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Break-Even Analysis Break-Even Analysis
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Page 1: Break-Even Analysis (2)

Break-Even AnalysisBreak-Even Analysis

Page 2: Break-Even Analysis (2)

Defined:Defined:Break-even analysis examines the Break-even analysis examines the

cost tradeoffs associated with cost tradeoffs associated with demand volume.demand volume.

Page 3: Break-Even Analysis (2)

Overview: Overview: Break-Even AnalysisBreak-Even Analysis• Benefits Benefits • Defining PageDefining Page• Getting StartedGetting Started• Break-even AnalysisBreak-even Analysis

– Break-even pointBreak-even point– Comparing variablesComparing variables

• Algebraic ApproachAlgebraic Approach• Graphical ApproachGraphical Approach

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Benefits and Uses:Benefits and Uses:• The evaluation to determine necessary The evaluation to determine necessary

levels of service or production to avoid levels of service or production to avoid loss.loss.

• Comparing different variables to Comparing different variables to determine best case scenario.determine best case scenario.

Page 5: Break-Even Analysis (2)

Defining Page:Defining Page:• USPUSP = Unit Selling Price= Unit Selling Price

• UVCUVC = Unit Variable costs= Unit Variable costs

• FC FC = Fixed Costs= Fixed Costs

• Q Q = Quantity of output units = Quantity of output units sold (and manufactured) sold (and manufactured)

Page 6: Break-Even Analysis (2)

Defining Page: Defining Page: Cont.Cont.• OIOI = Operating Income= Operating Income

• TRTR = Total Revenue= Total Revenue

• TCTC = Total Cost= Total Cost

• USPUSP = Unit Selling Price= Unit Selling Price

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Getting Started:Getting Started:• Determination of which equation Determination of which equation

method to use:method to use:– Basic equationBasic equation– Contribution margin equationContribution margin equation– Graphical displayGraphical display

Page 8: Break-Even Analysis (2)

Break-even analysis:Break-even analysis:Break-even pointBreak-even point• John sells a product for $10 and it cost John sells a product for $10 and it cost

$5 to produce (UVC) and has fixed cost $5 to produce (UVC) and has fixed cost (FC) of $25,000 per year(FC) of $25,000 per year

• How much will he need to sell to break-How much will he need to sell to break-even?even?

• How much will he need to sell to make How much will he need to sell to make $1000?$1000?

Page 9: Break-Even Analysis (2)

Algebraic approach:Algebraic approach:Basic equationBasic equation

Revenues – Variable cost – Fixed cost = OIRevenues – Variable cost – Fixed cost = OI(USP x Q) – (UVC x Q) – FC(USP x Q) – (UVC x Q) – FC = OI = OI $10Q - $5Q – $25,000$10Q - $5Q – $25,000 = $ 0.00 = $ 0.00 $5Q = $25,000$5Q = $25,000 Q = 5,000Q = 5,000

What quantity demand will earn $1,000?What quantity demand will earn $1,000? $10Q - $5Q - $25,000$10Q - $5Q - $25,000 = $ 1,000 = $ 1,000$5Q$5Q = $26,000 = $26,000 Q Q = 5,200 = 5,200

Page 10: Break-Even Analysis (2)

Algebraic approach:Algebraic approach:Contribution Margin equationContribution Margin equation (USP – UVC) x Q = FC + OI(USP – UVC) x Q = FC + OI QQ = FC + OI= FC + OI UMCUMC QQ = $25,000 + 0= $25,000 + 0 $5$5 QQ = 5,000= 5,000

What quantity needs sold to make $1,000?What quantity needs sold to make $1,000? QQ = $25,000 + $1,000= $25,000 + $1,000 $5$5 QQ = 5,200= 5,200

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Graphical analysis:Graphical analysis:DollarsDollars70,00070,00060,00060,00050,00050,00040,00040,00030,000 30,000 20,000 20,000 10,000 10,000 Break-even pointBreak-even point 00

