# Break-even analysis – part 1

What does it mean when a business breaks even?

Basically, that it is neither making a profit or a loss.  That seems simple enough to understand but this area of cost accounting is difficult for many of us to get our heads around.

We spend a lot time trying to remember all the formulae that are used in break-even analysis rather than putting our efforts into thinking about what we are analysing and what the figures actually tell us about the business they relate to.  So in this article we are going to concentrate on the basic principles behind break-even analysis to gain a better understanding of what we need to do and why, before we look at how to do it.

Before we can understand break-even analysis we need to be able to categorise costs and know how each category behaves:

• Fixed Costs – costs that do not change with output.
• Variable Costs – costs that vary in direct proportion to output.

If this is an area you struggle with, reading Fixed, Variable and Semi-variable costs would be beneficial before continuing.

Then we need to apply this underpinning knowledge to the relationships between costs and income:

• All costs have to be paid out of income.
• Fixed costs have to be paid regardless of how much income is generated by sales as they do not change with output.
• Variable costs are only incurred when there is output.

So in theory, if we don’t generate a sale we don’t incur the variable cost.  This works in theory and practice for a service. For example, if a taxi driver doesn’t have any customers then no petrol will get used.  However, in manufacturing you could argue that the variable costs involved in making a product are incurred regardless of whether that product is sold or not.  Whilst that is true, in break-even analysis, we work on the basis that we will manufacture the exact number of units sold.

The above point is crucial as break-even analysis is simply trying to work out how many of each product we must sell (and therefore produce) in order to cover fixed costs as well as variable costs.  Each unit that we sell must cover its variable cost and make a contribution to the fixed costs within the selling price.  When enough units have been sold to cover all of the fixed cost then the product has ‘broken even’.  In other words, until the break-even point is reached, we are not making any profit.  After the break-even point is reached, the part of the selling price that was contributing to the fixed costs is now contributing to the profits of the organisation instead.

Let’s think about the taxi driver again and imagine he has £10,000 worth of fixed costs to cover each year.  He also incurred £5 of variable costs every time he travels 10 business miles and he charges £25 for 10 business miles to generate his sales income.

As he doesn’t incur the variable costs if he doesn’t have a job, then they can be removed from the equation as by definition when a job does come in, enough income will be generated to pay for them.  His fixed costs however, have to be covered regardless of how many jobs he gets.

Therefore it is really important for the taxi driver to know how many jobs he’ll need in order to have enough money to pay his fixed costs.  Remember though, that for every 10 business miles he travels he’ll generate £25 but incur £5 of variable costs.  Therefore only £20 of the sales income is actually unaccounted for and this is the ‘contribution’.  It is a contribution to paying the fixed costs and once enough ‘£20 contributions’ have been made to add up to £10,000, then all the other ‘£20 contributions’ in the year are profit.

So to answer the question how many 10 business mile jobs does he need to do in order to have enough money cover his fixed costs, he must:

1. Calculate the contribution by deducting the variable costs from the selling price to see how much is unaccounted for:

£25 – £5 = £20

1. Then calculate how many contributions are needed to cover the fixed cost, which can be turned around when he does the maths as that’s the same as fixed costs divided by contribution:

£10,000 ÷ £20 = 500 jobs

1. Double check his calculation to see if his answer seems reasonable. 500 jobs that each make a £20 contribution will eventually provide exactly £10,000 to pay the fixed costs.

All this means is that the taxi driver needs 500 jobs to break-even.  This is because jobs number 1-499 don’t provide enough contribution to pay all his costs so he’s making a loss.  Job number 501, however, will generate £10,020 once he has paid all his variable costs, and out of that he can cover his £10,000 worth of fixed cost and have £20 of profit left over.

This is the theory and principles behind break-even analysis and whilst it is simply the concept of a business neither making a profit or loss, the underpinning knowledge and understanding required to get to grips with it, is extensive.

In part two of this article we’ll go onto to look at how we can present break-even information in different ways and use it as the basis of further analysis.

Gill Myers is a self-employed accounts consultant. She has taught AAT qualifications since 2005 and written numerous articles and e-learning resources.