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How does cost-volume-profit analysis link costs, volume and profit, and how is the target-profit output found?

Apply cost-volume-profit analysis to find the output needed for a target profit using the contribution approach

A focused answer to the H2 Principles of Accounting outcome on CVP analysis. The contribution and contribution-to-sales ratio, the profit equation, finding output for a target profit, and the assumptions behind the model.

Generated by Claude Opus 4.810 min answerUpdated 2026-06-06

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

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What this dot point is asking
The answer
Examples in context
Try this

What this dot point is asking

SEAB wants you to apply cost-volume-profit (CVP) analysis to find the output needed for a target profit, using the contribution approach. CVP is the analytical core of short-run planning: it links how costs behave, how much is sold, and how much profit results. The central insight is that once costs are split into fixed and variable, profit becomes a simple function of contribution and volume, so any planning question, such as the output for a desired profit, can be solved with one formula.

The answer

Contribution and the C/S ratio

CVP rests on contribution (sales less variable cost). Two forms are used:

Contribution per unit $=$ selling price $-$ variable cost per unit.
Contribution-to-sales (C/S) ratio $= \dfrac{\text{contribution per unit}}{\text{selling price}}$ , equivalently total contribution over sales.

The C/S ratio gives the proportion of each sales dollar that is contribution, useful when working in revenue rather than units.

The profit equation

Profit is total contribution less fixed costs:

\text{Profit} = (\text{units} \times \text{contribution per unit}) - \text{fixed costs}

Rearranging to find the units needed for a chosen profit:

\text{Units for target profit} = \frac{\text{fixed costs} + \text{target profit}}{\text{contribution per unit}}

And in revenue terms:

\text{Sales for target profit} = \frac{\text{fixed costs} + \text{target profit}}{\text{C/S ratio}}

These two formulas answer almost every CVP planning question once you have the contribution figures.

The assumptions

CVP assumes a straight-line world: costs split cleanly into fixed and variable, constant variable cost and selling price per unit, fixed costs constant within the relevant range, and (for planning) production equal to sales with a constant sales mix. These hold reasonably for modest changes but break down over wide ranges, where prices fall, bulk discounts apply, and fixed costs step up. So CVP is a planning tool for the relevant range, not a universal truth.

Worked example

A company sells a product for $\$ 25 $with variable cost$ \ $15$ per unit and fixed costs of $\$ 120,000 $. Management wants a profit of$ \ $60\,000$ . Find the units and revenue required, and the profit if it actually sells $20\,000$ units.

Step 1: Contribution figures

Contribution per unit $= 25 - 15 = \$ 10 $. C/S ratio$ = \dfrac{10}{25} = 0.4$.

Step 2: Units for the target profit

\frac{120\,000 + 60\,000}{10} = \frac{180\,000}{10} = 18\,000 \text{ units}

Step 3: Revenue for the target profit

\frac{180\,000}{0.4} = \$450\,000 \quad (\text{check: } 18\,000 \times 25 = \$450\,000)

Step 4: Profit at 20,000 units

\text{Profit} = (20\,000 \times 10) - 120\,000 = 200\,000 - 120\,000 = \$80\,000

So $18\,000$ units (or $\$ 450,000 $of revenue) hits the$ \ $60\,000$ target, and selling $20\,000$ units yields $\$ 80,000$. The contribution approach turns each question into a one-line calculation.

Examples in context

Example 1. Pricing a new product. A start-up estimates fixed costs of $\$ 80,000 $and a contribution of$ \ $20$ per unit at a $\$ 50 $price. To break even it needs$ \dfrac{80,000}{20} = 4,000 $units; to make a$ \ $40\,000$ profit it needs $\dfrac{120\,000}{20} = 6\,000$ units. CVP lets the founders test whether the market is large enough to reach a profitable volume before they commit, which is the model's planning value.

Example 2. Judging a cost change. A factory considers automation that raises fixed costs by $\$ 50,000 $but cuts variable cost by$ \ $4$ per unit, lifting contribution per unit. CVP recalculates the target-profit output under the new cost structure, showing whether the higher contribution justifies the extra fixed cost at the expected sales level. This is how CVP informs decisions about the mix of fixed and variable costs.

Try this

Q1. A product has contribution $\$ 8 $per unit and fixed costs$ \ $48\,000$ . Find the units for a $\$ 16,000$ profit. [2 marks]

Cue. $\dfrac{48\,000 + 16\,000}{8} = \dfrac{64\,000}{8} = 8\,000$ units.

Q2. Selling price is $\$ 30 $, variable cost$ \ $18$ . Find the C/S ratio. [2 marks]

Cue. Contribution $= 30 - 18 = \$ 12 $; C/S ratio$ = \dfrac{12}{30} = 0.4 $(or$ 40%$).

Q3. Explain why CVP analysis is unreliable for very large increases in output. [3 marks]

Cue. Beyond the relevant range fixed costs step up, bulk discounts may cut variable cost per unit, and prices may have to fall to sell more, so the constant-price and constant-cost assumptions no longer hold.

Exam-style practice questions

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

Original7 marksA product sells for

\

with variable cost

24

per unit. Fixed costs are

\

96\,000

. (a) Find the contribution per unit and the contribution-to-sales ratio. (b) Find the number of units needed for a target profit of

40\,000

. (c) Find the sales revenue needed for that profit.

Show worked answer →

(a) Contribution per unit $= 40 - 24 = \$ 16 $. Contribution-to-sales (C/S) ratio$ = \dfrac{16}{40} = 0.4 \text{ (or } 40%)$.

(b) Units for target profit $= \dfrac{\text{fixed costs} + \text{target profit}}{\text{contribution per unit}} = \dfrac{96\,000 + 40\,000}{16} = \dfrac{136\,000}{16} = 8\,500 \text{ units}$ .

(c) Sales revenue for target profit $= \dfrac{\text{fixed costs} + \text{target profit}}{\text{C/S ratio}} = \dfrac{136\,000}{0.4} = \$ 340,000 $. (Check:$ 8,500 \times 40 = \ $340\,000$ .)

Markers reward the $\$ 16 $contribution and$ 0.4 $C/S ratio,$ 8,500 $units for the target profit, and sales revenue of$ \ $340\,000$ .

Original5 marksState four assumptions underlying cost-volume-profit analysis and explain why they limit its use for large changes in output.

Show worked answer →

Four assumptions of CVP analysis:

Costs split neatly into fixed and variable, with variable cost per unit constant.
Selling price per unit is constant regardless of volume.
Fixed costs are constant within the relevant range.
Production equals sales (no inventory change), and for multi-product firms the sales mix is constant.

These assumptions limit CVP for large changes in output because, beyond the relevant range, fixed costs step up (more capacity needed), bulk-buying may cut variable cost per unit, and selling prices may have to fall to sell much higher volumes. The straight-line model then no longer holds, so CVP is most reliable for modest changes around the current level.

Markers reward four valid assumptions and a clear explanation that real costs and prices are not linear over wide ranges, so CVP breaks down for large output changes.