1000 2000 3000 4000 5000 60001000 2000 3000 4000 5000 6000 QuantityQuantity

Total Revenue Total Revenue LineLine

Total Cost LineTotal Cost Line

Page 12: Break-Even Analysis (2)

Graphical analysis:Graphical analysis:Cont.Cont.DollarsDollars70,00070,00060,00060,00050,00050,00040,00040,00030,00030,00020,00020,00010,000 10,000 Break-even pointBreak-even point 0 0

1000 2000 3000 4000 5000 60001000 2000 3000 4000 5000 6000 QuantityQuantity

Total Cost LineTotal Cost Line

Total Revenue Total Revenue LineLine

Page 13: Break-Even Analysis (2)

Scenario 1: Scenario 1: Break-even Analysis SimplifiedBreak-even Analysis Simplified• When total revenue is equal to total cost When total revenue is equal to total cost

the process is at the break-even point.the process is at the break-even point.

TC = TRTC = TR

Page 14: Break-Even Analysis (2)

Break-even Analysis:Break-even Analysis: Comparing different variables Comparing different variables• Company XYZ has to choose between Company XYZ has to choose between

two machines to purchase. The selling two machines to purchase. The selling price is $10 per unit.price is $10 per unit.

• Machine A: annual cost of $3000 with Machine A: annual cost of $3000 with per unit cost (VC) of $5.per unit cost (VC) of $5.

• Machine B: annual cost of $8000 with Machine B: annual cost of $8000 with per unit cost (VC) of $2.per unit cost (VC) of $2.

Page 15: Break-Even Analysis (2)

Break-even analysis:Break-even analysis:Comparative analysis Part 1Comparative analysis Part 1• Determine break-even point for Machine Determine break-even point for Machine

A and Machine B.A and Machine B.

• Where: V = FCWhere: V = FC SP - VCSP - VC

Page 16: Break-Even Analysis (2)

Break-even analysis:Break-even analysis:Part 1, Cont.Part 1, Cont.Machine A: Machine A:

vv = $3,000= $3,000 $10 - $5$10 - $5= 600 units= 600 units

Machine B:Machine B: vv = $8,000= $8,000 $10 - $2$10 - $2 = 1000 units= 1000 units

Page 17: Break-Even Analysis (2)

Part 1: ComparisonPart 1: Comparison• Compare the two results to determine Compare the two results to determine

minimum quantity sold.minimum quantity sold.

• Part 1 shows:Part 1 shows:– 600 units are the minimum.600 units are the minimum.– Demand of 600 you would choose Demand of 600 you would choose

Machine A. Machine A.

Page 18: Break-Even Analysis (2)

Part 2: ComparisonPart 2: ComparisonFinding point of indifference between Finding point of indifference between

Machine A and Machine B will give the Machine A and Machine B will give the quantity demand required to select quantity demand required to select Machine B over Machine A. Machine B over Machine A.

Machine A Machine A = Machine B= Machine B FC + VCFC + VC == FC + VC FC + VC$3,000 + $5$3,000 + $5 QQ = $8,000 + $2Q= $8,000 + $2Q

$3Q$3Q = $5,000= $5,000 QQ = 1667= 1667

Page 19: Break-Even Analysis (2)

Part 2: ComparisonPart 2: ComparisonCont.Cont.• Knowing the point of indifference we will Knowing the point of indifference we will

choose:choose:

• Machine A when quantity demanded is Machine A when quantity demanded is between 600 between 600 and 1667.and 1667.

• Machine B when quantity demanded Machine B when quantity demanded exceeds 1667.exceeds 1667.

