What you'll learn
Cost-volume-profit analysis answers the questions an owner actually asks before committing to anything: how many must we sell to stop losing money, how many to earn the profit we want, and how far can sales fall before we are in trouble. It rests entirely on contribution — selling price less variable cost — and therefore entirely on the fixed/variable split established in cost classification.
The central insight is that fixed costs do not change with volume, so every unit sold contributes the same amount towards covering them. Once enough units have been sold to cover the fixed costs completely, the business breaks even, and every unit after that adds its full contribution straight to profit. That is why profit rises faster than sales beyond break-even, and why a business just below break-even is in a very different position from one just above it.
By the end of this topic you should be able to calculate contribution and the contribution to sales ratio, find the break-even point in units and in revenue, compute the volume needed for a target profit, measure the margin of safety, and state the assumptions that limit the whole technique.
Key terms and definitions
Contribution per unit — selling price per unit less variable cost per unit.
Contribution to sales (C/S) ratio — contribution per unit divided by selling price, expressed as a percentage. Also called the profit-volume ratio.
Break-even point — the level of activity at which total contribution exactly equals fixed costs, so profit is nil.
Margin of safety — the amount by which current or budgeted sales exceed the break-even point, in units, in revenue, or as a percentage.
Target profit volume — the sales volume required to achieve a stated profit.
Break-even chart — a graph plotting total cost and total revenue against activity, intersecting at the break-even point.
Profit-volume chart — a graph plotting profit directly against activity, crossing the horizontal axis at break-even.
Core concepts
Contribution, and why it is the unit of account
Contribution is what each unit gives the business towards its fixed costs. Before break-even it is absorbing those costs; after break-even there are none left to absorb, so it becomes profit.
Thinking in contribution rather than profit per unit is what makes the technique work, because profit per unit is not a stable figure — it depends on how many units the fixed costs are spread over, so it changes at every volume. Contribution per unit does not change at all within the relevant range.
The three core formulas
Break-even in units = fixed costs ÷ contribution per unit. You are asking how many units of contribution are needed to cover the fixed costs.
Break-even in revenue = fixed costs ÷ C/S ratio. Use this where a question gives revenue and costs but no unit figures, which is common for a business selling a mix of products.
Target profit volume = (fixed costs + target profit) ÷ contribution per unit. The target profit is simply treated as an additional fixed cost to be covered.
All three are the same idea. Work out what has to be covered, then divide by what each unit contributes.
Margin of safety
The margin of safety measures how much sales can fall before the business starts making a loss. It can be stated in units, in revenue, or — most usefully — as a percentage of current sales.
A business selling 8,000 units with a break-even of 5,000 has a margin of safety of 3,000 units, or 37.5% of its sales. That is a genuinely informative figure: sales could fall by more than a third before losses begin.
A low margin of safety is a risk indicator, and it is where the interpretation marks sit. Two businesses with identical profits can have very different margins of safety, and the one with high fixed costs and high contribution per unit will have the lower margin — it is more exposed to a downturn and more rewarded by an upturn.
The charts
On a break-even chart, activity runs along the horizontal axis and money up the vertical. Fixed cost is a horizontal line; total cost starts at the fixed cost level and slopes upward at the variable cost per unit; total revenue starts at the origin and slopes upward more steeply. The two lines cross at break-even, and the vertical gap between them beyond that point is profit.
A profit-volume chart plots profit directly. It starts below the axis at minus the fixed costs, rises at the contribution per unit, and crosses the axis at break-even. It shows profit at any volume more readily, at the cost of not showing costs and revenues separately.
More than one product: the weakest assumption
Almost every real business sells several products with different contributions per unit, and break-even then has no single answer — it depends on which products are sold.
The standard treatment is to work with a weighted average contribution per unit, based on the expected sales mix, or to use the C/S ratio of the business as a whole and compute break-even in revenue rather than in units. Either way a mix has to be assumed, and the answer is only as good as that assumption.
The vulnerability is easy to state and worth stating. A business can hit its total revenue target exactly and still miss break-even, because it sold more of the low-margin lines and fewer of the high-margin ones than the mix assumed. Total sales met, profit missed.
For a Caribbean business with seasonal trade — a hotel, a restaurant, a shop selling both everyday goods and tourist items — the mix shifts through the year as a matter of course. That makes constant mix the weakest of all the assumptions, and naming it as such is a better evaluation point than repeating the linearity objection everyone makes.
The assumptions, and why they matter
Everything above rests on assumptions that are convenient rather than true. Costs are assumed to behave linearly, with variable cost per unit constant at all volumes. Selling price is assumed constant however much is sold. Fixed costs are assumed genuinely fixed. Production is assumed equal to sales, so inventory does not change. Where several products are sold, the sales mix is assumed constant.
Each of these breaks down in practice: bulk discounts reduce variable cost per unit, selling more may require price cuts, and fixed costs step up beyond a capacity threshold. All of it holds only within the relevant range.
This is not a reason to dismiss the technique. It is a reason to state the range over which a conclusion holds, which is what an evaluation question rewards.
Worked examples
Example 1 — Contribution and the C/S ratio (4 marks)
A product sells for $50 with a variable cost of $30.
Contribution per unit = $50 − $30 = $20. C/S ratio = $20 ÷ $50 × 100 = 40%.
