Transcript Lecture 9

Updated: 29 April, 2007
FINA 522: Project Finance and Risk
Management
Lecture Nine
0
RISK ANALYSIS
What is risk?
• Risk generally describes the possible
deviation from a projected outcome.
• To project any uncertain outcome into the
future you need to have a “predictive
model”.
• A predictive model could be a simple
formula or a very complex worksheet.
2
Decision-Making Under Uncertainty
1.Risk analysis
• How to identify, analyze, and interpret the
expected variability in project outcomes
2.Risk diversification and management
• How to diversify unsystematic risk
• How to redesign and reorganize projects
in order to reallocate risk
3
Risk Analysis
1. WHY?
• Project returns are spread over time
• Each variable affecting NPV is subject to a high level
of uncertainty
• Information and data needed for more accurate
forecasts are costly to acquire
• Need to reduce the likelihood of undertaking a "bad"
project while not failing to accept a "good" project
4
A good predictive model in project appraisal depends on:
Correct methodology
Cash-Flow Projections
Accurate data
Marketing Module
Input Data
Technical Module
Input Data
5
Uncertainty and Forecasting
We use the past to forecast the future
Ability to forecast accurately depends on:
Variable Value
Past Events
•
Forecasts
•
•
•
x
x
x
x
x
x
x
x
x
x
Past
o
o
o
o
o
x
Present
Future
•
•
How similar past events are to the
object of forecast
How big is the sample of past events
How recent are past events
How consistent the outcome
historically
How far into the future is the forecast
How dependent the outcome is on
previous years (trend) and on other
projected variables (correlations)
Time
6
Inputs are projected as certainties
(Base Case Scenario)
• When we provide inputs to a predictive
model we use one particular probability
distribution – the Deterministic Probability
Distribution.
• By that we assign 100% probability that the
single value of the input we use in the
projection will actually arise.
7
Forecasting the outcome of a future event:
Single-value estimate
The deterministic
probability distribution
Variable
value
Probability
MAXIMUM
1.0
 Mode
 Average
 Conservative
estimate
MINIMUM
Now
Time
Variable value
8
From a frequency to a probability distribution
Frequency
Variable values
Probability
MAXIMUM
1
5
3
5
1
3
MINIMUM
1
Now
Time
.5
.3
1
Minimum
Maximum
Variable value
.1
Minimum
.1
Maximum
Variable value
= Observations
9
Multi-value probability
distributions
Probability
Probability
Normal
Min.
Values
Uniform
Max.
Probability
Min.
Max.
Probability
Triangular
Min.
Values
Values
Step
Max.
Min.
Values
Max.
10
Multi-value probability distributions as their
inputs to a predictive model.
• Any possible deviation in any of the critical
input variables of a predictive model from
their base case values will generate a new
scenario with a different outcome (or
outcomes).
• There are potentially an infinite number of
combinations of input values possible, each
causing a different set of results.
11
2. Alternative Methods of Dealing
With Risk
2.1 Sensitivity Analysis
2.2 Scenario Analysis
2.3 Monte Carlo Risk Analysis
(or Simulation Analysis)
12
2.1 Sensitivity Analysis
• Test the sensitivity of a project's outcome (NPV or the key
variable) to changes in value of one parameter at a time
• "What if" analysis
• Allows you to test which variables are important as a source
of risk
• A variable is important depending on:
A) Its share of total benefits or costs
B) Likely range of values
• Sensitivity analysis allows you to determine the direction of
change in the NPV
• Break-even analysis allows you to determine how much a
variable must change before the NPV or these key variable
moves into its critical range turns negative
13
Another Important Use of Sensitivity Analysis
• Sensitivity analysis on the PV of each row of the
spreadsheet (Banker’s, Owner’s and Economy’s
point of view) is the best way to de-bug a
spreadsheet
• If results do not make sense then it is likely that
there is an computation or logistical error in the
spreadsheet
14
Sensitivity Analysis for the Mindanao Poverty Reduction Case
World T.P. Price
(S.F. FOB) US$/Ton
587
637
687
737
787
837
887
937
987
1037
1087
Divergence from
Original Cost
Estimate
-10%
-5%
0%
5%
10%
15%
20%
25%
30%
35%
40%
Real NPV
(Million Pesos)
-228
-103
22
147
272
397
522
647
772
897
1022
Real NPV
(Million Pesos)
190
169
147
125
103
82
60
38
17
-5
-27
Inflation
Rate
5%
8%
11%
14%
17%
20%
23%
26%
29%
32%
35%
Capacity
Utilization
Factor
60%
65%
70%
75%
80%
85%
90%
95%
100%
105%
110%
Real NPV
(Million Pesos)
161
147
136
126
118
111
105
99
94
89
84
Real NPV
(Million Pesos)
-189
-147
-105
-63
-21
21
63
105
147
189
231
15
• For Tomato Paste Plant Capacity Utilization is
critical.
