1. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 1-1 Developed By: Dr. Don Smith, P.E. Department of Industrial Engineering Texas A&M University College Station, Texas Executive Summary Version Chapter 13 Breakeven Analysis

2. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 1-2 LEARNING OBJECTIVES 1.Breakeven point 2.Two-alternative breakeven 3.Spreadsheets

3. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 1-3 Sct 13.1 Breakeven Analysis for a Single Project  Given P, F, A, i, n  If all of the parameters (variables) 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 for or approximate the unknown parameter

4. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 1-4 Solving for a Breakeven Value  Three approaches to solve for breakeven 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 functions PV, FV, RATE, IRR, NPV, PMT, and NPER are part of the solution process (use Excel’s Goal Seek or Solver)

5. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 1-5 Cost – Revenue Model Approach  A popular application of Breakeven (BE) is where cost-revenue-volume relationships are studied  Define cost and revenue functions and assume some linear or non-linear cost or revenue relationships  One objective: Find a parameter value -- termed Q BE -- that will minimize costs or maximize profits

6. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 1-6 Fixed Costs  Essentially constant for all values of the variable (parameter) in question;  If no level of activity, fixed costs continue;  Must shut down the activity before fixed costs can be altered downward significantly;  To buffer fixed costs one must work on improved efficiencies of operations.

7. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 1-7 Fixed Cost Examples  Fixed Costs – Cost that do not vary with production or activity levels  Costs of buildings;  Insurance;  Fixed overhead;  Equipment capital recovery;  etc.

8. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 1-8 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.

9. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 1-9 Variable Cost Examples  Costs that vary with the level of activity;  Direct labor such as wages;  Materials;  Indirect costs;  Marketing;  Advertising;  Warranty;  etc.

10. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 1-10 Total Costs  Total Cost = Fixed Costs + Variable Costs TC = FC + VC  Profit Relationships Profit = Revenue – Total Cost P = R – TC = R – (FC + VC)

11. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 1-11 Cost – Revenue Relationships  Linear Models  Non-linear models  Linear and non-linear models are used as approximations to reality  Typical cost relationships are shown on following slides

12. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 1-12 Linear and Nonlinear Cost Relationships

13. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 1-13 Basic Linear Cost Relationship Q, Level of activity per time unit C o s t Fixed Cost ( level) Variable Cost Total Cost

14. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 1-14 Basic Non-linear Cost Relationship Q, Level of activity per time unit C o s t Fixed Cost ( level) Variable Cost Total Cost

15. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 1-15 Breakeven  The breakeven (BE) point Q BE is the point where the revenue and total cost relationships intersect  For non-linear relations, it is possible to have more than one Q BE point

16. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 1-16 Breakeven…  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

17. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 1-17 Reduction of Variable Cost Figure 16-2Effect on the breakeven point when the variable cost per unit is reduced. BE point changes when the VC is lowered

18. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 1-18 Non-linear BE Analysis  For non-linear analysis the point of maximum profit is of interest  And, multiple BE points may exist

19. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 1-19 Non-linear Analysis Figure 16-3Breakeven points and maximum-profit point for a nonlinear analysis. Breakeven points and profit maximization for a non-linear model

20. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 1-20 Sct 13.2 Breakeven Analysis Between Two Alternatives  Given two alternatives (assume mutually exclusive)  Need to determine a common variable or economic parameter common to both alternatives  Parameter could be:  Interest rate,  First cost (investment),  Annual operating cost,  etc.

21. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 1-21 Breakeven for two alternatives Total cost relationships for two alternatives. Note the intersection of the two TC plots. Both alternatives are equal at BE point

22. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 1-22 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 BE plot might look like ….

23. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 1-23 Breakeven for Three Alternatives Breakeven for Three Alternatives

24. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 1-24 Sct 13.3 Spreadsheet Application: Using Excel’s SOLVER for Breakeven Analysis  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.  For a properly constructed model SOLVER will require that the analyst:  Specify a target cell (the objective);  Identify one or more changing cell(s) that will have to change to achieve the desired target cell value

25. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 1-25 Target Cell  The target cell MUST contain a valid Excel formula or function  Options of what can happen to the target cell:  Maximize the target cell value  Minimize the cell value  Set to some predetermined cell value (e.g., 0 or $10,000)  The target cell cannot be a cell reference

26. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 1-26 Changing Cell(s)  SOLVER requires the analyst to identify one or more cells that must change to achieve the desired result in the target cell  Changing cells are, in reality, the decision variables in the model  One or more cells are identified that directly or indirectly impact the target cell.

27. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 1-27 Achieving the Target Cell Objective  If the model is properly constructed and the cell formulas/functions are logically linked then:  SOLVER will iterate the designated changing cells until the target cell value is achieved as closely as possible.  SOLVER will generate either exact or closely approximated decision variable values  See Example 13.5. Note application of Excel financial functions PMT and PV

28. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 1-28 Chapter Summary  Breakeven point for a variable X is normally expressed as:  Units per time period;  Hours per month;  etc.  At exactly breakeven (Q BE ) one is indifferent regarding a project

29. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 1-29 Summary - continued  Typical breakeven models are:  Linear  Non-linear  Two or more alternatives can be compared using breakeven analysis  BE analysis can be a form of sensitivity analysis  Complex models can be evaluated using Excel’s SOLVER tool

30. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 1-30 Chapter 13 End of Set