1

BREAKEVEN ANALYSISBREAKEVEN ANALYSIS

IntroductionIntroduction

What is Break-even Analysis?What is Break-even Analysis?

Break-even in comparing alternative propositionsBreak-even in comparing alternative propositions

Break-even in single project analysisBreak-even in single project analysis

Break-even in decision makingBreak-even in decision making

OptimisationOptimisation

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INTRODUCTIONINTRODUCTION

Break-even analysis – a powerful management toolBreak-even analysis – a powerful management tool

A tool for cost comparisonA tool for cost comparison Example: How can we choose between two different Example: How can we choose between two different

options for a required piece of equipment?options for a required piece of equipment? A tool for single project analysisA tool for single project analysis

Example: How many units are required to be sold Example: How many units are required to be sold before the project yields a positive profit?before the project yields a positive profit?

A tool for decision makingA tool for decision making Example: is an investment in a marketing initiative that Example: is an investment in a marketing initiative that

is believed to have a certain benefit worth undertaking?is believed to have a certain benefit worth undertaking?

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COMPARING ALTERNATIVESCOMPARING ALTERNATIVES

In situations where the alternatives are affected in some In situations where the alternatives are affected in some way by a common variableway by a common variable

Total cost of Option 1 = TCTotal cost of Option 1 = TC11

Total cost of Option 2 = TCTotal cost of Option 2 = TC22

There exists a common, independent decision variable There exists a common, independent decision variable affecting both Options – ‘x’affecting both Options – ‘x’

€

TC1 = f1(x)

€

TC2 = f2(x)

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EQUIPMENT SELECTION EQUIPMENT SELECTION EXAMPLEEXAMPLE

2 pump options2 pump options Electric: Capital cost + Annual maintenance + Energy Electric: Capital cost + Annual maintenance + Energy

costcost Diesel: Capital cost + Hourly maintenance + Hourly Diesel: Capital cost + Hourly maintenance + Hourly

operator cost + Energy costoperator cost + Energy cost 4 year project life4 year project life 12% interest rate12% interest rate

Which is the lowest cost option?Which is the lowest cost option?

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PROBLEM SOLVING PROCESSPROBLEM SOLVING PROCESS

Identify the common, independent decision variableIdentify the common, independent decision variable

Translate the cost information for each option into cost Translate the cost information for each option into cost function formfunction form

Do the number crunchingDo the number crunching

Solve analytically or graph both cost functionsSolve analytically or graph both cost functions

Locate the break-even value (the intersection of the two Locate the break-even value (the intersection of the two cost functions)cost functions)

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SOLUTION 1SOLUTION 1

Common, independent decision variableCommon, independent decision variable ‘‘h’, pump operational hours per yearh’, pump operational hours per year

Cost function for Pump 1Cost function for Pump 1 Initial costInitial cost Annual Equivalent Annual Equivalent Annual maintenance costAnnual maintenance cost Annual amount Annual amount Energy costEnergy cost Hourly rate Hourly rate

Cost function for Pump 2Cost function for Pump 2 Initial costInitial cost Annual Equivalent Annual Equivalent Maintenance costMaintenance cost Hourly rate Hourly rate Energy costEnergy cost Hourly rate Hourly rate Operator costOperator cost Hourly rate Hourly rate

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SOLUTION 2SOLUTION 2

Common cost function:Common cost function:

Total Annual Equivalent Cost = Annual Cost + Hourly Rate * Total Annual Equivalent Cost = Annual Cost + Hourly Rate * hh

Equation of a straight lineEquation of a straight line

y (TAEC) = m (Hourly rate). x (h) + c (Annual cost)y (TAEC) = m (Hourly rate). x (h) + c (Annual cost)

Result is two straight lines, one for each optionResult is two straight lines, one for each option

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SOLUTION 3 – NUMBER SOLUTION 3 – NUMBER CRUNCHINGCRUNCHING

Pump 1Pump 1

Initial Capital cost Initial Capital cost = 1,800 m.u.= 1,800 m.u.

