Valuing Project Financing Using Monte Carlo Simulation, With Application
to the Expansion of a Chemical Company
by
Meghan Gibbons
Submitted to the Department of Mechanical Engineering
in Partial Fulfillment of the Requirements for the Degree of
Bachelor of Science in Mechanical Engineering
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
v,',/ea*0t
May 2005
i
OFTECHNOL03Y
JUN 0
© 2005 Meghan Gibbons
LIBRARIES
All rights reserved
The author hereby grants MIT permission to reproduce and to distribute
publicly paper and electronic copies of this thesis document in whole or in part.
Signature
ofAuthor:....
Signature of Author: ...........
..
~.......-..
..................... ;.....................................
~Dea~tment
of Mechanical Engineering
,,q ~
May 6, 2005
Certifiedby :. .......... .... ..
.....-
.............
.. ..................................
7/
Stewart C. Myers
GordoWYBillard Professor of Finance
Thesis Surervisor
Accepted by:..............................................................................................
Ernest G. Cravalho
Professor of Mechanical Engineering
Chainnrman,
Undergraduate Thesis Committee
1
2005
Valuing Project Financing Using Monte Carlo Simulation, With Application to the
Expansion of a Chemical Company
By
Meghan Gibbons
Submitted to the Department of Mechanical Engineering
On May 6, 2005 in Partial Fulfillment of the
Requirements for the Degree of Bachelor of Science in
Mechanical Engineering
ABSTRACT
The purpose of this thesis is to analyze the specific project value of a chemical company
that undertook a major expansion in the late 1990s. The actual details of the investment
were unique and conditional on the level of cumulative internal rate of return for the
project. This thesis evaluates the project value and the terms of the project financing using
Monte Carlo simulation, which is able to take into account the path-dependent nature of
the cash flow model. The results of this research are of interest to investors facing similar
financing terms or similar investment opportunities in the future.
2
Acknowledgements
I would like to extend a special thanks to Professor Stewart Myers, who provided guidance
and instruction throughout this process. I truly value all of his support and patience. I am
also extremely grateful to The Brattle Group - especially Lynda Borucki, who allowed me
access to critical background information and also spent time going through extensive
documentation with me.
3
Table of Contents
1.
Introduction...................................................................5
2.
The Investment Opportunity...............................................
2.1
2.2
6
Use of Documents..............................................
Overview of Project Details.................................
6
6
3.
Application of Monte Carlo Simulation.................................
9
4.
Project Model................................................................
5.
4.1
4.2
Structure and Input Variables ................................
Base Case Assumptions.......................................
11
12
4.3
How the Model Generates Output ........................
12
Simulation Results and Interpretation...................................
13
5.1
5.2
5.3
5.4
5.5
6.
11
The Base Case ..................................................
Varying the Standard Deviation.............................
Varying the Target Rate.......................................
The Effect of Including Fixed Costs........................
Changing the Distribution Percentage.....................
13
15
19
23
26
Conclusion...................................................................29
6.1
6.2
Summary of Results............................................
Areas of Further Work........................................
29
31
7.
Appendix ......................................................................
32
8.
List of References............................................................
54
4
1.
Introduction
This thesis investigates the unique project financing of a specific manufacturing
project using Monte Carlo simulation. Due to the path-dependent nature of this particular
investment, and the complication of many critical underlying variables, it was necessary to
use simulation in order to generate a probability distribution of possible outcomes.
Through the careful inspection of company documents, a model was set up to represent the
possible cash flows over a given time horizon. This thesis details the setup of the model
and further explains the incorporation of the model into the Monte Carlo procedure.
Finally, results of repeated simulations facilitate analysis of the degree to which certain
unique terms of the financial agreement affect value to outside investors.
Moreover, this thesis emphasizes the complications that arise as a result of a path-
dependent project. The investment opportunity is described and analyzed in terms of its
path-dependent nature. A clear need is established for a more sophisticated valuation
method in order to accurately judge the investment opportunity, and Monte Carlo
simulation is presented as a very viable solution. Furthermore, simulations facilitated the
valuation and anmalysis
of this investment by allowing the alteration of many key variables.
This type of sensitivity analysis would be of particular interest to investors who are faced
with the challenge of trying to evaluate the potential profit or loss of a similar type of
investment.
5
2.
2.1
The Investment Opportunity
Use of Documents
Documents and contracts detailing the project were fortunately available and easily
accessible during the writing of this thesis. However, these documents obviously contain a
large amount of private information relevant to the company and investors who undertook
this project. In order to respect the privacy rights of their agreement, this thesis relies on
an altered version of most quantities mentioned in the actual signed documents. Overall,
the focus of this thesis is not to use exact numbers but to demonstrate a methodology for
valuation.
2.2 Overview of Project Details
In the late 1990s, a large chemical company was interested in financing a major
expansion of their chemical plant. The company had to consider several key aspects
regarding the potential expansion. Beyond the costs of completing the project itself, the
expanded plant would require additional fixed costs, which would include energy costs as
well as costs of inputs necessary in the production of standard chemicals. Another
important issue was the degree to which the expansion would increase overall production
efficiency. The company also had to bear in mind taxes and the possible benefit of tax
shields from incurred debt. At the same time, the company lacked a comprehensive model
to help value the investment.
One fundamental issue was the type and source of funding. The company decided
that the expansion would be financed with $400 million of bank debt as well at $100
million in equity. Of the total equity, the company itself contributed $50 million, and
6
outside investors contributed the remaining $50 million. The debt was incurred in the
initial year and paid off annually through the tenth year. Interest payments were a fixed
percentage of the remaining principal each year. This information provides the necessary
details to understand the underlying financial structure of the project. Moreover, it is
important to take this financial structure into account when making assumptions in the cash
flow model.
Another fundamental issue was the determination of how the outside investors
would receive value for investing in the project. In this situation, the contract specified
that the net cash flows from the project would be divided equally between the outside
investors and the company. This condition would hold until the outside investors hit a
cumulative target internal rate of return of 16%. Once this target IRR was reached or
surpassed once, the investors would no longer receive any cash flows from that point on,
thus terminating their investment in the project. The company would receive all
subsequent cash flows. The sequence of events was especially important in this situation,
as the outside investors would still receive the cash flow that put them up to or beyond
their target IRR; they were just restricted from obtaining any subsequent amount after that
point.
This rule demonstrates the challenging issue of path-dependence. Outside investors
were critically dependent on their cumulative IRR, since they would only receive future
cash flows if the target IRR rule were satisfied. For example, with a $50 million
investment and 16% target, the IRR rule would begin with the conditional statement: If 50(1.16) + C1
> 0,
then stop, and otherwise continue. The next level of branching would
reference "-50(1.16) + Cl" as X1, such that the new condition would be: If Xl ( 1.16) + C2 >
7
0, then stop, and otherwise continue. The future cash flow stream is thus directly
dependent on all previous cash flows. The decision whether or not to continue in the
project must be evaluated at every node in the tree. The specific challenge is that the exact
stream of cash flows must be stored and used to evaluate the cumulative IRR with each
new move in the tree. This path-dependent nature presents a critical problem that must be
overcome to determine the NPV obtained by outside investors.
Several key calculations were performed in order to determine the profitability of
the investment. The project model in this case focuses on the net present value of the
project as a whole, as well as the net present value of the outside investors. Obviously the
outside investors prefer a project that will give them the largest possible net present value.
This thesis looks at several main input values that affect the net present value to outside
investors under the financial terms of this project. These quantities include standard
deviation, target IRR, fixed costs, as well as the percentage of project cash flows going to
the outside investors. Simulations were rerun with each of these quantities varied and
comparisons were then made to an initial base case. This repeated procedure revealed the
impact on the value obtained by outside investors due to changes in any of the above
inputs.
Overall, the terms of the original agreement specified many key variables that had
to be incorporated into the project model. The type of funding and the specific terms
critically established the basic financial structure of the project. This information
facilitates realistic calculations and analysis regarding how project financing affects the
value obtained by outside investors.
8
3.
