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

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

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

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

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

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

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

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

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

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

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

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

13.1 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

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

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

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

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

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

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

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

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

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

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

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