equals total cost, or equivalently total contribution exactly equals fixed costs. The break-even output is therefore fixed costs divided by the contribution per unit, because each unit's contribution chips away at the fixed costs until they are covered. With fixed costs of £45,000 and a contribution of £15 per unit, the break-even output is £45,000 / £15 = 3,000 units. Below 3,000 units the firm makes a loss; above it, every further unit's £15 contribution is profit. Break-even is a fundamental planning tool: it tells a firm the minimum it must sell to survive.

The break-even chart draws the picture. Output is on the horizontal axis and money (revenue and costs) on the vertical axis. The total revenue line rises from the origin (£50 per unit); the total cost line starts at the level of fixed costs (£45,000, paid even at zero output) and rises with the £35 variable cost of each unit. The two lines cross at the break-even point of 3,000 units and £150,000 of revenue. To the left of the crossing the total cost line is above the revenue line (a loss); to the right the revenue line is above (a profit); and the vertical gap between the lines beyond break-even is the profit at that output. The chart makes visible how contribution accumulates to cover fixed costs and then to generate profit.

The margin of safety is the amount by which the actual or planned output exceeds the break-even output - the cushion of sales the firm could lose before it slipped into loss. It is calculated as actual output minus break-even output, and can be expressed as a percentage of actual output. At a planned output of 4,000 units with a break-even of 3,000, the margin of safety is 1,000 units, or 25% of planned output - the firm could lose a quarter of its sales and still break even. A large margin of safety means the firm can absorb a fall in demand; a small one means it is dangerously close to loss, so the margin of safety is a crucial measure of risk.

Once above break-even, profit can be found directly as the margin of safety multiplied by the contribution per unit - here 1,000 x £15 = £15,000 - which agrees with total contribution minus fixed costs (£60,000 - £45,000 = £15,000), a useful check. Break-even analysis is valued for its simplicity and its power as a 'what-if' planning tool: a firm can see instantly how the break-even point moves if the price, the variable cost or the fixed costs change. But its assumptions are strong - that all output is sold, that price and variable cost per unit are constant at every level of output, and that costs split cleanly into fixed and variable - so it is a first-pass planning tool to be used with awareness of its limits, not a precise prediction.

\text{Break-even output} = \frac{\text{Fixed costs}}{\text{Contribution per unit}}

Break-even output

The output at which total contribution exactly covers fixed costs. Here 45,000 / 15 = 3,000 units.

\text{Margin of safety} = \text{Actual output} - \text{Break-even output}

Margin of safety

The cushion of sales before a loss. Here 4,000 - 3,000 = 1,000 units, or 25% of output.

\text{Break-even revenue} = \frac{\text{Fixed costs}}{\text{C/S ratio}}

Break-even revenue

Break-even in sales value. Here 45,000 / 0.30 = 150,000, matching 3,000 units x 50.

Worked example

Break-even, margin of safety and profit

A firm has fixed costs of £45,000, a selling price of £50 and a variable cost of £35 per unit, and plans to make and sell 4,000 units. Calculate the contribution per unit, break-even output, margin of safety and profit, and comment.

Contribution and break-even
Contribution = £50 - £35 = £15 per unit. Break-even = fixed costs / contribution = £45,000 / £15 = 3,000 units (£150,000 of revenue).
Margin of safety
Margin of safety = 4,000 - 3,000 = 1,000 units, which is 1,000 / 4,000 = 25% of planned output.
Profit and comment
Profit = margin of safety x contribution = 1,000 x £15 = £15,000 (check: total contribution 4,000 x £15 = £60,000, less fixed costs £45,000 = £15,000). A 25% margin of safety is a moderate cushion, but the figures assume all 4,000 units sell at £50 - a weaker market would erode it quickly.

Result: Contribution £15, break-even 3,000 units, margin of safety 1,000 units (25%) and profit £15,000 - a moderate cushion that rests on the assumption that all 4,000 units are sold at £50.

Typical mistakes

Dividing fixed costs by the selling price instead of by the contribution per unit when finding break-even.
Presenting break-even as a precise prediction, ignoring that it assumes all output is sold at a constant price and cost.

Active revision

Fixed costs £45,000, selling price £50, variable cost £35 per unit, planned output 4,000 units. Calculate the break-even output, margin of safety and profit, and comment on the risk.

Active recall

Recall the key points — then reveal.

Sources: AQA A-level Accounting 7127 specification (AQA)

Cost-volume-profit and target profit#

AdvancedAQA 7127 3.10

Target-profit output

Fig. 3Cost-volume-profit: fixed costs plus the desired profit, divided by contribution, gives the required output - 5,000 units for a £30,000 target profit.