Annual Equivalent Annual Equivalent = Initial Cost * A/P(12,4)= Initial Cost * A/P(12,4)

= 1,800 * 0.3292 = 1,800 * 0.3292

= 592.56 m.u.= 592.56 m.u.

Annual maintenance costAnnual maintenance cost = 360.00 m.u.= 360.00 m.u.

Total Annual costTotal Annual cost = 952.56 m.u.= 952.56 m.u.

Hourly rateHourly rate = 1.10 m.u. / hour= 1.10 m.u. / hour

Total Annual Equivalent costTotal Annual Equivalent cost = 952.56 + 1.10*h ………= 952.56 + 1.10*h ………(1)(1)

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SOLUTION 4 – NUMBER SOLUTION 4 – NUMBER CRUNCHINGCRUNCHING

Pump 2Pump 2

Initial Capital cost Initial Capital cost = 550 m.u.= 550 m.u.

Annual Equivalent Annual Equivalent = Initial Cost * A/P(12,4)= Initial Cost * A/P(12,4)

= 550 * 0.3292 = 550 * 0.3292

Total Annual costTotal Annual cost = 181 m.u.= 181 m.u.

Hourly rateHourly rate = 0.60 + 1.40 + 0.35 m.u. / = 0.60 + 1.40 + 0.35 m.u. / hourhour

= 2.35 m.u. / hour= 2.35 m.u. / hour

Total Annual Equivalent costTotal Annual Equivalent cost = 181.00 + 2.35*h ………(2)= 181.00 + 2.35*h ………(2)

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SOLUTION 5 – SOLVESOLUTION 5 – SOLVE

AnalyticalAnalytical Total Annual Equivalent costTotal Annual Equivalent cost = 952.56 + 1.10*h ………= 952.56 + 1.10*h ………

(1)(1) Total Annual Equivalent costTotal Annual Equivalent cost = 181.00 + 2.35*h ………= 181.00 + 2.35*h ………

(2)(2) Break-even is when these are equal, i.e. Break-even is when these are equal, i.e.

952.56 + 1.10*h = 181.00 + 2.35*h952.56 + 1.10*h = 181.00 + 2.35*h

771.56 = 1.25*h771.56 = 1.25*h

h = 617.25h = 617.25

Alternative Analysis

0

500

1000

1500

2000

2500

3000

100 200 300 400 500 600 700 800 900 1000Annual operational hours

Total Annual Equivalent

Cost

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MULTIPLE – ALTERNATIVE MULTIPLE – ALTERNATIVE PROBLEMSPROBLEMS

The same solution approach appliesThe same solution approach applies Reduce all problems to common cost functionReduce all problems to common cost function Graphical solution is best way of visualising the Graphical solution is best way of visualising the

solutionsolution

Multiple Alternatives

0

500

1000

1500

2000

2500

10 20 30 40 50 60 70 80 90 100110 120130140 150160 170180190 200

Decision Variable

Total Cost

V < 50 Blue50 < V < 150 Green150 < V Red

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BREAK-EVEN IN A SINGLE BREAK-EVEN IN A SINGLE PROJECTPROJECT

Definition of CostsDefinition of Costs

Fixed: “A cost is said to be fixed if it does not change in Fixed: “A cost is said to be fixed if it does not change in response to changes in the level of activity”response to changes in the level of activity”

Variable: “The cost that is directly associated with the Variable: “The cost that is directly associated with the production of one unit”production of one unit”

Cv

Cf

TotalCost(Ct)

Volume (v)€

Ct =Cf + v *Cv

Total CostTotal Cost

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COST – VOLUME – PROFIT COST – VOLUME – PROFIT EXAMPLEEXAMPLE

Telephone:Telephone: Annual line rental chargeAnnual line rental charge 25.00 m.u.25.00 m.u.

