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REPORT
Investment Risk Analysis in a New Production
Division using Monte Carlo simulation
Term Paper-Cost Analysis and Engineering Economy
REP
PREPARED BY
Arun V Sankar
A0134606L
NUS ISS EBAC
Sem 2 2015/16
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TABLE OF CONTENTS
1. Executive Summary.........................................................................................3
2. Problem Description........................................................................................4
3. Cash Flow Model Development......................................................................5
4. Base Case Solution .........................................................................................6
5. Understanding Key Uncertainty......................................................................7
Tornado Diagram
Spider Diagram
6. Observations from Tornado and Spider Diagram .........................................13
7. Rainbow Diagram..........................................................................................14
8. Probabilistic Risk Analysis............................................................................15
Monte Carlo Simulation Description
Histogram of Annual Worth
Risk Profile
Risk Profile Comparison
9. Conclusion ....................................................................................................19
10.Reference ...................................................................................................20
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1. Executive Summary
This report tries to understand and analyse the risk involved in planning to
start a new production division against an alternative option of adopting an existing
technology for the production. When the outcomes are considered deterministic the
decision rule is to go for the highest Net Present Value of alternatives available but
when the outcomes are not certain where various input values that decides the cash
flow varies, it is better to go with simulating random scenarios for uncertain input
variables selected from appropriate probability distribution. Here we have used
Monte Carlo Simulation to perform the Cost analysis and compare the alternatives.
This report first identifies the best alternative in Base Case Solution and using
this base case scenario we include uncertainty to it by inputting range of values to
the factors considered and effect plus importance of each factors to the project is
evaluated using Tornado and Spider Diagram. Rainbow Diagram is plotted to
identify the breakeven quantity of production that distinguishes one project over
other. Instead of analytical methods being used to determine the returns of the
projects, we can use Monte Carlo Simulation to derive the mean and standard
deviation of returns. The variables which were found to be sensitive are used to
make a random trial and these values are used to compute the AW of the trial (here
all non-sensitive variables are fixed at their base value).After identifying sensitive
factors we perform Probabilistic Risk Analysis for each alternative and compare
their risk profile. Here we are assuming that AW (in $) may be approximated by a
normal distribution. Best alternative under uncertainty is chosen among the
alternatives.
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2. Problem Description
ABC Pte. Ltd is into surgical tools production where they are deliberating to
start a new production line for making blood bags which is a new venture to their
existing product line. They have shortlisted two production lines that can make
blood bags that meets their standard. Production line 1 (New Design) uses a more
delicate and modern technology which requires lesser manpower thus cut down the
production cost while Production line 2(Old Design) is lesser expensive in terms of
initial investment. Since the medical equipment field is fast enough in terms of new
product innovation, they don’t find to see more than five-year operation period for
the product line after which a total overhaul of technical equipment of the division is
expected.
Other information:
Particulars New Design Old Design
Initial Cost($) 200000 150000
Annual Revenue($) 800000 800000
Lifetime(years) 5 5
Salvage Value($) 100000 50000
Selling price (per unit) 8 8
MARR (%) 10 10
Production per year 100000 100000
Operators required 20 40
Machine Troubleshoot($) 25000 10000
Inline Leak Testing($) 5000 3000
Spare parts($) 5000 2000
Manpower cost/hour($) 10 10
Output per hours 1000 800
Material Cost per unit($) 3 3
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3. Cash Flow Models Development
Cash Flow Modelling is the process of assessing a client’s current and
forecasted wealth, along with inflows (income) and outflows (expenditure) to create
a picture of their finances both now and in the future. It is a means of helping to
foresee the future cash flow in order to help establish their ability to achieve their
lifestyle objectives, their capacity for loss and risk, and then start to build a financial
plan. A more sensible way to approach future cash flow is by discounting them to
arrive at a present value estimate, which is used to evaluate the potential for
investment. If the value arrives at through analysis is higher than the current cost of
the investment, the opportunity may be considered feasible. Cash flow modeling
also improves understanding of the cash impact of investment decisions, and it
improves access to capital, as capital providers have more confidence.
