Calculate and interpret break-even
Calculate contribution, break-even output, margin of safety and profit, and interpret the limits of numerical and graphical analysis.
Section 5.4 · Costs
Cambridge International AS & A Level Business 9609, 2026–2028 syllabus and 2029 syllabus, section 5.4.4. Cambridge states that both current versions have no significant changes affecting teaching. This lesson maps only its named section; other sections and full paper practice remain separate. Written practice is self-checked
Before you begin
- No previous business course is assumed. Use the lesson's definitions before applying them to the business context.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What is unit contribution?
What you will learn
- Calculate unit contribution and break-even output
- Calculate margin of safety and profit
- Interpret a break-even chart and its assumptions
Break-even links costs, price and output
Contribution per unit = selling price−variable cost per unit. Break-even output = fixed costs ÷ contribution per unit. At break-even, total revenue equals total costs and profit is zero under the model.
Margin of safety = actual or budgeted output−break-even output. Profit = total contribution−fixed costs, or contribution per unit × output−fixed costs. State whether output is in units or revenue and use a consistent period.
Charts and assumptions limit the result
On a simple break-even chart, total revenue starts at zero and rises with output at a constant selling price; total cost starts at fixed costs and rises with variable costs. Their intersection is break-even; the distance between actual output and break-even represents margin of safety.
The model assumes costs, price and output relationships stay stable over a relevant range, and often assumes all units made are sold. Product mix, price changes, capacity limits, quality, demand uncertainty and step-fixed costs can make real outcomes differ. Break-even supports judgement; it does not predict success with certainty.
Pause and explain
Fixed costs are $9,000 and contribution is $15 per unit. What is break-even output?
Worked example
Fixed costs are $12,000, selling price is $30 and variable cost is $18 per unit. Calculate contribution per unit, break-even output and profit at 1,250 units.
Show the worked solution
- Contribution per unit = 30−18=$12.
- Break-even output = 12,000÷12.
- Profit at 1,250 units = 1,250×12−12,000.
Answer Contribution is $12 per unit. Break-even output is 1,000 units. At 1,250 units, profit is $15,000−$12,000=$3,000, assuming the stated linear model and that all units are sold.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
A product sells for $45, variable cost is $30 and fixed costs are $21,000. Calculate contribution, break-even output and margin of safety if expected sales are 1,800 units.
Give me a hint
Find unit contribution first, then break-even and subtract it from expected output.
Compare my reasoning
- Contribution per unit = 45−30=$15.
- Break-even = 21,000÷15.
- Margin of safety = 1,800−break-even output.
Contribution is $15 per unit. Break-even output is 1,400 units. Margin of safety is 1,800−1,400=400 units.
Look for these in your work
- Contribution is correct
- Break-even output is correct
- Margin is calculated using expected minus break-even output
Using the same product, calculate profit at 1,800 units and state one assumption behind the calculation.
Give me a hint
Multiply unit contribution by output and subtract fixed costs.
Compare my reasoning
- Total contribution = 15×1,800.
- Profit = total contribution−21,000.
- Assume all 1,800 units are sold at the stated price and costs remain stable.
Total contribution is $27,000, so profit is $27,000−$21,000=$6,000. This assumes the units are sold, price and variable cost remain constant and fixed costs do not change over the relevant range.
Look for these in your work
- Profit calculation is correct
- Contribution and fixed costs are distinguished
- A model assumption is stated
A break-even chart shows total revenue crossing total cost at 2,000 units. The business expects to sell 1,700 units. Interpret its position and give one reason the chart could misstate risk.
Give me a hint
Compare expected output with break-even and consider whether assumptions hold.
Compare my reasoning
- Expected sales are 300 units below break-even.
- Under the model this indicates a loss at 1,700 units.
- Demand, selling price or costs may vary from the chart's assumptions.
Expected sales are 300 units below break-even, so the chart implies a loss if its assumptions hold. The risk may be misstated if price, variable cost or demand changes, or if capacity and product mix do not match the linear model.
Look for these in your work
- Position relative to break-even is correct
- Implication is conditional
- A material model limitation is named
Common mistakes
- Dividing fixed cost by selling price instead of contribution
- Confusing margin of safety with break-even output
- Treating break-even as a sales forecast or guarantee
What can you explain now?
What is unit contribution?
Compare with the explanation
Selling price minus variable cost per unit
It is the amount per unit available to cover fixed costs and profit.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
How do contribution, break-even output, margin of safety and profit relate, and what assumptions sit behind a break-even chart?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.