• What can cause Capacity Utilization to be low?
1. Technical problems with the plant.
2. The demand for product does not exist at the price that
covers the costs
3. The plant can not get adequate supplies of raw materials.
Factsheet:
– this plant eventually run into financial troubles
– could not attain adequate supplies of raw
materials
16
Cautionary Notes for Sensitivity Analysis
1. Range and probability distribution of variables
• Sensitivity analysis doesn't represent the possible range of
values
• Sensitivity analysis doesn't represent the probabilities for
each range. Generally there is a small probability of being
at the extremes.
2. Direction of effects
For most variables, the direction is obvious
A) Revenue increases
NPV increases
B) Cost increases
NPV decreases
C) Inflation
Not so obvious
17
Cautionary Notes for Sensitivity Analysis
3. One-at-a-Time Testing Is Not Realistic
• One-at-a-time testing is not realistic because of correlation
among variables
A) If Q sold increases, costs will increase
Profits = Q (P - UC)
B) If inflation rate changes, all prices change
C) If exchange rate changes, all tradable goods' prices and foreign
liabilities change
• One method of dealing with these combined or correlated
effects is scenario analysis
18
2.2 Scenario Analysis
• Scenario analysis recognizes that certain variables are interrelated. Thus a small number of
variables can be altered in a consistent manner at the same time.
• What is the set of circumstances that are likely to combine to produce different "cases"
or "scenarios"?
A. Worst case / Pessimistic case
B. Expected case / Best estimate case
C. Best case / Optimistic case
Note: Scenario analysis does not take into account the Probability of cases arising
• Interpretation is easy when results are robust:
A. Accept project if NPV > 0 even in the worst case
B. Reject project if NPV < 0 even in the best case
C. If NPV is positive in some cases and negative in other cases, then results are not
conclusive
• Difficult to define what scenario’s to specify without first
examining the range of possible outcomes by a Monte
Carlo Analysis.
• Scenario analysis is a good way to communicate the results
of a Monte Carlo analysis.
19
2.3 Monte Carlo Method of Risk
Analysis
• A natural extension of sensitivity and scenario analysis
• Simultaneously takes into account different probability
distributions and different ranges of possible values for key
project variables
• Allows for correlation (covariation) between variables
• Generates a probability distribution of project outcomes
(NPV) instead of just a single value estimate
• The probability distribution of project outcomes may assist
decision-makers in making choices, but there can be
problems of interpretation and use.
20
Monte-Carlo Simulation
• Monte Carlo simulation is a methodology
that handles the complexity arising from
projecting multi-value probability
distributions as inputs to a model.
• Practically this is only possible to be
applied with the use of a computer and
specialised software.
21
The Risk Analysis Process
Forecasting model
Risk variables
Preparation of a
model capable of
predicting reality
Selection of key
project variables
Correlation
conditions
Setting of
relationships for
correlated variables
Probability distributions (step 1)
Probability distributions (step 2)
Definition of range
limits for possible
variable values
Allocation of
probability weights
to range of values
Simulation runs
Analysis of results
Generation of
random scenarios
based on
assumptions set
Statistical analysis
of the output of
simulation
22
Simple Model
Variables
Relationships
Result
B-C
R=1
B=3
C=2
23
The Financial Model
Cash Flow
Owner’s View
Cash Flow
Project View
Projected
Profit & Loss
Project Cost
& Financing
Plan
Loans
Depreciation
Projected
Projected
Sources &
Balance Sheets
Applications
Taxation
Assumptions
24
Taking uncertainty into consideration
Inputs
Model
Output
25
The Monte-Carlo Simulation process
1. Identify the critical/most uncertain
input variables in a projected model –
risk variables.
2. Substitute single-value assumptions
with probability distributions which
tend to express the possible variability
for each of the identified risk variables.
