A new bakery in Abuja sells loaves at ₦600 each. The owner knows that rent, salaries and the oven lease are paid whether or not anyone buys bread. The question every owner asks is simple: how many loaves must we sell each month before we stop losing money? And a second question follows: if we plan to sell more than that, how far can sales fall before the plan fails?
Cost-volume-profit (CVP) analysis answers both. It is an application of marginal costing. It shows how cost and profit change when the volume of activity changes. This topic explains the assumptions of CVP analysis, the concepts of contribution and the contribution to sales ratio, how to calculate the break-even point in units and in revenue, and how to measure the margin of safety.
It builds on the relevant costs for specific decisions topic, which also uses contribution. The next topic covers the contribution to sales ratio, target profit and target revenue.
In 30 seconds
CVP analysis shows how costs and profits change with volume, and applies marginal costing. Contribution = sales − variable costs (include variable selling costs); profit = contribution − fixed costs. C/S ratio = contribution per unit ÷ selling price per unit. Break-even point (units) = fixed costs ÷ contribution per unit. Break-even point (revenue) = fixed costs ÷ C/S ratio, which is the same as units × price.
Margin of safety = budgeted sales − break-even sales, in units or revenue, and as a percentage of budgeted sales; it is how far sales can fall before a loss. The method assumes that costs are fixed or variable, variable cost and price per unit are constant, and fixed costs are constant. Full marks come from the right formula, a clear unit label, and an interpretation.
The nature of CVP analysis
CVP analysis shows how costs and profits change with the volume of activity. It applies marginal costing, and it rests on these assumptions:
- Costs are either fixed or variable.
- The variable cost per unit is the same at all levels of activity.
- Total fixed costs are constant in each period, whatever the output.
- The selling price per unit is constant, so the contribution per unit is constant, and so is the contribution to sales ratio.
- If price, variable cost per unit and fixed costs do not depend on volume, profit is maximised by maximising total contribution.
Contribution
Contribution is sales revenue less variable costs. Profit is contribution less fixed costs. Variable costs include every cost that varies with units sold, including variable selling and distribution costs, so a product with a variable production cost of ₦22 and a variable selling cost of ₦3 has a variable cost of ₦25 a unit. Total contribution = contribution per unit (CPU) × units sold.
At low volumes the contribution does not cover fixed costs and there is a loss; as volume rises the contribution rises, the loss falls, and somewhere there is a volume at which profit is zero. That is the break-even point.
The contribution to sales ratio
The C/S ratio is contribution per unit ÷ selling price per unit, which is the same as total contribution ÷ total sales. It shows how much of each naira of sales is left after variable costs to cover fixed costs and profit. It is constant at all volumes under the assumptions above. Sales revenue can be found from contribution by dividing by the C/S ratio.
Break-even and margin of safety
Break-even point is the volume of sales in a period at which profit is zero. Management uses it to find the minimum sales needed to avoid a loss, and to judge the risk in the budget by comparing budgeted sales with it.
- Method 1, units. Total contribution at break-even equals fixed costs, so break-even units = fixed costs ÷ contribution per unit. Multiply by the price for revenue.
- Method 2, revenue. Break-even revenue = fixed costs ÷ C/S ratio. Divide by the price for units. The two methods give the same answer.
Break-even units that are not whole numbers are rounded up to the next whole unit, because part of a unit cannot be sold. The loss would continue until the next unit is sold.
Margin of safety
The margin of safety is the difference between budgeted sales and break-even sales, in units or in revenue. It is the greatest amount by which actual sales can fall below budget without a loss. It is often given as a percentage of budgeted sales: margin of safety ratio = margin of safety ÷ budgeted sales, which is the same percentage whether it is measured in units or revenue. A high margin of safety means a low risk of loss.
Using the model
- Sales strategy: the effect on profit of a price change, which changes both the contribution per unit and the break-even point.
- Cost control: the effect of changes in fixed or variable cost on the break-even point.
- New products: the minimum sales needed to justify a launch. Production costs are often known with some accuracy, but sales volume is hard to predict, so the model can be flexed to show different volumes.
Where profit at two volumes is known, the contribution per unit is the change in profit divided by the change in units, because fixed costs do not change. Fixed costs then follow from contribution minus profit at either volume.
Layouts
- Contribution per unit = price − variable production cost − variable selling cost.
- C/S ratio = contribution per unit ÷ price.
- Break-even units = fixed costs ÷ contribution per unit. Break-even revenue = fixed costs ÷ C/S ratio = units × price.
- Margin of safety (units) = budgeted units − break-even units. (Revenue) = budgeted revenue − break-even revenue.
- Margin of safety ratio = margin of safety ÷ budgeted sales × 100.
- Budgeted profit = budgeted units × contribution per unit − fixed costs.
