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ENGINEERING ECONOMY Fifth Edition
Blank and Tarquin
Mc
Graw
Hill
CHAPTER 13
BREAKEVEN ANALYSIS
Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University
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ENGINEERING ECONOMY Fifth Edition
Blank and Tarquin
Mc
Graw
Hill
CHAPTER 13
Learning Objectives
Blank & Tarquin: 5th edition. Ch.13 Authored by Dr. Don Smith, Texas A&M University
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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.
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ENGINEERING ECONOMY Fifth Edition
Blank and Tarquin
Mc
Graw
Hill
CHAPTER 13
13.1
Breakeven Analysis for a Single
Project
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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.
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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).
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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 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.
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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.
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13.1 Variable Costs
Costs that vary with the level of
activity;







Direct Labor – wages;
Materials;
Indirect costs;
Marketing;
Advertising;
Warranty;
Etc.
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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.
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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.
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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}.
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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 is
shown on the next slide.
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Figure 16-1 Linear and nonlinear revenue and cost relations used
in breakeven analysis.
WCB/McGraw-Hill
© The McGraw-Hill Companies, Inc., 1998
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13.1 Basic Cost Relationship (Linear)
C
O
S
T
Total Costs
Variable Costs
Fixed Costs ( level)
Q – Level of Activity per time unit
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13.1 Non-linear Models
Non-linear Models;

One or more of the relationships is (are)
non-linear;
Example Follows:
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13.1 Basic Cost Relationship (Linear)
C
O
S
T
Total Costs
Variable Costs
Fixed Costs ( level)
Q – Level of Activity per time unit
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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.
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13.1 Reduction of Variable costs
BE point
Changes
When the
VC’s are
Lowered.
Figure 16-2 Effect on the breakeven point when the variable cost per unit is
reduced.
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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!
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13.1 Non-linear Analysis
Breakeven Points
And Profit
Maximization for
A Non-linear Model
Figure 16-3 Breakeven points and maximum-profit point for a
nonlinear analysis.
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ENGINEERING ECONOMY Fifth Edition
Blank and Tarquin
Mc
Graw
Hill
CHAPTER 13
Breakeven Analysis Between
Two Alternatives
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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.
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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)…….
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13.2 Breakeven for Two Alternatives
Total Cost
Relationships for
Two alternatives.
Note the intersection
Of the two TC
Plots. Both alternatives
Are equal.
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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 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 ….
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Breakeven for Three Alternatives
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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.
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ENGINEERING ECONOMY Fifth Edition
Blank and Tarquin
Mc
Graw
Hill
CHAPTER 13
13.3
Spreadsheet Application – Using
Excel’s Solver for Breakeven
Analysis
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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.
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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.
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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;
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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.
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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.
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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.
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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
Cell to change – first
Cost of Machine 1
Target Cell
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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%.
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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.
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ENGINEERING ECONOMY Fifth Edition
Blank and Tarquin
Mc
Graw
Hill
CHAPTER 13
Chapter Summary
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13 – Summary
Breakeven point for a variable X is
normally expressed as:

Units per time period;

Hours per month;

Etc.
At breakeven, QBE one is indifferent
regarding a project.
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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.
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ENGINEERING ECONOMY Fifth Edition
Blank and Tarquin
Mc
Graw
Hill
CHAPTER 13
End of Slide Set
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