Break-even is the sales volume at which the model’s total revenue equals its total cost. The business has covered those included costs but has made neither a profit nor a loss. The calculation connects a fixed cost for a period with the amount each sold unit contributes after its variable cost.
All workshops and figures below are fictional classroom models, not forecasts or investment advice. One product is made and sold in whole units. Output equals sales, there is no opening or closing finished stock, and no tax or finance costs are included. State these assumptions before using the result.
Separate total fixed cost from variable cost per unit
In this model, fixed cost stays unchanged across the stated output range during one month. Variable cost per unit stays constant, so total variable cost rises with the number made and sold. “Fixed” does not mean a cost can never change; it means the amount is fixed within this period and relevant range.
Let q be units sold in the month. Total revenue = selling price per unit × q. Total cost = monthly fixed cost + variable cost per unit × q. Contribution per unit = selling price per unit − variable cost per unit. Profit in the model = total contribution − fixed cost.
When contribution per unit is positive, the equality point is fixed cost ÷ contribution per unit. This denominator is not the selling price alone. Each sale must first cover its variable cost before the remaining amount can contribute towards fixed cost and, after that, profit.
Worked case 1: a paper-folder workshop
Plainfold makes paper folders. Monthly fixed cost is KSh 8,400, the selling price is KSh 180 per folder and variable cost is KSh 110 per folder. These amounts stay constant from zero to 240 folders per month, the stated relevant range. Every produced folder is assumed sold at the stated price.
Contribution per folder = 180 − 110 = KSh 70. Break-even quantity = 8,400 ÷ 70 = 120 folders. At 120 folders, revenue is 120 × 180 = KSh 21,600. Total cost is 8,400 + (120 × 110) = KSh 21,600. Equality is checked using the full totals, not just the formula.
| Folders made and sold | Fixed cost (KSh) | Variable cost (KSh) | Total cost (KSh) | Revenue (KSh) | Profit or loss (KSh) |
|---|---|---|---|---|---|
| 0 | 8,400 | 0 | 8,400 | 0 | −8,400 |
| 40 | 8,400 | 4,400 | 12,800 | 7,200 | −5,600 |
| 80 | 8,400 | 8,800 | 17,200 | 14,400 | −2,800 |
| 120 | 8,400 | 13,200 | 21,600 | 21,600 | 0 |
| 160 | 8,400 | 17,600 | 26,000 | 28,800 | 2,800 |
| 200 | 8,400 | 22,000 | 30,400 | 36,000 | 5,600 |
| 240 | 8,400 | 26,400 | 34,800 | 43,200 | 8,400 |
The horizontal axis shows folders made and sold per month; the vertical axis shows KSh per month. Revenue begins at zero and rises by KSh 180 per folder. Total cost begins at KSh 8,400 and rises by KSh 110 per folder. The lines cross at 120 folders and KSh 21,600. To the left, cost exceeds revenue; to the right, revenue exceeds cost within the stated range.
The graph joins the values with straight lines to show the model. Actual sales in this case are whole folders. At 119 folders, contribution is KSh 8,330 and the loss is KSh 70; at 121 folders, contribution is KSh 8,470 and the profit is KSh 70. The table’s forty-unit spacing does not mean only multiples of forty are possible.
Worked case 2: a fractional equality point
A second workshop makes card wallets. Its monthly fixed cost is KSh 6,500, price KSh 150 per wallet and variable cost KSh 95 per wallet. The assumptions hold from zero to 180 whole wallets sold per month.
Contribution is 150 − 95 = KSh 55. The algebraic equality point is 6,500 ÷ 55 = 118.1818… wallets. A fraction of a wallet cannot be sold in this case. The smallest whole-unit sales quantity that avoids a loss is therefore 119, not 118.
- At 118: revenue = KSh 17,700; total cost = 6,500 + 11,210 = KSh 17,710; loss = KSh 10.