Application of Monte Carlo Simulation
Monte Carlo simulation is a useful method in cases in which varying cash flows
extend over many years into the future. Project financing often involves variables and
inputs that are not well understood, thus making a valuation very tedious and difficult. A
detailed model of the project facilitates a more comprehensive evaluation of the investment
opportunity. Monte Carlo simulation can use such a detailed project model to generate a
probability distribution for the overall value of a path-dependent project that extends over
many years.
Path-dependence is difficult to value because the stream of future cash flows relies
directly on knowledge of all prior cash flows. Certain criteria are evaluated with each
forthcoming cash flow, and this evaluation directly involves the series of previous cash
flows. At each point in time, the criteria determine whether or not the series is continued
based on the current cash flow, as well as the previous stream of cash flows. Thus, a
critical aspect of the expansion project is that it establishes a path-dependent investment
opportunity. As specified above, the investors are critically dependent on their cumulative
internal rate of return, earned from year zero onward. The path-dependent nature is a
crucial issue that must be addressed in order to determine the net present value obtained by
outside investors. Since the rule, establishing when the investors are "out," is predefined
as a certain cumulative IRR, the Monte Carlo method can be used to simulate and value the
path-dependent nature of this investment.
In general, the use of Monte Carlo simulation provides the means to avoid
difficulties that would arise in a complicated valuation, such as a path-dependent project.
9
Indeed, the specification of a particular cash flow stream over the next 30 years would
allow a straightforward calculation of present value. However, in cases that involve
multiple variables or extend over many years, it is often a difficult and time-consuming
process to come up with one project value. By using Monte Carlo simulations, it is
possible to establish multiple variables and forecast calculations that extend far into the
future. Rather than guessing specific cash flows and calculating one possibly inaccurate
value, computer simulations take samples for each variable based on specified probability
distributions and subsequently come up with probability distributions for quantities chosen
to be forecasted. These forecasted values, for example, can be the present value of the
project overall or even the cash flow from a certain year during the life of the project.
Monte Carlo simulation involves a number of distinct steps. It is necessary to start
with a model of the project that establishes a structure of possible cash flows over a certain
time. For example, this type of cash flow model can be conveniently represented as an
expanding binomial tree. At each node in the tree, probabilities are specified for the next
two branches that indicate a movement upward or downward in the cash flow tree. Once
the model and probabilities are set up, simulations can be run in which the computer
generates possible cash flows of the project in each year based on the probability
distributions specified for the unknown quantities. Many iterations of the simulation result
in probability distributions of cash flows for each year of the project. From these results,
further present value calculations and analysis can be performed.
10
4.
Project Model
4.1 Structure and Input Variables
Before running Monte Carlo simulations, the project model was set up to portray
the series of cash flows as a typical binomial tree extending from year zero to year 30.
Every branching step is the passage of one year, and each cash flow node is a simple
estimation of revenue minus fixed costs.
Figure 1: Initial Branching of a Binomial Tree
As a model of the real project, the binomial tree references key input variables that
affect project valuation. The risk-free rate was assumed to be 6%, indicating the safe return
of a U.S. treasury bond. The standard deviation, representing the degree of uncertainty of
cash flows, was initially set at 15%, somewhat less than the stock market variability of
around 20%. In other words, the expansion project was assumed to be relatively safe. The
probabilities of upward and downward movements are calculated automatically using the
entered standard deviation in order to obtain an expected rate of return that is equivalent to
the risk-free rate. This concept is more commonly referred to as the risk-neutral rate of
11
growth over any given year. The binomial tree uses these main input values, along with
the initial revenue amount, to calculate cash flows over the 30-year life of the project.
4.2 Base Case Assumptions
In order to start with a simple base case, certain assumptions were made regarding
initial terms of the project. The total investment in the project was kept at $500 million.
However, the base case assumed that the project was completely equity-financed and
included no portion of debt. The equity contribution was thus the total $500 million, with
the outside investors and the company each contributing $250 million. Furthermore, fixed
costs were initially assumed to be zero, and consequently the binomial tree only relied on
the beginning revenue value, estimated at $53 million, which gave a project NPV of $45
million.
In the base case, the outside investors received 50% of the project cash flows, and
their initial target IRR was assumed to be 11%. These input values were chosen in order to
establish a realistic level from which further comparisons could be made. The overall
terms of the agreement remained the same: the outside investors received their percentage
of project cash flows until they reached or surpassed their cumulative target IRR, in which
case they were out of the investment and all cash flows went to the company.
4.3 How The Model Generates Output
Overall, the simulations are path-dependent due to the fact that they must start at
year zero and go forward in time. Again, the path-dependent nature of this problem is
what dictates the need for Monte Carlo simulations. As the binomial tree shows, each
subsequent cash flow branches off of the previously-calculated entry. In other words, each
cell's calculation directly stems from the previous calculated cash flow. Monte Carlo
12
simulations also step forward through the tree in such a path-dependent fashion.
Moreover, running thousands of iterations provides a probability distribution of possible
cash flows for each year. The model was set up as a binomial tree that started with the
spreadsheet shown in Principles of Corporate Finance (Brealey and Myers, 2003, p. 626).
All necessary calculations, such as the routine for calculating the IRR, were written into
the model. Crystal Ball Software, produced by Decisioneering Inc., was used as a macro.
For each iteration, the program runs through the tree one time. A random number
is generated in order to specify an upward or downward movement at each consecutive
node in the cash flow model. The random numbers are generated from a continuous
uniform distribution, ranging from zero to one. This specification allows there to be a
clear cut-off level between zero and one that establishes which random numbers constitute
an upward-move or a downward-move at any given node. Thus, the generated string of
random numbers actually indicates a string of "up" and "down" moves in the binomial
tree. The program generates a random number for every year and then stops. Once this
series of up and down moves is established, the project's cash flows are calculated for each
of 30 years.
5.
Simulation Results and Interpretation
5.1 The Base Case
The base case detailed above provides a useful starting point. As shown in Table 1,
the key input values and investor terms are stated. Three graphs show the probability
distributions of cash flows to outside investors in years five, 15, and 30, respectively.
fourth graph in the table is the NPV to outside investors, and the final graph shows the
13
The
NPV of the project. The average value in each graph is also specifically noted, and all
subsequent tables follow this same format. In the base case, due to the fact that there are
no fixed costs or debt repayments, all cash flows to the outside investors are actually
positive. These assumptions, for example, allow outside investors to earn an average cash
flow of $8.5 million, even in the 3 0 th year:
.
CrystWa
Ball Acadeic
Fccast:
Edtimn
CFa y r 30
Nt for Cormercial Use
5,000 Trials
Freqiemy Chat
4,892 Dsplayed
.146
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.110
547.5
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-n
.
.073
9
CD
.0
.037
182.5 IQ
.000
0
0.00
7.12
1425
M
21.37
2&49
From Table 1: Base Case, Cash Flow to Outside Investors Year 30
However, the varying magnitude over the 30 years of the project causes there to be cases in
which investors realize a negative net present value for their investment. As the graphs
indicate, the outside investors earned an average net present value of $8.4 million in the
base case. The corresponding mean NPV of the project was $45 million. These quantities
provide a realistic starting point since the outside investors would earn between a three to
four percent return on their assumed investment of $250 million. The graphs of the NPV
to outside investors and the project NPV reveal similar shapes, although it is worthwhile to
note that the first shows more of a bimodal distribution. Resulting shape changes were
studied in more detail as the key input values were varied.
14
Crystal Ball Acaderric
Edtin
Forecast: NPV of Atsicb Investor
Ndtfor Corrrercia Use
Frercy
5,000 Tnals
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- 96
-
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5 . .....
.............. 24
I-
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Mc
0
I
$32.46
M
($44.54
($121.54)
$186.47
$109.47
From Table 1: Base Case, NPV to Outside Investors
CrystalBall AcaderticEdtimn
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forConmercia Use
Forecast: PrIect NR/
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4,905 Dsplayed
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.007 ..........
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....7
($3o100)
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............
