Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005

© 2005 by McGraw-Hill, New York, N.Y All Rights Reserved1-1

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, 6th Edition, 2005

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LEARNING OBJECTIVESLEARNING OBJECTIVES

1. Breakeven point

2. Two-alternative breakeven

3. Spreadsheets

Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005

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Sct 13.1 Breakeven Analysis for a Single Sct 13.1 Breakeven Analysis for a Single ProjectProject

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, 6th Edition, 2005

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Solving for a Breakeven ValueSolving 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, 6th Edition, 2005

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Cost – Revenue Model ApproachCost – 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 QBE --

that will minimize costs or maximize profits

Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005

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Fixed CostsFixed 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.

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Fixed Cost ExamplesFixed 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, 6th Edition, 2005

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Variable CostsVariable 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.

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Variable Cost ExamplesVariable Cost Examples

Costs that vary with the level of activity; Direct labor such as wages; Materials; Indirect costs; Marketing; Advertising; Warranty; etc.

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Total CostsTotal Costs

Total Cost = Fixed Costs + Variable Costs

TC = FC + VC Profit Relationships

Profit = Revenue – Total Cost

P = R – TC

= R – (FC + VC)

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Cost – Revenue RelationshipsCost – Revenue Relationships

Linear Models Non-linear models Linear and non-linear models are used as

approximations to realityTypical cost relationships are shown on

following slides

Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005

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Linear and Nonlinear Cost Linear and Nonlinear Cost RelationshipsRelationships

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Basic Basic LinearLinear Cost Relationship 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, 6th Edition, 2005

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Basic Basic Non-linearNon-linear Cost Relationship Cost Relationship

Q, Level of activity per time unit

Cos t

Fixed Cost ( level)

Variable Cost

Total Cost

Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005

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BreakevenBreakeven

The breakeven (BE) point QBE is the point

where the revenue and total cost relationships

intersect

For non-linear relations, it is possible to have

more than one QBE point

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Breakeven…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

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Reduction of Variable CostReduction of Variable Cost

Figure 16-2Figure 16-2 Effect on the breakeven point when the variable cost per unit is reduced.Effect on the breakeven point when the variable cost per unit is reduced.

BE pointchanges when the

VC islowered

Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005

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Non-linear BE AnalysisNon-linear BE Analysis

For non-linear analysis the point of maximum

profit is of interest

And, multiple BE points may exist

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Non-linear AnalysisNon-linear Analysis

Figure 16-3Figure 16-3 Breakeven points and maximum-profit point for a nonlinear analysis.Breakeven points and maximum-profit point for a nonlinear analysis.

Breakeven pointsand profit

maximization fora non-linear model

Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005

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Sct 13.2 Breakeven Analysis Between Two Sct 13.2 Breakeven Analysis Between Two AlternativesAlternatives

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.

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Breakeven for two alternativesBreakeven for two alternatives

Total costrelationships for two alternatives.

Note the intersectionof the two TC

plots. Both alternativesare equal at BE point

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Three Alternative AnalysisThree 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 ….

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Breakeven for Three AlternativesBreakeven for Three Alternatives

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Sct 13.3 Spreadsheet Application: Using Sct 13.3 Spreadsheet Application: Using Excel’s Excel’s SOLVERSOLVER for Breakeven Analysis 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

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Target CellTarget 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

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Changing Cell(s)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.

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Achieving the Target Cell ObjectiveAchieving 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

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Chapter SummaryChapter Summary

Breakeven point for a variable X is normally

expressed as: Units per time period;

Hours per month;

etc.

At exactly breakeven (QBE) one is indifferent

regarding a project

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Summary - continuedSummary - continuedTypical 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, 6th Edition, 2005

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Chapter 13Chapter 13End of SetEnd of Set