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Study notes

Calculating Breakeven Output - Changes & Margin of Safety

  • Levels: AS
  • Exam boards: AQA, Edexcel, OCR, IB

It is important to be able to assess what might cause the breakeven output of a business to change and to be able to calculate and assess the impact of such changes. Let's take a look at an example of how to do this.

Below is a summary of how breakeven output and contribution per unit changes as other key variables change:

The purpose of looking at the effect of changes in assumptions is to understand what happens to profit as key data in the business changes. This is usually referred to as "what-if analysis".

What-if analysis can be done using any of the three methods. However, it is much easier and quicker to use the break-even formulae rather than drawing charts of new tables. We'll use the formulae for our worked example below.

Here is the starting data for our example:

Gordon's Seafood Restaurant

Gordon Romsey is planning to open a new seafood restaurant in the popular Cornish village of Padstow to compete with his good friend Rick Strain. His business plan makes the following assumptions:

Average selling price per meal: £40

Average variable cost per meal: £10

Monthly fixed costs: £9,300

Let's take a look at some calculations to see what happens if these assumptions change:

(1) The contribution per unit & current break-even output
(2) The current margin of safety assuming that Gordon sells 1,200 meals per month
(3) What would happen to break-even output if the average selling price per meal increased to £50
(4) What the margin of safety would be if monthly fixed costs were 20% higher but there was no change in the number of meals served per month and the average selling price stays at £40 per meal

Remember that the "margin of safety" is the difference between actual (or forecast) output and the breakeven output.

So, using our breakeven formulae, we can quickly get to the answers. Here's how:

Question (1)

Contribution per unit = £40 - £10 = £30

Break-even output = fixed costs / contribution per unit = £9,300 / £30 = 310 meals per month

Question (2)

Margin of safety = current output less break-even output = 1,200 meals – 310 meals = 890 meals

Question (3)

An increase of £10 in the average selling price per meal would increase the contribution per unit to £40 (i.e. £50 - £10).

So the break-even output will now be £9,300 / £40 = 233 meals per month (rounded up)

That means that the break-even output has fallen from 310 to 233 meals. Gordon's restaurant has to sell fewer meals before it breaks even. That's good news!

Question (4)

Fixed costs will be 20% higher: that means fixed costs will be £9,300 x 1.2 = £11,160

Break-even output will now be £11,160 / £30 = 372 meals per month

[note: the break-even output has risen (bad news) because fixed costs have gone up]

Margin of safety now = 1200 meals – 372 meals = 828 meals per month

The margin of safety has fallen (bad news)

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