.33.25
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$15000
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0I
o
qO
From Table 1: Base Case, NPV of Project
5.2 Varying the Standard Deviation
One of the fundamental input variables in the cash flow model is the standard
deviation. This quantity determines the magnitude of each up-move or down-move in the
tree. The base case involved a standard deviation of 15%, which is reflected in the
variability of cash flows as the binomial tree branches out over the 30 years. However, by
15
changing this quantity, it is possible to gain insight regarding the affect to the net present
value of outside investors as well as to the present value of the project as a whole.
The standard deviation was first increased from 15% to 20%. Table 2 includes
graphs showing selected years of cash flows received by outside investors. The last two
graphs depict the overall net present value obtained by outside investors and the net
present value of the whole project, respectively, as reproduced below.
CrystalBall AcadenicEdticn
Nctfor Conmercil Use
5,000 Tndals
Forecast: NPVof Otsid
Investor
FrequercyChat
4,994 Dsplayed
.019
95
.014
71.25
Z'
-n
.010
I
47.5
n
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0
.010
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$23.77
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($157.12)
$11421
From Table 2: NPV to Outside Investors, St. Dev. 20%
CrystalBall Acaderic Edticn
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5,000 TriEls
Forecast: Proect NR/
4,877 Displayed
Frequercy Chat
.03D
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.022
111
-n
0
.015
74
.0
.007
37
.000
0
($40QO)
($10o)
$200
M
$5X00
From Table 2: NPV of Project, St. Dev. 20%
16
$8QO00
n
"1'1
.0
Increasing the standard deviation had the effect of decreasing the average net
present value of outside investors to -$5.8 million, demonstrating an unprofitable
investment. Aicomparison of probability distributions with the base case revealed that
outside investors received around the same average cash flow over the first few years.
However, their cash flows over the second half of the project declined relative to the base
case. This change contributed to the lower net present value due to the increased standard
deviation. Overall, the value to outside investors was affected more than the value of the
whole project. The net present value of the project remained relatively close to its value in
the base case.
An increase in standard deviation is essentially increasing the variability of the
upward and downward movements of cash flows over the 30 years. This effect causes
larger variability over a longer time horizon and explains why outside investors saw a
larger impact further out in the project life. This variability is further enforced by
comparing the ranges of net present values obtained by the outside investors. For example,
the base case provided a net present value ranging from -$134 to $186 million. With the
increased standard deviation, the range became -$160 to $238 million. The higher
standard deviation also resulted in a graph of investors' NPV that revealed a more
pronounced bimodal structure. There was also an increased likelihood of being out of the
investment at an earlier stage but with a lower NPV. As the simulations will show,
opposite results occurred when the standard deviation was lowered.
The standard deviation was subsequently decreased from the base case of 15% to
10%. Decreasing the standard deviation had the effect of increasing the mean net present
value obtained by the outside investors to around $19.2 million, representing roughly an
17
8% return on the invested $250 million. A comparison of probability distributions with the
base case revealed that outside investors received, as before, around the same average cash
flow over the first few years. The decrease in standard deviation caused cash flows over
the second half of the project to increase in comparison with the base case. This change
contributed to the higher net present value obtained by outside investors. Moreover, the
value to outside investors was once again affected more than the value of the project as a
whole. The net present value of the project increased slightly to $45.9 million. Again, a
comparison of the following graphs reveals that the shape of outside-investor NPV begins
to approach the shape of the project NPV with the lower standard deviation. The first
graph also reveals less of a bimodal shape compared to previous version.
CrystalBallAcaderic Edtion Foreast: NPV of Ojtsikb Investor
Nct forCommercil Use
5,000 Tials
Freqercy Chart
4,996 Displayed
.oz3
117
.018
87.75
.012
58.5
ZD
S
_n
c
0
.06
29L25 coo
.00
0
($94.3
($30.04)
$3424
M
From Table 3: NPV to Outside Investor, St. Dev. 10%
18
$16281
Faeast:
Crystal13alAcademicEdtic
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From Table 3: NPV of Project, St. Dev. 10%
In summary, the 10% standard deviation provided the case that was the most
beneficial to both the outside investors as well as to the overall project value. The
simulations revealed that the value of outside investors was more sensitive to the change in
standard deviation than was the project value itself.
5.3 Varying the Target Rate
One of the key determinants of value to outside investors was the specified
cumulative IRR target, which the base case assumes to be 11%. By altering this
percentage, it was possible to study the sensitivity the outside investors' value to the target
IRR. This rate was especially important in this type of investment because it determined
the cut-off point after which investors no longer received any value from the project. The
outside investors would want large payoffs without surpassing the limit set by the IRR.
The ideal outcome would be an IRR of 10.99% over 30 years. To study the effects of this
target rate, the initial 11% was increased and decreased by different amounts, and
subsequently Monte Carlo simulations were rerun each time in order to compare the
resulting probability distributions.
19
The target IRR was initially increased to 16% and then to 21%, while keeping the
other assumptions of the base case the same. These increases should effectively allow the
outside investors to obtain more cash flows before surpassing the target rate. The mean net
present value of outside investors did increase to $19.5 and $21.3 million, in the 16% and
21% cases, respectively. Furthermore, the graph displaying the probability distribution of
net present values to outside investors reveals that the higher target rate significantly
increased the range maximum. The range minimum was roughly the same as it was in the
base case. However the range maximum extended to almost $585 and then $680 million,
as the IRR was increased each time. The graphs demonstrate that the higher target rate
effectively increases the range maximum while only somewhat increasing the mean NPV
obtained by investors. As expected, the net present value of the project remained around
the same value due to the fact that the new target rates did not affect the overall project
cash flows. In both sequential increases, the graphs of outside investors' NPV closely
resemble each other as well as the graph of the project NPV. The following two graphs of
cash flows to investors correspond to the 21% IRR case, and to the 16% IRR case:
Crystal Ball Acaderic Edtimn
Forecast:
PV of Otsib Investor
NdotforComnTercilUse
5,000Trials
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Freiemy
Chat
4,890 Displayed
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635
.013
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.00
31.75
.00
0
($13356)
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($2.02)
$77.52
M
$18307
From Table 4: NPV to Outside Investors, 21% IRR
20
$2 61
Crysta BaldlAcadeic
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Frecast: NPV of O(tsicb Investor
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29
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($2.24)
$69.82
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$167.88
$3S93
From Table 5: NPV to Outside Investors, 16% IRR
The target rate was subsequently decreased to 9% and to 6%, and results were
compared with the previous cases. A lower target should essentially cause investors to
reach their ending point sooner in the life of the project. The mean net present value of the
outside investors decreased to -$3.2 million and -$23.8 million, respectively. The graphs
indicate a larger change from the base case compared to the previous example in which the
IRR was increased. Results indicate that the lower rate significantly decreases the range
maximum of net present value for investors. The range minimum again remained the same
as in the base case, while the range maximum decreased to $38 million with the 6% target
rate. Overall, these results reveal that the outside investors are more negatively affected by
a lowered target rate than they are positively affected by an increased target rate.
Moreover, the mean NPV is shown to increase at a decreasing rate as the target IRR is
raised.
The two cases of lowered IRR targets reveal interesting graphs of the NPV to
outside investors. As was previously the case when the IRR was increased, the same
21
graphs more closely resemble the project NPV graph. In the cases of lowered IRR, the
graphs become flatter except for a spike that develops toward the right of the distribution.
In the case when the IRR is equal to the risk-free rate of 6%, the graph becomes extremely
flat with a spike at around $7 million. The following two graphs demonstrate the results of
lowering the IRR:
Crystal Ball Acaderric
Edticn
Frecast: NPVof Otsikb Investor
Nct forCornTercil Use
5,000 Tris
Freqercy Chart
4,996 D siJay ed
.031
155
.023
116.2
-n
Z
M
.016
77.5 .0
.OOD
3875
.000
0
0
CL
X
($131.03)
($69.93)
($883)
M
$113.36
$5
From Table 6: NPV of Outside Investors with 9% IRR
Crystal Ball Acaderric
Edtin
Frecast: NPV of Outsicb Investor
Nct for CoTnercial Use
5,000 Tndals
4,955 Dspayed
Freqercy Chart
.136 -
.10Q2
.m.
.11 .06
682
. ...............
I.........................................................................................................
511.5
..........................................
..................................................................................................................
..... .........................................