- At 119: revenue = KSh 17,850; total cost = 6,500 + 11,305 = KSh 17,805; profit = KSh 45.
Rounding up identifies a feasible no-loss threshold, not exact equality. There is no whole number of wallets at which this particular model gives exactly zero profit. Ordinary rounding to the nearest whole number would give 118 and leave a loss, so it does not answer the question.
Worked case 3: non-positive contribution
A third workshop has monthly fixed cost of KSh 2,400, a selling price of KSh 90 per item and variable cost of KSh 95 per item. Contribution is −KSh 5. Its model profit is −5q − 2,400, which is negative for every non-negative sales quantity.
Dividing 2,400 by −5 produces −480, but a negative sales quantity is not a feasible break-even point. Each additional sale increases the loss by KSh 5 under these assumptions. At zero sales the loss is KSh 2,400; at 100 sales it is KSh 2,900.
If the selling price instead equalled the variable cost, contribution would be zero. With positive fixed cost of KSh 2,400, sales would make no contribution towards that fixed amount. There would still be no break-even volume. Division by zero is undefined; it must not be reported as zero units.
Test an assumption change
Return to Plainfold. Suppose variable cost rises to KSh 120 per folder while fixed cost remains KSh 8,400 and price remains KSh 180. New contribution is KSh 60 and break-even is 8,400 ÷ 60 = 140 folders. At 140, both revenue and total cost are KSh 25,200.
The threshold rises by twenty folders. That shows the effect of the stated cost change with everything else held constant. It does not establish that customers will buy 140 folders, or that a price increase would leave demand unchanged. A calculated threshold is a requirement within the model, not evidence that the required sales will happen.
Three solved practice tasks
Task 1: calculate a below-threshold result
Using Plainfold’s original figures, find the result at 100 folders.
Solution: Revenue is 100 × 180 = KSh 18,000. Cost is 8,400 + 100 × 110 = KSh 19,400. The loss is KSh 1,400. Alternatively, contribution is KSh 7,000, which is KSh 1,400 below fixed cost.
Task 2: increase fixed cost only
Fixed cost becomes KSh 9,800 while the original price and variable cost remain KSh 180 and KSh 110. Find and check break-even.
Solution: Contribution remains KSh 70. Break-even is 9,800 ÷ 70 = 140 folders. Revenue is KSh 25,200 and cost is 9,800 + 15,400 = KSh 25,200.
Task 3: test the relevant range
Suppose Plainfold’s original costs apply only up to a maximum of 100 folders monthly. Does the calculated 120-folder threshold show achievable break-even?
Solution: No. The threshold lies outside the stated capacity and relevant range. At the maximum of 100, the model still shows a KSh 1,400 loss. Extending the straight lines does not prove that the same costs apply beyond capacity.
Limitations that belong with the answer
This model assumes a single product, constant unit price and variable cost, fixed cost unchanged within the relevant range, and output equal to sales. It omits timing of receipts and payments, uncertain demand and costs outside its defined scope. Break-even therefore does not prove cash availability, long-term viability or suitability for investment. Changing the assumptions requires a fresh calculation.
Frequently asked questions
What is contribution?
Selling price minus variable cost per unit. Total contribution helps cover fixed cost before producing model profit.
Is contribution per unit the same as profit per unit?
No. Fixed cost still needs to be covered.
Why does the total-cost line start above zero?
Fixed cost is incurred in this model even when no units are made or sold.
When should I round up?
When a fractional threshold must be converted into the minimum whole-unit quantity that avoids a loss.
What happens with zero contribution?
With positive fixed cost, no sales volume can cover it under the unchanged model.
Can break-even predict demand?
No. It calculates required volume; it does not establish how many customers will buy.
Can monthly costs be mixed with annual sales?
No. Use one consistent period for revenue, variable cost and fixed cost before comparing them.
Reference
The basic single-product contribution formula is described by the U.S. Small Business Administration break-even guide. All figures, checks and the graph here are original.
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