Cost per callCost per call 0.10 m.u.0.10 m.u. Cost for 100 callsCost for 100 calls Line rental + call costLine rental + call cost 35.00 m.u. [0.35]35.00 m.u. [0.35] Cost for 500 callsCost for 500 calls Line rental + call cost Line rental + call cost 75.00 m.u. [0.25]75.00 m.u. [0.25]

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TotalCost(Ct)

Volume (v)100 500

35

75

Average CostAverage Cost

““Average cost is the Average cost is the total cost of providing total cost of providing a product or service, a product or service, divided by the number divided by the number that are provided.”that are provided.”

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LINEARITY OF VARIABLE COSTSLINEARITY OF VARIABLE COSTS

Variable costs = Variable costs = ff (volume), but the relationship is not (volume), but the relationship is not linearlinear

Limitations on linearityLimitations on linearity

Bulk purchase price break pointBulk purchase price break point

Demand fluctuationsDemand fluctuations

Economic climateEconomic climate

Production capabilityProduction capability

Efficiency & Productivity changesEfficiency & Productivity changes

Technology changesTechnology changes

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REALISTIC COST FUNCTIONSREALISTIC COST FUNCTIONS

FixedCost

Volume

VariableCost

Volume

TotalCost

Volume

+

=

Relevant Range

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CVP ANALYSISCVP ANALYSIS

Profit (P) = Sales Revenue (SR) – Total Costs (CProfit (P) = Sales Revenue (SR) – Total Costs (Ctt))

SR = Selling Price (SSR = Selling Price (Spp) * Volume (V)) * Volume (V)

CCtt = Fixed Costs (C = Fixed Costs (Cff) + Variable Costs (CV)) + Variable Costs (CV)

Marginal cost: “The cost of providing one additional Marginal cost: “The cost of providing one additional unit/itemunit/item

CCvv = Marginal Cost (C = Marginal Cost (Cvv) * Volume) * Volume

Break-even when P=0Break-even when P=0€

P = SpV − (C f +CvV )

P = (Sp −Cv )V −C f

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BREAK-EVEN ANALYSISBREAK-EVEN ANALYSIS

Cf

Gradient= (Sp - Cv)

Break-EvenVolume

Profit

Volume

fvp

vfp

CVCSP

VCCVSP

−−=

+−=

)(

)(

)( vp

fbe CS

CV

−=

At Breakeven P = 0

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SINGLE PRODUCT DECISIONSSINGLE PRODUCT DECISIONS

You buy and sell a product which sells for 15.00 m.u. each. You buy and sell a product which sells for 15.00 m.u. each. The cost for you to purchase the product is 3.00 m.u. In The cost for you to purchase the product is 3.00 m.u. In order for you to trade you require premises and equipment order for you to trade you require premises and equipment which, in total, represent a fixed cost to you of 25,000 m.u. which, in total, represent a fixed cost to you of 25,000 m.u. Your total planned volume for the year of the product is Your total planned volume for the year of the product is 4,000 units.4,000 units.

1)1) How many units do you need to sell to break-even?How many units do you need to sell to break-even?2)2) How many units do you need to sell to make 1,000 m.u. How many units do you need to sell to make 1,000 m.u.

profit?profit?3)3) Would it be worth the introduction of advertising at a Would it be worth the introduction of advertising at a

cost of 6,000 m.u. to increase sales to 4,450?cost of 6,000 m.u. to increase sales to 4,450?4)4) What impact would a 10% drop in selling price have on What impact would a 10% drop in selling price have on

the break-even volume?the break-even volume?

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SOLUTION - 1SOLUTION - 1

Problem 1) How many units to breakeven?

P = (Sp - Cv) * V - Cf

Definition of Break-Even : P = 0 )( vp

fbe CS

CV

−=

Profit

£25k

Break-EvenVolume = 2083.3

Break-EvenVolume = 2084

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SOLUTION - 2SOLUTION - 2

Problem 2) How many units to make £1000 profit?