341
n
e
nC
-
.034 ..........................................................................................................................
.................
.00 .'"- .,mhllnllllmllllh
($120.65)
($80.94
($4123)
M
v
($1.52)
From Table 7: NPV of Outside Investors with 6% IRR
22
170.5
,
0
$33.19
5.4 The Effect of Including Fixed Costs
The addition of fixed costs to the model allows further study of the main inputs
affecting investors' value. To start, a fixed amount of $30 million was subtracted from
each node in the tree. To facilitate comparison with the base case, the revenue was
increased from $53 to $93.195 million. This alteration provided the same base-case NPV
calculated by simply extending the amount of revenue minus fixed costs over 30 years and
discounting back to year zero.
The graphs in Table 8 show several key differences resulting from the inclusion of
fixed costs. The average cash flows to outside investors were larger in the initial years of
the project. However, as shown in the
significantly.
15th and
30
th
years, the average cash flow decreased
For example, year 30 of the base case revealed an average cash flow to
outside investors of $8.5 million. However, when fixed costs were added, this average
cash flow sunk to -$0.09 million in the thirtieth year. The addition of fixed costs caused
investors' average cash flows to be lower in later years since more nodes in the tree
generate negative cash flows later in the project. Thus, larger negative cash flows are
possible later in the life of the project as the binomial tree extends its branches over time.
Overall the mean net present value obtained by outside investors diminished to -$19.9
million, representing a situation any investor would want to avoid. The mean net present
value of the project remained in area of $42 million. This result reinforces the fact that the
revenue increase helped offset the increase in fixed costs in terms of overall project value.
The following graph, taken from Table 8, shows the resulting shape of the NPV to
outside investors in the case that included fixed costs of $30 million. Similar to the case in
which the IRR was decreased, this graph also reveals a flattened shape with a spike.
23
Crystal Ball Acaderic
Edticn
Faorecast: PV of Otsikb Investor
Ndt forConrrmercial
Use
5,000 Tdns
FreqJercy Chat
4,988 Dsplayaed
.034
171
.
12B2
-I
X
855
.017
.00
rp
*0
n
4275
.000
($23937)
0
($127.01)
($14.66)
M
$97.70
$210Q06
From Table 8: NPV to outside investors with fixed costs of $30 million
For further comparison, the simulations were run again using a different fixed cost.
Keeping the overall net present value of the project the same as before, the new fixed cost
was increased to $50 million and the initial revenue was set at $119.99 million. Since
revenue was increased by slightly more than fixed costs were increased, the input may
initially imply larger payoffs for the outside investors. However, the simulations
demonstrate that the higher revenue and higher fixed costs actually have the opposite
effect. In this case, average cash flows to outside investors were even higher in the
beginning years of the project. However, especially in the second half of the project life,
cash flows declined sharply. In year 30, investors obtained an average of -$5 million. The
graph of investors' net present value shows the negative impact resulting from fixed costs
of $50 million. The outside investors obtained a mean net present value of -$43.19
million, revealing an even worse investment opportunity than the previous case. The graph
also demonstrates a similar shape to the previous case with fixed costs of $30 million.
24
However, this graph has become slightly flatter with a narrow spike. This graph is also
similar in shape to the situation involving a lowered IRR target.
Crystal Ba Acadaric
Edtimn
Frecast: NIPVof Outsib Investor
Not for Conmrercil Use
Frequercy Chat
5,000 Tndals
5,000 Displayed
200
.040
.030
.02o
C,
n
.0
.010
50
.OO
0o
($33Q41)
($19341)
($56.41)
$8.59
$217.60
M
From Table 9: NPV to Outside Investors with fixed costs of $50 million
Overall, these two examples involving different levels of fixed costs emphasize
several important issues. The value that outside investors expect to gain from their
investment is extremely dependent not just on the expected NPV of the project but on the
actual level of revenue relative to fixed costs, as well. As simulations demonstrated, the
project could be valued at the same net present value but the value obtained by outside
investors depended critically on initial estimates of revenue and fixed costs. A project with
higher initial revenue may imply a more profitable investment. However, a project with
the same NPV but higher estimated revenue and a higher estimate of fixed costs actually
negatively impacts value to outside investors. In general, investors may have the tendency
to focus on the resulting amount of revenue minus fixed costs. These simulations
demonstrate the importance of the actual individual levels of revenue and fixed costs. In
the case with fixed costs of $30 million, net income was initially $93.2 - $30 = $63.2.
25
When fixed costs were $50 million, net income was $119.99 - $50 = $70 million. The
inclination may be to place higher value on the situation with the higher net income. On
the other hand, the equal estimate of net present value may seem to imply that the two
situations would result in similar outcomes for investors. However the graphs demonstrate
that the magnitude of fixed costs has a negative impact that outweighs the small increase in
initial revenue. Thus, the case in which there is higher revenue and higher fixed costs
actually results in a much worse outcome to investors' net present value.
5.5 Changing the Distribution Percentage
An essential part of the contract was the percent of cash flows that outside investors
would get each year. Previously kept at the specified 50%, this distribution percentage
was altered in order to determine its overall effect on investors' value. This particular
input variable provides an interesting situation in which a tradeoff exists concerning
receiving larger cash flows earlier but increasing the risk of reaching the target IRR sooner.
Likewise, a decreased distribution percentage lowers the chance of reaching the target rate
but spreads lower cash flows over a longer stretch of time. Without further examination
through simulations, neither case presents itself as the obvious choice.
The distribution percentage was initially increased from 50% to 75%. As expected,
graphs of the initial years revealed a higher average cash flow to outside investors. Graphs
of years 15 and 30 also reveal much higher probabilities of the investors being "out" by
that time (Table 10). The resulting mean NPV to outside investors rose to $64 million.
Moreover, the shape of the graph reveals a flattened lower tail, with an upsurge in value
that is pushed toward the front of the distribution.
26
Crystal allAcaderic Edticn
Nt for Cormrerci Use
Forecast: CFO yr 15
Frequercy Chat
5,000 Trials
4,911 DiEsplayed
1781
.356
.267
-n
.
w
.178
c
890.5
C
.0
0
4452
CL
.....................................................................................
i
................................
I..
p
o.O0
0
4
41.68
3126
2Q0.84
M
10.42
From Table 10: Cash Flow to Outside Investors in Year 15, 75% Distribution
CrystalBallAcadeic Edtin
Nd for Corrnerci Use
5,000 Tnils
4,918 Dispayed
Frequercy Chat
-
.:41 -
.410 .
,
Frecast: CFO yr 30
....................
.
-n
Cl
.
.274 ......
. ...................
-
=683.7
683.7,.
0
I.......................................................................................................................................
I
I
I
0.00
I-
~ ~ ~ ~~
I.
l I.
I.
I.
I.
=
I
.
o
11.30
M
16.95
I4
2260
0
From Table 10: Cash Flow to Outside Investors in Year 30, 75% Distribution
27
Crystal Ball Academic Edtin
Not for Corrercil
Frecast: NPV of
tsikd Investor
Use
5,000 Trids
Frequercy Chat
4,869 Displayed
.040
198
.030
148.5
-rl
m
._
99
0
..~
o
.0
.020
.010
495
.000
0
($36.05)
$14.46
$64.97
M
$11547
2
$16598
From Table 10: NPV to Outside Investors, 75% Distribution
For further comparison, the distribution percentage was also decreased to 25%.
This change presents the case of receiving lower cash flows over a longer period of time.
As expected, outside investors received lower average cash flows in the initial years of the
project, and had a much lower probability of being "out" of the investment in years 15 and
30. As the graph below indicates, the mean NPV of outside investors decreased to -$114
million. Compared to the previous case, the shape of investor NPV more closely
resembles the graph of the project NPV with more of a lognormal distribution.
Regarding the tradeoff between percentage of cash flow and likelihood of
surpassing the target IRR, simulations revealed that outside investors would definitely
prefer the higher distribution percentage. In this case, they obtained a significantly more
profitable investment by receiving larger sums of cash in the initial years, while giving up
a longer life of their investment.
