1. Adopted and modified by Dr. W-.W. Li of UTEP, Fall, 2003
ENGINEERING ECONOMY Fifth Edition Mc
Graw
Hill
Blank and Tarquin
CHAPTER 13
BREAKEVEN ANALYSIS
Adopted and modified by Dr. W-.W. Li of UTEP, Fall, 2003
Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University

2. 13.1 Understanding Breakeven
Given P, F, A, i, n;
If all of the parameters shown above are known except one, then the unknown parameter can be calculated or approximated;
A breakeven value can be determined by setting PW, FW, or AW = 0 and solve or approximate for the unknown parameter.
Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University

3. 13.1 Solving for a Breakeven Value
Two approaches for solving for an unknown parameter:
1. Direct Solution manually if only one interest factor is involved in the setup;
2. Trial and Error – manually if multiple factors are present in the formulation;
3. Spreadsheet model where the Excel financial functions { PV, FV, RATE, IRR, NPV, PMT, and NPER are part of the modeling process: (use Goal Seek or Solver).
Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University

4. 13.1 A Cost – Revenue Model Approach
A popular application of Breakeven (BE) is where cost – revenue – volume relationships are studied;
We define cost and revenue functions and assume some linear or non-linear cost or revenue relationships to model;
One objective: Find a parameter that will minimize costs or maximize profits – termed QBE.
Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University

5. Fixed Costs – Cost that do not vary with production or activity levels
13.1 Cost Models
Fixed Costs – Cost that do not vary with production or activity levels
e.g., Costs of buildings, Insurance, Fixed Overhead, Equipment capital recovery, etc.
Variable Costs - Costs that vary with the level of activity
e.g., Direct Labor (wages), Materials, Indirect costs, Marketing, Advertising, Warranty, Etc.
Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University

6. 13.1 Fixed Costs and Variable Costs
Essentially constant for all values of the variable in question
If no level of activity, fixed costs continue
Must shut down the activity before fixed costs can be altered downward
Variable Costs
Variable Costs change with the level of activity
More activity – greater variable costs
Less activity – lover variable costs
Variable costs are impacted by efficiency of operation, improved designs, quality, safety, and higher sales volume.
Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University

7. Total Cost = Fixed Costs + Variable Costs; TC = FC + VC;
13.1 Total Costs
Total Cost = Fixed Costs + Variable Costs;
TC = FC + VC;
Profit Relationships;
Profit = Revenue – Total Cost
P = R – TC
P = R –{FC + VC}.
Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University

8. 13.1 Cost – Revenue Relationships
Linear Models;
Non-linear models;
Linear and non-linear models are used as approximations to reality;
A basic linear Cost Relationship is shown on the next slide.
Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University

9. The McGraw-Hill Companies, Inc., 1998 WCB/McGraw-Hill
Figure 16-1 Linear and nonlinear revenue and cost relations used in breakeven analysis.
The McGraw-Hill Companies, Inc., 1998
WCB/McGraw-Hill
Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University

10. 13.1 Basic Cost Relationship (Linear)
Total Costs C O S T
Variable Costs
Fixed Costs ( level)
Q – Level of Activity per time unit
Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University

11. 13.1 Basic Cost Relationship (Non-linear)
Total Costs C O S T
Variable Costs
Fixed Costs ( level)
Q – Level of Activity per time unit
Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University

12. 13.1 Breakeven (BE)
The breakeven point, QBE is the point where the revenue and total cost relationships intersect:
For non-linear forms, it is possible to have more than one QBE point.
Revenue and Total cost relationships tend to be static in nature;
May not truly reflect reality of the dynamic firm;
However, the breakeven point(s) can be useful for planning purposes.
Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University

13. 13.1 Reduction of Variable costs
Figure 16-2 Effect on the breakeven point when the variable cost per unit is reduced.
BE point
Changes
When the
VC’s are
Lowered.
Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University

14. 13.1 Non-linear Analysis Breakeven Points And Profit Maximization for
Figure 16-3 Breakeven points and maximum-profit point for a nonlinear analysis.
Breakeven Points
And Profit
Maximization for
A Non-linear Model
Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University

15. 13.2 Breakeven Analysis for Two Alternatives
Given two alternatives (assume mutually exclusive)
Need to determine a common variable or economic parameter common to both alternatives;
Could be:
Interest rate,
First cost (investment),
Annual operating cost,
Etc.
Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University

16. 13.2 Breakeven Analysis for Two Alternatives
Total Cost
Relationships for
Two alternatives.
Note the intersection
Of the two TC
Plots. Both alternatives
Are equal.
Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University

17. 13.2 Two Alternative Analysis
The preferred approach is to define either a:
Present worth relationships or,
Annual worth relationships and,
Set to two expressions equal and solve for the parameter or variable of interest.
Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University

18. 13.2 Three Alternative Analysis
If three alternatives are present…
Compare the alternatives pair-wise or,
Use a spreadsheet model to plot the present worth or annual worth over a specified range of values.
A typical three alternative plot might look like ….
Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University

19. Breakeven for Three Alternatives
Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University

20. Use of spreadsheet models and plotting aids are suggested.
13. 2 Non-linear Breakeven
When variable cost relationships are non-linear, the analysis becomes more complicated;
Use of spreadsheet models and plotting aids are suggested.
Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University

21. 13.3 Use of Excel’s Solver Tool
SOLVER is one of many built-in Excel analysis tools;
Solver has been designed to aid in more complex forms of “goal seeking” and performing “what-if” evaluations of properly constructed models.
See Appendix A, Section A.4 of the text.
Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University

22. 13.3 SOLVER
For a properly constructed model, solver will require that the analyst:
Specifies a target cell (the objective);
One or more cell(s) that will have to change in order to achieve the desired target cell value.
Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University

23. 13.3 See Example 13.5 Example 13.5 page 436.
Note the application of the financial functions PMT and PV in this model.
Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University

24. Choice of what parameters to study are left up to the analyst.
13.3 Additional Analysis
The example also shows what the net cash flow for machine 1 must be to equate to Machine 2.
Choice of what parameters to study are left up to the analyst.
Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University