Accounting Share · Worked practice
How many units cover the costs?
Practice contribution margin, break-even volume and target profit with a simple product example.
Try each question before opening its solution. Keep your calculations in your own notes; this page does not save your progress.
Your scenario
A business sells one product for $50 per unit. Variable cost is $30 per unit, and fixed costs are $4,000 for the period. Assume selling price and variable cost per unit stay constant, fixed costs stay constant within the relevant range, and all units produced are sold. Ignore tax and financing costs.
1. Calculate contribution per unit
How much does each sale contribute toward fixed costs and then profit?
Show the contribution calculation
Contribution per unit = Selling price − Variable cost = $50 − $30 = $20. The contribution margin ratio is $20 ÷ $50 = 40%.
Contribution is not the same as profit: fixed costs still need to be covered.
2. Find the break-even point
Calculate break-even units and break-even sales revenue.
Show break-even units and revenue
Break-even units = Fixed costs ÷ Contribution per unit = $4,000 ÷ $20 = 200 units.
Break-even sales revenue = $4,000 ÷ 0.40 = $10,000, also 200 × $50.
Check: Revenue $10,000 − Variable costs $6,000 − Fixed costs $4,000 = $0 profit.
3. Calculate profit at 300 units
Show the profit calculation
Revenue = 300 × $50 = $15,000. Variable costs = 300 × $30 = $9,000. Total contribution = $6,000. Profit = $6,000 − $4,000 = $2,000.
4. Reach a target profit of $3,000
How many units must be sold under the same assumptions?
Show the target-profit calculation
Required units = (Fixed costs + Target profit) ÷ Contribution per unit = ($4,000 + $3,000) ÷ $20 = 350 units.
Check: 350 × $20 contribution − $4,000 fixed costs = $3,000 profit. If a calculation gives a fractional unit and only whole units can be sold, round the required units up.
5. Measure the margin of safety
If actual sales are 300 units, what is the margin of safety?
Show margin of safety
Margin of safety = Actual sales − Break-even sales = 300 − 200 = 100 units, or $5,000 of sales revenue.
Margin of safety percentage = 100 ÷ 300 × 100 = 33.33%, approximately. Use actual sales, not break-even sales, as the denominator.
Challenge: Variable cost rises to $34
Keep selling price at $50 and fixed costs at $4,000. Find the revised break-even units.
Show the revised break-even point
New contribution per unit = $50 − $34 = $16. Break-even units = $4,000 ÷ $16 = 250 units. The lower contribution means more sales are needed to cover the same fixed costs.
Before you apply the result
CVP is a simplified model. Changes in product mix, capacity, prices or cost behavior can change the answer. State the relevant range and assumptions before using a result in a real decision.
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