Calculate the break-even point in units and sales revenue from fixed costs, price and variable cost, plus the volume needed for a target profit.
업데이트 검증한 예제: 4
Each unit contributes $10.00 toward fixed costs, so you need 5,000 units ($125,000.00 of sales) before the business makes a profit.
| Volume vs break-even | 단위 | Revenue | Total cost | Profit |
|---|---|---|---|---|
| 50% | 2,500 | $62,500.00 | $87,500.00 | −$25,000.00 |
| 75% | 3,750 | $93,750.00 | $106,250.00 | −$12,500.00 |
| 100% | 5,000 | $125,000.00 | $125,000.00 | $0.00 |
| 125% | 6,250 | $156,250.00 | $143,750.00 | $12,500.00 |
| 150% | 7,500 | $187,500.00 | $162,500.00 | $25,000.00 |
| 200% | 10,000 | $250,000.00 | $200,000.00 | $50,000.00 |
Rounded up to whole units: selling one unit fewer would leave a loss.
The break-even point is the sales volume at which revenue equals total cost. Each unit sold contributes its price minus its variable cost, the contribution margin, toward fixed costs, so the break-even volume is Q = F ÷ (p − v). Break-even revenue is the fixed costs divided by the contribution margin ratio, (p − v) ÷ p.
With the defaults, fixed costs of 50,000, a price of 25 and a variable cost of 15 per unit, each unit contributes 10, a 40% margin ratio. Break-even comes at 5,000 units, or 125,000 of revenue, and a target profit of 20,000 would take 7,000 units.
The model is linear: price and variable cost per unit stay constant, and fixed costs do not step up as volume grows. Break-even units are rounded up, because one unit fewer would leave a small loss.
검증 출처: Python decimal: 50000 / (25 − 15) = 5000 units; 5000 × 25 = 125000
검증 출처: Python decimal: 10000 / 3 = 3333.33…, ceiling 3334; revenue 10000 / (3/7) = 23333.33
검증 출처: Python decimal: 0 / 4.5 = 0 — every unit sold is profit from the first
검증 출처: Python decimal: (50000 + 20000) / 10 = 7000 units; × 25 = 175000
Divide fixed costs by the contribution margin per unit, price minus variable cost. With fixed costs of 50,000, a price of 25 and a variable cost of 15, break-even is 50,000 ÷ 10 = 5,000 units. When the division is not whole, round up: 10,000 ÷ (7 − 4) = 3,333.33, so 3,334 units are needed.
The contribution margin is what each sale leaves after its variable costs, available to cover fixed costs and then profit: price − variable cost per unit. At a price of 25 and a variable cost of 15 it is 10 a unit. As a share of price, the contribution margin ratio, it is 10 ÷ 25 = 40%.
Divide fixed costs by the contribution margin ratio. With 50,000 of fixed costs and a 40% ratio, break-even revenue is 50,000 ÷ 0.40 = 125,000, the same as 5,000 units × 25. The revenue form is useful when a business sells many products with a similar margin ratio.
Add the target profit to the fixed costs and divide by the contribution margin: (F + target) ÷ (p − v). Earning 20,000 on top of 50,000 of fixed costs at a margin of 10 a unit takes 70,000 ÷ 10 = 7,000 units, or 175,000 of revenue at a price of 25.
A small price change moves break-even a lot, because it changes the margin on every unit. With 50,000 of fixed costs and a variable cost of 15, raising the price from 25 to 27 lifts the margin from 10 to 12 and cuts break-even from 5,000 to 4,167 units; cutting the price to 23 raises it to 6,250 units.
정확도는 입력값과 계산 방법의 가정에 따라 달라집니다. 십진 연산은 유효숫자 50자리를 사용하지만, 추정값·수치해석 방법·원본 데이터의 정밀도는 더 낮을 수 있습니다. 표시값을 반올림해도 이러한 한계는 사라지지 않습니다. 독립적인 출처의 풀이와 대조한 계산 예시: 4. 예를 들어 “Fixed 50,000, price 25, variable cost 15”은 Python decimal: 50000 / (25 − 15) = 5000 units; 5000 × 25 = 125000와 대조해 확인합니다.
Corporate Finance Institute — Break-even analysis; Horngren, Datar & Rajan — Cost Accounting: A Managerial Emphasis, ch. 3 (cost-volume-profit analysis).
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이 계산기에는 독립적인 출처에서 답을 얻은 계산 예제가 4개 있습니다. 테스트 모음에서 실행되며 여기에서도 실행할 수 있습니다.
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