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Cost-Volume-Profit Analysis (SACE Stage 2 Accounting)

Syllabus dot point

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

8 min read

Quick answer

Cost-volume-profit (CVP) analysis splits costs into fixed and variable, then uses the contribution margin per unit (selling price minus variable cost) to find the break-even point: Break-even units=Fixed costsContribution margin per unit\text{Break-even units} = \dfrac{\text{Fixed costs}}{\text{Contribution margin per unit}}. Above break-even the business makes a profit.

Jump to a section
  1. What this dot point is asking
  2. Fixed and variable costs
  3. Contribution margin
  4. The break-even point
  5. The contribution margin ratio and break-even chart
  6. Using CVP for decisions
  7. Exam-style questions

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.

Fixed and variable costs

Fixed costs stay the same in total regardless of output over a relevant range (for example rent, salaries, insurance). Variable costs change in direct proportion to output (for example materials, packaging, sales commission per unit).

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.

Contribution margin

Contribution margin per unit=Selling price per unit−Variable cost per unit\text{Contribution margin per unit} = \text{Selling price per unit} - \text{Variable cost per unit}

Once total contribution covers all fixed costs, every further unit's contribution becomes 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.

Break-even point

Break-even (units)=Fixed costsContribution margin per unit\text{Break-even (units)} = \frac{\text{Fixed costs}}{\text{Contribution margin per unit}}

Break-even (sales $)=Break-even units×Selling price\text{Break-even (sales \$)} = \text{Break-even units} \times \text{Selling price}

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.

Break-even and target profit

A business sells a single product

Selling price is 5050 per unit, variable cost is 3030 per unit, and fixed costs are 80 00080\,000 per year.

Each unit sold contributes toward fixed costs first and then toward profit. We find how many units are needed to cover all fixed costs, then extend the analysis to a target profit.

Step 1: Calculate the contribution margin per unit

The contribution margin is what each unit earns toward fixed costs after covering its own variable cost:

Contribution margin per unit=50−30=$20.\text{Contribution margin per unit} = 50 - 30 = \$20.

Step 2: Find the break-even point in units

At break-even, total contribution exactly covers fixed costs and profit is zero:

Break-even (units)=80 00020=4 000 units.\text{Break-even (units)} = \frac{80\,000}{20} = 4\,000 \text{ units}.

Step 3: Find the break-even point in sales dollars

Multiply the break-even units by the selling price to express the result in dollars:

Break-even (sales $)=4 000×50=$200 000.\text{Break-even (sales \$)} = 4\,000 \times 50 = \$200\,000.

To verify: at 4 0004\,000 units, revenue =200 000= 200\,000; total cost =80 000+(30×4 000)=200 000= 80\,000 + (30 \times 4\,000) = 200\,000. Profit is zero, confirming break-even.

Step 4: Find the units needed for a target profit of $30 000\$30\,000

Add the target profit to fixed costs, because that total must be covered by contributions:

Units for target profit=80 000+30 00020=110 00020=5 500 units.\text{Units for target profit} = \frac{80\,000 + 30\,000}{20} = \frac{110\,000}{20} = 5\,500 \text{ units}.

Step 5: Calculate the margin of safety

If the business expects to sell 7 0007\,000 units, the margin of safety is the gap between expected sales and break-even:

Margin of safety=7 000−4 000=3 000 units(or $150 000 in sales).\text{Margin of safety} = 7\,000 - 4\,000 = 3\,000 \text{ units} \quad \text{(or } \$150\,000 \text{ in sales).}

Sales could fall by this amount before the business makes a loss.

Final answer: Break-even is 4 0004\,000 units ($200 000\$200\,000 in sales). A target profit of $30 000\$30\,000 requires 5 5005\,500 units. At expected sales of 7 0007\,000 units, the margin of safety is 3 0003\,000 units.

The contribution margin ratio and break-even chart

For businesses that think in sales dollars rather than units, the contribution margin ratio (contribution margin per unit divided by selling price, expressed as a percentage) gives the break-even point directly in dollars: Break-even sales=Fixed costsContribution margin ratio\text{Break-even sales} = \dfrac{\text{Fixed costs}}{\text{Contribution margin ratio}}. With a $20 contribution on a $50 price, the ratio is 40%40\%, so 80 00080\,000 of fixed costs needs 80 000/0.40=200 00080\,000 / 0.40 = 200\,000 of sales to break even, agreeing with the unit calculation. SACE also expects you to read a break-even chart: total sales revenue and total cost are both plotted against output, the break-even point is where the two lines cross, the vertical gap to the left of that point is the loss area and the gap to the right is the profit area, and the margin of safety is the horizontal distance from expected sales back to break-even.

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.

Assumptions and limits

CVP assumes selling price and variable cost per unit are constant, fixed costs are fixed within the relevant range, and (for a multi-product business) the sales mix is stable. Outside the relevant range these assumptions break down, so CVP is a planning guide, not an exact prediction.

Common error

Dividing fixed costs by the selling price instead of by the contribution margin. Break-even uses contribution margin per unit (price−variable cost\text{price} - \text{variable cost}), because only the contribution is available to cover fixed costs. Using the full selling price understates the number of units needed and gives a misleadingly low break-even point.

Exam-style questions

Questions in the style of SACE Board exam questions on this dot point, each with a worked answer. They are written by ExamExplained unless tagged "Past paper"; the year shows the paper a question is modelled on.

2022 SACE Stage 2-style2 marks
Calculate the break-even point for 2022 for Espress Yourself's coffee machines. (Selling price $950 per unit; variable costs per unit: cost price $175 and delivery expense $5; fixed costs $130,000.)
Show worked answer →

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 2-style4 marks
From 10 July 2022 the supplier will increase the cost price of coffee machines from $175 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 $175 to $200 changes the contribution margin per unit.

Effect on break-even point: new variable cost per unit = 200 + 5 = $205, 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).

Practise this

Sources & how we know this

Based on the official SACE Board subject outline. Not yet individually reviewed by a person; always check SACE Board and your school's materials for current rules.

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