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
2
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?
3
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)
4
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?
5
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)
6
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
7
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
8
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)
9
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)
10
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
11
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
12
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
13
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]
25
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.”
14
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
15
REALISTIC COST FUNCTIONSREALISTIC COST FUNCTIONS
FixedCost
Volume
VariableCost
Volume
TotalCost
Volume
+
=
Relevant Range
16
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
17
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
18
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?
19
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
20
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
21
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!
22
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%
23
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.
24
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”
25
CONTRIBUTIONCONTRIBUTION
Marginal Contribution = Selling Price - Variable Cost
Revenue /Cost
Cf
Volume
Sales Revenue
Variable Costs
Contribution
Total Contribution = (Selling Price - Variable Cost) * Volume
26
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
27
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
28
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
29
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
30
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
31
OPTIMISATION CASE STUDYOPTIMISATION CASE STUDY
Sometown CompressorsSometown Compressors