28
Crystal Ball Acadeic
Edticn
Frecast: NPV of QJtsi
Investor
Nct forConrmrcial Use
5,000 Trials
Frequercy Chat
4,869 Dsplayed
.026 -129
~~~~~~~~~~~~~~~~9675
019
.013
.64.5
I-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~I
k-.00 . .......
.......
3 2
0....................
ADo
0
($191.91)
($14.71)
($89.51)
M
($38.30
$12.90
From Table 11:NPV to Outside Investors, 25% Distribution
6.
Conclusion
6.1 Summary of Results
This thesis looks at the use of Monte Carlo simulation to evaluate project financing
by studying a detailed example involving a financing deal for an expanding chemical
company. Although a seemingly simple problem, the expansion project actually revealed
an investment opportunity that necessitated a more sophisticated method of valuation than
was available at the time. Despite the confidentiality of exact numerical values of the
project, a carefully-chosen base case was presented to represent the same type of
investment opportunity that was part of the original project financing. This thesis
specifically focuses on the sensitivity of value obtained by outside investors to several key
input values detailed in the terms of the project.
Simulations facilitated the valuation and analysis of this investment by allowing the
alteration of many key variables, including the cumulative target IRR as well as to the
distribution percentage of cash flows. Key tradeoffs were examined such as the inclusion
29
of fixed costs, accompanied by higher revenue. In this particular example, results
demonstrated that larger fixed costs, despite an offsetting increase in revenue, created a
much worse investment opportunity for outside investors. Another key tradeoff studied
was the balance of receiving larger sums of cash with a higher risk of reaching the
cumulative IRR limit as opposed to receiving smaller amounts of cash with a higher
likelihood of remaining in the investment longer. Although not immediately apparent,
simulations clearly demonstrated the beneficial outcome of the larger distribution
percentage for a shorter time horizon. The graph of investors' NPV with the higher
distribution percentage was of similar shape to the previous graphs involving a decreased
IRR. Both situations forced investors out of their investment earlier. On the other hand,
the graphs that involved increasing the IRR, and the graph that involved lowering the
distribution percentage, were also similar in shape to each other as well as to the graph of
project NPV. These two cases allowed investors to remain in the project for a longer
period of time. Thus, the particular shapes of investors' payoff distributions revealed a
critical dependence on the length of time of the investment. At the same time, similar
shapes of payoffs, indicating roughly the same time horizon, did not necessarily indicate
anything about the actual value of the investment itself. For example, the lowered IRR
provided a negative mean NPV to outside investors, while the similarly-shaped graph of a
75% distribution percentage showed high levels of profit. In summary, the ability to
simulate and value important variations of the investment provides critical knowledge
concerning the sensitivity of investors' value to these variations. Moreover, Monte Carlo
simulations provide the essential method to examine the path-dependent nature of this
investment.
30
6.2 Areas of Further Work
There are many interesting related issues to address stemming from this thesis.
With this particular project, the expansion can be further studied by experimenting with
different time horizons. In this thesis, the life of the project was estimated to be 30 years.
However, similar calculations could be performed to compare the same project over
different time horizons and the subsequent effect it would have on value to outside
investors. In addition, further studies could be done that include a financing structure
involving debt to be paid off over any number of years. One could even go into details
concerning the effects of default at different point in the binomial tree.
In addition, many creative situations could be set up to encourage further study.
For example, the valuation could include the option of project abandonment as part of the
financial strategy. Broadening possibilities further, experiments could be done with
varying risk-free rates. These areas of further study are obviously a mere sampling of the
possible situations of project financing to address. Fortunately, with the help of Monte
Carlo methods, many projects and conditional events can be simulated and valued.
31
Table 1: Base Case
Key Input Values:
INVEST
500
|C1
|
FC
RF
0
6.00%
% to
Outside
Investors
Target
53
St. Dev. |
15.0%
UP
1.161834
| DOWN
| PROB
0.861
0.371
1- PROB
0.629
Investor Terms:
50%
CrystalBallAcadernic
Edticn
Ndtfor CorrmercilUse
5,000 Trials
IRR
11%
Forecast: CF
yr 5
Frequemy Chat
4,960 Displayed
.351
1757
.176
878.5 -
n
CD,
0
4392 ,
.00
0
1252
2Q0.18
27.85
M
3552
4318
Average Cash Flow, Year 5: $23 million
CrystalBallAcadaeicEdtin
Nd forComercia Use
5,000 Tnds
Forecast: CFa yr 15
Freqiecy Chat
4,838 Dsplayed
208
1038
-
...............
.0
778.5
-n
_
..........
....................
........................................
..........
...............
....................
I
......................................................................
I...
.104 ....................................
519 .C,
0
I
wCL
nm
.vuv
: 259.5
.........................
.....................
...........
I...................I.....
I
0.00
.ll
I
19.76
M
Average Cash Flow, Year 15: $16 million
32
29.63
4
39.51
0
......................................................................
Crytal BallAcadenicEdticn
Ndct
forCormercil Use
5,000 Trials
Fcrecast: CI
yr 30
Frqercy Chat
4,892 Dsplayed
.146
730
.110
547.5
-n
.073
-365 .0-
.0
k-
CL
._
.037
182.5,
0
0.Oo
7.12
14.25
M
21.37
2849
Average Cash Flow, Year 30: $8.5 million
CrystalBallAcademicEdticn Frecast: NPVof Otsid
Ndot
forCormmrcil Use
5,D) THals
Investor
Frecercy Chart
4,965 Dsplayed
.019
96
.014
72
-n
.0
._
.010
-48
=
0
24
0
0
.000
($121.54)
$32.46
M
($44.54)
$10947
$18647
Average NPV to Outside Investors: $8.4 million
CrystalBallAcademic
Edticn
NctforCornTercia Use
Fcraecast:
Prect NV
Freqery Chat
5,00 Tals
4,905 Dsplayed
.027
133
.020
99.75
-"r
.0
Z
.0
Lo
0.
o
.013
665 -0
CD
.007
33.25
,
.oo
0
($3o30.o)
($75.00)
$150.00
M
Average NPV of Project: $45 million
33
$37500
$60o.00
Table 2: Standard Deviation 20%
Key Input Values:
INVEST
500
|C1
53
FC
0
RF
6.00%
% to
Outside
Investors
Target
St.Dev.
20.0%
UP
1.221403
I
DOWN
0.819
PROB
0.382
Investor Terms:
IRR
11%
50%
CrystalBallAcadericEdticn
NotforComTercialUse
Faecast: CFO yr 5
5,000Tds
Freqemy Chat
4,967 Displayed
- 1705
.41A4
....... I..............
256 ..........................
2'
:3 171 ...........
................................................................................................................
-1n
-
......................
.....................................
-852.5 .........................................................................
......................
.....................................
.0
-426.2
.........................................................................
cx.
905
.171
oo ... ..
I
....
9.75
19.86
2.97
M
40.08
- 0
4
5Q19
Average Cash Flow, Year 5: $23 million
CrysalBallAaderic Edtion
Notfor CorrmercilUse
5,000 Tndals
Forecast: CFO yr 15
Freqiercy Chart
4,850 Displayed
2C2
1012
-1,
.0
0~
.101
5C6
.051
253
0
.00
0
0.00
10.64
2129
M
Average Cash Flow, Year 15: $13.6 million
34
31.93
4257
=
1 -PROB
0.618
CrystaBallAcadericEdticn
NctforCom-ercia'Use
Fcrecast:CFa yr 30
5,00 Trils
Frequercy Chat
4,901 Dsplayed
59.5
.129
-1
m
._
399 =
.
0
W~ .040
199.5,
0
.000
0.00O
21.05
1403
M
7.02
2806
Average Cash Flow, Year 30: $6.55 million
CrystalBallAcadaenric
Edticn Frecast:
Nct orComnerciaUse
5,C0DTnals
NPVof Otsicb
Investor
Frqency Chat
4,994 Dsplayed
.
.019
95
-71.25
.014 -
.0m
.010-
.................... 47.5
.005-
....................2375
k-
CL
._
w
($157.12)
$11421
-n
CD
r-
.0
I
f0
A
$234.65
M
Average NPV of Outside Investors: -$5.77 million
CrystalBallAcaderricEdticn
Nct forCommrcil Use
5,CO Trids
Frecast: Raqect NR/
Freqxery Chat
4,877 Dsplayed
148
.030
111
.015
74
-n
CD
.
