Break Even Analysis

Break-Even Analysis Greg Hiatt May 5, 2002

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

Overview:

Break-Even Analysis • • • •

Benefits Defining Page Getting Started Break-even Analysis – Break-even point – Comparing variables • Algebraic Approach • Graphical 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 equation – Contribution margin equation – Graphical display

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?

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

Algebraic approach:

Contribution Margin equation (USP – UVC) x Q = FC + OI Q = FC + OI UMC Q = $25,000 + 0 $5 Q = 5,000

What quantity needs sold to make $1,000?

Q = $25,000 + $1,000 $5 Q = 5,200

Graphical analysis: Doll ars 70,000 Total Cost 60,000 Line 50,000 40,000 30,000 20,000 Total Revenue 10,000 Break-even point Line 0 1000 2000 3000 4000 5000 6000 Quantity

Graphical analysis: Cont.

Dol lars 70,000 Total Cost 60,000 Line 50,000 40,000 30,000 20,000 Total Revenue 10,000 Break-even point Line 0 1000 2000 3000 4000 5000 6000 Quantity

Scenario 1:

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

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.

Break-even analysis:

Comparative analysis Part 1 • Determine break-even point for Machine A and Machine B. • Where: V =

FC SP - VC

Break-even analysis: Part 1, Cont. Machine A:

Machine B:

v = $3,000 $10 - $5 = 600 units v = $8,000 $10 - $2 = 1000 units

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.

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 FC + VC $3,000 + $5 Q $3Q Q

= = = = =

Machine B FC + VC $8,000 + $2Q $5,000 1667

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.

Part 2: Comparison Graphically displayed

Doll ars 21,000 18,000 Machine A 15,000 12,000 9,000 Machine B 6,000 3,000 0 500 1000 1500 2000 2500 3000 Quantity

Part 2: Comparison

Graphically displayed Cont. Doll ars 21,000 18,000 Machine A 15,000 12,000 9,000 Machine B 6,000 3,000 Point of indifference 0 500 1000 1500 2000 2500 3000 Quantity

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: Answer

Revenues – Variable cost - Fixed cost = OI

(USP x Q) – (UVC x Q) – FC $30Q - $10Q – $100,00 $20Q Q

= OI = $ 0.00 = $100,000 = 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: 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

Exercise 2: Answer Cont. Machine A FC + VC $5,000 + $5 Q $4Q Q

= = = = =

Machine B FC + VC $15,000 + $1Q $10,000 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.