The idea in one paragraph
Some costs change with how much you sell, such as materials and sales commissions. These are variable costs. Others stay the same whatever you sell, such as rent and salaries. These are fixed costs. Each unit sold brings in its price and uses up its variable cost, leaving a contribution towards covering fixed costs. Once total contribution equals fixed costs, you break even. Every unit after that adds to profit.
That chain of thought produces every formula in this topic. If you remember the logic, you can rebuild the formulas under exam pressure.
The core formulas
| Measure | Formula | Meaning |
|---|---|---|
| Contribution margin per unit | Price minus variable cost per unit | What each unit contributes to fixed costs and profit |
| Contribution margin ratio | Contribution margin divided by price | The share of each sales dollar that contributes |
| Break-even in units | Fixed costs divided by contribution margin per unit | Units to cover all costs |
| Break-even in revenue | Fixed costs divided by contribution margin ratio | Sales dollars to cover all costs |
| Units for a target profit | (Fixed costs plus target profit) divided by contribution margin per unit | Volume needed for the desired profit |
| Margin of safety | (Expected sales minus break-even sales) divided by expected sales | How far sales can fall before a loss |
| Degree of operating leverage | Total contribution margin divided by operating profit | How strongly profit responds to a change in sales |
A worked example
Single product (hypothetical)
A company sells a product for $40. Variable cost is $24 per unit. Fixed costs are $60,000 a year.
- Contribution margin: 40 minus 24 is $16 per unit. The ratio is 16 divided by 40, which is 40 percent.
- Break-even units: 60,000 divided by 16 is 3,750 units.
- Break-even revenue: 3,750 times $40 is $150,000. Check with the ratio: 60,000 divided by 0.40 is also $150,000.
- Target profit of $20,000: (60,000 plus 20,000) divided by 16 is 5,000 units, or $200,000 of sales.
- Margin of safety if expected sales are 5,000 units: (5,000 minus 3,750) divided by 5,000 is 25 percent.
- Operating leverage: total contribution at 5,000 units is $80,000 and profit is $20,000, so leverage is 4.0. A 10 percent increase in sales to 5,500 units gives contribution of $88,000 and profit of $28,000, which is 40 percent higher.
Show each formula and substitution in your answer, then state the result in words, such as the company must sell 3,750 units a year to cover its costs.
What-if analysis: price, cost and volume changes
CVP is most useful for testing decisions. Change one input at a time and recalculate the break-even point.
| Scenario (from the example) | New contribution per unit | New break-even units | Change |
|---|---|---|---|
| Base case | $16 | 3,750 | |
| Raise price to $42 | $18 | 3,334 | About 416 fewer units needed |
| Variable cost rises to $26 | $14 | 4,286 | About 536 more units needed |
| Fixed costs rise 10 percent to $66,000 | $16 | 4,125 | 375 more units needed |
| Price falls to $38 | $14 | 4,286 | About 536 more units needed |
This shows why small changes in price matter. A $2 price rise moves the contribution by 12.5 percent, and break-even falls by about 11 percent. Comment on the practical limit too: a higher price may reduce volume, so the real test is whether the lower break-even is reached with the new demand.
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Get an instant quoteMore than one product
With several products, break-even depends on the sales mix. The usual method assumes a fixed mix and treats each bundle of products as one unit.
Two products (hypothetical)
Fixed costs are $120,000. Product A sells for $20 with variable cost $12, so contribution is $8. Product B sells for $50 with variable cost $30, so contribution is $20. The expected mix is 3 units of A for every 1 of B.
- Contribution per bundle (3 A plus 1 B): 3 times 8 plus 20 is $44.
- Bundles to break even: 120,000 divided by 44 is 2,727.3, so 2,728 bundles.
- Units: product A, 3 times 2,728 is 8,184; product B, 2,728.
If the mix shifts toward the lower-contribution product, break-even rises. Mention that when you discuss risks, because mix is one of the assumptions most likely to be wrong.
Practice problem with solution
A product sells for $25 with a variable cost of $15 a unit. Fixed costs are $45,000 a year. Find the break-even point, the volume for a $15,000 profit, the margin of safety at that volume, and the effect of a 10 percent rise in variable cost.
Solution
- Contribution margin: 25 - 15 = $10 a unit, a ratio of 40 percent.
- Break-even: 45,000 / 10 = 4,500 units, or 4,500 x 25 = $112,500 of sales.
- Target profit of $15,000: (45,000 + 15,000) / 10 = 6,000 units.
- Margin of safety at 6,000 units: (6,000 - 4,500) / 6,000 = 25 percent.
- Variable cost up 10 percent: new variable cost is 16.50, so contribution is 8.50. Break-even rises to 45,000 / 8.50 = 5,294.1, which rounds up to 5,295 units, about 18 percent more than before. A cost rise of 10 percent has a much larger effect on break-even because it takes 15 percent of the contribution margin.
Assumptions and limits to mention
| Assumption | Why it may not hold |
|---|---|
| Costs separate cleanly into fixed and variable | Many costs are mixed or step costs, such as supervisors who are needed once volume passes a threshold |
| Price and variable cost per unit are constant | Discounts for volume, supplier price changes and overtime change them |
| Linear relationship within a relevant range | Outside the normal range of activity, the behavior of costs changes |
| Sales mix stays constant | Customers buy different products over time |
| Production equals sales | Inventory changes shift costs between periods |
A short paragraph on assumptions shows you know that CVP is a planning tool and not a forecast. Referring to the relevant range, in particular, is something markers often look for.
Present the analysis clearly
A CVP assignment usually asks for numbers and sometimes a graph. A break-even chart plots total revenue and total cost against volume. Total cost starts at the fixed cost line and rises with volume. The lines cross at break-even. The gap to the left is a loss and to the right is profit. Label axes, mark the break-even point and shade the margin of safety if requested.
In Excel you can build this quickly with a column of volumes, formulas for revenue, variable cost, fixed cost and profit, and a scatter chart with lines. See our guide on Excel formulas for business students. Include a short written recommendation, for example: break-even is achievable within nine months at forecast sales, but the margin of safety of 12 percent is thin if a competitor cuts price.
- Separate fixed and variable costs first Everything depends on classifying costs correctly.
- Show every formula and substitution Marks are for method as well as the answer.
- Round sensibly Round break-even units up to the next whole unit, because you cannot sell part of one.
- Test one change at a time In what-if analysis, change a single input and say what it does.
- End with a recommendation Say what the numbers mean for the decision.
If you want help with CVP calculations, a break-even chart or an Excel model, you can get an instant quote.