.007
37
,
.000
o
.0
.0
0
($400. )
($10oo)
$a)Q0oo
M
Average NPV of Project: $42 million
35
$5Q00o
$8D0.00
Table 3: Standard Deviation 10%
Key Input Values:
INVEST
FOC
C I
500
53
0
RF
St. Dev.
UP
DOWN
PROB
1 - PROB
6.00%
10.0%
1.105171
0.905
0.338
0.662
Investor Terms:
% to
Outside
Investors
Target
50%
11%
IRR
CrystalBallAcaderic Edticn
Nct forCorrmerciaUse
5,000 Trias
Fcrecast: CFOI yr 5
FreqRmy Chat
4,979 Dsplayed
1626
244
-n,
-q
.0
o
813 .0
.163
=
C.T
.081
406.5
,
.000
0
21.33
1607
2658
M
31.84
37.10
Average Cash Flow, Year 5: $23 million
CrystalBallAcademic
Edticn
NotforCornercid Use
5,00 Tnals
Fcrecast: CFO yr 15
Freqercy Chat
4,962 Dsplayed
221
1106
. .............................................................
...............................................................................................
. 829.5
.0
-n
I..............................
...... ................................................................................
I...........
. 553
.111 ...................
.0
0
iL
. ..........................................
...... ...... ....I..................................
....................
.................................
. 276.5
a-
I
.000
0.00
17.91
M
Average Cash Flow, Year 15: $17.3 million
36
2686
I
n
4
35.81
.=
co
CrystalBallA cadeic Edtion
Ndot
forCorr nercialUse
Frecast: CFO yr 30
5,00 Tri S
Fregency Chart
4,86; 2
splayed
- 758
.152
-568.5
.114
-n
-q
._
3
CID
- 379=
.076
C.,
1
. wo
.038
::::
1F
I
4,:::
: -
I
.000
189.5
plyI
-0
0.00
0.0J
1289
M
6.45
25.79
2579
19.34
Average Cash Flow, Year 30: $10.25 million
CrystalBallAcaderic Edtion
NotforComm;rcialUse
5,CO0Trials
.023
Farecast:
NW
of Outsicbk Investor
FreqJecy Chat
splayed
4,9 )6
117
r
.... ................................................................I.....................
I.......
.018 .......................................
. -87.75
4Z'
.
w
.0
0
k
-n
............................................................
.- 55 .0
I.......
I .......
.012.......................
.....................
. 29254
.006 .....................
.....
11
.000
($94.33)
11111
($3D.04)
II
4
0
$16281
$3424
M
Average NPV of Outside Investors: $19.22 million
CrystalBallAcademic
Edticn
Nt forCorrmnercial
Use
Frecast: Rlect NRI/
Frq
5,02 Tnds
y Chart
4,933 D splay ed
.026
13D
.020
97.5
-n
._
.3
.013
65
.007
325,
M
.0
0
.000
($2o0.00)
0
($50.00)
$10000
M
Average NPV of Project: $45.9 million
37
$25Q00
$400.00
CT
=
Table 4: IRR 21%
Key Input Values:
|
|C1 I
53
INVEST
500
FC
0
T
RF
6.00%
| St. Dev. |
UP
| DOWN
15.0%
1.161834
0.861
|
PROB
0.371
Investor Terms:
% to
Outside
Investors
50%
Target
IRR
21%
CrystalBallAcademic
Edticn
NotforCormerciaUse
5,00 Tries
Fcrecast: CFC yr 5
Freqery Chal
4,969 Dsplayed
1639
.246
-n
.164
819.5 C.,
.0
o
L
4G9.7 4
0L
0
.000
1252
20.45
28.39
M
3633
4426
Average Cash Flow, Year 5: $22.9 million
CrystalBallAcadenic Edticn
Nt forConrercil Use
5,000 Tnals
Frecast: CFa yr 15
Freqery Chart
4,904 Dsplayed
1009
.................
.151
I..................
....................................................
.....
-n
._
0i
CD,
......................................
..........................................................................................
504.5-~
.101 ........................
C.,
wm
O
- .......... .................................. .............
252.2
..................................
.000
O
3.77
14.74
2570
M
Average Cash Flow, Year 15: $17.1 million
38
3667
47.63
47.63
| 1 - PROB
0.629
CryFtalBallAcadeTicEdtin
NotforComercil Use
5,0(XD00
Tnsal
Forecast: CFa yr 30
Freercy Chat
4,875 Dsplayed
.153
765
.115
573.7
.077
-n
4
382.5 =
.=
,,
12
3
1912 Q
.000
0
0.00
1026
20.52
M
30.78
41.04
Average Cash Flow, Year 30: $10.94 million
CrystalBallAc adaric Edtia
NotforCome rcial Use
5,C00 Trias
.025-
Forecast: NV of OJtsi
Investor
Chart
Freqiecy
|
4,890 isplayed
I-
I- 127
.019 ......
._,
.,
o
.0
0
X
........... 9525
-I1
n
..- 65 -=
............
.013
n
C'D
.......
...........
.31.75 Q
.006
.000
IF35S)($
13356)
($2B.02)
$7.5
$18.07
$77.52
M
$18307
-0
6q
$28.61
Average NPV of Outside Investors: $19.47 million
CrystalBallAcadric Edticn
NotforComTerciaUse
5,0CDTrials
Forecast: Prqect NFV
4,903 Usplayed
Frequeruy Chat
.027
133
.020
99.75
-rl
-
.0
.013
0
.o.007
CD,
665 .0
CD
3325 4
.000
($300.00)
0
($75.00)
$150.00
M
Average NPV of Project: $42.1 million
39
$375.00
$6D00
Table 5: IRR 16%
Key Input Values:
INVEST
01
500
53
i
FC
RF
St. Dev.
UP
DOWN
PROB
1 - PROB
0
6.00%
15.0%
1.161834
0.861
0.371
0.629
Investor Terms:
% to
Outside
Investors
50%
Target
.
IRR
16%
CrystalBallAcaderaicEdticn
NdtforConTrercial
Use
5,0W Tndals
Frcast:
CFOi yr 5
Freqercy Chart
4,968 Dsplayed
.346
1730
.260
-n
.173
865
M
.087
432.5
1,
.0
0
.0o00
-q
1252
2Q04
27.56
M
3509
4261
Average Cash Flow, Year 5: $23 million
CrystalBallAcaderricEdticn
Ndct
forCorrrrercialUse
5,000 Tnials
Fcrecast: CF) yr 15
Freqery
Chart
4,926 Dsplayed
1055
211
791.2
-n
.1
.0
0
ICL
.106
527.5 =
.053
263.7
.000
0
0.0)
11.16
2232
M
Average Cash Flow, Year 15: $17.3 million
40
33.48
44.64
CrystalBallAcadanicEdticn
NdtforComrTercilUse
5,0 Tidals
Forecast: CFO yr 30
Frqercy Chat
4,922 Dsplayed
.145
724
.109
543
-n
0-
.072
362
0._
-=
C.,
181
W
.000
0
0.00
9.14
18.28
M
27.42
3656
Average Cash Flow, Year 30: $11.6 million
Crysal Ball Acadaric Edticn
Frecast: NPVof Ctskb Investor
NdotorCormercil Use
5,C00 Tnials
Freqemy
4,893 Bisplayed
Chat
.023
116
.017
87
-q
.012
58
.006
29
-~
0
k-
0L
.000O
0
($12630)
($12&3J)
($28.24)
$167.88
$26593
59
M
Average NPV of Outside Investors: $21.28 million
CrysialBallAcadeanic
Edtimn
Ndot
forCorrmercidUse
Ferecast: Raject NR/
5,OWTals
Freqercy Chat
4,909 Dsplayed
.020
99
'
.0
.013
66
.007
33Q
.000o
0
0
L.
CL
-n
C.
