1. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Blank & Tarquin: 5 th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University 1 CHAPTER 13 BREAKEVEN ANALYSIS McMc Graw Hill ENGINEERING ECONOMY Fifth Edition Blank and Tarquin

2. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Blank & Tarquin: 5 th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University 2 CHAPTER 13 Learning Objectives McMc Graw Hill ENGINEERING ECONOMY Fifth Edition Blank and Tarquin

3. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University3 Learning Objectives 1. The Breakeven Point. 2. Breakeven Analysis Between Two Alternatives. 3. Spreadsheet Application – Using Excel’s Solver for Breakeven Analysis. 4. Chapter Summary.

4. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Blank & Tarquin: 5 th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University 4 CHAPTER 13 13.1 Breakeven Analysis for a Single Project McMc Graw Hill ENGINEERING ECONOMY Fifth Edition Blank and Tarquin

5. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University5 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.

6. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University6 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).

7. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University7 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 Q BE.

8. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University8 13.1 Cost Models – Fixed Costs Fixed Costs – Cost that do not vary with production or activity levels Costs of buildings; Insurance; Fixed Overhead; Equipment capital recovery; etc.

9. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University9 13.1 Variable Costs Costs that vary with the level of activity; Direct Labor – wages; Materials; Indirect costs; Marketing; Advertising; Warranty; Etc.

10. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University10 13.1 Fixed 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; To buffer fixed costs one must work on improved efficiencies of operations.

11. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University11 13.1 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.

12. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University12 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}.

13. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University13 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.

14. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University14 © The McGraw-Hill Companies, Inc., 1998 WCB/McGraw-Hill Figure 16-1Linear and nonlinear revenue and cost relations used in breakeven analysis.

15. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University15 13.1 Basic Cost Relationship (Linear) Q – Level of Activity per time unit COSTCOST Fixed Costs ( level) Variable Costs Total Costs

16. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University16 13.1 Non-linear Models Non-linear Models; One or more of the relationships is (are) non-linear; Example Follows:

17. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University17 13.1 Basic Cost Relationship (Linear) Q – Level of Activity per time unit COSTCOST Fixed Costs ( level) Variable Costs Total Costs

18. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University18 13.1 Breakeven The breakeven point, Q BE is the point where the revenue and total cost relationships intersect: For non-linear forms, it is possible to have more than one Q BE point.

19. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University19 13.1 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.

20. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University20 13.1 Reduction of Variable costs Figure 16-2Effect on the breakeven point when the variable cost per unit is reduced. BE point Changes When the VC’s are Lowered.

21. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University21 13.1 Non-linear BE illustration For non-linear analysis the point of maximum profit is of interest; And, multiple BE’s may exist; See the next slide!

22. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University22 13.1 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

23. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Blank & Tarquin: 5 th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University 23 CHAPTER 13 Breakeven Analysis Between Two Alternatives McMc Graw Hill ENGINEERING ECONOMY Fifth Edition Blank and Tarquin

24. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University24 13.2 Two Alternative Analysis 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.

25. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University25 13.2 Breakeven for two alternatives Common analysis considers: Revenue or Costs Common to both options. Assume a linear revenue-cost relationship…… See figure 13-7 (next slide)…….

26. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University26 13.2 Breakeven for Two Alternatives Total Cost Relationships for Two alternatives. Note the intersection Of the two TC Plots. Both alternatives Are equal.

27. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University27 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.

28. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University28 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 ….

29. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University29 Breakeven for Three Alternatives

30. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University30 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.

31. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Blank & Tarquin: 5 th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University 31 CHAPTER 13 13.3 Spreadsheet Application – Using Excel’s Solver for Breakeven Analysis McMc Graw Hill ENGINEERING ECONOMY Fifth Edition Blank and Tarquin

32. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University32 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.

33. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University33 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.

34. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University34 13.3 Target Cell The target cell MUST contain a valid Excel formula or function; One can: Maximize the target cell value or, Minimize the cell value 0r, Set to some predetermined cell value (like “0”, etc.); The target cell cannot be a cell reference;

35. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University35 13.3 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.

36. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University36 13.3 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 “change” cells until the target cell value is achieved as close as possible. Solver will generate either exact decision variable values or closely approximated decision cell values.

37. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University37 13.3 Target Cell Achievement If the proper linkages are built into the model, solver can achieve values for the various decision values; At times, solver might not find feasible values for the decision variables.

38. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University38 13.3 See Example 13.5 Example 13.5 page 436. Note the application of the financial functions PMT and PV in this model.

39. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University39 13.3 Figure 13-10 Example 13.5 Target Cell Cell to change – first Cost of Machine 1

40. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University40 13.3 Changing Cell for Ex. 13.5 The objective here is to find the breakeven value of Machine 1’s initial first cost so that the two machines are economically identical at the 10% interest rate. The analysis shows that if Machine 1 could be purchased for $6,564 then the two alternatives will have the same annual worth at 10%.

41. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University41 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 analyist.

42. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Blank & Tarquin: 5 th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University 42 CHAPTER 13 Chapter Summary McMc Graw Hill ENGINEERING ECONOMY Fifth Edition Blank and Tarquin

43. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University43 13 – Summary Breakeven point for a variable X is normally expressed as: Units per time period; Hours per month; Etc. At breakeven, Q BE one is indifferent regarding a project.

44. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University44 13 Summary Typical models are: Linear or, 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 feature.

45. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Blank & Tarquin: 5 th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University 45 CHAPTER 13 End of Slide Set McMc Graw Hill ENGINEERING ECONOMY Fifth Edition Blank and Tarquin