IE 415/515: SUMMER 2015
LAB 2:
Simulating in Excel with Crystal Ball
1. Introduction
In this laboratory exercise, you will work in teams of two, and use Monte Carlo
simulation to:
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Conduct engineering economic analysis considering the uncertainty in cash
flow estimates,
Estimate the probabilities of outcomes in scenarios with randomly
distributed components.
Unlike lab assignment #1, you will be using an Excel add-in called Crystal Ball that
facilitates the execution of Monte Carlo simulations.
2. Engineering Economics – Net Present Value
In engineering economy, the net present value or NPV is the value of a series of
cash flows over time at time zero (present time). The calculation of NPV accounts
for the time value of money specified through an interest rate (often referred to as
the minimum attractive rate of return, MARR). The interest rate is typically an
annual interest rate, and a common assumption is that cash flows occur at the end
of a time period. For example, the NPV of cash flow x occurring in year five at
interest rate i is:
𝑁𝑃𝑉 =
𝑥
(1 + 𝑖)5
In this lab all cash flows will be annual cash flows, and the interest rate will be an
annual rate.
3. Simulation With Crystal Ball
Crystal Ball allows cells in a spreadsheet model to represent random variables, and
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facilitates Monte Carlo simulation by automatically generating realizations of the
random variables. Each cell that represents a random variable in a Monte Carlo
spreadsheet simulation is called an assumption.
Crystal Ball will also tabulate and store statistics for results computed as a
function of spreadsheet cells. The cells that Crystal Ball keeps track of are called
forecasts
The lab TAs will give you a short tutorial on using Crystal Ball. It will be
assumed that all students are familiar the concepts of random variables (discrete
and continuous), probability density functions, probability mass functions, and
cumulative distribution functions. The Crystal Ball topics covered are:
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Assumptions
Forecasts
Copy and pasting Crystal Ball data
Random number generation
Sampling methods
Running and pausing simulations
Simulation output displays, and copying and pasting output.
4. Lab Assignment
NPV Analysis
Two alternative heating systems are being considered, gas and electric, for a
temporary building to be used for 5 years. The gas system will cost $6K to
install (at year 0). It is estimated that this system will have a salvage value of
$500 after 5 years, and will have annual fuel and maintenance costs of $1K.
The electric system will cost $8K to install and has an estimated 5 year salvage
value of $1.5K. The estimated annual fuel and maintenance costs are $750 per
year. The assumed MARR (interest rate) = 6%.
a. Based on a net present value analysis (NPV) using the estimated costs as
known cash flows, which system is preferred and why (assuming all other
factors are equal)?
b. Assume the salvage value and annual fuel and maintenance costs are
independent random variables. The fuel and maintenance cost for each year
may be different. Each annual cost will vary uniformly ±50% around the
estimated costs given earlier (e.g., Uniformly distributed between $500 and
$1500 for gas). The salvage values will vary according to a triangular
distribution. For the gas system enter a “likeliest” value of $500, a minimum of
$250, and a maximum of $600. For the electric system set the “likeliest” value
to $1500, the minimum to $500, and the maximum to $1750. Incorporate this
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into a spreadsheet simulation using “Monte Carlo” sampling. Simulate 50000
times (use a seed = 999).What is the average and the standard deviation of the
difference NPV(gas)-NPV (electric) generated from the simulation? Make sure
this figure is labeled and highlighted in your spreadsheet. Which system is
preferred and why?
What to turn in
E-mail your completed spreadsheets to the TAs (ie415lab@gmail.com). Include the
following:
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Names of team members(File Name: Last Name-Last Name-Lab#),
Add documentation to make the spreadsheet understandable. This is a
judgment call so add more rather than less documentation. Assignments
that are too hard to understand will be penalized.
A separate sheet with the answers requested. Clearly label all answers.
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