Breakeven analysis answers a question every client asks: how much must we sell before we stop losing money? In the Case Study it also supports pricing, risk and tender decisions. This topic covers the three uses of breakeven, the three methods of calculating it, cost-volume-profit analysis and its limits, with a worked example.
In 30 seconds
The breakeven point is where total revenue equals total cost, so there is neither profit nor loss. Find it from unit contribution: fixed costs divided by selling price less variable cost per unit. The same logic gives the lowest price that avoids a loss and the margin of safety, which is how far sales can fall before a loss arises.
Cost-volume-profit analysis rests on assumptions such as constant mix and linear costs, so state them and flex the key figures.
Three uses of breakeven analysis
Breakeven. Identify the contribution of a product or activity by separating fixed and variable costs, then find the sales revenue or number of units at which the business breaks even. An approximation of contribution can be gross profit, revenue less direct costs, and in many cases a sensible approximation is a mark of good financial data analysis.
Remember that the line between fixed and variable costs is flexible: over long periods nearly all costs can change.
Pricing. Pricing is the corollary of breakeven. It identifies the lowest price at which a new or existing product can be sold without making a loss. That can matter greatly in a price war, especially in a recession.
Margin of safety. This is how far sales can fall before a loss occurs, that is, the excess of budgeted revenue over breakeven revenue. It also shows the size of the cushion for errors in your estimates. The smaller the margin, the more critical each estimated figure becomes, just as a small gap between profit and loss makes the audit materiality level more critical.
Include all relevant costs. If relevant information seems to be missing, perform the calculation as requested first, then add your estimate of the missing figure. State it as an assumption and quantify its effect.
Three methods of finding the breakeven point
| Method | How it works |
|---|---|
| Equation method | Set sales revenue equal to variable costs plus fixed costs and solve for volume |
| Contribution margin method | Contribution margin is revenue less variable costs. Unit contribution margin (UCM) equals unit selling price (USP) less unit variable cost (UVC). Breakeven units = fixed costs ÷ UCM |
| Graphical method | Plot total revenue and total cost against units. They meet at the breakeven point, and the gap between them shows profit or loss at any output. A contribution graph is an alternative |
Cost-volume-profit analysis
Cost-volume-profit (CVP) analysis studies how different activity levels affect financial results. It shows the effect on profit of changes in volume, costs and selling prices. Volume gets the focus because, in the short run, price and the cost of materials and labour are usually known fairly well, but sales volume is not.
The usual question from a business owner is whether the company will make a profit this year, and the honest answer is often that it depends on volume. CVP works out the volume needed to break even and also the units needed to reach a target profit.
Limits of CVP analysis
- Either one product is sold, or several are sold in a constant mix.
- Volume is assumed to be the only factor that changes revenue and cost. In practice there can be economies of scale, and a higher volume may need a lower price.
- Total cost and total revenue are assumed to be linear, which holds only in the short run and over a limited range.
- Costs are split into fixed and variable, though some are semi-fixed, such as a telephone line with a rental and a call charge.
- Fixed costs stay constant only over a relevant range of activity that the business knows well.
Worked example
Scenario (fictitious figures). Ladipo Packaging Ltd sells a carton at ₦500. Variable cost is ₦300 a unit and fixed costs are ₦4 million a month. Budgeted sales are 25,000 units a month. Analyse the position.
- Unit contribution.
500 − 300 = ₦200. - Breakeven units.
4,000,000 ÷ 200 = 20,000 units, which is ₦10 million of revenue. - Margin of safety.
25,000 − 20,000 = 5,000 units, which is 20% of budget or ₦2.5 million of revenue. - Target profit of ₦2 million.
(4,000,000 + 2,000,000) ÷ 200 = 30,000 units. - Lowest price at budget volume.
Total cost is 4,000,000 + (25,000 × 300) = ₦11.5 million, so the lowest price that avoids a loss is 11,500,000 ÷ 25,000 = ₦460. - Flex. If variable cost rises by 10% to ₦330, unit contribution falls to ₦170 and breakeven rises to about 23,530 units. The margin of safety shrinks to about 1,470 units, or 5.9%, so a small further fall in sales brings a loss.
The conclusion is that the business is profitable on budget but very sensitive to input costs. Management should secure supplier prices or raise the selling price before committing to further fixed costs.
Common mistakes
- Using gross profit as contribution without saying that it is an approximation.
- Leaving out relevant costs, or inserting a missing figure without disclosing and quantifying it.
- Calculating breakeven but not the margin of safety, so the risk is not shown.
- Treating the fixed and variable split as exact.
- Ignoring the assumptions of constant mix and linear cost.
Quick revision
- Breakeven units = fixed costs ÷ unit contribution.
- Margin of safety = budgeted sales less breakeven sales.
- Lowest price: total cost at the expected volume ÷ units.
- Target profit units = (fixed costs + target profit) ÷ unit contribution.
- Limits: single product or constant mix, linear costs, fixed costs only within a range.
Practice questions
These are original questions in the style of the Institute of Chartered Accountants of Nigeria exam. Try each one before you open the answer.
Question 1. Selling price is ₦80, variable cost is ₦50 and fixed costs are ₦600,000. Breakeven units are:
- 7,500
- 12,000
- 20,000
- 30,000
Show the answer
C. Unit contribution is 30, and 600,000 ÷ 30 = 20,000 units.
Question 2. Budgeted sales are 25,000 units and breakeven is 20,000 units. The margin of safety as a percentage of budget is:
- 5%
- 20%
- 25%
- 80%
Show the answer
B. 5,000 ÷ 25,000 = 20%.
Question 3. With the same figures as question 1, units needed to earn a ₦300,000 profit are:
- 20,000
- 25,000
- 30,000
- 40,000
Show the answer
C. (600,000 + 300,000) ÷ 30 = 30,000.
Question 4. Which is an assumption of CVP analysis?
- Costs are never semi-fixed
- Volume is the only factor that changes revenue and cost
- Prices rise as volume rises
- Fixed costs change with every unit
Show the answer
B. This is one of the listed assumptions, and it may not hold in practice.
Question 5 (6 marks). Explain the margin of safety and state three limitations of cost-volume-profit analysis.
Model answer
Show the model answer to Question 5
Margin of safety (3 marks). It is how far sales can fall below budget before a loss occurs, the excess of budgeted revenue over breakeven revenue. (1.5) It shows the risk and the cushion for errors in the estimates: the smaller it is, the more critical each estimate becomes. (1.5)
Limitations (3 marks, one each, any three). It assumes one product or a constant mix. Volume is assumed to be the only variable that changes. Costs and revenues are assumed linear, which holds only in the short run. Costs may be semi-fixed. Fixed costs are constant only within a relevant range.
The next topic covers product mix, profitability and short-term and long-term decisions.
Pathfinder on Breakeven, cost-volume-profit analysis and pricing decisions
These are the ICAN Pathfinder questions that test this topic. ICAN owns the questions and the suggested solutions, so we point you to them and do not copy them. Open your Pathfinder, attempt each question under exam conditions, then check your answer against the notes above.
The case lists sales and costs for three product lines and says no fixed costs go if one is dropped. Practise separating contribution from allocated fixed costs.
Revise first: Three methods of finding the breakeven point
The board wants a new product judged on its numbers. Breakeven, margin of safety and flexing the key figures all apply.
Revise first: Worked example
Source: ICAN Pathfinder, Case Study. Diets covered: November 2014 and May 2024.
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