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Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University 1

Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

CHAPTER 13

BREAKEVEN ANALYSIS

Mc

GrawHill

ENGINEERING ECONOMYSixthEdition Blank and

Tarquin

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Chapter 13 Learning Objectives

1. The Breakeven Point.2. Breakeven Analysis Between Two

Alternatives.

3. Spreadsheet Application UsingExcels Solver for BreakevenAnalysis.

4. Chapter Summary.

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13.1 Understanding Breakeven

Given P, F, A, i, n;If all of the parameters shownabove are known except one, then

the unknown parameter can becalculated or approximated;

A breakeven value can bedetermined by setting PW, FW, or

AW = 0 and solve or approximatefor the unknown parameter.

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13.1 Solving for a Breakeven Value

Two approaches for solving for anunknown parameter: 1. Direct Solution manually if only one

interest factor is involved in the setup;

2. Trial and Error manually if multiplefactors are present in the formulation;

3. Spreadsheet model where the Excelfinancial functions { PV, FV, RATE, IRR,

NPV, PMT, and NPER are part of themodeling process: (use Goal Seek orSolver).

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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 functionsand 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 .

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13.1 Cost Models Fixed Costs

Fixed Costs Cost that do not varywith production or activity levels Costs of buildings;

Insurance;

Fixed Overhead;

Equipment capital recovery;

etc.

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13.1 Variable Costs

Costs that vary with the level ofactivity; Direct Labor wages;

Materials;

Indirect costs;

Marketing;

Advertising;

Warranty; Etc.

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13.1 Fixed Costs

Essentially constant for all valuesof the variable in question;

If no level of activity, fixed costs

continue;Must shut down the activity beforefixed costs can be altereddownward;

To buffer fixed costs one mustwork on improved efficiencies ofoperations.

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13.1 Variable Costs

Variable Costs change with thelevel of activity;

More activity greater variable

costs;Less activity lover variable costs;

Variable costs are impacted byefficiency of operation, improved

designs, quality, safety, and highersales volume.

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13.1 Total Costs

Total Cost = Fixed Costs + VariableCosts;

TC = FC + VC;

Profit Relationships;Profit = Revenue Total Cost

P = R TC

P = R {FC + VC}.

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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 isshown on the next slide.

C i ht Th M G Hill C i I P i i i d f d ti di l

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The McGraw-Hill Companies,WCB/McGraw-

Figure 16-1 Linear and nonlinear revenue and cost relations used in breakeven analysis.


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13.1 Basic Cost Relationship (Linear)

Q Level of Activity per time unit

C

O

S

T

Fixed Costs ( level)

Variable Costs

Total Costs


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13.1 Non-linear Models

Non-linear Models; One or more of the relationships is

(are) non-linear;

Example Follows:

Copyright The McGraw Hill Companies Inc Permission required for reproduction or display

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13.1 Basic Cost Relationship (Linear)

Q Level of Activity per time unit

C

O

S

T

Fixed Costs ( level)

Variable Costs

Total Costs


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13.1 Breakeven

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.


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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.

Copyright The McGraw-Hill Companies Inc Permission required for reproduction or display

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13.1 Reduction of Variable costs

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

BE point

ChangesWhen the

VCs are

Lowered.


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Copyright The McGraw Hill Companies, Inc. Permission required for reproduction or display.

13.1 Non-linear BE illustration

For non-linear analysis the point of

maximum profit is of interest;

And, multiple BEs may exist;

See the next slide!


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13.1 Non-linear Analysis

Figure 16-3 Breakeven points and maximum-prof i t point for a nonlinear analysis.

Breakeven Points

And ProfitMaximization for

A Non-linear Model


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CHAPTER 13

Section 13.2

Breakeven Analysis Between

Two Alternatives


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13.2 Two Alternative Analysis

Given two alternatives (assumemutually exclusive)

Need to determine a commonvariable or economic parametercommon to both alternatives;

Could be: Interest rate,

First cost (investment), Annual operating cost,

Etc.


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py g p , q p p y

13.2 Breakeven for two alternatives

Common analysis considers: Revenue or

Costs

Common to both options.

Assume a linear revenue-costrelationship

See figure 13-7 (next slide).


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py g p , q p p y

13.2 Breakeven for two alternatives

Total Cost

Relationships forTwo alternatives.

Note the intersection

Of the two TC

Plots. Both alternatives

Are equal.


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y g y

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.


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13.2 Three Alternative Analysis

If three alternatives are presentCompare the alternatives pair-wiseor,

Use a spreadsheet model to plotthe present worth or annual worthover a specified range of values.

A typical three alternative plot

might look like .


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Breakeven for Three Alternatives


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13. 2 Non-linear Breakeven

When variable cost relationshipsare non-linear, the analysisbecomes more complicated;

Use of spreadsheet models andplotting aids are suggested.


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CHAPTER 13

Section 13.3

Spreadsheet Application UsingExcels Solver for Breakeven

Analysis


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13.3 Use of Excels Solver Tool

SOLVER is one of many built-inExcel analysis tools;

Solverhas been designed to aid inmore complex forms of goalseeking and performing what-ifevaluations of properly constructedmodels.

See Appendix A, Section A.4 of thetext.


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13.3 SOLVER

For a properly constructed modelsolver 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 desiredtarget cell value.


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13.3 Target Cell

The target cellMUST contain avalid Excel formula or function;

One can: Maximize the target cellvalue or,

Minimize the cell value 0r,

Set to some predetermined cell value(like 0, etc.);

The target cellcannot be a cellreference;


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13.3 Changing Cell(s)

Solver requires the analyst toidentify one or more cells that mustchange to achieve the desiredresult in the target cell;

Changing cells are, in reality, thedecision variables in the model;

One or more cells are identified

that directly or indirectly impactthe target cell.


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13.3 Achieving the Target CellObjective

If the model is properlyconstructed and the cellformulas/functions are logicallylinked then: Solverwill iterate the designated

change cells until the target cellvalue is achieved as close as possible.

Solverwill generate either exact

decision variable values or closelyapproximated decision cell values.

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13.3 See Example 13.5

Example 13.5 page 436.

Note the application of the

financial functions PMT and PV in

this model.


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13.3 Figure 13-10 Example 13.5

Target Cell

Cell to change first

Cost of Machine 1


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13.3 Changing Cell for Ex. 13.5

The objective here is to find thebreakeven value of Machine 1sinitial first cost so that the twomachines are economically

identical at the 10% interest rate.

The analysis shows that if Machine1 could be purchased for $6564

then the two alternatives will havethe same annual worth at 10%.


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13.3 Additional Analysis

The example also shows what thenet cash flow for machine 1 mustbe to equate to Machine 2.

Choice of what parameters tostudy are left up to the analyist.


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Chapter 13 Summary

Breakeven point for a variable X is

normally expressed as:

Units per time period;

Hours per month; Etc.

At breakeven, QBEone is indifferent

regarding a project.


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Chapter 13 Summary cont.

Typical models are: Linear or,

Non-linear.

Two or more alternatives can becompared using breakevenanalysis;

BE analysis can be a form of

sensitivity analysis;Complex models can be evaluatedusing Excels Solverfeature.


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End of Slide Set

Mc

GrawHill

ENGINEERING ECONOMYSixthEdition

Blank and

Tarquin

Chapter 13x

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