Cost-volume-profit (CVP) analysis extends break-even to answer 'what output do we need for a given profit?' and 'what happens to profit if price, cost or volume change?'. The key relationship is that the output required to achieve a target profit is the fixed costs plus the target profit, all divided by the contribution per unit - because the contribution must now cover both the fixed costs and the desired profit. With fixed costs of £45,000, a contribution of £15 per unit, and a target profit of £30,000, the required output is (£45,000 + £30,000) / £15 = £75,000 / £15 = 5,000 units, generating revenue of 5,000 x £50 = £250,000. The same logic in revenue terms uses the C/S ratio: required revenue = (fixed costs + target profit) / C/S ratio.

CVP analysis is powerful for 'what-if' planning because it lets a firm see quickly how a proposed change affects the break-even point and the profit. If the selling price rises, the contribution per unit rises, so break-even falls and profit at any given volume rises - but demand may fall, so the volume assumption must be revisited. If fixed costs rise (a bigger factory), break-even rises. If variable costs fall (a cheaper supplier), contribution rises and break-even falls. Managers use CVP to test the profit consequences of pricing decisions, cost changes and investment before committing, which is one of the most practical applications of management accounting.

The margin of safety and the target-profit calculation together let a manager frame a plan in terms of both survival and ambition. Break-even sets the floor (the minimum to avoid a loss); the target-profit output sets the goal (the sales needed to earn the desired return); and the margin of safety measures how much room there is between the expected outcome and the floor. Presenting a plan this way - here, break-even at 3,000 units, a target of 5,000 units for a £30,000 profit, and a margin of safety at the planned 4,000 units of 1,000 units - gives a clear, quantified picture of the risk and the reward.

As with break-even, the value of CVP analysis is inseparable from its assumptions, and evaluation turns on recognising them. It assumes a constant selling price and a constant variable cost per unit at all volumes (ignoring bulk discounts, price elasticity and economies of scale), a clean fixed/variable split, that all output is sold, and, for multi-product firms, a constant sales mix. Over a wide range of output these assumptions break down - fixed costs step up, discounts appear, the mix shifts - so CVP is most reliable over a limited 'relevant range' near current activity. Used within that range and with its assumptions in mind, it is an excellent decision-support tool; pushed beyond it, or treated as exact, it misleads.

\text{Output for target profit} = \frac{\text{Fixed costs} + \text{Target profit}}{\text{Contribution per unit}}

Target-profit output

Contribution must cover both fixed costs and the desired profit. Here (45,000 + 30,000) / 15 = 5,000 units.

\text{Revenue for target profit} = \frac{\text{Fixed costs} + \text{Target profit}}{\text{C/S ratio}}

Target-profit revenue

The same in sales value. Here (45,000 + 30,000) / 0.30 = 250,000, matching 5,000 units x 50.

Worked example

Output for a target profit

With fixed costs of £45,000, a contribution of £15 per unit and a selling price of £50, calculate the output and revenue needed to earn a target profit of £30,000. The firm plans to make 4,000 units - what is its margin of safety against this target?

Target-profit output
Output = (fixed costs + target profit) / contribution = (£45,000 + £30,000) / £15 = £75,000 / £15 = 5,000 units.
Target-profit revenue
Revenue = 5,000 x £50 = £250,000 (check via C/S ratio: £75,000 / 0.30 = £250,000).
Interpret against the plan
To earn £30,000 the firm must sell 5,000 units, but it only plans 4,000, which yields £15,000 profit - so on current plans it falls 1,000 units short of the target and must raise volume, price or contribution to reach it.

Result: 5,000 units (£250,000 of revenue) are needed for a £30,000 profit; the planned 4,000 units fall 1,000 short, earning only £15,000 - so the target requires higher volume or a bigger contribution.

Typical mistakes

Forgetting to add the target profit to fixed costs before dividing by contribution.
Applying CVP far outside the relevant range where its constant-price and constant-cost assumptions fail.

Active revision

Fixed costs £45,000, contribution £15 per unit, selling price £50. Calculate the output and revenue needed for a target profit of £30,000, and the margin of safety if the firm plans 4,000 units.

Active recall

Recall the key points — then reveal.

Sources: AQA A-level Accounting 7127 specification (AQA)

Short-term decision making with marginal costing#

AdvancedAQA 7127 3.10

Limiting-factor decision

Fig. 4When labour is scarce, rank by contribution per labour hour: product A (£10/hr) beats product B (£6/hr) despite B's higher contribution per unit.

