1. PROJECT:
DECISION MAKING
MODELS
APPLICATION OF SENSITIVITY ANALYSIS
FOR INVESTMENT PROJECT EVALUATION
TABLE OF CONTENTS
Topic Page no.
Introduction to Sensitivity Analysis 3
Conventional methods used for Investment Decision Making 3
Sensitivity Analysis: Importance 4
2. Set of criteria for Evaluation 5
Concepts used in Evaluation 5
Application in Investment decision making through an example 6
Conclusion 8
References 9
INTRODUCTION:
What is Sensitivity Analysis?
As per our text bookIntroduction to Management Science : A Quantitative
ApproachSensitivity Analysis is the study of how changes in the coefficients of an
Optimization Model affect the Optimal Solution . Using Sensitivity Analysis we
can answer questions such as the following :
1 – How will the changes in the Objective Function effect the Optimal Solution?
2 – How will the changes in the right hand side of a constraint effect the optimal
solution?
3. In this Project we will study one practical application of the conceptof Sensitivity
Analysis.
Conventional methods used for Investment DecisionMaking are:
Name How it works Drawback Where it should
be Method used
Break –even
Analysis
It is one of the
simplest points for
making such
decisions. It is the
point where firm
incurs neither loss
nor gain. In this
case we use data
on only one
representative year
of the complete
life cycle.
This method is
incapable of giving a
true picture of the
investment project
because it has many
weaknesses
It should only be
used for initial
analysis of the
project.
It is used to give
the firm an idea
about the
minimum level of
sales that they
need to maintain in
order to remain
sustainable (not
necessarily
profitable
Theoryof Games
And Decision
Making Models
It provides
mathematical
model for the
problems and then
gives their
solutions
For managerial
decisions we have
to use its matrix
form
Types :
Games against
intelligent
opponent
Games against
Nature
The degree of
knowledge about the
future can be
completely
unpredictable so the
application of Theory
of Games may or may
not work
It should be used
when we have
more accurate
knowledge of the
future conditions
4. Sensitivity Analysis:
What is
Sensitivity
Analysis
In simple terms it is the effect of changes of input values on the
final values
In Investment we have to find determine the effect of input values
like income, cost, value of Investment etc. on the total project
evaluation
Why is it
important in
Investment
Project
Evaluation
If we don’tperform the Sensitivity Analysis then there is a good
chance that the decision which we make will be inaccurate to some
extent because we can never be completely sure that the decision
that we have made is an accurate one
In case of an inaccurate decision this analysis helps us in
understanding the extent to which various inputs will affect our
final output
What output
will Sensitivity
analysis give
to us
It will yield the maximum and minimum values of an input that
allows the realization of an Investment Project
Set of criteria for Evaluation
Set of
Output
Values
Net present values
Internal Rate of Return
Payback period
Set of Input
Values
Income
Cost
Discount rate
Value of investment
5. Concepts usedin Evaluation
Net present
value
The Net Present Value is the sum of present values of all the
annual net incomes earned during the project duration
Mathematically it is given as:
*Source: Research Paper Sensitivity Analysis In Investment
Projects
Internal Rate
of Return
It is the Discount at which the Net Present Value is zero.
Mathematically It is given as:
*Source: Research Paper Sensitivity Analysis In Investment
Projects
Pay-back
Period
It is the period for which the net income (after discount) per year
will cover the total value of investments (after discount).
*Source: Research Paper Sensitivity Analysis In Investment
6. Projects
Steps to be followedfor sensitivity analysis are as follows: (these are general
steps and may vary depending on the problem at hand)
1. We decide to quantitative criteria that we will use for Investment project
evaluation.
2. We look at all input values and choosethe input values that we will analyze
to find their impact on the output
3. We find out the range in which these values can move so that the project is
still profitable
4. After getting these results we analyze and interpret these results so that we
can make some improvements (in any)
Application in Investment decisionmaking through an example:
In Investment Decision Making we need to consider several key input parameters
such as: the criterion of Net present value, IRR etc.
Let us consider Net Income as an example. The formula for Net Income will be
given as follows:
*Source: Research Paper Sensitivity Analysis in Investment Projects
Now to analyze the possible values in the future we need to vary the values of the
input parameters as follows:
Here p = discount rate factor
7. The parameters that we will vary p , k
The parameters that are constant d , m
*Source: Research Paper Sensitivity Analysis in Investment Projects
Following Table shows how the sensitivity Analysis needs to be done for the Net
Income Value
One RealInvestment Projectof MetalProcessing Industry
In the example that we have considered we will calculate the Net Income with the
help of following formula:
Now we after calculation we found out that following values are used the example:
I $1751587
i 15%
Condition is that
IF Net present
value >0
acceptable
IF Net Present
Value <0
unacceptable
Excelsheetto display the Net PresentValues
9. In this project I studied the Investment Project Evaluation and decision making
when the future conditions were uncertain. Under these uncertain circumstances
we can use methods like: Break Even Analysis, Theory of Games, Decision
Making Theory and Sensitivity Analysis.
I studied the use of Sensitivity Analysis to determine the changes in Output subject
to changes in inputs. I studied one example of Metal Industry where two inputs
were changed and value of NPV was observed (only positive values were
acceptable).
Overall I understood how , by observing the change in these output values we can
determine some improvement in our Investment decisions. I also realized that even
though we can never be 100% sure about whether our investment decision is going
to work or not we can still use the various quantitative methods available to us and
increase the odds of success to a great extent
References:
10. 1. An Introduction to Management Science, Quantitative Approaches to
Decision Making, Anderson D. R., Sweeney D. J. and Williams T. A.,
Eleventh Edition, South-Western College Publication, Cengage Publication
2. Operations Research: An introduction, Taha, H. A., Eighth Edition, Pearsons
Education.
3. Research Paper Sensitivity Analysis In Investment Projects written by Petar
Jovanovic
4. http://handbook.cochrane.org/chapter_9/9_7_sensitivity_analyses.html
5. http://cbkb.org/toolkit/sensitivity-analysis/
