Defined:Defined:

Break-even analysis examines the Break-even analysis examines the cost tradeoffs associated with cost tradeoffs associated with demand volume.demand volume.

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

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.

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)

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

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

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?

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

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

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

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

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

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.

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

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

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.

Part 2: ComparisonPart 2: Comparison

Finding 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

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.

Part 2: ComparisonPart 2: ComparisonGraphically displayedGraphically displayed

DollarsDollars21,00021,00018,00018,00015,00015,00012,00012,000 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

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

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?

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

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

Exercise 2:Exercise 2:AnswerAnswer

Step 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 unitsMachine B:Machine B:

vv = $15,000= $15,000 $10 - $1$10 - $1

= 1667 units= 1667 units

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.

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.

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.