26
Forecasting Model
Forecasting Model
$
Sales price
Volume of sales
Variables Formulae
12
V1
100
V2
1,200
F1 = V1  V2
Materials
300
F2 = V2  V4
Wages
400
F3 = V2  V5
Expenses
200
Cash outflow
900
F4 = F2 + F3 + V3
Net Cash Flow
300
F5 = F1 – F4
Cash inflow
V3
Relevant assumptions
Material cost per unit
3.00
V4
Wages per unit
4.00
V5
27
Set Probability Distributions
Simulation model
$
X
Sales price
Volume of sales
Cash inflow
12
V1
100
V2
-0.8
Y
Risk variables
1,200
Materials
300
Wages
400
Expenses
200
Cash outflow
900
Net Cash Flow
300
Relevant assumptions
Material cost per unit
3.00
Wages per unit
4.00
V4
28
The Monte-Carlo Simulation process
3. Set correlation conditions to limit the
possibility of generating internally
inconsistent scenarios during a
simulation.
4. Identify the critical calculated results
you wish to apply the analysis on –
model results.
29
Set correlation conditions
Simulation model
$
X
Sales price
Volume of sales
Cash inflow
12
V1
100
V2
-0.8
Y
Risk variables
1,200
Materials
300
Wages
400
Expenses
200
Cash outflow
900
Net Cash Flow
300
Relevant assumptions
Material cost per unit
3.00
Wages per unit
4.00
V4
30
Correlated variables – Generating Relationship Data
Correlated Variables
(r = 0.8), 200 runs
Volume of sales (dependent variable)
130
120
110
100
90
80
70
8
9
10
11
12
13
14
15
16
Sales price (independent variable)
31
The Monte-Carlo Simulation process
5. Run simulation creating a sample of
computer scenarios based on inputs from the
probability distributions and with respect to
any correlation conditions set.
6. Analyse results generated in the simulation
run, calculating statistical measures and
plotting probability distribution graphs of the
results, which indicate all the potential
outcomes and their likelihood of occurrence.
32
Simulation Runs
33
Distribution of results (net cash flow)
Cumulative probability
1.0
0.8
0.6
0.4
0.2
0.0
-300
-200
-100
0
100
200
300
400
500
600
Dollars
p
1
n
where: p = probability weight for a single run
n = sample size
34
Net present value distribution (different project perspectives)
Cumulative probability
1.00
0.80
0.60
0.40
0.20
0.00
-300000
-200000
Banker's view
-100000
0
100000
Ow ner's view
200000
300000
Economy's view
35
Cash
Flow
Mastering Cash Flow - What lies beneath the projections?
Base-Case Cash flow
Time
36
Cash
The impact of uncertainty on the projected cash flow
Flow
Upside Cash flow
NET CASH FLOW
Base-Case Cash flow
Debt Service
Downside Cash flow
Time
Key Benefits
• Risk Measurement
• Risk Mitigation
• Risk Management
37
Interpretation of Risk Analysis Results
38
39
Case 1: Probability of negative NPV=0
Cumulative probability
-
0
Probability
+
-
0
NPV
+
NPV
DECISION : ACCEPT
40
Case 2: Probability of positive NPV=0
Cumulative probability
-
Probability
0
+
-
NPV
0
+
NPV
DECISION : REJECT
41
Case 3: Probability of zero NPV greater than 0 and
less than 1
Probability
Cumulative probability
-
+
0
-
+
0
NPV
NPV
DECISION : INDETERMINATE
42
Case 4: Mutually exclusive projects
(given the same probability, one project always shows a
higher return)
Cumulative probability
Project A
Probability
Project B
-
+
NPV
Project B
Project A
-
+
NPV
DECISION : CHOOSE PROJECT B
Case 4: Non-intersecting cumulative probability
distributions of project return for mutually exclusive projects
43
Case 5: Mutually exclusive projects
(high return vs. low loss)
Cumulative probability
Project A
Probability
Project B
-
Project A
+
NPV
Project B
-
+
NPV
DECISION : INDETERMINATE
Case 5: Intersecting cumulative probability
distributions of project return for mutually exclusive projects
44
Expected Loss Ratios:
Example of project outcomes
expected value of project
Return
Probability
Expected Value
-10
x
0.2
=
-2.0
-5
x
0.3
=
-1.5
10
x
0.4
=
4.0
15
x
0.1
=
1.5
Total
Expected value
of losses
Expected value
of gains
2.0
45
Expected Loss Ratios
Probability
el 
-
Expected Loss
Expected Gain  Expected Loss
0
-3.5
Expected value
of loss
NPV
+
+5.5
Expected value
of gain
46
Risk under conditions of limited liability
Probability
Adjusted probability
distribution to reflect
liability limits
-
Equity
Liability
Limit
0
Expected value
increases
Ev(0) Ev(1)
NPV
+
47
Advantages of risk analysis
•
It enhances decision making on marginal projects.