0
CD,
($300.o)
($75.00)
$150.00
M
Average NPV of Project: $43 million
41
$37500
$6Q00
Table 6: IRR 9%
Key Input Values:
INVEST
500
FC
0
I C1 I
53
I
RF
6.00%
I St. Dev.I
15.0%
UP
1.161834
I
DOWN
0.861
PROB
0.371
Investor Terms:
% to
Outside
Investors
50%
Target
IRR
9%
CrystalBallAcadeic Edticn
NdtforCorercia Use
Forecast: CFO yr 5
Freecy
5,00) Trds
Chat
4,968 Dsplayed
1673
.251
r-n
,-h
.0
836.5 =~=
.167
C,
.0
0
.084
418.2
,
0
1252
2Q0.38
28.25
M
3611
4398
Average Cash Flow, Year 5: $23 million
CrystalBallAcaderricEdticn
Ndot
forCorrrcil Use
Forecast: CFO yr 15
5,000 Trils
Freqercy
Chart
4,902 Dsplayed
20
999
.150
7492
.100
499.5 .0
-n
.0
.0
CD,
.0
0
249.7
0
.000
0.0
9.29
18.59
M
Average Cash Flow, Year 15: $14.2 million
42
27.88
37.17
1 - PROB
0.629
Crytal BallAcaderic Edticn
Nt forComercia Use
Forecast: CFO yr 30
5,00 Tnls
Fregiery Chat
4,872 Displayed
-1173
---
.176. .......
- 879.7
...................
I.......................................................................................................................................
-n
............
m
,, 117
*_
3
.117 -......
o
...................................
.............................................................................................
I.....................
- 586.5 M
2
CD
..... ........................I................................
............................................................
.059 .........................
0 2
.-293.2
iL
-
INII[
,V'
- _
I
.1 1
-I--,
- --
0.00
5.74
11.48
M
1722
qI
2296
-
Average Cash Flow, Year 30: $6.4 million
CrystalBallAcadrmicEdticn Forecast: NPV of QOtski Investor
NotforComrercialUse
Frqercy Chart
5,COOTrals
4,996 Dsplayed
.031
155
.023
116.2
.016
77.5 .-
.Z
-n
,
n
&oc
00
3875 I
0
OOO
0
($8.83)
M
($131.03)
$11336
Average NPV of Outside Investors: -$3.2 million
CrystalBallAcadericEdticn
Nt for ComrercialUse
Forecast: Rqect NPVR/
5,O Tals
FreqJecy Chart
4,906 Clsplay od
.026
132
.020
99
-n
M
._
-
66 -~
.013
L-
33
.0o
.007
0
($30Q0)
($75.00)
$150.00
M
Average NPV of Project: $41.2 million
43
$37500
$6D.00
Table 7: IRR 6%
Key Input Values:
INVEST
500
C1
53
FC
0
RF
6.00%
St. Dev.
15.0%
UP
1.161834
DOWN
0.861
PROB
0.371
Investor Terms:
% to
Outside
Investors
50%
6%
CrystalBallAcadenicEdticn
Ndot
forComercial Use
5,00 Tndals
Forecast: CFO yr 5
Freqercy Chat
4,967 Dsplayed
.354
1769
-n
884.5 =
.177
4CT'
-._w
442.2 4
.00
0
1252
2028
2805
M
35.82
4358
Average Cash Flow, Year 5: $22.8 million
Edticn
CrystalBallAcademic
NdtforCormercidUse
5,000 Tnds
Forecast: CFl yr 15
Frequercy Chat
4,971 Dsplayed
200
748.5
-r,
.0
CT'
.100
499
.050
249.5
,
.000
0
.
.0
I-
0.
EL
0.00O
8.08
1616
M
Average Cash Flow, Year 15: $11.24 million
44
2424
3322
1 - PROB
0.629
CrysfalBallAcader
nicEdticn
Ndot
forCormercil Use
5,(Cx: Trials
Forecast: CFO yr 30
Freqiercy Chat
4,920 Elsplayed
5_
A~
.14C
-
OAA 7
- zq4 I
.367 ......
-rn
q
.11
I
.0
.| I
nmY'
iiiii
.vw
I
I
..........................................................................................................................................................
I I
I
611.7
,I- , .122
12 -......
......
I
I
I
I
I
I
O
0.00
3.74
7.48
M
11.22
4
14.96
0
Av.,rage Cash Flow, Year 30: $3.28 million
CrystalBallAcaderic Edtion Forecast: NPVof Otsicb Investor
No forCormrercial
Use
Frequercy Chat
5,000 Trials
4,955 [Esplay d
.136
682
.102
511.5
.,
-n
CID
341 .0
CID
=
.0
,w
L
.034
,
170.5
.000
0
($12Q0.65)
($80.94)
($41.23)
M
($1.52)
Average NPV of Outside Investors: -$23.78 million
CrystalBallAcadenicEdticn
Nct forCorrnercialUse
5,X0 Trials
Fcrecast: Proect NR/
Frmqery
Chart
4,907
splay ad
.026
130
.020
97.5
-n
=
w
.013
65
325,
0.007
0
($300.
C0)
($75.00)
$150.00
M
Average NPV of Project: $41 million
45
$375.00
$60o.00
3
rD
Table 8: Fixed Costs $30 Million
Key Input Values:
INVEST
500
C1
|
93.195
FC
30
RF
6.00%
% to
Outside
Investors
Target
St. Dev.
15.0%
UP
1.161834
DOWN
0.861
PROB
0.371
Investor Terms:
IRR
l
50%
11%
CrystalBallAcade'icEdticn
NdtforCorrmercilUse
Forecast: CFO yr 5
5,000Tris
Frequercy Chart
4,970 Dsplayed
1725
.64b -
...............
I.......................................
.........................................................................................................
-n
3
M
.0
............................
..................................
... ................................................................
.173 ...........................
862.5 8
............................
......................................
.......................................
I.......................
431.2
0~
nm
7.01
2Q15
3329
M
46.43
4
5956
0
Average Cash Flow, Year 5: $25.5 million
CrystalBallAcade-raic
Edticn
NdtforCormercil Use
5,0 Tnals
Forecast: CFC yr 15
Freecy Chat
4,936 Dsplayed
.210
1048
....................
.......................................................................................
.
.157 .....................................................
-n
.0I.
CID
.............................
.......... ....................
...........................
..........................................................
. 524 =
.0
0~
.......... , ....
-8.37
......... ........... ................ .................................
4.44
17.25
M
Average Cash Flow, Year 15: $9.2 million
46
3Q06
4
4288
222G
, ='
=
0
1 - PROB
0.629
CrystalBallAcadericEdticn
NOtforCorrmercilUse
5,000 Tridals
r~A
/.17
Fcrecast: CFO yr 30
Freecy Chat
4,868 Dsplayed
- 1172
-
.176 .............................
- 879
-n
'
;
.117-
.- 586 3
o
I.09
0~~~~~~~~
.
....................................
....................................................................CD
..............
1........I......................................
I
. ............
.. .... ...
I I
IN
.'L/'O.J
'u
·
-293
:...
.I
qI
-173
-1a73
-3.82
6.09
M
15.99
0
25.90
Average Cash Flow, Year 30: -$0.1 million
Crystal Ball Academic Edtin
NdforCorrrercil
Frecast: NPV of Otsib
Investor
Use
5,000Tnls
Freqercy Chart
4,988Dsplayei
.034
171
.029
128.2
Z'1
=
.017
-8553
co
n
=
.oo9
4275 I
M
.0
A'
-n
'"ql
.
.000
($239.37)
0
($127.01)
($14.66)
M
$97.70
$21Q0.06
Average NPV of Outside Investors: -$19.9 million
Fareast:Rqect N/
CrystalBallAcadericEdticn
Ndtfor Comnercil Use
5,0(I) Tnls
4,905 Dsplayed
Frequercy Chart
-139
.21 ......................
.1042
.021. ............................
-n
0
.014.
.....................
.69.5 3
C.
n
0
....................
34.75 ,
.0070
.O
rK-~
P
($750.0)
I.l.|.JI
($31250)
$125.00
M
Average NPV of Project: $42.1 million
47
$56250
0O
I
$1,000.00
Table 9: Fixed Costs $50 Million
Key Input Values:
INVEST |
C1
|
500
119.991
FC
50
|
RF
6.00%
St. Dev.