In short-term decisions, marginal costing focuses on contribution and on the costs that actually change as a result of the decision (relevant costs), ignoring fixed costs that will be incurred anyway and sunk costs already spent. A special-order decision illustrates the principle: if a firm with spare capacity is offered a one-off order at a price below its normal price, it should accept if the price still exceeds the variable (marginal) cost, because the order then makes a positive contribution to fixed costs that are already covered by normal sales - adding to profit even though the price is below full cost. The relevant comparison is price against variable cost, not price against full cost.

A make-or-buy decision applies the same relevant-cost logic. In deciding whether to make a component in-house or buy it from a supplier, the firm compares the variable cost of making it (plus any fixed costs that would actually be avoided or incurred by the decision) with the bought-in price. Fixed overheads that will be incurred regardless are irrelevant to the comparison. If making it costs less in relevant terms, and capacity is available, the firm makes; otherwise it buys - subject always to qualitative factors such as the reliability and quality of the supplier and the risk of depending on an outside source.

The limiting-factor (key-factor) decision is the most important marginal-costing application and a frequent exam task. When a scarce resource - labour hours, machine hours, materials - limits how much a firm can produce, and it makes several products, it should allocate the scarce resource to the products that earn the most contribution per unit of that limiting factor, not the most contribution per unit of product. The procedure is: calculate each product's contribution per unit, divide by the amount of the limiting factor each unit uses to get contribution per unit of limiting factor, rank the products by that figure, and allocate the scarce resource to the highest-ranked first. This maximises total contribution and therefore profit from the constrained resource.

A worked ranking shows why the per-unit-of-product figure can mislead. Suppose product A earns £20 contribution and uses 2 labour hours (£10 per hour), while product B earns £24 contribution and uses 4 labour hours (£6 per hour), and labour is the limiting factor. Product B has the higher contribution per unit, but product A earns more per scarce labour hour, so when labour is the constraint the firm should make product A first - it wrings more contribution from each precious hour. Marginal costing thus gives a clear, correct answer to constrained-resource decisions, but the numbers must always be tempered by qualitative and longer-term factors: the effect on customers if a product is dropped, contractual commitments, and the fact that a resource shortage may be temporary.

\text{Contribution per unit of limiting factor} = \frac{\text{Contribution per unit}}{\text{Limiting factor used per unit}}

Limiting-factor ranking

Rank products by this figure and allocate the scarce resource to the highest first, to maximise total contribution.

Worked example

Allocating a scarce resource

A firm makes two products. Product A earns £20 contribution per unit and uses 2 labour hours; product B earns £24 per unit and uses 4 labour hours. Only 4,000 labour hours are available and both products can be sold in any quantity. Decide how to use the labour and the maximum contribution.

Contribution per labour hour
Product A: £20 / 2 = £10 per labour hour. Product B: £24 / 4 = £6 per labour hour. Although B has the higher contribution per unit, A earns more per scarce hour.
Rank and allocate
Rank A first (£10/hr) and B second (£6/hr). With labour the binding constraint and both products sellable, devote all 4,000 hours to product A: 4,000 / 2 = 2,000 units of A.
Maximum contribution and caveat
Maximum contribution = 2,000 units x £20 = £40,000 (versus 1,000 units of B x £24 = £24,000). But the firm should check qualitative factors - whether dropping B loses customers or breaches commitments - before abandoning B entirely.

Result: Make product A (higher contribution per scarce labour hour): 2,000 units for £40,000 of contribution, well above the £24,000 from B - subject to checking the effect of dropping product B on customers and commitments.

Typical mistakes

Ranking products by contribution per unit rather than per unit of the limiting factor.
Including irrelevant fixed or sunk costs in a special-order or make-or-buy decision.

Active revision

Product A earns £20 contribution using 2 labour hours; product B earns £24 using 4 labour hours. Labour is limited to 4,000 hours. Determine which product to make and the maximum contribution, and note one qualitative factor.

Active recall

Recall the key points — then reveal.

Sources: AQA A-level Accounting 7127 specification (AQA) · Ofqual - GCE AS and A level qualifications (Ofqual)

References & sources

Sources

AQA

AQA A-level Accounting 7127 specification

Ofqual

Ofqual - GCE AS and A level qualifications

Marginal costing

4 sections~19 min reading time3 competenciesLevel Standard 1 · Advanced 3

Marginal costing

Key points

Contribution and profit

Key points

Break-even, margin of safety and profit

Key points

Output for a target profit

Key points

Allocating a scarce resource

Sources

Marginal costing

Key points

Contribution and profit

Key points

Break-even, margin of safety and profit

Key points

Output for a target profit

Key points

Allocating a scarce resource

Sources