The Proper Care and Feeding of a MySQL Database for Busy Linux Admins -- SCaLE 13x Feb 21st 2015
Chapter 13x
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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.
C i ht Th M G Hill C i I P i i i d f d ti di l
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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
C i ht Th M G Hill C i I P i i i d f d ti di l
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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)
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.
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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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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