A LevelAccountingCambridge (CIE)Revision NotesFundamentals of Cost & Management AccountingMarginal CostingBreak-even Analysis

Break-even Analysis (Cambridge (CIE) A Level Accounting): Revision Note

Exam code: 9706

Seina Murakami

Written by: Seina Murakami

Reviewed by: Dan Finlay

Updated on

Break-even charts

What is a break-even chart? 

  • A break-even chart is a graphical representation of costs, revenue, and profit at different levels of output 

  • The number of units sold or produced is plotted on the horizontal axis

  • The costs and revenue in monetary terms ($) are plotted on the vertical axis

  • The line for fixed cost is horizontal because it doesn’t change with the output level

  • The lines for variable cost and revenue increase as output level increases

  • The line for total cost

    • starts at the same value as the fixed cost

    • and is parallel to the line for variable cost

  • The break-even point is the point at which total revenue equals total costs 

    • Total costs are covered by sales 

    • No profit or loss is made 

Graph showing break-even analysis with lines for revenue, total cost, variable cost, and fixed cost intersecting at the break-even point.
Break-even chart

Examiner Tips and Tricks

You will never be required to construct a break-even chart in the exam. You just need to be able to interpret them and use them in calculations.

Calculations using a break-even chart

How do I calculate the break-even point? 

  • The formula for the number of units required to break-even is:

    • Break minus even space point space in space units space equals space fraction numerator Total space fixed space costs over denominator Contribution space per space unit end fraction

    • If your answer is a decimal, you should always round your answer up to the next whole number

  • There are two formulas for the sales revenue required to break-even:

    • Break minus even space point space in space sales space revenue space equals Break minus even space units cross times Selling space price space per space unit

    • Break ひく even スペース point スペース in スペース sales スペース revenue スペース イコール スペース Contribution スペース to スペース sales スペース ratio 分の Total スペース fixed スペース costs 分数の終わり

Graph showing break-even point where revenue and total cost lines intersect. X-axis is number of units, Y-axis is dollars.
Break-even point

Examiner Tips and Tricks

You can use whichever formula you want. However, if a question first asks you to find the contribution to sales ratio, then it is easier to use that to find the break-even point.

If you forget the formulas, you can easily derive them using algebra. Let x be the number of units sold, S be the selling price per unit, F be the fixed cost and V be the variable cost per unit.

table row Revenue equals cell Total space cost end cell row cell S x end cell equals cell F plus V x end cell row cell S x minus V x end cell equals F row cell x open parentheses S minus V close parentheses end cell equals F row x equals cell fraction numerator F over denominator S minus V end fraction end cell end table

Worked Example

The following forecasted data is available.

$

Total fixed costs

100 000

Direct materials

3 000

Direct labour

5 000

Other direct costs

6 000

Sales revenue (10 000 units)

200 000

Calculate the break-even point in units.

Answer: 

Calculate the total variable cost

Variable costs = Direct materials + Direct labour + Other direct costs 

= $3 000 + $5 000 + $6 000 

= $14 000 

Calculate the total contribution

Contribution = Revenue - Variable costs 

= $200 000 - $14 000

= $186 000 

Calculate the contribution per unit

Contribution per unit = Total contribution ÷ Number of units 

= $186 000 ÷ 10 000 

= $18.60 per unit 

Calculate the break-even point in units

Break-even point in units = Total fixed costs ÷ Contribution per unit 

  = $100 000 ÷ 18.6 

  = 5 376.34

Round up to the next whole number

Break-even point in units is 5 377 units

How do I calculate the level of output required to achieve a target profit? 

  • The formula for the number of units required to achieve a target profit is:

    • Level スペース of スペース output スペース required スペース in スペース units スペース イコール スペース Contribution スペース per スペース unit 分の Total スペース fixed スペース costs スペース たす スペース Target スペース profit 分数の終わり

    • If your answer is a decimal, you should always round your answer up to the next whole number

  • There are two formulas for the sales revenue required to achieve a target profit:

    • Level スペース of スペース output スペース required スペース in スペース sales スペース revenue スペース イコール スペース Contribution スペース to スペース sales スペース ratio 分の Total スペース fixed スペース costs スペース たす スペース Target スペース profit 分数の終わり

    • Level space of space output space required space in space sales space revenue space equals space Target space profit space units cross times Selling space price space per space unit

Graph showing two lines: red for revenue and blue for total cost, with an arrow indicating target profit difference, labelled axes in dollars and units.
Target profit

Worked Example

Total fixed cost $40 000 

Variable cost per unit $30 per unit 

Selling price per unit $50 per unit 

What is the level of output required in units and in sales revenue for a target profit of $60 000?

Answer: 

Calculate the contribution per unit

Contribution per unit = Selling price per unit - Variable cost per unit 

= $50 -$ 30 

= $20 per unit 

Calculate the number of units required to make the profit

Level of output required in units = (Total fixed costs + Target profit) ÷ Contribution per unit

= ($40 000 + $60 000) ÷ $20 

= 5 000 units

The level of output required to achieve a target profit of $60 000 is 5 000 units

Multiply this by the selling price per unit

5 000 × $50

= $250 000

Or calculate the contribution to sales ratio and use the relevant formula

Sales to contribution ratio = $20 ÷ $50 = 0.4

Level of output required in sales revenue = (Total fixed costs + Target profit) ÷ Contribution to sales ratio

= ($40 000 + $60 000) ÷ 0.4

= $250 000

The level of output required to achieve a target profit of $60 000 is $250 000 in sales revenue

How do I calculate the margin of safety? 

  • The margin of safety is the difference between actual/forecast output and the break-even level of output

  • It shows how much sales can fall before a business reaches the break-even point

  • The formula for the number of units in the margin of safety is:

    • Margin space of space safety space in space units space equals space Actual divided by forecasted space production space units space minus space Break minus even space point space units

Graph showing revenue and total cost lines intersecting, with margin of safety highlighted. Axes labelled as dollars and number of units.
Margin of safety

Worked Example

Forecasted production 15 000 units.

Break-even point units 10 000 units.

Calculate the margin of safety in units.

Answer: 

Use the formula

Margin of safety in units = Forecasted production - Break-even point in units 

= 15 000 - 10 000 

Margin of safety is 10 000 units 

Uses & limitations of break-even analysis

What are the uses of break-even analysis?

  • Break-even analysis can calculate break-even point, level of output to achieve target profit, margin of safety which helps management with marketing decisions

  • The visual graphical representation is easy to understand

  • Assists short-term decision-making 

    • Such as setting selling prices

What are the limitations of break-even analysis?

  • Fixed costs are treated as staying the same, but they may only stay fixed up to a certain point

    • i.e. they may be stepped

  • Analysis is only based on budgets 

  • Costs may change due to changes in market

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Author
Reviewer
Seina Murakami

Author: Seina Murakami

Expertise: Accounting Content Creator

Seina studied Pharmacology at UCL, though her professional passion lies deeply in the world of accounting and finance. With an A* in CIE A-Level Accounting and extensive experience tutoring IGCSE and IAL students, she specializes in making complex financial concepts accessible. From developing comprehensive revision resources to collaborating with faculty on lesson materials, Seina is dedicated to helping students bridge the gap between struggling with content and mastering it.

Dan Finlay

Reviewer: Dan Finlay

Expertise: Maths Subject Lead

Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.