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Risk Simulation
Lecture No. 40
Chapter 12
Contemporary Engineering Economics
Copyright, © 2016
Contemporary Engineering Economics, 6th edition
Park
Copyright © 2016 by Pearson Education, Inc.
All Rights Reserved
What is Monte Carlo Simulation?
 Definition: A computerized mathematical
technique that allows the decision-maker to
account for risk in quantitative analysis and
decision making
 How Monte Carlo Simulation Works
By building models of possible results by
substituting a range of values (random
sampling)—a probability distribution—for any
factor that has inherent uncertainty.
Contemporary Engineering Economics, 6th edition
Park
Copyright © 2016 by Pearson Education, Inc.
All Rights Reserved
Logical Steps Involved in Simulating a
Risky Investment
Contemporary Engineering Economics, 6th edition
Park
Copyright © 2016 by Pearson Education, Inc.
All Rights Reserved
Monte Carlo Sampling
o Unit demand (X): a
discrete distribution
o Unit price (Y): a
triangular distribution
o Salvage value (S): a
uniform distribution
Contemporary Engineering Economics, 6th edition
Park
Copyright © 2016 by Pearson Education, Inc.
All Rights Reserved
A Sampling Scheme for Discrete and
Continuous Random Variables
 Step 1: Define the cumulative
probability distribution for
each random variable.
 Step 2: Generate a uniform
random deviate U(0,1).
 Step 3: Place the random
deviate generated on the
vertical axis (F(.)) of the
cumulative distribution.
 Step 4: Determine the
corresponding value on the
horizontal axis, which is
viewed as the sample value
from that distribution.
Contemporary Engineering Economics, 6th edition
Park
Copyright © 2016 by Pearson Education, Inc.
All Rights Reserved
Observed NPW Values ($), Based on 200
Iterations
Contemporary Engineering Economics, 6th edition
Park
Copyright © 2016 by Pearson Education, Inc.
All Rights Reserved
Simulated NPW Frequency Distribution
•
•
Mean = $44,245
Standard deviation = $18,585
Contemporary Engineering Economics, 6th edition
Park
Copyright © 2016 by Pearson Education, Inc.
All Rights Reserved
Simulation Result Based on 200 Iterations
Contemporary Engineering Economics, 6th edition
Park
Copyright © 2016 by Pearson Education, Inc.
All Rights Reserved
Risk Simulation with Crystal Ball™
 Crystal Ball is an add-in to Microsoft Excel, so you just create
an Excel worksheet to determine the NPW.
o Create a Cash Flow Statement with Excel
o Define Uncertainty
o Pick Your Bottom Line
o Simulate
o Analyzing the Simulation Result Screen
Note: @RISK could provide the same flexibility in creating input files
and obtaining the simulation results.
Contemporary Engineering Economics, 6th edition
Park
Copyright © 2016 by Pearson Education, Inc.
All Rights Reserved
Step 1: Create a Cash Flow Statement with Excel
 Create an Excel worksheet
as a function of input
variables, so any change in
input variables can
automatically update the
bottom line “NPW.”
Contemporary Engineering Economics, 6th edition
Park
Copyright © 2016 by Pearson Education, Inc.
All Rights Reserved
Step 2: Define Uncertainty
We will treat the unit price
(Y), the demand (X), and the
salvage value (S) as random
variables.
o Let the cursor point to the
cell where the input
random variable is to be
defined.
o Go to the menu bar and
click on “Define
Assumption” which brings
on the types of random
variable to be assigned.
Contemporary Engineering Economics, 6th edition
Park
Copyright © 2016 by Pearson Education, Inc.
All Rights Reserved
Step 3: Define Forecast
In developing the
NPW distribution,
we do the following:
o Let cursor point to
cell F15.
o Select the “Define
Forecast”
command in the
tool menu bar. The
cell formula in F15
would look like:
=NPV(B14,C43:G43)+B43
Contemporary Engineering Economics, 6th edition
Park
Copyright © 2016 by Pearson Education, Inc.
All Rights Reserved
Step 4: Simulate
o Click the “Run
Preference” button
from the tool bar to
specify the number of
iterations desired.
o Click the “Start” button
from the tool bar menu
to simulate.
Contemporary Engineering Economics, 6th edition
Park
Copyright © 2016 by Pearson Education, Inc.
All Rights Reserved
Step 5: Analyzing the Simulation Result Screen
Crystal Ball provides a wide
range of graphing options for
interpreting and presenting
the simulation results.
o Click the “Create Report”
button to display
cumulative graphs,
Tornado charts,
histograms, and other
summary statistics.
• Mean: $40,995
• Variance: (18,730)2
Contemporary Engineering Economics, 6th edition
Park
Copyright © 2016 by Pearson Education, Inc.
All Rights Reserved