A table of figures says that the company breaks even at 45,000 units. A chart says it in a way that a director can see across the boardroom: the revenue line crossing the cost line, the loss on one side, the profit on the other, and the budget sitting to the right of the crossing with a visible gap between them.
Charts do not give any information that the formulae do not, but they show the shape of the relationship, they show every volume at once, and they make the margin of safety visible.
This topic explains how to construct and read a break-even chart and a profit-volume (P/V) chart, the difference between the two forms of break-even chart, how to find the data for a chart from two profit figures, and the uses and limits of charts. It builds on the target profit topic. The next topic covers multi-product CVP analysis.
In 30 seconds
A break-even chart plots, for all volumes of output and sales, total costs (analysed into variable and fixed), sales revenue, and so the profit (the gap between sales and total costs), the break-even point (where total costs equal sales) and, if budgeted sales are marked, the margin of safety.
The fixed cost line is horizontal; the total cost line starts at the fixed cost level at zero output and rises at the variable cost per unit; the sales line starts at the origin. In the second form, fixed costs are drawn on top of variable costs, which shows the total contribution.
A profit-volume (P/V) chart plots profit or loss against sales: it starts at a loss equal to fixed costs, rises with a slope equal to the contribution per unit (or the C/S ratio if sales revenue is on the axis) and crosses the axis at break-even. Full marks come from correctly labelled lines and the points read from them.
Break-even charts
A break-even chart shows, for all volumes of output and sales:
- total costs, analysed into variable and fixed costs
- sales revenue
- profit, the difference between sales and total costs
- the break-even point, where total costs equal sales revenue and profit is zero
It resembles a cost behaviour chart with sales revenue added.
If budgeted sales are shown, the margin of safety is the distance between the budgeted volume and the break-even volume.
How to draw one
- Choose the axes: volume of sales (units or revenue) along the bottom, naira up the side. Use a range that goes beyond the budget.
- Plot the fixed cost line, horizontal, at the level of fixed costs. It is the same at all volumes.
- Plot the total cost line. It starts at the fixed cost level at zero output and rises in a straight line. Find the total cost at a high volume (fixed costs + variable cost per unit × units) and join the two points. (In the usual form the variable costs are drawn on top of the fixed costs.)
- Plot the sales line, from the origin to sales at the same high volume, because the price is constant.
- Mark the break-even point where the sales and total cost lines cross. Label the loss area to the left and the profit area to the right.
- Mark the budgeted sales and show the margin of safety.
In the second form, fixed costs are drawn on top of variable costs: the variable cost line rises from the origin and the total cost line runs parallel above it. The total costs are exactly the same as in the first form. The advantage is that the total contribution is the gap between the sales line and the variable cost line, and at break-even the contribution equals the fixed costs.
Profit-volume charts
A profit-volume (P/V) chart is an alternative way of presenting CVP information. It shows the profit or loss at all levels of output and sales. At zero sales there is a loss equal to the fixed costs. The loss shrinks as sales volume rises, because contribution rises. The line crosses the horizontal axis at the break-even point and profit grows after it.
The slope of the line is the contribution per unit when volume is on the axis, and the C/S ratio when sales revenue is on the axis.
A line drawn horizontally at the level of the fixed cost loss shows the fixed costs, and the gap between the profit line and that line is the total contribution. The P/V chart is simpler than the break-even chart, because it plots one line, and it shows the profit at any volume directly. It is the basis of the multi-product chart in the next topic.
Finding the data for a chart
Often a question gives profit at two volumes instead of costs. The contribution per unit is the change in profit divided by the change in units, because fixed costs do not change. The variable cost per unit is the price less the contribution per unit. The fixed costs are the contribution at either volume less the profit at that volume.
With these the chart can be drawn and the break-even point and margin of safety read off.
Uses and limits
- Uses: they show profit and loss at all volumes at a glance; they show the margin of safety; they help non-accountants to see risk; they let managers test the effect of changes in price, variable cost and fixed costs by redrawing the line.
- Limits: they are only as reliable as the assumptions (constant price and variable cost per unit, constant fixed costs); they show a straight line where real behaviour may step or curve; a graph cannot be as precise as a formula, so the break-even point read from it should be checked by calculation.
Layouts for chart data
- Sales at volume V = V × price (and zero at zero volume).
- Total cost at volume V = fixed costs + V × variable cost per unit.
- Profit at volume V = V × contribution per unit − fixed costs.
- Contribution per unit from two profits.
(profit 2 − profit 1) ÷ (units 2 − units 1). - Fixed costs = contribution at a volume − profit at that volume.
