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How many units must a business sell to break even and reach a target profit?

Apply cost-volume-profit analysis to calculate the break-even point and inform pricing and output decisions

Cost-volume-profit analysis separates fixed and variable costs to find the break-even point and the sales needed for a target profit, supporting pricing and output decisions.

Generated by Claude Opus 4.78 min answer

Reviewed by: AI editorial process; not yet individually human-reviewed

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  1. What this dot point is asking
  2. Fixed and variable costs
  3. Contribution margin
  4. The break-even point
  5. Using CVP for decisions

What this dot point is asking

You need to classify costs as fixed or variable, calculate contribution margin, find the break-even point in units and dollars, and use CVP to make pricing and output decisions.

Fixed and variable costs

CVP analysis depends on separating costs by behaviour.

Total cost is Fixed costs+(Variable cost per unit×units)\text{Fixed costs} + (\text{Variable cost per unit} \times \text{units}).

Contribution margin

Each unit sold contributes toward covering fixed costs and then toward profit.

The break-even point

The break-even point is the level of sales at which total revenue exactly equals total costs, so profit is zero.

To find the units needed for a target profit, add the target to fixed costs:

Units for target profit=Fixed costs+Target profitContribution margin per unit\text{Units for target profit} = \frac{\text{Fixed costs} + \text{Target profit}}{\text{Contribution margin per unit}}

The margin of safety is how far sales can fall before reaching break-even: Actual sales−Break-even sales\text{Actual sales} - \text{Break-even sales}. A larger margin of safety means lower risk.

Using CVP for decisions

CVP answers practical questions: how a price change shifts break-even, whether a special order is worthwhile if it covers variable cost and contributes to fixed costs, and how much output is needed to reach a profit goal. Raising the selling price increases contribution margin and lowers the break-even point; cutting price does the reverse.

Exam-style practice questions

Practice questions written in the style of SACE Board exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

2022 SACE Stage 22 marksCalculate the break-even point for 2022 for Espress Yourself's coffee machines. (Selling price 950perunit;variablecostsperunit:costprice950 per unit; variable costs per unit: cost price 175 and delivery expense 5;fixedcosts5; fixed costs 130,000.)
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Break-even point (in units) = fixed costs / contribution margin per unit.

Step 1: contribution margin per unit = selling price - total variable cost per unit = 950 - (175 + 5) = 950 - 180 = $770.

Step 2: break-even units = 130,000 / 770 = 168.83, which rounds up to 169 units, because a part unit cannot be sold and 168 would not quite cover fixed costs.

At 169 machines sold, total contribution covers the $130,000 fixed costs and profit is zero.

Markers reward including both variable costs (cost price and delivery) in the contribution margin, the correct formula, and rounding up to the next whole unit.

2022 SACE Stage 24 marksFrom 10 July 2022 the supplier will increase the cost price of coffee machines from 175to175 to 200 per unit. Discuss the effects this change will have on the break-even point for sales of coffee machines and on the profitability of selling these coffee machines.
Show worked answer →

The cost price is a variable cost, so raising it from 175to175 to 200 changes the contribution margin per unit.

Effect on break-even point: new variable cost per unit = 200 + 5 = 205,socontributionmarginfallsfrom205, so contribution margin falls from 770 to 950−205=950 - 205 = 745. Break-even = 130,000 / 745 = 175 units (rounded up), higher than the previous 169. The business must now sell more machines to cover the same fixed costs.

Effect on profitability: with a lower contribution margin, each machine contributes $25 less, so total profit falls at any given sales level unless the business raises its selling price or cuts other costs. Margin of safety also shrinks.

Markers reward recalculating the contribution margin, showing the higher break-even, and explaining that profit per unit and total profit fall (and that the selling price may need to rise to protect margin).