4. Base Case Solution
The alternatives which we are considering is classified into Investment or Revenue
Projects where capital investments and operating costs are expected to produce
revenues and are discarded if found not feasible or not generating revenue. Usually
among the alternatives considered the project which is found to be more profitable
is selected.
New Design
Annual Revenue-Cost
$ 445,000+100,000
$ 445,000 $ 445,000 $ 445,000 $ 445,000
1 2 3 4 5
Initial Cost=
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$2,000,000
Cash Flow
New Design Old Design
Cash Flow Cash Flow
Initial Investment -$200,000.00 -$150,000.00
Annual Revenue $800,000.00 $800,000.00
Annual Direct Manpower cost -$20,000.00 -$50,000.00
Annual Direct Material cost -$300,000.00 -$300,000.00
Annual Overheads -$35,000.00 -$15,000.00
Salvage value $100,000.00 $50,000.00
Annual Worth (10%) = -Initial cost + Annual Revenue – Cost
AW (New Design, MARR=10%) = $408,620.25.
Old Design
$435,000+50,000
$ 435,000 $ 435,000 $ 435,000 $ 435,000
1 2 3 4 5
Initial Cost=
$1,500,000
Annual Worth (10%) = -Initial cost + Annual Revenue – Cost
AW (Old Design, MARR=10%) = $403,620.25
AW for New Design > Old Design; hence choose former in base case analysis
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5. Understanding Key Uncertainties
Base Case Analysis has assumed that all the cash flow information is known with
certainty while most of the real world situation demands cash flow not known in
certainty.
Here we have tried to list all variables where there is uncertainty possible and tried
to list the range between the variables can move. Eight variables in both alternatives
shown in table below (Letter U against the uncertain variables) are considered
uncertain with Low, Base, and High value specified for each.
New Design
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Old Design
Sensitivity Analysis helps to determine to what degree changes in values of
one or more variables would affect an investment decision. Sensitivity Analysis
returns factors or variables which have high impact on decision and those variables
are classified as sensitive in PW/AW or IRR of the project. Tornado and Spider
Diagrams are used to understand the sensitive variables.
Tornado Diagram shows how the PW/AW or IRR of a project changes when
each factor is varied (one at a time) over its range of possible values, while all the
other factors remain at their base values. Spider Diagram is a plot of the PW or IRR
against %-change of each uncertain factor (one at a time) whilst all the other factors
remain at their base values.
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6. Observations from Tornado and Spider Diagram
The width of the tornado diagram indicates the sensitivity of each factor. Here New
Design and Old Design has production price as the most sensitive factor followed by
selling price and material cost as 2nd and 3rd sensitive factor. It should be noted that
top five sensitive factors for both projects differ as 4th and 5th factors are different in
both cases.
Top 5 factors in Tornado Diagram are taken as sensitive and the rest of the factors
considered non-sensitive.
Nowhere has the projects gone below AW<0 for all ranges considered and hence
both alternatives are feasible at all times.
All the lines in Spider Diagram pass through its Base AW value.
Production per year, Selling Price, Material Cost, Salvage Value and Output per hour
have positive slope in Spider Diagram indicating increase in AW/PW value with
increase in these factors.
Material Cost, Manpower Cost, Machine Troubleshooting , Inline Leak Testing, Spare
Parts have negative slope indicating decrease in AW/PW value with increase in
factors.
It should be noted that for both the projects the factors behave similarly.
Swing % for the most sensitive factor ie. Production per year has 58% and 54% for
New Design and Old Design respectively indicating effect of change in factors on AW
has different impact, hence further analysis using Monte Carlo simulation can better
find out if New Design performs better than Old Design as found from Base Case
Solution.
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7. Rainbow Diagram
For further comparison of how each factors effect beyond lower-upper range we can
use Rainbow Diagram for it.
Here we have plotted AW against Production per year to find out the breakeven
quantity; breakeven quantity can be described as the quantity of production above
which one project is preferred over the other and vice versa.
Break Even Quantity for selecting New Design over Old Design is calculated as
83333 which concur with our Base Case Solution.