•
It screens new project ideas and aids the identification of investment
opportunities.
•
It highlights project areas that need further investigation and guides the
collection of information.
•
It aids the reformulation of projects to suit the attitudes and requirements
of the investor.
•
It induces the careful re-examination of the single-value estimates in the
deterministic appraisal.
•
It helps reduce project evaluation bias through eliminating the need to
resort to conservative estimates.
48
Advantages of risk analysis (cont.)
•
It facilitates the thorough use of experts.
•
It bridges the communication gap between the analyst and the decision
maker.
•
It supplies a framework for evaluating project result estimates.
•
It provides the necessary information base to facilitate a more efficient
allocation and management of risk among various parties involved in a
project.
•
It makes possible the identification and measurement of explicit liquidity
and repayment problems in terms of time and probability that these may
occur during the life of the project.
49
Finally two words of caution:
• Overlooking significant inter-relationships among the
projected variables can distort the results of risk analysis and
lead to misleading conclusions.
• The accuracy of the results of risk analysis can only be as
good as the predictive capacity of the model employed.
50
FINA 522: Project Finance and Risk
Management
Lecture on Crystal Ball
51
INTRODUCTION TO RISK
ANALYSIS PROGRAM
MICROSOFT EXCEL
& CRYSTAL BALL
INTRODUCTION TO RISK
ANALYSIS PROGRAM
MICROSOFT EXCEL
& CRYSTAL BALL
June 2006
WHY do we need Risk Analysis ?
• Project returns are spread over time, therefore
are subject to risk as they are the result of many
uncertain events.
• Each variable affecting NPV is subject to high
level of uncertainty
• Need to reduce the likelihood to undertake a
"bad" project while not failing to accept a "good"
project
Crystal ball risk software will help us
• identify, analyze, and interpret the expected
variability in project outcomes.
54
WHAT CRYSTAL BALL SOFTWARE DOES?
• Traditionally it is the most likely outcome (mode) that
has been presented for decision making.
• Monte Carlo analysis enables one to estimate the
expected values of the outcome of our project.
• It also allows us to estimate the impact on the expected
value and standard deviation of the outcomes when
contracts and other risk management techniques are
applied to the project.
55
Methods
• Sensitivity Analysis
• Monte Carlo Risk Analysis (or Simulation
Analysis) using Crystal Ball Software
56
Sensitivity Analysis
• Test the sensitivity of a project's outcome (NPV or IRR)
to changes in value of one or two parameter at a time
• "What if" analysis
• Allows you to test which variables are important as a
source of risk
• Sensitivity analysis allows you to determine the direction
of change of the NPV
57
Monte Carlo Method of Risk
Analysis
• A natural extension of sensitivity analysis
• Simultaneously takes into account different
probability distributions and different ranges of
possible values for key project variables.
• Allows for correlation between variables.
• Generates a probability distribution of project
outcomes (NPV) instead of just a single value
estimate
• The probability distribution of project outcomes may
assist decision-makers in making choices, but there
can be problems of interpretation and use.
58
Steps in Building a Monte Carlo Simulation
1.
2.
3.
•
•
Mathematical model: project evaluation spreadsheet
Identify variables which are sensitive and uncertain
Define uncertainty
Establish a range of options (minimum and maximum)
Allocate probability distribution
–
–
–
–
4.
•
•
5.
6.
