Breakeven Analysis for a Single Project
Chapter 13 – Breakeven
Analysis
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INEN 303
Sergiy Butenko
Industrial & Systems Engineering
Texas A&M University
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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
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Solving for a Breakeven Value
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Cost – Revenue Model Approach
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A popular application of Breakeven (BE) is
where cost-revenue-volume relationships are
studied
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Define cost and revenue functions and assume
some linear or non-linear cost or revenue
relationships
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Find a parameter value -- denoted QBE – the
break-even volume where cost equals revenue
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Find Q* that will minimize costs or maximize
profits
Three approaches to solve for breakeven for
an unknown parameter:
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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)
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Fixed Costs
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Variable Costs
Essentially constant for all values of the
variable (parameter) in question (say volume
for example)
Fixed Costs – Costs that do not vary with
production or activity levels. Some examples:
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Costs of buildings
Insurance
Equipment capital recovery
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Variable costs change with the level of
activity - usually proportional to activity
Costs that vary with the level of activity
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Direct labor such as wages
Materials
Marketing
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Total Costs
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Cost, Revenue Relationships
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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Linear or non-linear models capture the costvolume and revenue-volume relationships
Linear and non-linear models are used as
approximations to reality
Typical cost, revenue relationships are
shown on following slides
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Breakeven
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The breakeven (BE) point QBE is the point
where the revenue and total cost
relationships intersect
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For non-linear relations, it is possible to have
more than one QBE point
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Breakeven…
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Revenue and total cost relationships tend to
be static in nature
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May not truly reflect reality of the dynamics
of the firm
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However, the breakeven point(s) can be
useful for planning purposes
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Non-linear BE Analysis
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For non-linear analysis the point of
maximum profit is of interest
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And, multiple BE points may exist
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Breakeven Analysis Between Two
Alternatives
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Given two mutually exclusive
alternatives
Need to determine a variable or
economic parameter common to both
alternatives
Parameter could be Interest rate, First
cost (investment), Annual operating cost,
etc.
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Incremental ROR analysis (Ch. 8)
Replacement value (RV) analysis (Ch. 11)
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Three Alternative Analysis
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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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Example 13.3
Automatic
Initial cost
$23,000
Salvage
$4000
AOC
$3500
Life
10 yrs
Labor cost
$12/hr
M/C Output
8tons/hr
#operators reqd.
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Manual
$8000
$0
$1500
5 yrs
$8/hr
6tons/hr
3
automatic
manual
MARR = 10%
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Spreadsheet Application: Using Excel’s
SOLVER for Breakeven Analysis
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Target Cell
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:
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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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The target cell MUST contain a valid
Excel formula or function
Options of what can happen to the target
cell:
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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)
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Achieving the Target Cell Objective
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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If the model is properly constructed and
the cell formulas/functions are logically
linked then:
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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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Summary
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Typical breakeven models are:
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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
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