Breakeven Analysis (Introduction)

What breakeven is all about
• Understanding the breakeven position
is key to assessing the feasibility of a
start-up
• Calculating contribution and breakeven
is an important analytical method
• However, it makes certain assumptions,
so you need to be aware of the
limitations

Contribution
• Contribution looks at the profit made on
individual products
• It is used in calculating how many items
need to be sold to cover all the business'
total costs (variable and fixed)
• Contribution is the difference between
sales and variable costs of production

Contribution - formulae
Contribution = total sales less total variable
costs

Contribution per unit = selling price per unit less
variable costs per unit

Total contribution can also be calculated as:
Contribution per unit x number of units sold

Profit = Contribution less Fixed Costs

Contribution – example calculation
• Data Contribution per unit =
£10 - £5 = £5
– Quantity sold:
5,000 units
Total Sales = 5,000 x £10
– Selling price per = £50,000
Total Variable Costs = 5,000 x £5 =
unit: £10 £25,000
– Variable cost per Total Contribution =
£50,000 - £25,000
unit: £5 = £25,000
– Fixed costs:
Profit = £25,000 - £10,000
£10,000 = £15,000

breakeven output: introduction

• Three methods of calculating breakeven
level of output
• A table (or spreadsheet) showing sales
and costs over different levels of output
• A formula which you can use to
calculate breakeven output
• A graph which charts sales and costs

Breakeven analysis: key assumptions

• In order to do breakeven analysis, you have
to make some important assumptions
– Selling price per unit stays the same, regardless of
the amount produced
– Variable costs vary in direct proportion to output –
i.e. variable cost per unit is the same
– All output is sold
– Fixed costs do not vary with output – they stay the
same
• These assumptions are not always realistic
– a key limitation of breakeven analysis

Method 1 – Using a Table
Variable Fixed Total
Output Sales Profit
Costs Costs Costs
'000 £'000 £'000 £'000 £'000 £'000

0 0 0 40 40 -40
1 10 4 40 44 -34 breakeven occurs
where contribution
2 20 8 40 48 -28
equals fixed costs =
3 30 12 40 52 -22 between 6,000 & 7,000
4 40 16 40 56 -16 units
5 50 20 40 60 -10
6 60 24 40 64 -4
7 70 28 40 68 2
8 80 32 40 72 8
9 90 36 40 76 14
10 100 40 40 80 20

Method 2 – Using a formula
Contribution per unit = selling price per unit less variable cost per
unit

In this example, contribution per unit = £10 less £4 = £6 per unit

Using the formula:
breakeven output (units) = Fixed costs (£) / Contribution per unit (£)

breakeven output = £40,000 divided by £6 = 6,666
Note: breakeven output is always expressed in terms of units

So breakeven output = 6,666 units

Tip: If the information is available, it is always quicker and
easier to use a breakeven formula rather than use a table
or draw a chart

Method 3 – breakeven Chart

• We’ll lead you through the stages of
completing a breakeven chart
• You may be asked to complete a
breakeven chart in an exam
• However, it is most important to
understand the concepts used in
constructing the chart

breakeven chart – Step 1
100 The first step is to produce two axes:
90 The vertical axis shows the value of sales &
costs
80 The horizontal axis shows the output
Sales and costs (£’000)

70
60
50
40
30
20
10
0
1 2 3 4 5 6 7 8 9 10
Units of Output (‘000)

100 The next step is to add the fixed cost line.
Remember that we assume fixed costs don’t
90 change with the level of output. So the fixed cost
80 line (in red below) is a horizontal line, showing

£40,000.
70
60
50
Fixed costs
40
30
20
10
0
1 2 3 4 5 6 7 8 9 10

100 Next we add the variable costs. We assume that variable costs vary
directly with output. In our example, the variable cost per unit is £4.
90 So variable costs for 1,000 units will be £4,000, and at 5,000 units
80 they will be £20,000. Remember that you only need to plot a

couple of points to be able to draw the straight line (in yellow
70 below).
60
50
Fixed costs
40
30
Variable costs
20
10
0
1 2 3 4 5 6 7 8 9 10

Next step is to add the variable costs to the fixed costs for each level of output.
100 This is important. Remember that to calculate breakeven we need to know total
costs. The total cost line is shown in green on the chart.
90
80

70 Total costs
60
50
Fixed costs
40
30
Variable costs
20
10
0
1 2 3 4 5 6 7 8 9 10

Total sales
100
Having dealt with costs,
90 we can now draw the line
for total sales. Remember
80

that we assume that all
70 output is sold for the Total costs
same selling price (in this
60 case - £10 per unit). So
50 total sales for 2,000 units
will be £20,000; 10,000 Fixed costs
40 units will make £100,000
of sales. The total sales
30
line is drawn in blue Variable costs
20
10
0
1 2 3 4 5 6 7 8 9 10

The last step is to use these lines to identify certain information from the chart.
First, the breakeven output - the point where total sales = total costs. So the
output is the point where the total sales line crosses the total costs line (e.g.
where the blue line crosses the green line). Find this point on the chart and then
follow a vertical line down to the output (horizontal) axis. You can see this brings
us to 6,666
Another thing you can notice from the chart is the over a range of output, total
costs are higher than total sales (green line higher than the blue line). That
means that in this range, the business is making losses. This is the loss-making
range of output.
If the actual output is more than the breakeven output, the business will be
making a profit. In our example, any output more than 6,666 units will mean
profits are earned.
The difference between the actual output and the breakeven output is known as
the “margin of safety”. For example, if actual output were 8,000 units, then the
margin of safety = 8,000 units less 6,666 units = 1,334 units.

Total sales
100
90
80
70 Total costs
60
50
Fixed costs
40
30
Variable costs
20
10
0
1 2 3 4 5 6 7 8 9 10

Effects on breakeven
Change Effect on Effect on breakeven
Contribution per Unit Output

Higher selling price Higher Lower

Lower selling price Lower Higher

Higher variable cost per Lower Higher
unit

Lower variable cost per Higher Lower
unit

Increase in fixed costs No change Higher

Decrease in fixed costs No change Lower

Strengths of breakeven analysis
Strengths
Focuses on how long it will take before a start-up reaches profitability –
the required output

Helps entrepreneur & finance-providers better understand the viability
and risk of a business idea
Margin of safety calculation shows how much a sales forecast can prove
over-optimistic before losses are incurred

Illustrates the importance of keeping fixed costs down to a minimum

Calculations are quick and easy

Limitations of breakeven analysis
Limitations
Unrealistic assumptions – products are not sold at the same price at
different levels of output; fixed costs do vary when output changes

Sales are unlikely to be the same as output – there may be some build up
of stocks or wasted output too
Variable costs do not always stay the same. For example, as output rises,
the business may benefit from being able to buy inputs at lower prices
(buying power)
Most businesses sell more than one product

A planning aid rather than a decision-making tool

Exam Tips
• Focus your studies on understanding how various changes in
the business can affect the breakeven level of output. A
breakeven chart can help you illustrate this, but it is more
important to understand why the changes affect breakeven
output, and what a business can do in response
• Don't assume that breakeven analysis is a proven, scientific
method. It makes lots of assumptions about the ability of the
business to identify which costs are variable and which are
fixed - in reality this can be quite tough
• breakeven analysis is particularly useful for a new business or
for any business which is loss-making or barely making profits

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Breakeven Analysis (Introduction)

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