•
•
Normal distribution
Triangular distribution
Uniform distribution
Step distribution
Identify and define correlated variables
Positive or negative correlation
Strength of correlation
Simulate model
Analysis of results
Statistics
Distributions
59
ORGANIZATION CHART
FOR CASH-FLOW MODEL
TABLE OF
PARAMETERS
LINK
CASH
FLOWS
LINK
LINK
SENSITIVITY
ANALYSIS
RISK ANALYSIS
60
DETERMINISTIC ANALYSIS
(Unit Price of Goods)
$150
$250
$350
61
SENSITIVITY ANALYSIS
(Unit Price of Goods)
$150
$250
$350
62
MONTE CARLO
RISK ANALYSIS
(Unit Price of Goods)
$150
$250
$350
63
Upgrading a Gravel Road to Tar
Risk Analysis
Guidelines for Crystal Ball©
Steps to Follow:
Step 1: Complete Financial Analysis
Step 2: Identify “Risk Assumptions” and
“Risk Forecasts”
Step 3: Choose a Probability Distribution and
Correlations for Risk Assumptions
Step 4: Define Risk Assumptions and Correlations
Step 5: Define Risk Forecasts
Step 6: Configure Risk Simulation
Step 7: Running a Risk Simulation
Step 8: Prepare a Risk Report
Step 9: Interpretation of Results
65
Step 1: Complete Financial Analysis
(Deterministic Case)
• Finalize the financial/economic analysis of
project
• Calculate NPV, IRR, Debt Service Ratios
• All these will be “deterministic case” under the
base assumptions in Table of Parameters
• Risk analysis will model changes in the base
assumptions
66
Step 2: Identify “Risk Assumptions” and
“Risk Forecasts”
• Risk assumptions – parameters that will be
changed (prices of inputs and outputs, growth
rates, any other risky and uncertain variables)
• Risk forecasts – results, at which we look during
the risk analysis (NPVs, IRRs, Debt Service
Ratios, Distributions, etc.)
• In Road case, all risk assumptions and forecasts
are already given
67
Step 3: Choose a Probability Distribution
and Correlations for Risk Assumptions
• Each risk assumption must be assigned a probability
distribution
• If you don’t know the appropriate probability
distribution – find it either from past data, or use
whatever information available to develop subjective
probability distribution.
• There are many types of probability distributions
available
• Some variables may be correlated with each other –
their exact relationship must be identified
• In Road case, probability distributions for risk
assumptions are already given
68
Step 4: Define Risk Assumptions and
Correlations
• Click on the CELL in Table of Parameters, which will be defined as a
risk assumption
• For example:
Traffic Growth Rate Cell: E8
• In CELL menu choose:
Define Assumption…
69
• Choose from available types of distributions
• Press “More” for other types
• Press “Fit…” to estimate probability distribution
from actual data (if you have any)
• Once chosen, press “OK”, this assumption has
triangular distribution.
70
• Insert the distribution as given.
• For example: Traffic Growth Rate Cell E8 (Triangular)
Assumption Name
Minimum Value
Maximum Value
Mean
(Likeliest)
• Insert the distribution as given 
Minimum
Likeliest
Maximum
0.00
0.04
0.08
71
• For triangular distribution, fill-in:
– Assumption Name
– Minimum and Maximum Values
– Press “Enter” to update display
• Press “OK” (risk assumption is defined)
72
• Investment Cost-over run has step distribution
• Fill-in the following fields in the box:
Custom Distributions
Minimum
-0.20
-0.10
0.00
0.10
Maximum
-0.10
0.00
0.10
0.20
Probability
19%
24%
44%
13%
Assumption Name
Minimum and
Maximum Values
for Each Step
Probability of Occurrence
for Each Step
73
• For custom distribution, fill-in:
–
–
–
–
–
Assumption Name
Minimum and Maximum Values for a Step
Probability of Occurrence for that Step
Press “Enter” to update display
Continue with other steps
• Finally, press “OK” (risk assumption is defined)
• Note: if mistakenly entered, steps can be edited
later by clicking on them, changing to new values
and pressing “Enter” and then “OK”.
74
• Maintenance Costs Savings Factor has triangular
• Continue with ALL other assumptions
• For example: Maintenance Costs Savings Factor (Triangular)
Triangular Distribution
Minimum
Likeliest
Maximum
-0.10
0.00
0.10
Assumption Name
Minimum Value
Maximum Value
Mean
75
•
•
•
•
This example shows, how to define the correlation between two
variables.
In this assignment, we assume that traffic growth rate and the
maintenance costs saving factor have correlation coefficient of -0.6
Click on the value which have correlation then go to the define
assumption
Press “Correlate…” in the assumption of maintenance costs saving
factor
76
•
After click on the correlation, the following screen appears.
Assumption Name
Correlation Coefficient
•
•
•
•
•
•
Press “Select Assumption” (in this
case Traffic Growth Rate)
Fill-in the correlation coefficient (in
this case -0.6)
Press “Enter” to update display
Repeat procedure for all
assumptions being correlated
Finally, press “OK” (correlations are
defined)
See the picture on the right.
77
• VOC Savings Factor has normal distribution
• Continue with ALL other assumptions
• For example:
VOC Savings Factor Cell: F22 (Normal)
Normal Distribution
Mean
Standard Dev.
