Calculate the sales at which profit is exactly zero (the break-even point) from sales and costs. The key is to split costs into variable costs, which grow in proportion to sales, and fixed costs, which stay the same regardless of sales. You can also check the sales needed for a target profit and see the profit and loss regions on a break-even chart.
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Result
Break-even sales = fixed costs ÷ contribution margin ratio
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Profit = sales − variable costs − fixed costs
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Variable cost ratio = variable costs ÷ sales
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Contribution margin ratio = 1 − variable cost ratio
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Break-even ratio = break-even sales ÷ sales
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Margin of safety ratio = 1 − break-even ratio
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Sales needed for the target profit = (fixed costs + target profit) ÷ contribution margin ratio
The calculation uses a simple model in which the variable cost ratio and fixed costs stay constant regardless of sales. The quantity is rounded up to a whole unit.
See it as a graph
Other inputs stay at their current values while the chosen input varies from 1/4 to 4 times its current value. The red dot is the current value.
What is the break-even point?
The break-even point is the level of sales at which sales and costs are exactly equal and profit is zero. Above it the business makes a profit; below it, a loss. Costs are split into variable costs, such as materials and purchased goods, which rise in proportion to sales, and fixed costs, such as rent and salaries, which stay the same regardless of sales. In the example “Sales 1,000, variable costs 600, fixed costs 300”, 60% of sales goes to variable costs, so covering the fixed costs of 300 with the remaining 40% (the contribution margin) needs sales of 300 ÷ 0.4 = 750.
Contribution margin and margin of safety
Sales minus variable costs is the contribution margin (marginal profit), and its share of sales is the contribution margin ratio. Each extra unit of sales raises profit by the contribution margin ratio. Break-even sales are fixed costs ÷ contribution margin ratio. The margin of safety ratio shows how far current sales are above the break-even point: (sales − break-even sales) ÷ sales. In the example it is (1000 − 750) ÷ 1000 = 25%, so sales can fall by 25% before the business makes a loss.
Target profit and quantity
The sales needed for a target profit come from covering the fixed costs plus the target profit with the contribution margin: (fixed costs + target profit) ÷ contribution margin ratio. When the unit price and variable cost per unit are known, each unit sold earns a contribution margin of unit price − variable cost per unit, so the break-even quantity is fixed costs ÷ contribution margin per unit. In the example “Find the quantity from a product's unit price”, ¥1.5 million in fixed costs ÷ (¥2,500 − ¥1,500) = 1,500 units.
Lowering the break-even point
Lowering the break-even point lets a business make a profit on smaller sales and makes it more resilient in a downturn. The ways to do it are to cut fixed costs or to lower the variable cost ratio (raise the contribution margin ratio), for example by leasing equipment, negotiating lower material prices or raising prices. Automating a factory lowers the variable cost ratio but raises fixed costs, so the decision depends on the expected sales.
The variable cost ratio is 20 ÷ 50 = 0.4, so the contribution margin ratio, the part of sales available to cover fixed costs, is 1 − 0.4 = 0.6. Break-even sales are the sales at which the contribution margin exactly covers the fixed costs, so 24 ÷ 0.6 = ¥40 million. The current sales of ¥50 million are above the break-even point, and the profit is 50 − 20 − 24 = ¥6 million.
The contribution margin ratio is 1 − 0.7 = 0.3, so break-even sales are 45 ÷ 0.3 = ¥150 million. The margin of safety ratio expresses how far current sales exceed the break-even point as a share of sales: (200 − 150) ÷ 200 = 25%. It means the company does not fall into a loss until sales drop by 25%, and the larger it is, the more resistant the company is to falling sales. Break-even sales ÷ sales = 75% is the break-even ratio, and the two add up to 100%.
The contribution margin, sales minus variable costs, must cover both the fixed costs and the target profit. The contribution margin ratio is 1 − 0.6 = 0.4, so the required sales are (30 + 10) ÷ 0.4 = ¥100 million. As a check, with sales of ¥100 million the variable costs are ¥60 million, so the profit is 100 − 60 − 30 = ¥10 million.
Each chip sold earns a contribution margin of 4,000 − 2,400 = ¥1,600. To cover the fixed costs of ¥800 million with this margin, 800 million ÷ 1,600 = 500,000 units must be sold, and the sales at that point (the break-even sales) are 500,000 × 4,000 = ¥2 billion. In general, the more advanced the process, the larger the fixed costs for masks and design, so a product with a small sales volume may never reach its break-even point.
If sales are S (in ¥ million), operating profit is S − 0.4S − 27 = 0.6S − 27, and this must equal 0.15S, so 0.45S = 27 and S = ¥60 million. In other words, of the contribution margin ratio of 0.6, 0.15 is kept as profit and the remaining 0.45 covers the fixed costs. As a check, at sales of ¥60 million operating profit is 36 − 27 = ¥9 million, and 9 ÷ 60 = 15%.
If sales are S (in ¥ million), the profit of plan A is 0.4S − 10 and that of plan B is 0.55S − 16. They are equal when 0.15S = 6, that is, S = ¥40 million (both profits are then ¥6 million). Above this, plan B, with its higher contribution margin ratio, increases profit faster and is better; below it, plan A, with its lower fixed costs, is better. An investment such as automation that raises fixed costs to lower the variable cost ratio pays off when sufficient sales can be expected.
FAQ
How do I split variable and fixed costs?
By whether a cost rises in proportion to sales (or production). Materials, cost of goods purchased, sales commissions and outsourcing are usually treated as variable costs; rent, depreciation, salaried staff and insurance as fixed costs. In practice some costs, such as electricity, have both characteristics.
How are the break-even ratio and the margin of safety related?
The break-even ratio is break-even sales ÷ sales, and the margin of safety ratio is 1 − the break-even ratio, so the two add up to 100%. A lower break-even ratio (higher margin of safety) means the business is better able to withstand a fall in sales.
What is shown for a loss-making business?
Profit is negative, the break-even ratio exceeds 100% and the margin of safety is negative. You can see how much sales must grow to reach the break-even point.
How does this appear on exams?
The strategy area of IT certification exams such as Japan's Fundamental Information Technology Engineer Examination and IT Passport often asks for break-even sales from sales, variable costs and fixed costs, or for the sales or quantity needed to reach a target profit.