Knowing the break-even point answers one question. Knowing how far above it you are answers a more important one: how much can things go wrong before we lose money? That cushion is the margin of safety.
And because many people absorb numbers better as pictures, cost-volume-profit (CVP) information is often shown as a chart, in which the break-even point, the loss area, the profit area and the margin of safety can all be read off at a glance.
This topic covers the margin of safety (in units, in revenue and as a percentage), what it says about risk, how to construct and read the traditional break-even chart, the contribution version of the chart, and the profit/volume (P/V) chart. A single example is carried through the calculations and the three charts, so you can see that they all show the same facts in different ways.
In 30 seconds
Margin of safety = budgeted (or actual) sales − break-even sales, in units or naira. As a ratio, margin of safety % = margin of safety ÷ budgeted sales. It is the most that sales can fall below budget before a loss is made. A break-even chart plots a total revenue line (from the origin), a fixed cost line, and a total cost line (starting at fixed costs).
They cross at the break-even point. Below it is the loss area; above it, the profit area. In the contribution version, fixed costs are stacked on top of variable costs, so contribution is the gap between revenue and the variable cost line.
A P/V chart plots profit against volume: it starts at a loss equal to fixed costs, crosses zero at break-even and has a slope equal to contribution per unit.
The example used throughout
Zaria Bags Ltd sells a bag at ₦50. The variable cost is ₦30 per bag. Fixed costs are ₦400,000 a period. Budgeted sales are 25,000 bags.
| Measure | Working | Result |
|---|---|---|
| Contribution per bag | ₦50 − ₦30 | ₦20 |
| C/S ratio | 20 ÷ 50 | 40% |
| Break-even point | ₦400,000 ÷ ₦20 | 20,000 bags |
| Break-even revenue | 20,000 × ₦50, or ₦400,000 ÷ 0.40 | ₦1,000,000 |
| Budgeted profit | 25,000 × ₦20 − ₦400,000 | ₦100,000 |
The margin of safety
The margin of safety is the difference between budgeted sales and break-even sales. It is the maximum amount by which actual sales can fall short of the budget without a loss in the period. It can be stated three ways:
- as a quantity of units = budgeted sales units − break-even units;
- as an amount of sales revenue = budgeted revenue − break-even revenue; and
- as a percentage of budgeted sales = margin of safety ÷ budgeted sales.
| Form | Working | Result |
|---|---|---|
| Units | 25,000 − 20,000 | 5,000 bags |
| Revenue | ₦1,250,000 − ₦1,000,000, or 5,000 × ₦50 | ₦250,000 |
| Percentage | 5,000 ÷ 25,000 | 20% |
A 20% margin of safety means that sales could fall up to 20% below budget and the company should still make a profit. A useful link: margin of safety % = profit ÷ contribution. Here ₦100,000 ÷ ₦500,000 = 20%, because every unit above break-even adds its contribution entirely to profit.
Why it matters
- It is a risk measure. A high margin of safety means a low risk of loss. A low one means the business is vulnerable to small changes in demand, competition or the economy, so it needs close monitoring.
- It gives a buffer against changes in sales conditions. A larger margin signals healthier finances, with more room to handle sales declines without a loss.
- Higher fixed costs tend to push the break-even point up and the margin of safety down.
- It changes with sales, costs and prices, so it should be recalculated.
- It can be applied to a product or a department as well as the whole company, giving more focused insight.
Further calculations
From the margin of safety ratio to fixed costs. A firm has monthly sales of ₦800,000, a margin of safety of 25% and a monthly profit of ₦60,000. Break-even revenue = (1 − 0.25) × ₦800,000 = ₦600,000. Contribution at ₦800,000 less contribution at ₦600,000 equals the profit, because fixed costs are covered at the break-even point: C/S ratio × (₦800,000 − ₦600,000) = ₦60,000, so the C/S ratio = 30%. Contribution at ₦800,000 = ₦240,000, so fixed costs = ₦240,000 − ₦60,000 = ₦180,000. To earn ₦120,000, sales must be (₦180,000 + ₦120,000) ÷ 0.30 = ₦1,000,000.
Effect of a change in costs. If fixed costs in the main example rise by ₦40,000 to ₦440,000, break-even becomes ₦440,000 ÷ ₦20 = 22,000 bags and the margin of safety falls to 3,000 bags (12%). A higher cost base lowered the cushion from 20% to 12%.
