Contribution margin

Definition and units

Contribution margin is revenue less variable costs. It covers fixed costs before producing operating profit. State the period, scope and currency. OpenStax, Managerial Accounting, §3.1

For one constrained machine in the capacity example, A contributes $40 per unit and needs two hours. B contributes $15 and needs half an hour. B ranks first at $30 per bottleneck hour versus A at $20. This ordering assumes one binding resource, the stated demand limits and no minimum orders.

Let p be selling price per unit, v variable cost per unit, q units sold, and F total fixed operating costs for the same period:

For a single product with positive sales, the ratio is also (p − v) ÷ p. It uses sales as the denominator, not variable cost. A percentage without its denominator is ambiguous; it could otherwise be mistaken for a markup. OpenStax, §3.1

Classify costs by behavior

Contribution analysis separates variable and fixed costs rather than manufacturing and non-manufacturing costs. Variable selling costs, such as sales commissions, belong above contribution alongside variable production costs. Fixed manufacturing and fixed selling/administrative costs are deducted afterward. Gross margin instead deducts cost of goods sold from revenue, before selling and administrative expenses. The two subtotals answer different questions. Penn State, contribution margin versus gross margin

Cost behavior must be assessed over a stated activity range and time horizon. A fixed total can remain unchanged while its cost per unit falls as volume rises; that does not make it variable. Mixed costs need separation into their fixed and variable portions, and step costs can change when another crew, shift or machine becomes necessary. Do not classify a whole account solely from its name or assume all labour is variable. OpenStax, cost-behavior patterns, §2.2

Reconciled example: contribution versus gross margin

Original illustrative assumptions: one product, one month, USD, 1,000 units produced and sold, no inventory changes, and no interest or income tax. Selling price is $100/unit; variable manufacturing cost is $50/unit and variable selling cost $10/unit. Fixed manufacturing cost is $20,000/month; fixed selling/administrative cost is $10,000/month. All costs are included once.

Unit contribution is $40, its ratio is 40%, and gross margin is 30% of sales. Both formats reconcile to $100,000 revenue less $90,000 costs. The difference is classification, under the explicit no-inventory-change assumption. Do not generalize the reconciliation to a situation where a change in inventory defers fixed manufacturing costs under absorption costing. Penn State, income-statement formats

With these unchanged assumptions, break-even volume is $30,000 ÷ $40 = 750 units, equivalent to $75,000 sales. At 1,000 units, the extra 250 units generate $10,000 above fixed costs. This is a model result, not a sales forecast. ACCA's CVP treatment requires constant unit selling price and variable cost, fixed costs within the relevant range, and a constant mix for multiple products. Recalculate when those assumptions change. ACCA, cost-volume-profit analysis

Sales mix: weight the ratio correctly

For several products, calculate the overall ratio from total contribution divided by total sales. A simple average of product percentages ignores their different sales weights. A unit mix and a revenue mix are also different descriptions; identify which one the model holds constant. Multi-product break-even analysis depends on the assumed mix remaining stable. OpenStax, multi-product CVP, §3.4

Separate illustrative mix case, with prices and costs fixed:

The overall ratio is $9,500 ÷ $25,000 = 38%, not the simple average of A's 40% and B's 30%, which is 35%. At $7,600 fixed costs, this mix gives $1,900 operating profit and a modeled break-even sales value of $7,600 ÷ 38% = $20,000. The figures reconcile: $25,000 − $15,500 variable costs − $7,600 fixed costs = $1,900. A shift toward B changes the ratio and break-even sales value.

Constrained resource: rank contribution per bottleneck unit

Where one resource is binding and fixed costs are unchanged, rank products by unit contribution divided by scarce-resource usage per unit, subject to demand and commitments. Ranking by contribution per product unit can waste capacity. ACCA also distinguishes this approach from throughput accounting, which uses a different cost convention. Do not substitute selling price less direct materials for contribution without changing the model explicitly. ACCA, Performance Management examiner's report, March 2019, pp. 10–11

Separate capacity example: retain A's $40 and B's $15 unit contributions, but assume A needs two bottleneck hours and B half an hour. A contributes $20/hour; B contributes $30/hour. With 100 hours available, maximum demand of 120 B units, sufficient A demand and no minimum orders, make 120 B first: 60 hours and $1,800 contribution. The remaining 40 hours make 20 A and $800 contribution. Total contribution is $2,600, using all 100 hours. Making only 50 A would contribute $2,000. The $600 improvement depends on the stated constraints, not on B having a higher unit margin.

Multiple binding resources, indivisible batches, setup changes or customer commitments require additional modeling; the simple one-resource ranking is insufficient.

Decision boundaries

For an incremental order or product-line decision, identify changes in cash flows and any contribution displaced elsewhere. Fixed costs can be relevant when the decision changes them; allocated costs that remain regardless of the decision are not savings. Positive contribution alone is not a complete acceptance rule when capacity has another use or a new commitment is required. ACCA, relevant costs

Related references

• Cost structure and cost bases
• Break-even quantity
• Actual costing