Chapter 9: Simulation
Concepts and Methods
Project risk analysis by
simultaneous adjustment
of forecast values.
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Introduction
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Simulation allows the repeated
solution of an evaluation model.
Each solution randomly selects
values from predetermined
probability distributions.
All solutions are summarized into
an overall distribution of NPV
values.
This distribution shows
management how risky the
project is.
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Simulation Terminology
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The treatment of risk by using simulation
is known as ‘stochastic’ modeling.
Other names for our term ‘Simulation’,
are - ‘Risk Analysis’, ‘Venture
Analysis’,’Risk Simulation’, ‘Monte Carlo
Simulation’.
The name ‘Monte Carlo Simulation’
helps visualization of repeated spins of
the roulette wheel, creating the selected
values.
Each execution of the model is known as
a ‘replication’ or ‘iteration’.
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The Role of Simulation
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Follows the initial creation and basic testing
of the representative model.
Is sometimes used as a test of the model.
Emphasizes the need for formal forecasting,
and requires close specification of the
forecast variables.
Draws managements attention to the inherent
risk in any project.
Focuses attention on accurate model
building.
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Probability Distributions
of Forecast variables
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Uniform: upper and lower
bounds required.
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Probability Distributions
of Forecast variables
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Uniform: upper and lower
bounds required.
Triangular: pessimistic,
most likely, and optimistic
values required
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Probability Distributions
of Forecast variables
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Uniform: upper and lower
bounds required.
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Triangular: pessimistic,
most likely, and optimistic
values required
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Normal: mean and variance
required.
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Probability Distributions of Forecast
Variables
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Uniform: upper and lower
bounds required.
Triangular: pessimistic, most
likely, and optimistic values
required
Normal: mean and variance
required.
Exponential: initial value and
growth factor required.
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Process of Computation
per Replication
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A value of a variable is selected
from its distribution using a
random number generator.
For example: Sales 90 units;
selling price per unit $2,350;
component cost per unit $1,100;
labour cost per unit $280.
These values are incorporated
into the model, and an NPV is
calculated for this replication.
The NPV for this replication is
stored, and later reported as one
of many in an overall NPV
distribution.
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Making the Replications
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Each replication is unique.
Selection of values from the
distribution is made according
to the particular distributions
The automated process is driven
by a random number generator.
Excel add-ons such as ‘@Risk’
and ‘Insight’ can be used to
streamline the process.
About 500 replications should
give a good picture of the
project’s risk.
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Using the Output
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Management can view the risk
of the project.
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Probability of generating an
NPV between two given values
can be calculated.
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Probability of loss is the area to
the left of a zero NPV.
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Benefits and Costs of Simulation
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Focuses on a detailed definition and analysis of
risk.
Sophisticated analysis clearly portrays the risk
of a project
Gives the probability of a loss making project
Allows simultaneous analysis of variables
-- -- -- -- -- -Requires a significant forecasting effort.
Can be difficult to set up for computation.
Output can be difficult to interpret.
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