P = (Sp - Cv) * V - Cf

Volume for Profit = £1000

Profit

£26k

Volume = 2166.6

)( vp

fbe CS

CV

−=

Volume = 2167

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SOLUTION - 3SOLUTION - 3

Problem 3) Would it be worth the introduction of

advertising at a cost of £6,000 to increase

sales to 4450?

P = (Sp - Cv) * V - Cf

Profit for V = 4000 is £23,000

Profit for V = 4450 is £28,400

Gain in Profit = £5,400

Cost to Achieve Gain = £6,000

Hence Not Worth Pursuing!

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SOLUTION - 4SOLUTION - 4

Problem 4) What impact would a 10% drop in selling

price have on the break even volume. ?

P = (Sp - Cv) * V - Cf

)*9.0( vp

f

CS

CV

−=

Profit

£25k

Break-EvenVolume = 2381

Increase = 298 unitsor 14.3%

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CONTRIBUTIONCONTRIBUTION

Problem 3) Would it be worth the introduction of

advertising at a cost of £6,000 to increase

sales to 4450?

P = (Sp - Cv) * V - Cf

Profit for V = 4000 is £23,000

Profit for V = 4450 is £28,400

Gain in Profit = £5,400

Cost to Achieve Gain = £6,000

There is an alternative way of solving this.

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CONTRIBUTIONCONTRIBUTION

Problem 3) Would it be worth the introduction of

advertising at a cost of £6,000 to increase

sales to 4450?

P = (Sp - Cv) * V - Cf

Per unit Profit = (Sp - Cv) = £12

Increase in Volume with Advertising : 450 units

Increase in Profit = £12 * 450 = £5,400

Cost to Achieve Gain = £6,000

“£12 is the contribution or profit margin per unit”

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CONTRIBUTIONCONTRIBUTION

Marginal Contribution = Selling Price - Variable Cost

Revenue /Cost

Cf

Volume

Sales Revenue

Variable Costs

Contribution

Total Contribution = (Selling Price - Variable Cost) * Volume

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OPTIMISATION ANALYSISOPTIMISATION ANALYSIS

Some cost components vary directly with a common Some cost components vary directly with a common decision variable while others vary inversely with the decision variable while others vary inversely with the decision variabledecision variable

In such cases an optimum (lowest cost) existsIn such cases an optimum (lowest cost) exists The general form of such a cost function is:The general form of such a cost function is:

Where:Where: x = common decision variablex = common decision variable TC = Total costTC = Total cost A, B, C = constantsA, B, C = constants

€

TC = A + B.x +C

x

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OPTIMISATION ANALYSISOPTIMISATION ANALYSIS

The general form can be solved analytically and/or graphicallyThe general form can be solved analytically and/or graphically

€

dTC

dx= A −

C

x 2= 0

x =C

A

Optimisation Analysis

0100020003000400050006000700080009000

200 220 240 260 280 300 320 340 360 380 400 420 440 460 480 500 520 540 560 580Decision variable

Total cost

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ALTERNATIVE OPTIONS - 1ALTERNATIVE OPTIONS - 1

Single cross-overSingle cross-over Lowest cost option changes onceLowest cost option changes once

Alternative Options Optimisation

050001000015000200002500030000350004000045000

50150 250 350 450 550 650 750 850 950 1050115012501350145015501650175018501950

Decision variable

Total cost

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ALTERNATIVE OPTIONS - 2ALTERNATIVE OPTIONS - 2

Double cross-overDouble cross-over Lowest cost option changes twiceLowest cost option changes twice

Alternative Options Optimisation

0

5000

10000

15000

20000

25000

30000

35000

50100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000

Decision variable

Total cost

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ALTERNATIVE OPTIONS - 3ALTERNATIVE OPTIONS - 3

No cross-oversNo cross-overs Lowest cost option never changesLowest cost option never changes

Alternative Options Optimisation

050001000015000200002500030000350004000045000

50100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000

Decision variable

Total cost

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OPTIMISATION CASE STUDYOPTIMISATION CASE STUDY

Sometown CompressorsSometown Compressors