1. Break-Even Analysis
Greg Hiatt
May 5, 2002

2. Defined:
Break-even analysis examines the cost tradeoffs associated with demand volume.
Definition (Russell “operational management” p.236)

3. Overview: Break-Even Analysis
Benefits
Defining Page
Getting Started
Break-even Analysis
Break-even point
Comparing variables
Algebraic Approach
Graphical Approach

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

5. 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.

6. 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.

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

8. 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?

9. 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)

10. 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

11. 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

12. 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

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

14. 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.

15. 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)

16. 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.

17. 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.

18. 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.

19. 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.

20. 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.

21. 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.

22. 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?

23. 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.

24. 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?

25. 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.

26. 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.

27. 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.

28. 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.