The break-even chart
A break-even chart shows the relationship between costs, revenue and profit at different levels of activity. It shows the point at which total revenue equals total costs, the break-even point. The chart can be for a single product or, with a constant sales mix and varying contributions, for a multi-product business, in which case the break-even point is found for the business as a whole.
The elements of the chart
| Element | What it shows |
|---|---|
| Total revenue line | Sales income. A straight line starting at the origin (0 units, ₦0) with a slope equal to the selling price per unit |
| Fixed cost line | A horizontal line at the level of fixed costs. These costs do not change with volume |
| Variable costs | Shown by the slope of the total cost line, which rises with volume |
| Total cost line | Fixed plus variable costs. It starts at the fixed cost level on the vertical axis (costs are incurred even with no sales) and rises with the variable cost per unit |
| Break-even point | Where total revenue crosses total cost. Profit is zero |
| Loss area | Below break-even, where total cost is above revenue |
| Profit area | Above break-even, where revenue is above total cost. The wider the gap, the greater the profit |
| Margin of safety | The distance along the volume axis between budgeted sales and break-even sales |
How to draw it
- Put volume (units) on the horizontal axis and naira on the vertical axis. Choose a scale that covers beyond budgeted sales.
- Draw the fixed cost line: horizontal at ₦400,000.
- Draw the total cost line: from ₦400,000 at zero units to a second point, for example at 30,000 bags ₦400,000 + 30,000 × ₦30 = ₦1,300,000.
- Draw the revenue line: from the origin to a point, for example 30,000 bags × ₦50 = ₦1,500,000.
- Mark the break-even point where revenue and total cost cross: 20,000 bags and ₦1,000,000.
- Mark budgeted sales (25,000 bags) and show the margin of safety between the two.
- Label the loss and profit areas.
Interpreting the chart
- Before break-even revenue is less than total cost, so there is a loss. The vertical gap between the lines is the loss, and it widens as volume falls. At zero sales the loss equals fixed costs (₦400,000).
- At break-even revenue equals total cost. The business has covered its fixed and variable costs but made no profit. This is the minimum sales target.
- After break-even. revenue exceeds total cost. The vertical gap is the profit, and it widens as volume rises.
At 25,000 bags the gap is ₦1,250,000 − ₦1,150,000 = ₦100,000.
The contribution break-even chart
In a second version of the chart, the fixed costs are drawn on top of the variable costs. The variable cost line starts at the origin, and the total cost line is the same as before. But now runs parallel above the variable cost line, the gap between them being the constant fixed cost. The total cost line is the same in both versions.
The advantage is that contribution, the difference between the revenue line and the variable cost line, can be seen directly. At the break-even point, the contribution (the gap between revenue and variable cost) is exactly equal to fixed costs (the gap between variable cost and total cost).
The profit/volume (P/V) chart
A profit/volume chart shows the profit or loss at every level of output and sales. It plots profit (positive above the horizontal axis and negative below) against sales volume.
- At zero sales there is a loss equal to total fixed costs (−₦400,000).
- As volume rises, the loss shrinks because contribution is earned. The slope of the line is the contribution per unit (₦20 per bag), or the C/S ratio if volume is shown in naira.
- The line crosses the horizontal axis at the break-even point (20,000 bags).
- Above break-even there is a profit. At 25,000 bags the profit is ₦100,000, so the vertical gap at budgeted sales is the profit and the horizontal gap from break-even is the margin of safety.
A line parallel to the horizontal axis can be drawn at the fixed cost level (the loss at zero sales). Total contribution is then the vertical distance between the profit line and this fixed cost line.
| Break-even chart | P/V chart | |
|---|---|---|
| Shows | Revenue, costs and the points where they cross | Profit or loss directly at each volume |
| Break-even point | Where revenue crosses total cost | Where the profit line crosses zero |
| Profit at a given volume | Gap between revenue and total cost lines | Read straight off the vertical axis |
| Cost behaviour | Shows fixed and variable costs separately | Does not show costs, only the net effect |
The ideas in more depth
Charts give the same answers as formulas
Every point on a chart can be checked against the formulas. If your drawn break-even point does not agree with fixed costs ÷ contribution per unit, the chart has an error. Exam questions often ask for a calculation and a chart, and the two must agree.