Percentages are to one decimal place, break-even units are rounded up to whole units, and each answer is rounded once at the end.
Worked examples
Example 1: break-even and margin of safety. A company sells a product at ₦45. The variable production cost is ₦22 and the variable selling cost ₦3. Fixed costs are ₦900,000 a year. Budgeted sales are 60,000 units. Required: the contribution per unit and C/S ratio, the break-even point, the margin of safety and the budgeted profit.
- Contribution per unit.
45 − 22 − 3 = ₦20.
C/S ratio 20 ÷ 45 = 44.4%. - Break-even units.
900,000 ÷ 20 = 45,000 units.
Revenue 45,000 × 45 = ₦2,025,000.
Check: 900,000 ÷ 0.4444 = 2,025,000. - Margin of safety.
60,000 − 45,000 = 15,000 units, or 15,000 ÷ 60,000 = 25.0% of budgeted sales.
In revenue: 2,700,000 − 2,025,000 = ₦675,000. - Budgeted profit.
60,000 × 20 = 1,200,000
less 900,000 = ₦300,000. - Comment. Sales could fall by a quarter before a loss. That is a comfortable margin, but a competitor’s price cut could remove much of it.
Example 2: a price cut. Continue Example 1. Management considers cutting the price by 10%, with no change in costs. Required: the new break-even point and the margin of safety if sales stay at 60,000 units.
- New price.
45 × 0.90 = ₦40.5.
New contribution 40.5 − 25 = ₦15.5 a unit. - Break-even.
900,000 ÷ 15.5 = 58,064.5, rounded up to 58,065 units. - Margin of safety.
60,000 − 58,065 = 1,935 units, or 1,935 ÷ 60,000 = 3.2%. - Comment. A 10% price cut reduces contribution per unit by a quarter and nearly removes the margin of safety, so volume would have to rise a great deal to justify it.
Example 3: finding the cost structure from two profits. A firm made a profit of ₦300,000 on 60,000 units and ₦500,000 on 70,000 units. Required: the contribution per unit and the fixed costs.
- Contribution per unit.
(500,000 − 300,000) ÷ (70,000 − 60,000) = ₦20. - Fixed costs.
60,000 × 20 = 1,200,000
less profit 300,000 = ₦900,000.
Expect variants: the C/S ratio given instead of the unit costs, a margin of safety stated and the break-even to be found, costs changing next year, or break-even in naira only.
Common mistakes
- Leaving out variable selling costs from the contribution per unit.
- Using the profit per unit instead of contribution to find break-even.
- Mixing units and naira. Fixed costs divided by the C/S ratio gives revenue, not units.
- Not rounding break-even units up.
- Measuring the margin of safety against the wrong base. It is a percentage of budgeted sales.
- Forgetting the assumptions when asked for limits.
Quick revision
- Contribution = sales − variable costs. Profit = contribution − fixed costs. C/S = contribution ÷ sales.
- Break-even units = fixed ÷ CPU. Break-even revenue = fixed ÷ C/S.
- Margin of safety = budgeted − break-even; ratio = margin ÷ budgeted sales.
- Two profit points: CPU = change in profit ÷ change in units.
- Assumptions: fixed or variable, constant price and unit variable cost, constant fixed costs.
How the marks are earned
- Calculate: contribution, C/S ratio, break-even, margin of safety, each with its unit.
- Interpret: what the margin of safety means for risk.
- Discuss: assumptions and their effect on reliability.
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. CVP analysis is an application of:
- Absorption costing
- Activity based costing
- Marginal costing
- Life cycle costing
Show the answer
C. It uses contribution and fixed costs.
Question 2. Contribution equals:
- Sales minus variable costs
- Sales minus fixed costs
- Profit plus variable costs
- Sales minus all costs
Show the answer
A. Include variable selling costs.
Question 3. Break-even units equal:
- Contribution ÷ fixed costs
- Fixed costs ÷ contribution per unit
- Fixed costs ÷ price
- Profit ÷ contribution
Show the answer
B. At break-even, contribution equals fixed costs.
Question 4. Break-even revenue equals:
- Fixed costs × C/S ratio
- Contribution ÷ fixed costs
- Variable costs ÷ price
- Fixed costs ÷ C/S ratio
Show the answer
D. It equals break-even units times price.
Question 5. The margin of safety is:
- Budgeted sales minus break-even sales
- Break-even sales minus budgeted sales
- Fixed costs minus profit
- Contribution minus sales
Show the answer
A. It shows how far sales can fall before a loss.
Question 6. The margin of safety ratio is:
- Break-even ÷ budgeted
- Fixed ÷ variable
- Margin of safety ÷ budgeted sales
- Profit ÷ fixed
Show the answer
C. The same in units or revenue.
Question 7. The target volume in units for a target profit is:
- Profit ÷ price
- Fixed costs ÷ profit
- Variable ÷ contribution
- (Fixed costs + target profit) ÷ contribution per unit
Show the answer
D. Contribution must cover fixed costs and the target.
Question 8. At the break-even point, profit is:
- Maximum
- Zero
- Negative
- Equal to fixed costs
Show the answer
B. Contribution equals fixed costs.
Question 9. An assumption of CVP analysis is that:
- Fixed costs rise with output
- Price falls with volume
- Selling price and variable cost per unit are constant
- Costs cannot be classified
Show the answer
C. So contribution per unit is constant.
Question 10. A high margin of safety indicates:
- A low risk of making a loss
- A high risk of loss
- Sales below break-even
- No fixed costs
Show the answer
A. Sales can fall a long way before a loss.
Section B style: written questions
Question 11 (10 marks). (a) State FOUR assumptions of CVP analysis. (4 marks) (b) Explain what the break-even point and the margin of safety show management. (6 marks)
Question 12 (15 marks). A company sells a product at ₦80 with a variable cost of ₦32. Fixed costs are ₦720,000 and budgeted sales are 22,000 units.
(a) Calculate the contribution per unit and the C/S ratio. (3 marks) (b) Calculate the break-even point in units and revenue. (4 marks) (c) Calculate the margin of safety in units, as a percentage, and in revenue. (4 marks) (d) Calculate the budgeted profit. (2 marks) (e) Comment on the risk. (2 marks)
Question 13 (20 marks). A company has monthly sales of ₦150,000 and a profit of ₦9,000. Its margin of safety is 20% of budgeted sales.
(a) Calculate the break-even sales. (2 marks) (b) Calculate total costs at budgeted sales and at break-even, and from these the variable cost percentage and the fixed costs. (6 marks) (c) Calculate the C/S ratio. (2 marks) (d) Calculate the sales needed for a profit of ₦15,000. (4 marks) (e) Discuss the limitations of CVP analysis. (6 marks)
Model answers
Show the model answer to Question 11
(a) Any four:
- costs are fixed or variable
- variable cost per unit is constant
- total fixed cost is constant
- selling price per unit is constant
- contribution per unit and C/S ratio are constant
- a constant sales mix for several products (1 each)
(b) The break-even point is the sales volume at which there is neither profit nor loss, so it is the minimum sales to avoid a loss (2). Comparing budgeted sales with it shows the risk in the budget (1).
The margin of safety is budgeted sales minus break-even sales, the amount by which sales can fall before a loss (2); expressed as a percentage of budgeted sales it allows comparison. A high figure means low risk (1).
Show the model answer to Question 12
(a)
- 80 − 32 = ₦48
- C/S 48 ÷ 80 = 60.0% (3).
(b)
- 720,000 ÷ 48 = 15,000 units
- revenue 15,000 × 80 = ₦1,200,000 (4).
(c)
- 22,000 − 15,000 = 7,000 units
- 7,000 ÷ 22,000 = 31.8%
- revenue 1,760,000 − 1,200,000 = ₦560,000 (4).
(d)
- 22,000 × 48 = 1,056,000
- less 720,000 = ₦336,000 (2).
(e) Sales can fall by nearly a third before a loss, so the risk is low, though a price cut or a fall in demand would reduce it (2).
Show the model answer to Question 13
(a) Break-even sales = 80% × 150,000 = ₦120,000 (2).
(b)
- Total costs at budget 150,000 − 9,000 = ₦141,000; at break-even ₦120,000 (2).
- Difference in cost 21,000 over difference in sales 30,000 = 70% variable cost (2).
- Variable cost at budget 0.70 × 150,000 = 105,000
- fixed costs 141,000 − 105,000 = ₦36,000 (2).
(c) C/S ratio = 100% − 70% = 30% (2).
(d) (36,000 + 15,000) ÷ 0.30 = ₦170,000 (4).
(e) Costs are hard to split into fixed and variable; variable cost per unit may change with volume (overtime, discounts); fixed costs are fixed only within a range and may step up; the price may change with volume; products are not sold in constant ratios; the analysis ignores the uncertainty in estimates; the answers may be outside the range of the data (any six, 1 each).
Pathfinder on Break-even analysis and margin of safety
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.
Marginal mix for one plant, throughput accounting profitability, new plant marginal statement, break-even units and value, combined statement, RI viability.
Revise first: Layouts
Selling price, sales, break-even and margin of safety from contribution data; choose price-cut strategy; challenges in developing an MIS.
Revise first: Layouts
Product contribution/profit, drop a product, extra sales to cover advertising; relevant cost quote for a one-off job; incremental, differential, committed, sunk, opportunity cost.
Revise first: Layouts
Source: ICAN Pathfinder, Performance Management. Diets covered: March/July Diet, 2020 to May Diet, 2026. All 13 diets in the Pathfinder are mapped.
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