An owner who knows the break-even point knows how few loaves must be sold to stop the losses. The next question is more ambitious: how many must be sold to earn the profit the owner wants?
A distributor wants to earn ₦585,000 a year, a shop wants its sales to carry a ₦540,000 target, and a manufacturer wants next year’s profit to match this year’s even though the price, the variable cost and the rent are all about to change. Each of these is the same calculation with a different target.
The contribution needed is the fixed costs plus the target profit, and it is divided by the contribution per unit or by the contribution to sales ratio. This topic explains how to use the C/S ratio, how to find the sales in units and revenue for a target profit, how to deal with changes in price and cost, and how to work backwards from given ratios.
It builds on the break-even and margin of safety topic. The next topic covers break-even charts and profit-volume charts.
In 30 seconds
The C/S ratio = contribution per unit ÷ selling price; it is the same at every volume. Target volume (units) = (fixed costs + target profit) ÷ contribution per unit. Target revenue = (fixed costs + target profit) ÷ C/S ratio = units × price. Break-even is the special case where the target profit is zero. If the price, variable cost or fixed costs change, recalculate the contribution per unit and fixed costs first.
If the C/S ratio and the variable cost per unit are known, price = variable cost ÷ (1 − C/S ratio). Round units up. Full marks come from showing the total contribution needed, then the division, then both units and revenue if asked.
The C/S ratio and the target profit
The contribution to sales ratio measures how much of each naira of sales remains after variable costs, to pay for fixed costs and profit. It is the contribution per unit divided by the price per unit, and it equals total contribution divided by total sales at any volume, because price and variable cost per unit are assumed constant.
A C/S ratio of 60% means that ₦60 of every ₦100 of sales is contribution. Sales revenue can be found from contribution by dividing by the ratio. Because the ratio is constant, a change in sales revenue changes contribution, and profit, by that percentage of the change.
Target profit
Management often asks what sales are needed to earn a target profit. The total contribution must cover both the fixed costs and the target profit, so:
- Contribution needed = fixed costs + target profit.
- Target volume in units = contribution needed ÷ contribution per unit. Multiply by the price for the revenue.
- Target revenue = contribution needed ÷ C/S ratio. Divide by the price for units.
The two routes give the same answer. Break-even is the case where the target profit is zero. If a question gives a target profit after tax, divide it by one minus the tax rate to find the profit before tax first; where a question says nothing about tax, ignore it.
Changes in price and cost, and working backwards
- A change in price changes the contribution per unit and the C/S ratio, so the break-even and target volumes change.
- A change in variable cost per unit changes the contribution per unit and the C/S ratio.
- A change in fixed costs changes the contribution needed but not the contribution per unit.
- To match a profit next year, find this year’s profit, set it as the target, adjust the price and costs for next year, and use the new contribution per unit and fixed costs.
Sometimes a question gives ratios and asks for the price or cost. If the C/S ratio is 40%, then variable cost is 60% of the price, so price = variable cost per unit ÷ 0.60. If the margin of safety ratio is given, the break-even sales are (1 − margin of safety ratio) times budgeted sales.
With total costs at two sales levels, the variable cost percentage is the change in total cost divided by the change in sales. Fixed costs are total cost less variable cost.
Using the answers
A target volume should be compared with capacity and with likely demand. If the volume needed is more than the market will buy or the factory can make, the target is not realistic, and management must change price, cost or the target. The model assumes constant price and unit variable cost, so volumes far outside the normal range should be treated with caution.
Layouts
- C/S ratio = contribution per unit ÷ price.
- Contribution needed = fixed costs + target profit.
- Target units = contribution needed ÷ contribution per unit (round up). Target revenue = contribution needed ÷ C/S ratio.
- Price from the ratio = variable cost per unit ÷ (1 − C/S ratio).
- Next year’s contribution per unit = new price − new variable cost; new fixed costs = old × (1 + change).
Money is in naira, units are rounded up, and each answer is rounded once at the end.
Worked examples
Example 1: target profit. A product sells for ₦65 with a variable cost of ₦26. Fixed costs are ₦1,170,000 a year and the target profit is ₦585,000. Required: the contribution per unit, the C/S ratio, and the units and revenue needed.
- Contribution per unit and C/S ratio.
Contribution = 65 − 26 = ₦39
C/S ratio = 39 ÷ 65 = 60% - Contribution needed. Fixed costs plus the target profit must all come from contribution.
1,170,000 + 585,000 = ₦1,755,000 - Target units. Divide by the contribution per unit.
1,755,000 ÷ 39 = 45,000 units - Revenue.
45,000 × 65 = ₦2,925,000 - Check. Contribution needed divided by the C/S ratio gives the same revenue.
1,755,000 ÷ 0.60 = 2,925,000 ✓
Example 2: matching this year’s profit next year. This year a company sells 10,000 units at ₦60 with a variable cost of ₦24 and fixed costs of ₦300,000. Next year the price will rise by 5%, the variable cost by 10% and fixed costs by 8%. Required: the units needed to earn the same profit as this year.
