Break-Even Analysishttp://www.bized.ac.uk
• Break-Even Analysis is used to
– predict future profits/losses
– predict results eg produce Product A or Product
B
• Break-Even Point is when Sales Revenue
equals Total Costs
• at this point no profit or loss is incurred
• the firm merely covers its total costs
• Break-Even Point can be shown in graph
form or by use of formulae
Break-Even Analysishttp://www.bized.ac.uk
In order to calculate how profitable a product will be,
we must firstly look at the Costs involved There are two basic types of costs a company incurs.
• Variable Costs
• Fixed Costs
Variable costs are costs that change with changes in production
levels or sales. Examples include: Costs of materials used in the
production of the goods.
Fixed costs remain roughly the same regardless of sales/output
levels. Examples include: Rent, Insurance and Wages
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Break-Even Analysis
• TOTAL COSTS
– Total Costs is simply Fixed Costs and Variable Costs
added together.
TC = FC + VC
– As Total Costs include some of the Variable Costs then
Total Costs will also change with any changes in
output/sales.
– If output/sales rise then so will Total Costs.
– If output/sales fall then so will Total Costs.
Break-Even Analysis
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The Break-even point occurs when Total Costs equals
Revenue (Sales Income)
Revenues (Sales Income) = Total Costs
At this point the business is not making a Profit nor
incurring a Loss – it is merely covering its Total Costs
Let us have a look at a simple example.
Bannerman Trading Company
opens a flower shop.
Break-Even Analysis
Fixed Costs:
•
•
Rent: £400
Helper (Wages): £200
Variable Costs:
•
Flowers: £0.50 per bunch
Selling Price:
• Flowers: £2 per bunch
So we know that:
Total Fixed Costs = £600
Variable Cost per Unit = £0.50
Selling Price per Unit = £2.00
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Break-Even Analysis
SP = £2.00
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VC = £0.50
FC = £600
• We must firstly calculate how much income from each
bunch of flowers can go towards covering the Fixed
Costs.
This is called the Unit Contribution.
Selling Price – Variable Costs = Unit Contribution
£2.00 - £0.50 = £1.50
• For every bunch of flowers sold £1.50 can go towards
covering Fixed Costs
Break-Even Analysis
SP = £2.00
http://www.bized.ac.uk
VC = £0.50
Now to calculate how many units must
be sold to cover Total Costs (FC + VC)
Unit cont = £1.50
FC = £600
This is called the Break Even Point
Break Even Point =
Fixed Costs  Unit Contribution
£600  £1.50 = 400 Units
Therefore 400 bunches of flowers must be sold to Break
Even – at this the point the business is not making a
Profit nor incurring a Loss – it is merely covering its
Total Costs
Break-Even Analysis
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Lets try another example:
Selling Price per unit = £5
Variable Cost per unit = £2
Fixed Costs = £300
How many units must be sold in order to Break
Even?
Break-Even Analysis
SP = £5.00
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First calculate the Unit Contribution
SP – VC = Unit Contribution
£5.00 - £2.00 = £3.00
VC = £2.00
FC = £300
Now calculate Break Even point by using the
formula –
Fixed Costs  Unit Contribution
£300  £3.00 = 100 units
Therefore 100 units must be sold in order to Break
Even
Break-Even Analysis
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Lets try another example:
A firm has Fixed Costs of £1,200.
The Selling Price is £6 per unit and the
Variable Costs are £3 per unit.
How many units must be sold in order to Break
Even?
Break-Even Analysis
SP = £6.00
http://www.bized.ac.uk
First calculate the Unit Contribution
SP – VC = Unit Contribution
£6.00 - £3.00 = £3.00
VC = £3.00
FC = £1,200
Now calculate Break Even point by using the
formula –
Fixed Costs  Unit Contribution
£1,200  £3.00 = 400 units
Therefore 400 units must be sold in order to Break
Even
Break-Even Analysis
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Break Even can also be used to calculate Profit (or Loss)
at a given level of output
For example:
J Bannerman sells Golf Clubs. How much profit/loss is
made when 5000 golf clubs are sold?