15.0%
UP
| DOWN
1.161834
0.861
| PROB
0.371
Investor Terms:
% to
Outside
Investors
Target
50%
11%
IRR
CrystalBallAcademic
Edticn
Nct forComnercil Use
Forecast: CFO yr 5
5,000Tnis
Freqercy
Chart
4,970 Dsplayed
.334
1668
195
.250
-n
.
.167
834 =
¢3
J~
.083
417
.000
0
CW
3.34
21.12
3891
M
5669
7447
Average Cash Flow, Year 5: $27.1 million
CrystalBallAcadericEdticn
Nctfor Cornmnerci
Use
5,000 Tndals
Forecast: CFO yr 15
Freqecy Chat
4,799 D[splayed
215
1074
.161
805.5
-n,
.
-r
.107
537,
.054
268.5 Q
.0
0
h..
a-
0
.0OO
-18.68
-3.47
11.74
M
Average Cash Flow, Year 15: $5.12 million
48
2695
4216
1 -PROB
0.629
Crytal BallAcadenicEdticn
Ndot
forComercil Use
5,00 Trials
Forecast: CFO yr 30
Freqercy
4,900 Dsplayed
Chart
1409
.211
-rl
704.5 =
.141
.0
.o
CO
322
352.2
.070
.- il
.00
-23.36
I ~*1*
I
-11.46
1234
0.44
4
24.23
0
M
Average Cash Flow, Year 30: -$5.05 million
CrystalBallAcad'ric Edtimn Faorecast:INPVof OQtsic
Nd for ConTrmercil
Use
Frecry
5,000 Tals
Ivestor
Chat
5,000 Dsplayed
.040
20w
.030
-n
C'D
100 .0
.0
.0
o-
0L
.020
C.
.010
50
.003O
0o
($33Q
41)
($1941)
-
$217.60
($56.41)
M
Average NPV of Outside Investors: -$43.19 million
CryslalBallAcadmic Edtin
Ndtfor Cormercil Use
5,0(:OD
Trials
Forecast: Praect NFPV
Freqer:y Chat
4,882 Dsplayed
131
9825
-n
.0
.013
.0
00L
3275
.007
0
.003
($750.o)
($250.o0)
$250.00
M
Average NPV of Project: $36 million
49
$750.00
$1,25.00
Table 10: Distribution to Outside Investor 75%
Key Input Values:
INVEST
|C1
500
FC
RF
| St. Dev. |
UP
0
6.00%
15.0%
1.161834
53
| DOWN
| PROB
0.861
0.371
1- PROB
0.629
Investor Terms:
% to
Outside
Investors
75%
Target
IRR
11%
CrystalBallAccadenicEdticn
NotforComnercialUse
5,000 Tnel S
Forecast: CFOAyr 5
Freruy Chart
4,96C D splayed
1760
.352
... ..........................
............... ................ ..........................
-
264 ...........
._
,S
0
&
-n1
...........................
.....................................
.......................................................................
88D
8m- '
,.... ..... ....... .......................
... .................................
.. .....................................................................
.
.176
.0
.088oco08
440
Q
....................................
........................ .................................................
0
4
30.78
18.78
4279
M
66.81
54.80
Average Cash Flow, Year 5: $34.7 million
CrystalBallAcaderricEdticn
NdtforCorrmercial
Use
Forecast: CFO yr 15
Freqiercy Chat
5,000 Tnds
,
4,911 Dsplayed
-
.3U
,}.
;,b/
11
J~J
----4
-n,
C.
890.5
.178
...........................................................................................................................................................
.0
. ..... .....................................................................
I.........................................I.........................................
:
.
=
O
a. . 089
4452
t,1I
.vuv
O.00
.I
I
1Q42
I
r
2Q84
M
Average Cash Flow, Year 15: $12.4 million
50
I
I
3126
n
41.68
|
CrystalBallAcaderic Edticn
NotForCorrmercid
I Use
Forecast: CF1 yr 30
5,(00Tns
Frecemy Chat
4,918 splayed
- zib
.b4/
.410
.410 ......
274 ......
,,
,- I
.11 1--
-I
.,
t-,
. ......................................
.............................................................................
I
I
I.....................................
...........................................................................................................................................................
,,0
0
.137 ......
683.7
--
.00-
0.0)
-- --
---I
l
;
11.30
M
1695
l
-
0
J
j
4
2260
Average Cash Flow, Year 30: $4.5 million
CrystalBallAcaderic Edticn Forecast:NPVof
Nt fr ComnerciaUse
OLAtsiCb
Freerry
5,000Trils
Investor
Chat
4,869 splayed
.040
198
.033
148.5
.020
99
-q
4
._
Z
M
0
&
.010
49.5
,
.000
0
($36.05)
$14.46
$64.97
M
$115.47
.=
=n
$16598
Average NPV of Outside Investors: $64.44 million
CrysL,BallAcademicEdticn
Nt forCornTrerciai
Use
Forecast: Rqect NFV
Frequercy Chat
5,0(0 Tdls
._,
.
M
0
4,91 1
splay ad
.025
127
.019
9525
-n
635 .c
.013
.00
31.75
k-.003
0
($300O)
($75.00)
$15Q00
M
Average NPV of Project: $45.9 million
51
$37500
$600.00
Table 11: Distribution to Outside Investor 25%
Key Input Values:
INVEST
500
Cl
53
FC
0
RF
6.00%
% to
Outside
Investors
Target
25%
11%
St. Dev.
15.0%
UP
1.161834
DOWN
0.861
PROB
0.371
Investor Terms:
IRR
CrystalBallAcadaric Edticn
NctforCormercis Use
5,000 Triads
Fcrecast: CF
yr 5
Freqiery Chat
4,969 Dsplayed
1731
.346
-q
.173
=
865.5 C.
.087
42.7
0
0k-
Co
0
.000
10.10
1393
M
17.77
21.61
Average Cash Flow, Year 5: $11.5 million
CrystalBallAcadericEdticn
NdtforComrnercid
Use
5,000 Tridals
Forecast: CFI yr 15
Frequency Chat
4,903 Dasplayed
28
1040
.156
-n,
.0
.104
520
.000
0
0
1.40
6.70
11.99
M
Average Cash Flow, Year 15: $8.7 million
52
1729
2259
=
1 - PROB
0.629
CrystalBallAcademic
Edticn
NotforComercil Use
5,(X0 Trials
Forecast: CFO yr 30
4,887Esplayed
Freqemy Chart
.149
743
.111
557.2
-I1
.
Ii
._
.074
371.5 .0
.037
135.74
.O0
0
C
W
L.
027
9.83
M
5.05
14.61
19.39
Average Cash Flow, Year 30: $5.72 million
Edtim Forecast: NPV of Otsikb Investor
CrystalBallAcademic
NdotforCornmercil Use
Frec
y Chart
5,000Tals
4,869 Dsplayed
123
.019
9675
.013
64.5
-n
C"D
.
C
0
CL
.006
3225
.000
0
($191.91)
($140.71)
($89.51)
M
($38.30)
$12.90
Average NPV of Outside Investors: -$114.24 million
CrystalBallAcadenicEdtin
NdtforComnrercilUse
5,000 Trials
Forecast: Raect NRI
Freqemy
Chart
4,902 D[splayed
.030
112.5
.023
-n
.0
C.D
75
.015
C.
.0
0L.
C-
.0
.0c8
37.5
0
.0oo
($300.00)
($75.00)
$15Q0.00
M
Average NPV of Project: $43 million
53
$375.00
$60Q00oo
,
List of References
Bertsimas, Dimitris, and Robert M. Freund. Data, Models, and Decisions: The
Fundamentals of Management Science. Cincinnati: South-Western College
Publishing, 2000.
Brealey, R.A., and S. C. Myers. Principles of Corporate Finance 7 h Ed. New York:
McGraw Hill Book Company, 2003.
Myers, Stewart, ed. Modern Developments in Financial Management. New York:
Praeger, 1976.
54