Reading profit from the chart
On the break-even chart, profit at a given volume is the vertical gap between the revenue line and the total cost line. On the P/V chart it is the height of the line above the horizontal axis. With a fixed price and variable cost, every extra unit adds the same contribution, so the P/V line is straight.
Sensible limits for the chart
The chart is valid only within the relevant range, where fixed costs are constant and the unit price and variable cost are as stated. Extending the lines to very high volumes assumes capacity that may not exist.
What the chart cannot show
Charts assume a straight-line revenue and cost. They do not show discounts, step fixed costs, changes in sales mix, time or non-financial factors. They are useful for communication but not a replacement for careful analysis.
A multi-product chart
Background. With several products at a constant mix, the chart is drawn for the business as a whole, with volume measured in sales revenue and the line slope equal to the overall C/S ratio. The same break-even revenue, fixed costs ÷ overall C/S ratio, is found, and a P/V chart for the whole business has a slope equal to the overall C/S ratio.
Worked example: from two data points to a chart
Scenario. Kwara Garments Ltd estimates that annual sales of 6,000 shirts would give a profit of ₦20,000 and sales of 9,000 shirts a profit of ₦140,000. The selling price is ₦60. (a) Find the variable cost per shirt and the fixed costs. (b) Find the break-even point in units and naira. (c) Find the margin of safety if sales are expected to be 8,000 shirts. (d) Say what you would plot on a break-even chart.
- Contribution per shirt.
change in profit ÷ change in units = (₦140,000 − ₦20,000) ÷ (9,000 − 6,000) = ₦120,000 ÷ 3,000 = ₦40.
Variable cost = ₦60 − ₦40 = ₦20. - Fixed costs:
contribution at 6,000 shirts = ₦240,000, minus profit ₦20,000 = ₦220,000.
(Check at 9,000 shirts: ₦360,000 − ₦220,000 = ₦140,000. ✓) - Break-even.
₦220,000 ÷ ₦40 = 5,500 shirts, or 5,500 × ₦60 = ₦330,000. - Margin of safety at 8,000 shirts.
8,000 − 5,500 = 2,500 shirts, which is 31.25% of 8,000, or ₦150,000 of sales.
(Check: profit ÷ contribution = (8,000 × ₦40 − ₦220,000) ÷ (8,000 × ₦40) = ₦100,000 ÷ ₦320,000 = 31.25%. ✓) - Chart:
a fixed cost line at ₦220,000; a total cost line from ₦220,000 at zero shirts to, for example, ₦220,000 + 9,000 × ₦20 = ₦400,000 at 9,000 shirts; a revenue line from the origin to ₦540,000 at 9,000 shirts; the lines cross at 5,500 shirts (₦330,000).
Mark 8,000 shirts to show the margin of safety.
Using the margin of safety in decisions
The margin of safety helps managers judge proposals. Suppose Zaria Bags is offered a contract that would raise fixed costs by ₦100,000 (a new machine) and cut variable cost by ₦5 per bag. New contribution = ₦25, fixed costs ₦500,000, break-even = 20,000 bags (unchanged). At budgeted 25,000 bags the margin of safety is still 20%, but profit rises to 25,000 × ₦25 − ₦500,000 = ₦125,000. Profit is more sensitive to volume, because each bag now earns ₦25 instead of ₦20.
If demand fell to 21,000 bags, profit would be ₦25,000 (new) against ₦20,000 (old), and at 19,000 bags the loss would be ₦25,000 (new) against ₦20,000 (old). The new cost structure gains more when sales are good and loses more when they are poor, which is the risk-return trade-off in operating gearing.
A bank or investor often asks for the margin of safety, because a business that loses money after a small fall in sales is a risk. A margin of 20% or more is usually thought comfortable, but the right level depends on how stable demand is. A business that sells to a few large customers on contract needs a smaller margin than one selling a fashion product.
Reading charts in the exam
Examination questions on charts usually ask you to do one or more of the following. For each, there is a quick method.
| Task | Method |
|---|---|
| Find the break-even point from a chart | Read where revenue and total cost cross. Down to the volume axis for units, across to the naira axis for revenue |
| Find profit at a given volume | Break-even chart: vertical gap between revenue and total cost. P/V chart: height of the line |
| Find the margin of safety | Budgeted volume minus break-even volume on the horizontal axis |
| Find fixed costs | The intercept of total cost on the vertical axis, or the loss at zero sales on a P/V chart |
| Find variable cost per unit | Slope of the total cost line, or price minus the slope of the P/V line |
| Find contribution per unit | Slope of the P/V line, or revenue line slope minus total cost line slope |
Practise by drawing the chart for Zaria Bags yourself on graph paper, with ₦ on the vertical axis (scale 1 cm = ₦100,000) and units on the horizontal (1 cm = 2,500 bags). Check that your lines cross at 8 cm across and 10 cm up.