- Break-even = fixed costs ÷ contribution per unit; margin of safety = budget − break-even.
Money is in naira and each answer is rounded once at the end.
Worked examples
Example 1: data for a break-even chart. A product sells at ₦45 with a variable cost of ₦25. Fixed costs are ₦900,000. Budgeted sales are 60,000 units. Prepare the data for a break-even chart up to 80,000 units, and state the break-even point and margin of safety.
- Fixed cost line. ₦900,000 at every volume.
- Total costs. At 0 units 900,000.
At 80,000 units 900,000 + 80,000 × 25 = ₦2,900,000. - Sales. At 0 units 0.
At 80,000 units 80,000 × 45 = ₦3,600,000. - Break-even.
900,000 ÷ 20 = 45,000 units; revenue ₦2,025,000.
This is where the lines cross in the chart above. - Margin of safety.
60,000 − 45,000 = 15,000 units. - Budgeted profit.
60,000 × 20 − 900,000 = ₦300,000.
Example 2: the P/V chart. Use the same data. Required: the points for a P/V chart with volume on the axis.
- At 0 units. Loss of ₦900,000.
- At 45,000 units. Profit zero (break-even).
- At 60,000 units.
60,000 × 20 − 900,000 = ₦300,000. - At 80,000 units.
80,000 × 20 − 900,000 = ₦700,000. - Slope. ₦20 of profit for each extra unit, which is the contribution per unit.
Example 3: data from two profit figures. The selling price is ₦90. The company made a loss of ₦40,000 on 10,000 units and a profit of ₦200,000 on 16,000 units. Required: the contribution per unit, the variable cost, the fixed costs, break-even, and the margin of safety at 14,000 units.
- Contribution per unit.
(200,000 + 40,000) ÷ (16,000 − 10,000) = ₦40.
Variable cost 90 − 40 = ₦50.
C/S ratio 44.4%. - Fixed costs. At 10,000 units contribution 400,000; loss 40,000; so fixed costs ₦440,000.
- Break-even.
440,000 ÷ 40 = 11,000 units. - Margin of safety at 14,000 units.
3,000 units, or 3,000 ÷ 14,000 = 21.4%.
Expect variants: a chart in naira instead of units, a change in fixed costs or price to be shown on the same chart, and a question that asks you to read the profit at a given volume.
Common mistakes
- Starting the total cost line at zero. It starts at the fixed cost level.
- Drawing the fixed cost line sloping. It is horizontal.
- Starting the P/V line at zero. It starts at a loss equal to the fixed costs.
- Not labelling the lines, axes and the break-even point.
- Reading the break-even point only from the graph. Confirm by calculation.
- Mixing units and naira on one axis.
Quick revision
- Break-even chart: fixed line horizontal; total costs from fixed level; sales from origin; crossing is break-even; gap to budget is margin of safety.
- Second form: fixed costs on top of variable; shows contribution.
- P/V chart: starts at loss equal to fixed costs; slope contribution per unit; crosses axis at break-even.
- From two profits: CPU = change in profit ÷ change in units; fixed costs = contribution − profit.
How the marks are earned
- Draw: a mark for each correct line, axis labels and the break-even point.
- Calculate: the chart data, with the working.
- Interpret: the margin of safety and what a change would do.
Practice questions
These are original questions, written in the style of the Skills examination. Work each one before you open the answer.
Recall check: multiple choice
Question 1. On a break-even chart the break-even point is where:
- Fixed costs are zero
- Variable costs are zero
- Profit is maximum
- Total revenue equals total costs
Show the answer
D. Profit is zero there.
Question 2. The fixed cost line on a break-even chart is:
- Sloping upwards
- Horizontal
- Sloping downwards
- Curved
Show the answer
B. Fixed costs are the same at all volumes.
Question 3. At zero output the total cost line starts at:
- The fixed cost level
- Zero
- The sales line
- The break-even point
Show the answer
A. Fixed costs are incurred even with no output.
Question 4. The distance between budgeted sales and break-even on the chart is the:
- Contribution
- Fixed cost
- Margin of safety
- Profit
Show the answer
C. It is the fall that sales can take before a loss.
Question 5. A P/V chart shows:
- Only sales
- The profit or loss at each level of sales
- Only costs
- Only variable costs
Show the answer
B. It is a single line.
Question 6. At zero sales, the P/V line shows a loss equal to:
