Study tips: Break-even analysis series

• Part 1
• Part 2

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.

Categorising costs

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.

Covering fixed costs

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’s 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

2. 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

3. 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.

In summary

This is the theory and various principles behind break-even analysis and whilst it’s 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 on to to look at how we can present break-even information in different ways and use it as the basis of further analysis.

Read more on studying with AAT:

• Choose the best study method for success
• Study tips: Spreadsheets for accounting
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This is the first article in our 2-part series on the accruals concept.

Study tips: Accruals concept series

• The accruals concept part 1
• The accruals concept part 2

The accruals concept is one of the underpinning theories of accountancy and fundamental to many daily accounting activities, yet it is the concept that as students we struggle to understand the most. When we prepare year-end accounts we have to consider the accruals concept as part of the process so it is vital we understand the theory:

Income generated must be matched with expenses incurred, within a financial period, regardless of when the money is paid or received.

What is a prepayment?

A prepayment is an expense or some income that has been paid for or received this financial year but that belongs (needs to be matched to) next year.

Theory:    Income generated must be matched with expenses incurred ……

Practice:   We must match up the accounts on the statement of profit or loss (SoPL), including the expenses that have been spent to generate the net sales figure.

Theory:     …..in a financial period…..

Practice:   Let’s say we pay an annual insurance policy that runs from 1^st June to 31^st May but our accounting year runs from 1^st April to 31^st March.

The periods don’t match.  Within our financial year we need to include the last two months of the previous insurance policy and ten months of this policy.

Theory:     …..regardless of when the money is paid or was received.

Practice:    We are likely to pay for the insurance policy in one lump sum. So the expense incurred will have gone through the bank account in June and will cover all twelve months of the policy. Because the periods don’t match though, we can only include ten months on this year’s SoPL to match with this year’s sales, even though it’s all been paid for.

The other two months need to be pushed forward into next year’s accounts as that’s where they belong. In other words, two months of the policy have been pre-paid for next year. This has the effect of reducing this year’s expenses and increasing next year’s.

Let’s assume last year’s insurance cost £600 which would be a monthly amount of £50. If the annual premium has increased to £660 this year, the monthly cost has become £55.

To correctly match the insurance expense to our financial year we need:

2 months of last year’s policy                                     £100

10 months of this year’s policy                                   £550

Total insurance cost for current financial year       £650

We have to learn that there are three elements to these year-end adjustments:

1. Reversal of the previous year’s year-end adjustment
2. Accounting for this year’s activity i.e. what money has gone through the bank account
3. This year’s year-end adjustment

Once you have a prepayment or an accrual then it is likely to continue in the same pattern year after year as it becomes a cycle:

How is this reflected in the accounting records?

Let’s say our year-end is 31^st March. Last year we paid £600 for our insurance. However, we needed two months of that to be included in our current year. Therefore, at the end of last year we would have reduced the insurance by £100 and double entered that into the prepayments account.

By doing that we made a provision for the prepaid amount, just whilst we moved from one year to the next.

The balance on the prepayments account is shown on the statement of financial position (SoPF) as a current asset. This is because we own those two months of insurance, as the policy was paid in full in June but they can’t be matched to this year’s income so must not be included in the SoPL.

That was the position at the end of last year.  Now we need to think about this year’s accounts.

Remember the three elements:

1. Reversal of the previous year’s year-end adjustment:

It decreased the expense at the end of last year’s so it must increase the expense at the start of this year.

2. Accounting for this year’s activity ie. what money has gone through the bank:

3. This year’s year-end adjustment:

Finally, we have to decrease this year’s insurance expense because the last two months will be for next year.

All we need to do now is write off the balance on the Insurance account to the SoPL and balance the Prepayments account and show it on the SoFP.

Then the cycle will start again.

It might be worth pointing out that in this example we’ve done a lot of work for the sake of a net adjustment of £10. However, when the figures are scaled up for larger organisations and multiple transactions, then the zeros add up. If the concept of accruals was not applied the impact on reported profit figures would be significant.

In part two we’ll have a look at how the same theory of matching is applied to adjustments for accrued expenses as well as prepaid and accrued income.

Read part 2 now.

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Study tips: Break-even analysis series

• Part 1
• Part 2

In part one we looked at the underpinning theories and principles behind break-even analysis which are crucial to understanding this tricky subject.

If you haven’t read it then it would be a good idea to do so before continuing as we are going to re-visit the idea of the four components of break-even analysis: sales, variable costs, fixed costs and profit.

