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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. Definition (Russell “operational management” p.236)

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**Overview: Break-Even Analysis**

Benefits Defining Page Getting Started Break-even Analysis Break-even point Comparing variables Algebraic Approach Graphical Approach

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

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**Defining Page: USP = Unit Selling Price UVC = Unit Variable costs**

FC = Fixed Costs Q = Quantity of output units sold (and manufactured) 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.

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**Defining Page: Cont. OI = Operating Income TR = Total Revenue**

TC = Total Cost USP = Unit Selling Price 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.

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**Getting Started: 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 year How much will he need to sell to break-even? 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 $5Q = $25,000 Q = 5,000 What quantity demand will earn $1,000? $10Q - $5Q - $25,000 = $ 1,000 $5Q = $26,000 Q = 5,200 Equation (Horngren “Cost Accounting” p. 63)

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**Algebraic approach: Contribution Margin equation**

(USP – UVC) x Q = FC + OI Q = FC + OI UMC Q = $25, $5 Q = 5,000 What quantity needs sold to make $1,000? Q = $25,000 + $1,000 Q = 5,200 Equation (Horngren “Cost Accounting” p. 64) UMC = $10 - $5 = $5

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**Graphical analysis: Dollars 70,000 60,000 50,000 40,000 30,000 20,000**

10, Break-even point Quantity Total Cost Line Total cost line is a linear line based on the equation: y = VC*Q + FC y = $5Q + $25,000 Total revenue line is a linear line based on the equation y = USP * Q y = $10 * Q Break-even point is where TR = TC. Total Revenue Line

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**Graphical analysis: Cont.**

Dollars 70,000 60,000 50,000 40,000 30,000 20,000 10, Break-even point Quantity Total Cost Line 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 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. 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. 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.

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**Break-even analysis: Comparative analysis Part 1**

Determine break-even point for Machine A and Machine B. Where: V = FC SP - VC Equation (Russel “Operational Management” p.240)

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**Break-even analysis: Part 1, Cont.**

Machine A: v = $3,000 $10 - $5 = 600 units Machine B: v = $8,000 $10 - $2 = 1000 units The first step in finding out which process and/or machine is preferred is to find out the break-even point of each option.

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

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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 $3,000 + $5 Q = $8,000 + $2Q $3Q = $5,000 Q = 1667 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.

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Part 2: Comparison Cont. 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. 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.

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**Part 2: Comparison Graphically displayed**

Dollars 21,000 18,000 15,000 12,000 9,000 6,000 3,000 Quantity Machine A Machine B The Machine A line is a linear line based on the equation: y = UVC*Q + FC y = $5Q + $3,000 The 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.

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**Part 2: Comparison Graphically displayed Cont.**

Dollars 21,000 18,000 15,000 12,000 9,000 6,000 3, Point of indifference Quantity Machine A Machine B 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.

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**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?

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**Exercise 1: Answer (USP x Q) – (UVC x Q) – FC = OI**

Revenues – 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 Company ABC will break even when they sell 5000 units of their widgets.

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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. 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?

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**Exercise 2: Answer Step 1: Break-even analysis on both options.**

Machine A: v = $5,000 $10 - $5 = 1000 units Machine B: v = $15,000 $10 - $1 = 1667 units If answer is not a whole number then round to the nearest dollar.

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**Exercise 2: Answer Cont. Machine A = Machine B FC + VC = FC + VC**

$5,000 + $5 Q = $15,000 + $1Q $4Q = $10,000 Q = 2500 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. Required quantities to avoid loss. 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, 2000. Horngren, Charles T., George Foster, and Srikant M. Datar. Cost Account. 10th ed. Upper Saddle River, NJ: Pentice-Hall, 2000.

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