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8. Probabilistic Risk Analysis
Monte Carlo Simulation
Instead of analytical methods being used to determine the returns of the projects,
we can use Monte Carlo Simulation to derive the mean and standard deviation of
returns. The variables which were found to be sensitive are used to make a random
trial and these values are used to compute the AW of the trial (here all non-sensitive
variables are fixed at their base value). The random trials are repeated for 32000
times and results are accumulated to form distribution of AW which will give the
returns parameters. The underlying principle for the process is that when annual
cash flows in a multiple period project are mutually independent, the project’s AW
will tend to a Normal Distribution with mean E[AW)] and variance Var[PW)] as the
number of periods tends to infinity.
The table below shows the computed returns for both the design against all
sensitive variables taken for both the project.
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Histogram
New Design AW
Old Design AW
$200,000.00$250,000.00$300,000.00$350,000.00$400,000.00$450,000.00$500,000.00$550,000.00$600,000.00$650,000.00$700,000.00
0
500
1000
1500
2000
2500
3000
3500
4000
AW over useful life, Column Width = 25000
ColumnFrequency
Not For Commercial Or Instructional Use
SimVoi Trial Version Histogram For 32000 Trials
$250,000.00$300,000.00$350,000.00$400,000.00$450,000.00$500,000.00$550,000.00$600,000.00$650,000.00$700,000.00$750,000.00
0
500
1000
1500
2000
2500
3000
3500
AW over useful life, Column Width = 25000
ColumnFrequency
Not For Commercial Or Instructional Use
SimVoi Trial Version Histogram For 32000 Trials
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Risk Profile
New Design
Old Design
0.0
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0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
$200,000.00$250,000.00$300,000.00$350,000.00$400,000.00$450,000.00$500,000.00$550,000.00$600,000.00$650,000.00$700,000.00
CumulativeRelativeFrequency
AW over useful life
Not For Commercial Or Instructional Use
SimVoi Trial Version Cumulative Chart For 32000 Trials
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
$250,000.00$300,000.00$350,000.00$400,000.00$450,000.00$500,000.00$550,000.00$600,000.00$650,000.00$700,000.00$750,000.00
CumulativeRelativeFrequency
AW over useful life
Not For Commercial Or Instructional Use
SimVoi Trial Version Cumulative Chart For 32000 Trials
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Comparing the two alternatives
New Design Old Design
EV of AW $408,834.56 $457,109.80
St. Dev. $82,569.18 $85,111.81
Downside Risk 3.68373E-07 3.92163E-08
Upside Potential
Prob{AW>300000} 90.62 96.71
Prob{AW>400000} 54.26 74.88
Prob{AW>500000} 13.47 30.71
VaR(95%) -544648.77 -597106.25
0%
5%
10%
15%
20%
25%
30%
35%
40%
45%
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
100%
$0 $100,000 $200,000 $300,000 $400,000 $500,000 $600,000 $700,000 $800,000
ExcessProbability
AW
New Design Old Design
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9. Conclusion
Here we are assuming that AW (in $) may be approximated by a normal distribution
which concur with the histogram plotted and its mean and variance is calculated for
analysis.
Mean and Variance is calculated for both the alternatives and it is found that new
design has lesser mean to old design but new design variance is found to be slightly
lower value which can be a reason for new design being selected in Base Case
Solution.
Downside Risk is the probability that the project is economically infeasible and
value of risk calculated is 0; showing the project is feasible at almost all times.
Probability of achieving various upside potential is calculated and it is found that old
design dominates new design in all cases; thus we can conclude considering Old
Design instead of adopting a New Design for producing the Blood Bags.
Company had a plan to invest the same money in bond market which will give
returns of 5% but it is found that the revenue generated in an year from production
of Blood Bags already covers double of the initial investment made hence go with
the option of setting up production line using Old Design.
10. Reference:
1. The European Physical Journal B - Risk analysis in investment appraisal based on the
Monte Carlo simulation technique.
2. A Probabilistic Approach to Risk Analysis in Capital Investment Projects- C. D. Zinn
and W. G. Lesso.