- The fixed costs
- The variable costs
- Zero
- The contribution
Show the answer
A. Fixed costs are incurred with no contribution.
Question 7. With volume on the horizontal axis, the slope of the P/V line equals:
- The fixed cost
- The price
- The C/S ratio
- The contribution per unit
Show the answer
D. Each extra unit adds that much profit.
Question 8. A break-even chart with fixed costs drawn on top of variable costs shows clearly:
- The selling price
- The tax
- The total contribution
- The overheads
Show the answer
C. It is the gap between sales and variable costs.
Question 9. The P/V line crosses the horizontal axis at the:
- Budgeted sales
- Origin
- Break-even point
- Capacity
Show the answer
C. Profit is zero there.
Question 10. An advantage of a chart is that it:
- Shows profit and loss at all volumes at a glance
- Is more exact than a formula
- Removes the assumptions
- Shows tax
Show the answer
A. It also shows the margin of safety visually.
Section B style: written questions
Question 11 (10 marks). (a) Describe the steps in drawing a break-even chart. (6 marks) (b) State TWO differences between the break-even chart and the P/V chart. (4 marks)
Question 12 (15 marks). A product sells at ₦80 with a variable cost of ₦30. Fixed costs are ₦500,000. Budgeted sales are 14,000 units.
(a) Calculate the contribution per unit and break-even units. (3 marks) (b) Calculate the sales, fixed cost and total cost at 0 and 20,000 units for a chart. (4 marks) (c) Calculate the margin of safety in units and as a percentage. (3 marks) (d) Calculate the budgeted profit and the total cost at budget. (3 marks) (e) State what the chart would show at the budgeted level. (2 marks)
Question 13 (20 marks). The selling price is ₦120. A company made a loss of ₦90,000 on 9,000 units and a profit of ₦270,000 on 15,000 units.
(a) Calculate the contribution per unit, the C/S ratio and the fixed costs. (6 marks) (b) Calculate break-even and the margin of safety at 15,000 units. (4 marks) (c) Describe how you would draw a P/V chart for the data. (6 marks) (d) State TWO advantages and TWO limits of charts. (4 marks)
Model answers
Show the model answer to Question 11
(a) Draw axes with volume across and naira up (1). Draw the horizontal fixed cost line (1). Draw the total cost line starting at fixed costs and rising by the variable cost per unit (1). Draw the sales line from the origin (1). Mark the break-even point where sales and total costs cross (1). Mark the budget and the margin of safety, and label loss and profit areas (1).
(b) The break-even chart plots total costs and sales and shows profit as the gap between them, while the P/V chart plots profit or loss directly in one line (2). The P/V line starts at a loss equal to fixed costs and its slope is the contribution per unit, while the break-even chart starts the sales line at the origin and the cost line at fixed costs (2).
Show the model answer to Question 12
(a)
- 80 − 30 = ₦50
- break-even 500,000 ÷ 50 = 10,000 units (3).
(b)
- At 0 units: sales 0, fixed cost 500,000, total cost 500,000.
- At 20,000 units: sales ₦1,600,000, fixed cost ₦500,000, total cost 500,000 + 20,000 × 30 = ₦1,100,000 (4).
(c)
- 14,000 − 10,000 = 4,000 units
- 4,000 ÷ 14,000 = 28.6% (3).
(d) Profit 14,000 × 50 − 500,000 = ₦200,000; total cost at budget 500,000 + 14,000 × 30 = ₦920,000; sales ₦1,120,000 (3).
(e) The sales line is above the total cost line by ₦200,000 at 14,000 units, and the budget lies 4,000 units to the right of the break-even point (2).
Show the model answer to Question 13
(a)
- (270,000 + 90,000) ÷ (15,000 − 9,000) = ₦60 (2).
- C/S 60 ÷ 120 = 50.0% (2).
- Fixed costs: at 9,000 units contribution 540,000, loss 90,000, so fixed costs ₦630,000 (2).
(b)
- Break-even 630,000 ÷ 60 = 10,500 units (2).
- Margin of safety 15,000 − 10,500 = 4,500 units, or 30.0% (2).
(c) Label axes with volume and profit or loss (1). Plot the loss of 630,000 at zero sales (1). Plot the profit at 15,000 units, 15,000 × 60 − 630,000 = 270,000 (1). Join the points with a straight line (1). The line crosses the axis at 10,500 units, the break-even point (1). Mark the margin of safety to the budget (1).
(d) Advantages, any two: show profit and loss at all volumes at a glance; show the margin of safety; help non-accountants see risk; can test changes. Limits, any two: depend on constant price and unit variable cost; assume constant fixed costs; real costs may step or curve; less precise than formulae (1 each).
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