The ratio says that 40 cents in every dollar of sales is available to cover fixed costs and then to become profit.
Example 2 — Break-even in units and revenue (5 marks)
Fixed costs are $100,000.
Break-even in units = $100,000 ÷ $20 = 5,000 units. Break-even in revenue = 5,000 × $50 = $250,000.
Check using the ratio: $100,000 ÷ 0.40 = $250,000. The two routes agree, which is a useful cross-check and takes one line.
Example 3 — Target profit (4 marks)
The owner wants a profit of $60,000.
Required volume = ($100,000 + $60,000) ÷ $20 = $160,000 ÷ $20 = 8,000 units.
In revenue: 8,000 × $50 = $400,000.
Check: contribution at 8,000 units is 8,000 × $20 = $160,000, less fixed costs of $100,000, gives a profit of $60,000. It agrees.
Example 4 — Margin of safety (5 marks)
Budgeted sales are the 8,000 units from Example 3, and break-even is 5,000 units.
Margin of safety in units = 8,000 − 5,000 = 3,000 units. In revenue = 3,000 × $50 = $150,000. As a percentage = 3,000 ÷ 8,000 × 100 = 37.5%.
Interpretation: sales could fall by 37.5% before the business begins to make a loss. That is a comfortable position, and saying so — rather than only reporting the figure — is where the interpretation mark sits.
Example 5 — The effect of a price cut (5 marks)
The owner proposes cutting the price to $45 to win volume.
New contribution per unit = $45 − $30 = $15. New break-even = $100,000 ÷ $15 = 6,666.67, so 6,667 units (always round up — 6,666 units leaves fixed costs not quite covered).
Break-even has risen by 1,667 units, or a third. To earn the same $60,000 profit the business must now sell ($100,000 + $60,000) ÷ $15 = 10,667 units, against 8,000 before.
So the price cut requires roughly a 33% increase in volume just to stand still. Stating that requirement, rather than merely recalculating, is what turns the arithmetic into advice.
Common mistakes and how to avoid them
Dividing fixed costs by selling price. Divide by contribution per unit — the selling price includes the variable cost that has to be paid out again.
Rounding break-even down. Always round up to the next whole unit, or fixed costs are not fully covered.
Using profit per unit instead of contribution. Profit per unit changes with volume; contribution per unit does not.
Forgetting that target profit is added to fixed costs. Treat it as another amount to be covered.
Mixing units and revenue in the margin of safety. State which you are giving, and give the percentage where you can.
Applying the C/S ratio to units. It applies to revenue; contribution per unit applies to units.
Presenting a break-even figure with no assumptions stated. Linearity, constant price, constant mix and fixed costs staying fixed all have to hold.
How this links to your Internal Assessment
CVP is among the most useful techniques an Internal Assessment can apply, because the break-even point is a number the owner will immediately recognise as meaningful and very often has never calculated.
Derive the fixed and variable split from the actual records — the high-low method on real cost data is the honest route — then compute break-even, the margin of safety and the volume needed for the profit the owner says they want. Compare that required volume with what the business currently achieves and with what its capacity allows. If the target profit needs more units than the premises can produce, that is a finding worth more than any ratio.
Then test something. Model the effect of a price change or a rent increase, as in Example 5, and state what the business would have to achieve to absorb it. Sensitivity analysis of that kind demonstrates the technique is understood rather than merely executed.
Be explicit that your fixed/variable split rests on limited observations, and that CVP assumes a constant sales mix — which for a business selling several products is usually the weakest assumption of all.
Exam technique for cost-volume-profit analysis
Calculate contribution per unit first, before anything else, and write it down. Every other figure in the question depends on it, and an error here propagates through the whole answer.
Show the formula, then the substitution, then the answer with its unit — units, dollars or a percentage. A bare number is ambiguous and cannot earn full marks.
Cross-check break-even by the other route where both are available: units × price should equal fixed costs ÷ C/S ratio. It costs one line and catches most errors.
Command words matter here. Calculate the break-even point wants the working. Explain what the margin of safety measures wants the fall-in-sales interpretation, not the formula. Analyse the effect of a price reduction wants the new break-even and the volume increase needed to stand still. Evaluate the usefulness of CVP wants the assumptions set against the technique's practical value, and a stated conclusion.
If asked to draw a chart, label both axes with their units, mark the break-even point where the lines cross, and label the fixed cost line — the labelling carries marks independently of the accuracy of the lines.
Quick revision summary
- Contribution per unit = selling price − variable cost per unit; it is constant within the relevant range.
- C/S ratio = contribution ÷ selling price, applied to revenue rather than units.
- Break-even units = fixed costs ÷ contribution per unit; always round up.
- Break-even revenue = fixed costs ÷ C/S ratio.
- Target profit volume = (fixed costs + target profit) ÷ contribution per unit.
- Margin of safety = current sales − break-even, best expressed as a percentage of current sales.
- Beyond break-even, every unit adds its full contribution to profit.
- High fixed costs with high contribution per unit means a lower margin of safety: more exposed to a downturn, more rewarded by an upturn.
- Break-even chart shows costs and revenues; profit-volume chart shows profit directly.
- Assumptions: linear costs, constant price, constant mix, production equals sales, fixed costs genuinely fixed — all within the relevant range.
- A price cut raises break-even; state the extra volume needed just to stand still.