Common mistakes in the exam
- Calculating the margin of safety as a percentage of break-even sales instead of budgeted sales.
- Using actual sales for the margin of safety when the question gives budgeted sales, or the reverse.
- Starting the revenue line away from the origin, or the total cost line at zero instead of at fixed costs.
- Drawing the fixed cost line sloping instead of horizontal.
- Labelling the profit and loss areas the wrong way round.
- On a P/V chart, starting the line at zero instead of at the loss equal to fixed costs.
- Using unequal scales so that the break-even point cannot be read.
- Forgetting that the contribution chart and the traditional chart have the same break-even point.
Quick revision
- Margin of safety = budgeted sales − break-even sales. Percentage = margin ÷ budgeted sales. Also = profit ÷ contribution.
- High margin of safety = low risk. Higher fixed costs lower it.
- Break-even chart: revenue from origin; total cost from fixed costs; fixed cost horizontal; they cross at break-even.
- Contribution chart: fixed costs on top of variable costs; contribution is the gap between revenue and variable cost.
- P/V chart: starts at − fixed costs, crosses zero at break-even, slope = contribution per unit.
Practice questions
These are original questions written in the style of the Institute of Chartered Accountants of Nigeria (ICAN) exam. Try each one before you open the answer.
Section A style: multiple choice
Question 1. Budgeted sales 25,000 units, break-even 20,000 units. The margin of safety is:
- 5,000 units
- 20,000 units
- 45,000 units
- 25%
Show the answer
A. 25,000 − 20,000 = 5,000 units.
Question 2. In Question 1, the margin of safety as a percentage of budgeted sales is:
- 20%
- 25%
- 80%
- 5%
Show the answer
A. 5,000 ÷ 25,000 = 20%.
Question 3. A high margin of safety indicates:
- A low risk of making a loss
- A high risk of loss
- No fixed costs
- A loss
Show the answer
A. Sales can fall a long way before a loss.
Question 4. Break-even sales ₦600,000 and budgeted sales ₦800,000. The margin of safety ratio is:
- 25%
- 33%
- 75%
- 20%
Show the answer
A. ₦200,000 ÷ ₦800,000 = 25%.
Question 5. On a traditional break-even chart, the total cost line starts at:
- The origin
- The fixed cost level on the vertical axis
- The break-even point
- The variable cost level
Show the answer
B. Fixed costs are incurred even at zero sales.
Question 6. The revenue line on a break-even chart starts at:
- The origin
- The fixed cost level
- The break-even point
- The total cost line
Show the answer
A. No sales, no revenue.
Question 7. In the contribution version of the break-even chart, contribution is shown as the gap between:
- Revenue and variable costs
- Revenue and fixed costs
- Fixed and variable costs
- Total cost and fixed cost
Show the answer
A. Sales less variable costs.
Question 8. On a P/V chart, the line meets the vertical axis at:
- A loss equal to fixed costs
- Zero
- A profit equal to contribution
- The break-even point
Show the answer
A. At zero sales, only fixed costs are incurred.
Question 9. The slope of the P/V line (volume in units) equals:
- Contribution per unit
- Fixed cost per unit
- Selling price
- Variable cost per unit
Show the answer
A. Each extra unit adds its contribution to profit.
Question 10. Profit is ₦100,000 and contribution is ₦500,000. The margin of safety percentage is:
- 20%
- 5%
- 80%
- 50%
Show the answer
A. Profit ÷ contribution = 20%.
Section B style: written questions
Question 11 (10 marks). Explain the margin of safety and why managers use it. Describe the main features of a break-even chart.
Question 12 (20 marks). A firm estimates that annual sales of 8,000 units would give a loss of ₦20,000 and sales of 12,000 units a profit of ₦100,000. The selling price is ₦90.
