1. Contemporary Engineering Economics, 6 th edition Park Copyright © 2016 by Pearson Education, Inc. All Rights Reserved Risk Simulation Lecture No. 40 Chapter 12 Contemporary Engineering Economics Copyright, © 2016

2. Contemporary Engineering Economics, 6 th 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.

3. Contemporary Engineering Economics, 6 th edition Park Copyright © 2016 by Pearson Education, Inc. All Rights Reserved Logical Steps Involved in Simulating a Risky Investment

4. Contemporary Engineering Economics, 6 th 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

5. Contemporary Engineering Economics, 6 th 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.

6. Contemporary Engineering Economics, 6 th edition Park Copyright © 2016 by Pearson Education, Inc. All Rights Reserved Observed NPW Values ($), Based on 200 Iterations

7. Contemporary Engineering Economics, 6 th edition Park Copyright © 2016 by Pearson Education, Inc. All Rights Reserved Simulated NPW Frequency Distribution Mean = $44,245 Standard deviation = $18,585

8. Contemporary Engineering Economics, 6 th edition Park Copyright © 2016 by Pearson Education, Inc. All Rights Reserved Simulation Result Based on 200 Iterations

9. Contemporary Engineering Economics, 6 th 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.

10. Contemporary Engineering Economics, 6 th 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.”

11. Contemporary Engineering Economics, 6 th 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.

12. Contemporary Engineering Economics, 6 th 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

13. Contemporary Engineering Economics, 6 th 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.

14. Contemporary Engineering Economics, 6 th 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