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

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

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

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)

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

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.

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.

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.

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.

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)

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

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

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

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

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

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

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

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

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

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.

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

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 ….

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

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

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

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.

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 Note application of Excel financial functions PMT and PV

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

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

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