- This year’s profit. Total contribution less fixed costs.
10,000 × (60 − 24) = 360,000
360,000 − 300,000 = ₦60,000 - Next year’s figures. Raise each figure by its percentage.
Price = 60 × 1.05 = ₦63
Variable cost = 24 × 1.10 = ₦26.40
Contribution = 63 − 26.40 = ₦36.60
Fixed costs = 300,000 × 1.08 = ₦324,000 - Contribution needed. Fixed costs plus the same profit as this year.
324,000 + 60,000 = ₦384,000 - Units. Round up, because the target must be reached.
384,000 ÷ 36.6 = 10,491.8, so 10,492 units - Comment. Volume must rise by about 5% (10,492 ÷ 10,000), because fixed costs and variable cost rise faster than the price.
Example 3: price from the C/S ratio. A product has a variable cost of ₦30 a unit and a C/S ratio of 40%. Fixed costs are ₦420,000. Required: the price, and the break-even units and revenue.
- Price. The C/S ratio is 40%, so variable cost is the other 60% of the price.
Price = 30 ÷ 0.60 = ₦50
Contribution per unit = 50 − 30 = ₦20 - Break-even revenue. Fixed costs divided by the C/S ratio.
420,000 ÷ 0.40 = ₦1,050,000 - Break-even units.
1,050,000 ÷ 50 = 21,000 units - Check. Fixed costs divided by the contribution per unit.
420,000 ÷ 20 = 21,000 ✓
Expect variants: a target profit per unit sold, a target return on capital, a target after tax, sales in naira only, and several changes at once.
Other forms of target
A target may be stated as a profit per unit, as a margin on sales or as a return on capital employed. Convert it to a total profit first. A return of 15% on capital of ₦4,000,000 means a target profit of ₦600,000.
A margin of 12% on sales means that profit is 0.12 times revenue, so the contribution needed is fixed costs plus 0.12 times revenue. The revenue needed is fixed costs ÷ (C/S ratio − 0.12).
Example. Use the data of Example 1: a C/S ratio of 60% and fixed costs of ₦1,170,000. Find the revenue for a 12% margin on sales.
- Subtract the margin from the C/S ratio. This is the part of each naira of sales that pays the fixed costs.
0.60 − 0.12 = 0.48 - Divide the fixed costs.
1,170,000 ÷ 0.48 = ₦2,437,500 - Find the profit. It is 12% of revenue.
12% × 2,437,500 = ₦292,500 - Check. Contribution less fixed costs should give the same profit.
60% × 2,437,500 = 1,462,500
1,462,500 − 1,170,000 = 292,500 ✓
Common mistakes
- Forgetting to add the target profit to fixed costs.
- Dividing by the C/S ratio when units are asked for and not converting by the price.
- Using old unit cost after a price or cost change. Recalculate first.
- Raising fixed costs by the wrong percentage or applying it to variable cost.
- Not rounding units up.
- Ignoring the after-tax wording when it is given.
Quick revision
- Contribution needed = fixed costs + target profit.
- Target units = needed ÷ CPU; target revenue = needed ÷ C/S ratio.
- Price = variable cost ÷ (1 − C/S ratio).
- Matching profit next year: new CPU, new fixed costs, same profit target.
How the marks are earned
- Calculate: the contribution needed, the division, and both units and revenue.
- Adjust: show the new price, variable cost and fixed costs before the division.
- Comment: compare the target with capacity or demand.
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. The C/S ratio is:
- Fixed costs ÷ sales
- Contribution per unit ÷ selling price per unit
- Profit ÷ sales
- Variable cost ÷ contribution
Show the answer
B. It is constant at all volumes.
Question 2. Fixed costs are ₦200,000 and the C/S ratio is 40%. Break-even revenue is:
- ₦80,000
- ₦240,000
- ₦400,000
- ₦500,000
Show the answer
D. 200,000 ÷ 0.40 = 500,000.
Question 3. A contribution per unit of ₦8 and fixed costs of ₦600,000 give break-even of:
- 75,000 units
- 48,000 units
- 7,500 units
- 4,800 units
Show the answer
A. 600,000 ÷ 8 = 75,000.
Question 4. The sales in units needed for a target profit are:
- Profit ÷ price
- Fixed costs ÷ profit
- (Fixed costs + target profit) ÷ contribution per unit
- Fixed costs ÷ C/S ratio
Show the answer
C. Contribution must cover fixed costs and the target.
Question 5. The revenue needed for a target profit is:
- (Fixed costs + target profit) ÷ C/S ratio
- Target profit × C/S ratio
- Fixed costs × C/S ratio
- Variable costs ÷ profit
Show the answer
A. Divide by units’ price to get units.
Question 6. A variable cost of ₦30 and a C/S ratio of 40% give a price of:
- ₦42
- ₦75
- ₦50
- ₦12
Show the answer
C. 30 ÷ 0.60 = 50.
Question 7. If the selling price rises and variable cost stays the same, the C/S ratio:
- Falls
- Is unchanged
- Is zero
- Rises
Show the answer
D. Contribution per unit rises by more than the price.
Question 8. The contribution needed for a target profit equals:
- Fixed costs only
- Fixed costs plus target profit
- Variable costs plus profit
- Target profit only
Show the answer
B. Break-even is the case of zero target profit.
Question 9. If fixed costs rise by 10% and contribution per unit is unchanged, break-even units:
- Fall by 10%
- Stay the same
- Rise by 10%
- Double
Show the answer
C. Break-even is proportional to fixed costs.
Question 10. Profit equals:
- Contribution minus fixed costs
- Sales minus contribution
- Fixed costs minus contribution
- Sales plus variable costs
Show the answer
A. Contribution is sales less variable costs.
Section B style: written questions
Question 11 (10 marks). (a) Explain the C/S ratio and why it is useful. (4 marks) (b) State the formulae for the units and revenue needed to earn a target profit. (4 marks) (c) State how a price rise affects the break-even point. (2 marks)
Question 12 (15 marks). A product sells for ₦120 with a variable cost of ₦48. Fixed costs are ₦1,260,000 and the target profit is ₦540,000.
(a) Calculate the contribution per unit and the C/S ratio. (3 marks) (b) Calculate the break-even units. (3 marks) (c) Calculate the units and revenue needed for the target profit. (4 marks) (d) If the price were cut by 10%, calculate the units needed for the target profit. (3 marks) (e) Comment on the price cut. (2 marks)
Question 13 (20 marks). A company has monthly sales of ₦200,000 and a profit of ₦12,000. Its margin of safety is 10% of budgeted sales.
(a) Calculate the break-even sales. (2 marks) (b) Calculate total costs at budgeted sales and at break-even. (2 marks) (c) Calculate the variable cost percentage and fixed costs. (6 marks) (d) Calculate the C/S ratio. (2 marks) (e) Calculate the sales needed for a profit of ₦30,000. (4 marks) (f) State TWO uses of these results to management. (4 marks)
Model answers
Show the model answer to Question 11
(a) The C/S ratio is contribution per unit divided by the selling price per unit (1). It shows the part of each naira of sales available to cover fixed costs and profit (1). It is constant at all volumes, so revenue can be found from contribution (1), and it allows break-even and target sales in naira to be found without unit data (1).
(b) Units = (fixed costs + target profit) ÷ contribution per unit (2). Revenue = (fixed costs + target profit) ÷ C/S ratio (2).
(c) A price rise increases the contribution per unit and the C/S ratio, so the break-even point falls (2).
Show the model answer to Question 12
(a)
- Contribution per unit.
120 − 48 = ₦72 - C/S ratio.
72 ÷ 120 = 60% (3)
(b)
- Break-even units. Fixed costs divided by the contribution per unit.
1,260,000 ÷ 72 = 17,500 units (3)
(c)
- Contribution needed.
1,260,000 + 540,000 = ₦1,800,000 - Units.
1,800,000 ÷ 72 = 25,000 - Revenue.
25,000 × 120 = ₦3,000,000 (4)
(d)
- New contribution. The new price is ₦108.
108 − 48 = ₦60 - Units. The contribution needed is still ₦1,800,000.
1,800,000 ÷ 60 = 30,000 (3)
(e) A 10% price cut cuts the contribution per unit by a sixth and needs 20% more volume to earn the same profit, so it is worthwhile only if demand is likely to rise by more than that (2).
Show the model answer to Question 13
(a) 90% × 200,000 = ₦180,000 (2).
(b) At budget 200,000 − 12,000 = ₦188,000; at break-even ₦180,000 (2).
(c)
- Variable cost ratio. Change in cost divided by change in sales.
8,000 ÷ 20,000 = 40% (3) - Variable cost at budget.
0.40 × 200,000 = 80,000 - Fixed costs. Total cost at budget less variable cost.
188,000 − 80,000 = ₦108,000 (3)
(d) 100% − 40% = 60% (2).
(e)
- Add the amounts. Fixed costs of 108,000 plus 30,000.
108,000 + 30,000 = 138,000 - Divide by the C/S ratio. The ratio is 60%.
138,000 ÷ 0.60 = ₦230,000 (4)
(f) Any two, developed:
- set sales targets
- judge the risk in the budget
- test the effect of price and cost changes on profit
- decide whether a target is realistic given capacity and demand (2 each)
Pathfinder on C/S ratio, target profit and target revenue
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.
Multi-product break-even in units and value, revised budget, revenue for after-tax return.
Revise first: Layouts
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
Multi-product break-even in units and value; revised mix, target after-tax profit.
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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