break-even analysis greg hiatt may 5, 2002. defined: break-even analysis examines the cost tradeoffs...
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Break-Even AnalysisBreak-Even Analysis
Greg HiattGreg Hiatt
May 5, 2002May 5, 2002
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.