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Break-Even Analysis Greg Hiatt May 5, 2002

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

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Overview: Break-Even Analysis BenefitsBenefits Defining PageDefining Page Getting StartedGetting Started Break-even AnalysisBreak-even Analysis –Break-even point –Comparing variables Algebraic ApproachAlgebraic Approach Graphical ApproachGraphical Approach

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Benefits and Uses: The evaluation to determine necessary levels of service or production to avoid loss.The evaluation to determine necessary levels of service or production to avoid loss. Comparing different variables to determine best case scenario.Comparing different variables to determine best case scenario.

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Defining Page: USP= Unit Selling PriceUSP= Unit Selling Price UVC= Unit Variable costsUVC= Unit Variable costs FC = Fixed CostsFC = Fixed Costs Q = Quantity of output units sold (and manufactured)Q = Quantity of output units sold (and manufactured)

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Defining Page: Cont. OI= Operating IncomeOI= Operating Income TR= Total RevenueTR= Total Revenue TC= Total CostTC= Total Cost USP= Unit Selling PriceUSP= Unit Selling Price

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Getting Started: Determination of which equation method to use:Determination of which equation method to use: –Basic equation –Contribution margin equation –Graphical display

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Break-even analysis: Break-even point John sells a product for $10 and it cost $5 to produce (UVC) and has fixed cost (FC) of $25,000 per yearJohn sells a product for $10 and it cost $5 to produce (UVC) and has fixed cost (FC) of $25,000 per year How much will he need to sell to break-even?How much will he need to sell to break-even? How much will he need to sell to make $1000?How much will he need to sell to make $1000?

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Algebraic approach: Basic equation Revenues – Variable cost – Fixed cost = OI (USP x Q) – (UVC x Q) – FC = OI $10Q - $5Q – $25,000 = $ 0.00 $10Q - $5Q – $25,000 = $ 0.00 $5Q = $25,000 $5Q = $25,000 Q = 5,000 Q = 5,000 What quantity demand will earn $1,000? $10Q - $5Q - $25,000 = $ 1,000 $5Q = $26,000 Q = 5,200 Q = 5,200

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Algebraic approach: Contribution Margin equation (USP – UVC) x Q = FC + OI (USP – UVC) x Q = FC + OI Q= FC + OI Q= FC + OI UMC UMC Q= $25, Q= $25, $5 $5 Q= 5,000 Q= 5,000 What quantity needs sold to make $1,000? Q= $25,000 + $1,000 Q= $25,000 + $1,000 $5 $5 Q= 5,200 Q= 5,200

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Graphical analysis: Dollars70,00060,00050,00040,00030,00020,000 10,000 Break-even point Quantity Quantity Total Revenue Line Total Cost Line

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Graphical analysis: Cont. Dollars70,00060,00050,00040,00030,00020,000 10,000 Break-even point Quantity Quantity Total Cost Line Total Revenue Line

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Scenario 1: Break-even Analysis Simplified When total revenue is equal to total cost the process is at the break-even point.When total revenue is equal to total cost the process is at the break-even point. TC = TR TC = TR

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Break-even Analysis: Comparing different variables Company XYZ has to choose between two machines to purchase. The selling price is $10 per unit.Company XYZ has to choose between two machines to purchase. The selling price is $10 per unit. Machine A: annual cost of $3000 with per unit cost (VC) of $5.Machine A: annual cost of $3000 with per unit cost (VC) of $5. Machine B: annual cost of $8000 with per unit cost (VC) of $2.Machine B: annual cost of $8000 with per unit cost (VC) of $2.

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Break-even analysis: Comparative analysis Part 1 Determine break-even point for Machine A and Machine B.Determine break-even point for Machine A and Machine B. Where: V = FCWhere: V = FC SP - VC SP - VC

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Break-even analysis: Part 1, Cont. Machine A: v= $3,000 v= $3,000 $10 - $5 $10 - $5 = 600 units Machine B: v= $8,000 v= $8,000 $10 - $2 $10 - $2 = 1000 units = 1000 units

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Part 1: Comparison Compare the two results to determine minimum quantity sold.Compare the two results to determine minimum quantity sold. Part 1 shows:Part 1 shows: –600 units are the minimum. –Demand of 600 you would choose Machine A.

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Part 2: Comparison Finding point of indifference between Machine A and Machine B will give the quantity demand required to select Machine B over Machine A. Machine A = Machine B FC + VC= FC + VC FC + VC= FC + VC $3,000 + $5Q= $8,000 + $2Q $3Q= $5,000 $3Q= $5,000 Q= 1667 Q= 1667

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Part 2: Comparison Cont. Knowing the point of indifference we will choose:Knowing the point of indifference we will choose: Machine A when quantity demanded is between 600 and 1667.Machine A when quantity demanded is between 600 and Machine B when quantity demanded exceeds 1667.Machine B when quantity demanded exceeds 1667.

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Part 2: Comparison Graphically displayed Dollars21,00018,00015,00012,000 9,000 9,000 6,000 6,000 3,000 3, Quantity Quantity Machine A Machine B

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Part 2: Comparison Graphically displayed Cont. Dollars21,00018,00015,00012,000 9,000 9,000 6,000 6,000 3,000 Point of indifference 3,000 Point of indifference Quantity Quantity Machine A Machine B

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Exercise 1: Company ABC sell widgets for $30 a unit.Company ABC sell widgets for $30 a 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 basic algebraic approach?What is the break-even point using the basic algebraic approach?

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Exercise 1: Answer Revenues – Variable cost - Fixed cost = OI (USP x Q) – (UVC x Q) – FC = OI $30Q - $10Q – $100,00 = $ 0.00 $30Q - $10Q – $100,00 = $ 0.00 $20Q = $100,000 $20Q = $100,000 Q = 5,000 Q = 5,000

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Exercise 2: Company DEF has a choice of two machines to purchase. They both make the same product which sells for $10.Company DEF has a choice of two machines to purchase. They both make the same product which sells for $10. Machine A has FC of $5,000 and a per unit cost of $5.Machine A has FC of $5,000 and a per unit cost of $5. Machine B has FC of $15,000 and a per unit cost of $1.Machine B has FC of $15,000 and a per unit cost of $1. Under what conditions would you select Machine A?Under what conditions would you select Machine A?

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Exercise 2: Answer Step 1: Break-even analysis on both options. Machine A: v= $5,000 v= $5,000 $10 - $5 $10 - $5 = 1000 units Machine B: v= $15,000 v= $15,000 $10 - $1 $10 - $1 = 1667 units = 1667 units

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Exercise 2: Answer Cont. Machine A = Machine B FC + VC= FC + VC FC + VC= FC + VC $5,000 + $5Q= $15,000 + $1Q $4Q= $10,000 $4Q= $10,000 Q= 2500 Q= 2500 Machine A should be purchased if expected demand is between 1000 and 2500 units per year.Machine A should be purchased if expected demand is between 1000 and 2500 units per year.

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Summary: Break-even analysis can be an effective tool in determining the cost effectiveness of a product.Break-even analysis can be an effective tool in determining the cost effectiveness of a product. Required quantities to avoid loss.Required quantities to avoid loss. Use as a comparison tool for making a decision.Use as a comparison tool for making a decision.

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Bibliography: Russel, Roberta S., and Bernard W. Taylor III. Operations Management. Upper Saddle River, NJ: Pentice-Hall, Horngren, Charles T., George Foster, and Srikant M. Datar. Cost Account. 10 th ed. Upper Saddle River, NJ: Pentice-Hall, 2000.

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