0.00
0.12
Assumption Name
Deterministic Value
Standard Deviation
78
• Time Saving Factor has uniform distribution
• Continue with ALL other assumptions
• Some assumptions will have different probability distributions
• For example: Time Saving Factor
Cell: F23 (Uniform)
Uniform Distribution
Minimum
Maximum
-0.12
0.12
Assumption Name
Minimum Value
Maximum Value
79
Step 5: Define Risk Forecasts
• Click on the CELL in spreadsheet, which will be
defined as a risk forecast
• For example:
NPV (Economic) H149
• In CELL menu choose:
Define Forecast…
80
•
•
•
In the dialog box for risk forecast, fill-in:
–
Forecast Name
–
Units
Press “OK” (forecast is defined)
Repeat procedure for ALL, like PV of Road Agency,
PV of Light Vehicle Users and PV of Heavy
Vehicle Users; other risk forecasts to be defined
81
NOTES TO ADVANCED USER
• Parameters of risk assumptions and forecasts can
be copied by special Crystal Ball copy-paste
commands
• This saves time and effort in repeated tasks (e.g.
defining yearly inflation rate)
• Select the cell from which you want to copy risk
parameters --> in CELL menu choose COPY DATA
• Select the cell to which the risk parameters are
applied --> in CELL menu choose PASTE DATA
• ALL risk parameters can be removed in a cell by
choosing CELL menu – CLEAR DATA
82
Step 6: Configure Risk Simulation
• Any risk simulation must be properly configured
BEFORE running it
• In RUN menu choose:
Run Preferences…
83
• Set the necessary Number of Trials (5,000 runs
is usually considered to be sufficient)
• Switch OFF the following:
– Stop if specified precision is reached; and
– Stop if calculation error occurs
Set Number of
Trials
Switch OFF
Got to NEXT
stage
• Press “>>” to go to next stage …
84
• Choose Sampling Method:
– Monte Carlo (most often used)
– Latin Hypercube (computer memory intensive)
• Do NOT change any other parameters here
Sampling Method
• Press “>>” to go to next stage …
85
• Do NOT change Use Burst Mode When Idle
• Select one of the options in Minimize While
Running:
– All Spreadsheets (recommended)
• Switch ON the option of Suppress Forecast
Windows
Speed Options
Switch ON
• Press “OK” (configuration is complete)
86
Step 7: Running a Risk Simulation
• To start running a simulation, In RUN menu
choose:
Run
• Wait until it tells you that Maximum Number of
trials is Reached (sometimes takes a while…)
87
Step 8: Prepare a Risk Report
• Risk report is a sheet containing the summary of
the risk assumptions and forecasts parameters as
well as the final results of the simulation
• Forecasts should be formatted for easier visual
representation
• In RUN menu choose:
Forecast Windows
Select Open ALL
Forecasts
88
• In the forecast window, choose PREFERENCES
menu and select CHART…
89
• Make sure you select the following options:
• When done, press “APPLY TO ALL”
90
• Each forecast window should be adjusted for
range:
– NPV range: from –Infinity to Zero
– IRR range: from –Infinity to Discount Rate used
– Debt Service Ratios: from –Infinity to 1.50
Fill-in either 0 for
NPV, or Discount
Rate used for IRR,
or 1.50 for Debt
Service Ratio
and
press ENTER on
keyboard
91
• Create an Overlay Chart, in RUN menu choose:
Open Overlay Chart
Choose NPV
Forecasts
Press Choose
Forecasts…
Press OK
92
• Overlay chart should be also formatted for better
visual presentation, as shown below:
Press Chart
Prefs…
Press OK
93
• After completion of simulation, and format save its
results to a file
• You can later access the results of your risk simulation
WITHOUT running it again
94
• To generate a Report, in RUN menu
choose: Create Report…
Choose
Assumptions
NO
Percentiles
95
Step 9: Interpretation of Results
• Analyze the results, which will be presented
by:
– Overlay Chart (comparison of several NPVs)
– Forecast Charts for each risk forecast (NPVs, IRR,
Debt Service Ratios)
• Summary Statistics for each risk forecast
• Risk results must be compared with the
results of deterministic analysis
96
Commonly used and widely
understood descriptors
• Summary Statistics for a risk forecast:
97
• What do we need to do to manage
risks?
• Is risk management proposal
effective? – Need to test contracts.
98