Now I would like you to put yourself in the shoes of a business owner and think about what you would want to know about your business’s performance. Probably first on the list is whether it’s profitable. In order to answer that, you need to know how much is left of your sales income after you have covered all your costs.

Contribution is always the first calculation in any break-even analysis

By calculating the contribution we are removing the variable costs from the sales income thereby dealing with two of the four components.

Let’s say we manufacture beds. Each bed sells for £700 and has variable production costs of £450. The business has fixed costs of £500,000.

In theory, the variable costs can be avoided, so for break-even analysis we assume that they will be covered by the selling price and therefore deduct them to see what’s ‘left over’. In other words, the contribution. £700 less £450 means that we have a contribution of £250 per bed.

Break-even point is when we have enough contribution to exactly cover the fixed costs

As sales and variable costs have now been dealt with we can concentrate on component three, fixed costs.

By dividing the fixed costs by the contribution we can calculate how many beds we need to sell in order to have enough money to pay our bills. In this case, £500,000 ÷ £250 = 2,000 beds.

Note: be really careful about whether the figures you calculate represent monetary values or quantities as it is easy to get confused.

Break-even point can be described in a number of ways

The basic calculation we’ve just done tells us the number of units we need to sell in order to break-even. However, it may be more useful for us to know the value of the sales turnover required to break-even instead. They are fundamentally the same thing, just presented differently.

The simplest way to convert quantity to value, is to multiply the number of units by the unit value. In this case we know we need to sell 2,000 beds to break-even and that each one sells for £700.  Therefore, we need sales turnover of £1,400,000 (2,000 x £700) in order to generate enough sales income to cover our variable costs and have exactly £500,000 left to pay the fixed costs thereby breaking even.

Profits are generated by the contributions made by sales after the fixed costs have been paid.

Sales less variable costs equal contribution and fixed costs divided by contribution tells us the break-even point. So the only component left unaccounted for is profit.

Let’s say we sell 3,000 beds. We know that we need to sell 2,000 beds to break-even and that each one makes a contribution of £250 (£500,000). Therefore, the 1,000 beds sold after we’ve reached the break-even point will generate £250 of profit each (£250,000 in total) as the fixed costs will have already been covered.

Break-even point is used as the basis of further analysis – target profit

There’s not much point being in business if you only break-even. However, knowing the break-even point is fundamental to being able to plan for profitable business growth. Let’s say that as the owner of our bed company we want to make £70,000 profit this year. That’s all well and good but now we need to back it up with information that is meaningful for our production and sales teams. In other words, how many beds do we need to sell to achieve it?

We already know we have to sell enough beds to cover our £500,000 fixed costs and at that point we are no longer making a loss. But we’re not making any profit either, so now we’re adding the target profit of £70,000. Therefore, we need to sell enough beds to cover both.

The fixed costs of £500,000 plus the £70,000 target profit equal £570,000.

£570,000 divided by the contribution of £250 tells us we now need to sell 2280 beds.

The first 2000 will provide enough money to pay the fixed costs and the remaining 280 will generate the desired profit (280 x £250 = £70,000)

Margin of safety

Sales targets can also be set in terms of value as well as quantity. In combination with the break-even point these forecasts can be used to provide useful management information.

If the break-even point is where we must be in order to exactly cover our fixed costs then we’re making a loss until we reach it, and that’s a dangerous place for a business to be. However, as soon as we sell one unit more than the break-even we are making a profit and that’s much safer for our business’s future.

If we have a sales forecast of 3,500 beds, that indicates where we’d like to be. The difference between where we must be and where we’d like to be is called the margin of safety (MofS).

Ideally this difference should be as big as possible, as the further we move away from the break-even point and towards our forecast, then the safer and more profitable we become.

The difference between our forecast of selling 3,500 beds and our break-even point of 2,000 beds is a margin of safety of 1,500 beds.

That’s the same as £1,050,000 worth of sales (the MofS in units x selling price). We needed £1,400,000 to break-even and if we sell all 3,500 beds that’s £2,450,000 but anywhere in the middle would be profitable and safe.

In summary

Finally, it’s often useful to know how safe we are as a percentage of our forecast. In this case it is 43%, which is calculated as the MofS divided by the forecast multiplied by 100 (1,500 ÷ 3,500 x 100 = 43).  This means that 43% of the forecasted sales are on the safe side of the break-even point.

At the beginning of article one, we questioned why break-even analysis is such a tricky topic. I hope you now have a better understanding of what it actually means and how it is used. I also hope you’ll be able to work calculations out logically and will therefore forgive me for the lack of formulae.

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