Break-Even Analysis

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

Overview: Break-Even AnalysisBenefits Defining PageGetting StartedBreak-even AnalysisBreak-even pointComparing variablesAlgebraic ApproachGraphical Approach

Benefits and Uses:The evaluation to determine necessary levels of service or production to avoid loss.

Comparing different variables to determine best case scenario.

Defining Page:USP= Unit Selling Price

UVC= Unit Variable costs

FC = Fixed Costs

Q = Quantity of output units sold (and manufactured)

Defining Page: Cont.OI= Operating Income

TR= Total Revenue

TC= Total Cost

USP= Unit Selling Price

Getting Started:Determination of which equation method to use:Basic equationContribution margin equationGraphical display

Break-even analysis:Break-even pointJohn sells a product for Rs10 and it cost Rs5 to produce (UVC) and has fixed cost (FC) of Rs25,000 per year

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

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

Algebraic approach:Basic equationRevenues Variable cost Fixed cost = OI(USP x Q) (UVC x Q) FC = OI 10Q - 5Q 25,000 = 0.00 5Q = 25,000 Q = 5,000

What quantity demand will earn Rs1,000? 10Q - 5Q - 25,000 = 1,0005Q = 26,000 Q = 5,200

Algebraic approach:Contribution Margin equation (USP UVC) x Q = FC + OI Q= FC + OI usp-uvc Q= 25,000 + 0 5 Q= 5,000What quantity needs sold to make 1,000? Q= 25,000 + 1,000 5 Q= 5,200

Graphical analysis:Rs70,00060,00050,00040,00030,000 20,000 10,000 Break-even point 0 1000 2000 3000 4000 5000 6000 Quantity

Total Revenue LineTotal Cost Line

Graphical analysis:Cont.Dollars70,00060,00050,00040,00030,00020,00010,000 Break-even point 0 1000 2000 3000 4000 5000 6000 Quantity

Total Cost LineTotal Revenue Line

Scenario 1: Break-even Analysis SimplifiedWhen total revenue is equal to total cost the process is at the break-even point.

TC = TR

Break-even Analysis: Comparing different variablesCompany 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 B: annual cost of $8000 with per unit cost (VC) of $2.

Break-even analysis:Comparative analysis Part 1Determine break-even point for Machine A and Machine B.

Where: V = FC SP - VC

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

Part 1: ComparisonCompare the two results to determine minimum quantity sold.

Part 1 shows:600 units are the minimum.Demand of 600 you would choose Machine A.

Part 2: ComparisonFinding 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$3,000 + $5Q= $8,000 + $2Q $3Q= $5,000 Q= 1667

Part 2: ComparisonCont.Knowing the point of indifference we will choose:

Machine A when quantity demanded is between 600 and 1667.

Machine B when quantity demanded exceeds 1667.

Part 2: ComparisonGraphically displayedDollars21,00018,00015,00012,000 9,000 6,000 3,000 0 500 1000 1500 2000 2500 3000 Quantity

Machine AMachine B

Part 2: ComparisonGraphically displayed Cont.Dollars21,00018,00015,00012,000 9,000 6,000 3,000 Point of indifference 0 500 1000 1500 2000 2500 3000 Quantity

Machine AMachine B

Exercise 1:Company ABC sell widgets for $30 a unit.

Their fixed cost is$100,000

Their variable cost is $10 per unit.

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

Exercise 1:AnswerRevenues Variable cost - Fixed cost = OI

(USP x Q) (UVC x Q) FC = OI $30Q - $10Q $100,00 = $ 0.00 $20Q = $100,000 Q = 5,000

Exercise 2: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 B has FC of $15,000 and a per unit cost of $1.

Under what conditions would you select Machine A?

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

Exercise 2:Answer Cont.Machine A = Machine B FC + VC= FC + VC$5,000 + $5Q= $15,000 + $1Q $4Q= $10,000 Q= 2500

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

Summary:Break-even analysis can be an effective tool in determining the cost effectiveness of a product.

Required quantities to avoid loss.

Use as a comparison tool for making a decision.

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

*Definition (Russell operational management p.236)*Acronyms and terms (Horngren Cost Accounting p. 63)Unit selling price: The price received by the manufacture per unit sold.Unit variable cost: Cost that change in proportion to the changes in the level of activity.Fixed cost: Cost that remain unchanged over a given period regardless of the change in activity. *Operating income:Total revenues from operation minus cost of goods sold and operating cost.Total revenue: Total revenue that a company takes in.Total cost: All cost related to the companies operations.

*Equation (Horngren Cost Accounting p. 63)

*Equation (Horngren Cost Accounting p. 64)UMC = $10 - $5 = $5*Total cost line is a linear line based on the equation: y = VC*Q + FC y = $5Q + $25,000Total revenue line is a linear line based on the equation y = USP * Q y = $10 * QBreak-even point is where TR = TC.

*Any quantity sold in the red colored region will produce a loss, while any quantity in the green region will produce a positive cash flow*Equation (Russel Operational Management p.240)*The first step in finding out which process and/or machine is preferred is to find out the break-even point of each option. *By analyzing the break-even analysis we can see that a quantity demanded of less than 600 units would produce a loss for both Machine A and Machine B.*Point of indifference identifies the quantity demanded amount where either machine (or process) will suffice.

Below the point of indifference Machine A will be a good choice. The reason is that the fixed cost is lower and for smaller quantities demanded Machine A will cost less to operate.

Above the point of indifference Machine B will be the best choice. The reason is that the variable cost is lower and for larger quantities demanded Machine B will cost less to operate.

*The solution procedure for selecting the correct machine and/or process.Formulate a total cost equation for each variable.Calculate the point of indifference.Above the point of indifference choose the alternative with the lowest variable cost.Below the point of indifference choose the alternative with the lowest fixed cost.*The Machine A line is a linear line based on the equation: y = UVC*Q + FC y = $5Q + $3,000The Machine B line is a linear line based on the equation y = UVC * Q + FC y = $2 * Q + $8,000*The higher the VC the steeper the slope.

*Red filled area is when neither machine should be purchased. The red area represents the quantity demanded between 0 and 600.Pink filled area is when Machine A should be purchased. The pink area represents quantity demanded between 600 and 1667.Green filled area is when Machine B should be purchased. The green area represents the quantities demanded of 1667 and above.*Company ABC will break even when they sell 5000 units of their widgets.*If answer is not a whole number then round to the nearest dollar.