Break-even Analysis (Cambridge International A-Level Accounting)

Break-even charts

Spec point — how to interpret a break-even chart

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

Break-even chart

Exam Hint 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

Spec point — how to calculate the break-even point, contribution to sales ratio, level of output or sales to achieve a target profit, and margin of safety

How do I calculate the break-even point?

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

  • $\mathrm{Break}-\mathrm{even} \mathrm{point} \mathrm{in} \mathrm{units}=\frac{\mathrm{Total} \mathrm{fixed} \mathrm{costs}}{\mathrm{Contribution} \mathrm{per} \mathrm{unit}}$
  • 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:

  • $\mathrm{Break}-\mathrm{even} \mathrm{point} \mathrm{in} \mathrm{sales} \mathrm{revenue}=\mathrm{Break}-\mathrm{even} \mathrm{units}\times\mathrm{Selling} \mathrm{price} \mathrm{per} \mathrm{unit}$
  • $\mathrm{Break}-\mathrm{even} \mathrm{point} \mathrm{in} \mathrm{sales} \mathrm{revenue}=\frac{\mathrm{Total} \mathrm{fixed} \mathrm{costs}}{\mathrm{Contribution} \mathrm{to} \mathrm{sales} \mathrm{ratio}}$

Break-even point

Exam Hint 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.

$\begin{gathered} \text{Revenue} = \text{Total} \text{cost} \\ S x & = F + V x \\ S x - V x & = F \\ x ( S - V ) & = F \\ x = \frac{F}{S - V} \end{gathered}$

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

Final answer: 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:

  • $\mathrm{Level} \mathrm{of} \mathrm{output} \mathrm{required} \mathrm{in} \mathrm{units}=\frac{\mathrm{Total} \mathrm{fixed} \mathrm{costs}+\mathrm{Target} \mathrm{profit}}{\mathrm{Contribution} \mathrm{per} \mathrm{unit}}$
  • 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:

  • $\mathrm{Level} \mathrm{of} \mathrm{output} \mathrm{required} \mathrm{in} \mathrm{sales} \mathrm{revenue}=\frac{\mathrm{Total} \mathrm{fixed} \mathrm{costs}+\mathrm{Target} \mathrm{profit}}{\mathrm{Contribution} \mathrm{to} \mathrm{sales} \mathrm{ratio}}$
  • $\mathrm{Level} \mathrm{of} \mathrm{output} \mathrm{required} \mathrm{in} \mathrm{sales} \mathrm{revenue}=\mathrm{Target} \mathrm{profit} \mathrm{units}\times\mathrm{Selling} \mathrm{price} \mathrm{per} \mathrm{unit}$

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

Final answer: 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

Final answer: 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:

  • $\mathrm{Margin} \mathrm{of} \mathrm{safety} \mathrm{in} \mathrm{units}=\mathrm{Actual}/\mathrm{forecasted} \mathrm{production} \mathrm{units}-\mathrm{Break}-\mathrm{even} \mathrm{point} \mathrm{units}$

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

Final answer: Margin of safety is 10 000 units

Uses & limitations of break-even analysis

Spec point — the use and 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