(a) Calculate the variable cost per unit and the fixed costs. (6 marks)
(b) Calculate the break-even point in units and in naira. (4 marks)
(c) Calculate the margin of safety in units and as a percentage if sales are expected to be 11,000 units. (3 marks)
(d) Describe how you would draw a traditional break-even chart for this data. (4 marks)
(e) State three limitations of break-even charts. (3 marks)
A further written question
Question 13 (10 marks). A firm has monthly sales of ₦800,000, a margin of safety of 25% and a monthly profit of ₦60,000. (a) Calculate the break-even revenue. (2 marks) (b) Calculate the C/S ratio. (4 marks) (c) Calculate the fixed costs. (2 marks) (d) Calculate the sales required for a profit of ₦120,000. (2 marks)
Model answers
Show the model answer to Question 11
The margin of safety is the difference between budgeted sales and break-even sales, measured in units or naira, and often as a percentage of budgeted sales. It is the most by which actual sales can fall below budget without a loss.
Managers use it as a risk measure: a high margin means a low risk of loss and a low margin means vulnerability, which calls for close monitoring and perhaps changes in price, cost or sales effort. It also helps in decisions and can be applied to individual products or departments.
A break-even chart plots volume on the horizontal axis and naira on the vertical. It has a total revenue line from the origin, a horizontal fixed cost line, and a total cost line that starts at fixed costs and rises with variable cost. The lines cross at the break-even point. Below it is the loss area and above it the profit area.
Budgeted sales can be marked to show the margin of safety. In a second version, fixed costs are drawn above variable costs so that contribution can be seen.
Show the model answer to Question 12
(a)
- Contribution per unit.
(₦100,000 + ₦20,000) ÷ (12,000 − 8,000) = ₦120,000 ÷ 4,000 = ₦30. - Variable cost.
₦90 − ₦30 = ₦60. - Fixed costs.
12,000 × ₦30 − ₦100,000 = ₦260,000.
(b)
- Break-even = ₦260,000 ÷ ₦30 = 8,667 units (8,666.7).
- Revenue = 8,666.7 × ₦90 = ₦780,000.
- (C/S ratio 33.3%: ₦260,000 ÷ 0.3333 = ₦780,000.)
(c) Margin of safety = 11,000 − 8,667 = 2,333 units, which is 2,333 ÷ 11,000 = 21.2% of expected sales.
(d) Put units on the horizontal axis and naira on the vertical axis. Draw a horizontal fixed cost line at ₦260,000. Draw the total cost line from ₦260,000 at zero units to, for example, ₦980,000 at 12,000 units (₦260,000 + 12,000 × ₦60). Draw the revenue line from the origin to ₦1,080,000 at 12,000 units. Mark the break-even point where the lines cross (8,667 units, ₦780,000). Mark expected sales of 11,000 units and the margin of safety. Label the loss and profit areas.
(e) Any three:
- assumes constant price and unit variable cost
- assumes linear relationships
- assumes fixed costs constant in the range
- assumes a constant sales mix
- ignores external and non-financial factors
- unsuitable for long-term decisions
Show the model answer to Question 13
(a) Break-even sales = (1 − 0.25) × ₦800,000 = ₦600,000.
(b)
- The profit comes from the sales above break-even, which earn contribution only.
- C/S ratio × (₦800,000 − ₦600,000) = ₦60,000, so C/S ratio = ₦60,000 ÷ ₦200,000 = 30%.
(c)
- Contribution at ₦800,000 = 30% × ₦800,000 = ₦240,000.
- Fixed costs.
₦240,000 − ₦60,000 = ₦180,000.
(d) Sales = (₦180,000 + ₦120,000) ÷ 0.30 = ₦1,000,000.
Pathfinder on Margin of safety and break-even charts
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.
Items on break-even and margin of safety from budgeted figures. Check Section A of the diet for the exact wording.
Revise first: The margin of safety
An item asks for the break-even point in value from budgeted fixed overhead, which uses the same contribution ratio as the margin of safety.
Revise first: The example used throughout
Multiple-choice items often ask for the margin of safety in units or as a percentage, or what a point on a chart represents. Check Section A of every diet you practise.
Revise first: The break-even chart
Written questions may ask you to draw a break-even or P/V chart from given data and to read off the break-even point and margin of safety.
Revise first: The profit/volume (P/V) chart
Source: ICAN Pathfinder, Management Accounting. Diets covered: November Diet, 2025 and May Diet, 2026. May Diet, 2025 and November Diet, 2024 are not covered here.
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