Each Golf Club is sold for £20
Variable Costs per golf club are £10
Fixed Costs total £24,000
Break-Even Analysis
SP = £20.00
http://www.bized.ac.uk
VC = £10.00
Firstly, calculate Unit Contribution
FC = £24,000
SP – VC = Unit Contribution
Sales = 5,000 units
£20.00 - £10.00 = £10.00
Now calculate Total Contribution when 5,000 golf
clubs are sold
Unit Contribution x no of units = Total Contribution
£10.00 x 5,000 = £50,000
Now calculate Net Profit at 5,000 units
Total Contribution – Fixed Costs = Net Profit
£50,000 - £24,000 = £26,000
Break-Even Analysis
Lets try another example.
Variable Costs =
So:
SP = £2.50
Fixed
Costs =
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Flowers
£1.49
SP
= £2.50 £1,050
Rent
Paper
£0.01
Insurance
£200
VC = £1.50
Total
FC £1,250
(£3/300)
FC = £1,250
shop. Total VC £1.50
Caroline Wilson owns a florist
She buys each bunch of flowers for £1.49 and
special wrapping paper for £3 per roll. Each roll
of wrapping paper will wrap 300 bunches of
flowers. Rent of her premises is £1,050 per
month and she pays monthly insurance of £200.
Caroline sells each bunch of flowers for £2.50.
What do we know?
Break-Even Analysis
SP = £2.50
http://www.bized.ac.uk
VC
= £1.50
FC = £1,250
Calculate Caroline’s Break Even
Point and also how much Profit
would she make if she sold 2,000 bunches of flowers?
Firstly, calculate Unit Contribution
SP – VC = Unit Contribution
£2.50 - £1.50 = £1.00
Now calculate Break Even
Fixed Costs  Unit Contribution
£1,250  £1.00 = 1,250 units
Break-Even Analysis
How much Profit would she make
if she sold 2,000 bunches of flowers?
SP = £2.50
http://www.bized.ac.uk
VC
= £1.50
FC = £1,250
Unit Cont = £1.00
Now, calculate the profit at 2,000 bunches of flowers
Unit Contribution x No of Units = Total contribution
£1.00 – 2,000 units = £2,000
Total Contribution – Fixed Costs = Net Profit
£2,000 - £1,250 = £750
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Break-Even Analysis
Another Example
Calculate how many units need to be
produced in order to achieve a Net Profit of
£25,000 given the following information
Fixed Costs £30,000
Contribution per unit £10
Answer
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Net Profit = Total Contribution – Fixed Cost
£25,000 = Total Contribution - £30,000
therefore Total Contribution = £55,000
If unit contribution is £10
then 5,500 units will have to be produced in order to
achieve a Total Contribution of £55,000.
Therefore the number of units required to achieve a Net
Profit of £25,000 is 5,500 units
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Break-Even Analysis
The formulae used so far assumes that Unit
Costs are known ie Unit Selling Price and
Unit Variable Cost
When no unit costs are known, the
Profit/Volume Ratio should be used instead
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Profit Volume Ratio
P/V Ratio (Profit/Volume Ratio) =
Total Contribution / Sales
x 100
If asked to calculate the volume of sales needed to
Break-Even (when no unit costs are given) the
following formula should be used:
Sales at BEP = Fixed Costs / Profit/Volume Ratio
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Profit/Volume Ratio
For Example
Sales £60,000
Variable Costs £24,000
Fixed Costs £14,000
Calculate the P/V Ratio and the BEP
Answer
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Sales – Variable Costs = Total Contribution
£60,000 - £24,000 = £36,000
Total Contribution / Sales = P/V Ratio
(£36,000 / £60,000) x 100 = 60%
Fixed Costs / P/V Ratio = Sales at BEP
£14,000 / 60% = £23,333
Therefore £23,333 of Sales are necessary in order to
Break-Even
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Costs/Revenue
Break-Even Chart
TR
TC
VC
The Break-even point
occurs where total
revenue equals total
costs – the firm, in
this example would
have to sell Q1 to
generate sufficient
revenue (income) to
cover its total costs.
