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.
Cập nhật Ví dụ đã kiểm tra: 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 | Đơn vị | 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.
Nguồn đối chiếu: Python decimal: 50000 / (25 − 15) = 5000 units; 5000 × 25 = 125000
Nguồn đối chiếu: Python decimal: 10000 / 3 = 3333.33…, ceiling 3334; revenue 10000 / (3/7) = 23333.33
Nguồn đối chiếu: Python decimal: 0 / 4.5 = 0 — every unit sold is profit from the first
Nguồn đối chiếu: 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.
Độ chính xác phụ thuộc vào dữ liệu nhập và giả định của phương pháp. Phép tính thập phân dùng 50 chữ số có nghĩa, nhưng ước lượng, phương pháp số và dữ liệu nguồn có thể kém chính xác hơn; làm tròn khi hiển thị không loại bỏ các giới hạn đó. Ví dụ có lời giải đã đối chiếu với nguồn độc lập: 4. Ví dụ, “Fixed 50,000, price 25, variable cost 15” được kiểm tra bằng Python decimal: 50000 / (25 − 15) = 5000 units; 5000 × 25 = 125000.
Corporate Finance Institute — Break-even analysis; Horngren, Datar & Rajan — Cost Accounting: A Managerial Emphasis, ch. 3 (cost-volume-profit analysis).
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