Page 20: Break-Even Analysis (2)

Part 2: ComparisonPart 2: ComparisonGraphically displayedGraphically displayedDollarsDollars21,00021,00018,00018,00015,00015,00012,00012,000 9,000 9,000 6,000 6,000 3,000 3,000 00

500 1000 1500 2000 2500 3000500 1000 1500 2000 2500 3000 QuantityQuantity

Machine AMachine A

Machine BMachine B

Page 21: Break-Even Analysis (2)

Part 2: ComparisonPart 2: ComparisonGraphically displayed Cont.Graphically displayed Cont.DollarsDollars21,00021,00018,00018,00015,00015,00012,00012,000 9,000 9,000 6,000 6,000 3,000 3,000 Point of indifferencePoint of indifference 00

500 1000 1500 2000 2500 3000500 1000 1500 2000 2500 3000 QuantityQuantity

Machine AMachine A

Machine BMachine B

Page 22: Break-Even Analysis (2)

Exercise 1:Exercise 1:• Company ABC sell widgets for $30 a Company ABC sell widgets for $30 a

unit. unit.

• Their fixed cost is$100,000Their fixed cost is$100,000

• Their variable cost is $10 per unit. Their variable cost is $10 per unit.

• What is the break-even point using the What is the break-even point using the basic algebraic approach?basic algebraic approach?

Page 23: Break-Even Analysis (2)

Exercise 1:Exercise 1:AnswerAnswer

Revenues – Variable cost - Fixed cost = OIRevenues – Variable cost - Fixed cost = OI

(USP x Q) – (UVC x Q) – FC (USP x Q) – (UVC x Q) – FC = OI= OI $30Q - $10Q – $100,00 $30Q - $10Q – $100,00 = $ 0.00= $ 0.00

$20Q $20Q = $100,000= $100,000 Q Q = 5,000= 5,000

Page 24: Break-Even Analysis (2)

Exercise 2:Exercise 2:• Company DEF has a choice of two Company DEF has a choice of two

machines to purchase. They both make machines to purchase. They both make the same product which sells for $10.the same product which sells for $10.

• Machine A has FC of $5,000 and a per unit Machine A has FC of $5,000 and a per unit cost of $5.cost of $5.

• Machine B has FC of $15,000 and a per Machine B has FC of $15,000 and a per unit cost of $1.unit cost of $1.

• Under what conditions would you select Under what conditions would you select Machine A?Machine A?

Page 25: Break-Even Analysis (2)

Exercise 2:Exercise 2:AnswerAnswerStep 1: Break-even analysis on both options.Step 1: Break-even analysis on both options.Machine A: Machine A:

vv = $5,000= $5,000 $10 - $5$10 - $5= 1000 units= 1000 units

Machine B:Machine B: vv = $15,000= $15,000 $10 - $1$10 - $1 = 1667 units= 1667 units

Page 26: Break-Even Analysis (2)

Exercise 2:Exercise 2:Answer Cont.Answer Cont.

Machine A Machine A = Machine B= Machine B FC + VCFC + VC == FC + VC FC + VC$5,000 + $5$5,000 + $5 QQ = $15,000 + $1Q= $15,000 + $1Q

$4Q$4Q = $10,000= $10,000 QQ = 2500= 2500

• Machine A should be purchased if Machine A should be purchased if expected demand is between 1000 and expected demand is between 1000 and 2500 units per year.2500 units per year.

Page 27: Break-Even Analysis (2)

Summary:Summary:• Break-even analysis can be an effective Break-even analysis can be an effective

tool in determining the cost tool in determining the cost effectiveness of a product.effectiveness of a product.

• Required quantities to avoid loss.Required quantities to avoid loss.

• Use as a comparison tool for making a Use as a comparison tool for making a decision.decision.

Page 28: Break-Even Analysis (2)

Bibliography:Bibliography:Russel, Roberta S., and Bernard W. Taylor Russel, Roberta S., and Bernard W. Taylor

III. III. Operations Management. Operations Management. Upper Upper Saddle River, NJ: Pentice-Hall, 2000.Saddle River, NJ: Pentice-Hall, 2000.

Horngren, Charles T., George Foster, and Horngren, Charles T., George Foster, and Srikant M. Datar. Srikant M. Datar. Cost Account.Cost Account. 10 10thth ed. ed. Upper Saddle River, NJ: Pentice-Hall, Upper Saddle River, NJ: Pentice-Hall, 2000.2000.