BEP
FC
Q1
Output/Sales
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Costs/Revenue
Break-Even Chart
TR (p = £3)
TR (p = £2)
TC
VC
If the firm chose
At present, this
to set price higher
firms sells each
than £2 (say £3)
unit for £2 –
the TR curve
Break Even point
would be steeper –
is at Q1
they would not
have to sell as
many units to
break even
BEP
BEP
Q2
FC
Q1
Output/Sales
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Break-Even Chart
TR (p = £1)
Costs/Revenue
TR (p = £2)
TC
BEP
VC
If the firm chose
to set prices lower
(say £1) it would
need to sell more
units before
covering its costs
BEP
FC
Q1
Q3
Output/Sales
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Break-Even Chart
TR (p = £2)
Costs/Revenue
TC
Profit
VC
If youunits
sell sold
fewer
Any
units than
theEven
above
Break
Breakrepresents
Even Point,
Point
a
aProfit
loss is incurred
BEP
Loss
FC
Q1
Output/Sales
http://www.bized.ac.uk
Break-Even Chart
Costs/Revenue
TR (p = £3)
TR (p = £2)
Margin of
Ifhigher
weshows
sell
Asafety
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Break
Even
how
farlower
sales
more
than
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isEven
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IfPoint
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= 1000
wethe
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and
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= 1800,
make
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fall by 800
Profit
safety
would
units before
a
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made
TC
VC
BEP
Margin of Safety
FC
Q3
Q1
Q2
Output/Sales
LIMITING FACTORS
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• Under normal circumstances, the bestpaying product is that which shows the
highest contribution per £ of sales
• Certain circumstances make this
inappropriate eg
• a factory producing a particular range of
products may depend on a highly skilled
labour force
• If skilled labour is in short supply in the
locality of the factory, then labour is
termed a limiting, or key, factor
LIMITING FACTORS
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• The most important criterion now will be
the optimum use of labour
• This is expressed by the contribution per
labour hour
• Direct labour is only one example of a
limiting factor
• Other examples could be
– direct materials
– machine hours
– factory capacity
For Example
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• In a situation where labour is scarce (ie
direct labour = limiting factor), advise
management which of Products X and Y is
more profitable
Product X
Product Y
Selling Price
£100
£100
Contribution %
(P/V Ratio)
35%
30%
Direct Labour
Hours per unit
25 hours
20 hours
Answer
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Under normal circumstances Product X
would be the better paying product
because of its higher P/V Ratio
However, when the limiting factor is labour,
Product Y becomes the better paying
product:
Contribution Per Direct
Labour Hour
Product X
35% x £100
Product Y
30% x £100
25
20
= £1.40
= £1.50
PRODUCT MIX
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A business may produce a number of products but at
the same time be unable to meet total demand for
all products due to a limiting factor eg machine
hours or labour hours.
In this case the business would decide on the
optimum use of the limited resource by producing
all of the demand for the product which yields the
highest contribution per the limiting factor.
Having produced all of the demand from that
product, the business would produce the next
highest contribution per the limiting factor and so
on until full capacity is reached.
For example
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A business can produce Products A, B and C.
A
B
C
£2
£1
£3
Labour hours per unit
4
4
3
Total demand in units
5,000
5,000
10,000
Contribution per labour
hour
The factory is limited to 60,000 labour hours.
How many units of each Product should be produced
to maximise profit?
Answer
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Produce in the order of the highest Contribution
per Labour Hour ie C then A then B
Demand
C
10,000
A
5,000
Labour hrs/unit
3
4
Total lab hrs
30,000
20,000
Total labour hours required to produce all demand for
C then A = 50,000 labour hours.
Answer
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If Total Labour hours available equals 60,000
and 50,000 is used producing Products C
and A, then 10,000 labour hours are left to
produce as many units as possible for
Product B
Product B uses 4 labour hours per unit,
therefore only 2,500 units of Product B can
be produced within the available 60,000
labour hours
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Assumptions of Break Even
Analysis
• All Fixed and Variable costs can be
identified
• Variable costs are assumed to vary
directly with output
• Fixed costs will remain constant
• Selling prices are assumed to remain
constant for all levels of output
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Assumptions Continued
• The sales mix of products will remain
constant – break even charts cannot
handle multi-product situations
• It is assumed that all production will be
sold
• The volume of activity is the only
relevant factor which will affect costs
Limitations of Break Even
Analysis
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• Some costs cannot be identified as precisely
Fixed or Variable
• Semi-variable costs cannot be easily
accommodated in break-even analysis
• Costs and revenues tend not to be constant
• With Fixed costs the assumption that they
are constant over the whole range of output
from zero to maximum capacity is
unrealistic
Limitations Continued
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• Price reduction may be necessary to
protect sales in the face of increased
competition
• The sales mix may change with changes
in tastes and fashions
• Productivity may be affected by strikes
and absenteeism
• The balance between Fixed and Variable
costs may be altered by new technology