0 Lecture Nine FINA 522: Project Finance and Risk Management Updated: 29 April, 2007.

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Lecture Nine

FINA 522: Project Finance and Risk Management

Updated: 29 April, 2007

RISK ANALYSIS

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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.

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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

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Risk Analysis1. 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

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A good predictive model in project appraisal depends on:

Cash-Flow Projections Marketing Module

Technical Module

Input Data

Input Data

Correct methodology Accurate data

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Uncertainty and Forecasting

• 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)

x

x

x

x

xx

x

x

xx

x

o o o o o

TimePresentPast Future

Variable Value

Past Events Forecasts

We use the past to forecast the future

Ability to forecast accurately depends on:

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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.

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MAXIMUM 1.0

Mode Average Conservative

estimateMINIMUM

Now

The deterministicprobability distribution

Probability Variable

value

Time Variable value

Forecasting the outcome of a future event:Single-value estimate

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From a frequency to a probability distribution

MAXIMUM

1

5

53

31

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MINIMUM

MaximumNow Minimum

ProbabilityFrequencyVariable values

Time Variable value

.5

.3

.1.1MaximumMinimum

Variable value

= Observations

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Multi-value probability distributions

Normal

Probability

Values Max.Min.

Probability

Uniform

Values Max.Min.

Probability

Triangular

Values Max.Min.

Probability

Step

Values Max.Min.

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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.

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2. Alternative Methods of Dealing With Risk

2.1 Sensitivity Analysis

2.2 Scenario Analysis

2.3 Monte Carlo Risk Analysis(or Simulation Analysis)

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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

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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

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Sensitivity Analysis for the Mindanao Poverty Reduction Case

Inflation Rate5%8%11%14%17%20%23%26%29%32%35%

CapacityUtilization

Factor60%65%70%75%80%85%90%95%100%105%110%

Real NPV (Million Pesos)

16114713612611811110599948984

Real NPV(Million Pesos)

-189-147-105-63-212163

105147189231

World T.P. Price(S.F. FOB) US$/Ton

587637687737787837887937987

10371087

Divergence fromOriginal Cost

Estimate-10%-5%0%5%

10%15%20%25%30%35%40%

Real NPV (Million Pesos)

-228-10322

147272397522647772897

1022Real NPV

(Million Pesos)

19016914712510382603817-5

-27

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• 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

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Cautionary Notes for Sensitivity Analysis1. 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 effectsFor most variables, the direction is obvious

A) Revenue increases NPV increasesB) Cost increases NPV decreasesC) Inflation Not so obvious

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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

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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 caseNote: 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.

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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.

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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.

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The Risk Analysis Process

Probability distri-butions (step 1)

Definition of range limits for possible variable values

Risk variables

Selection of key project variables

Forecasting model

Preparation of a model capable of predicting reality

Probability distri-butions (step 2)

Allocation of probability weights to range of values

Simulation runs

Generation of random scenarios based on assumptions set

Correlation conditions

Setting of relationships for correlated variables

Analysis of results

Statistical analysis of the output of simulation

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Simple Model

B-C

Relationships ResultVariables

B=3

C=2R=1

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The Financial Model

Cash FlowOwner’s View

Cash FlowProject View

ProjectedProfit & Loss

ProjectedSources &

Applications

ProjectedBalance Sheets

Loans Depreciation TaxationProject Cost& Financing

PlanAssumptions

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Taking uncertainty into consideration

Inputs OutputModel

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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.

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Forecasting Model

Forecasting Model

$ Variables Formulae

Sales price 12 V1

Volume of sales 100 V2

Cash inflow 1,200 F1 = V1 V2

Materials 300 F2 = V2 V4

Wages 400 F3 = V2 V5

Expenses 200 V3

Cash outflow 900 F4 = F2 + F3 + V3

Net Cash Flow 300 F5 = F1 – F4

Relevant assumptions

Material cost per unit 3.00 V4

Wages per unit 4.00 V5

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Set Probability Distributions Simulation model

$ Risk variables

Sales price 12 V1


Cash inflow 1,200

Materials 300

Wages 400

Expenses 200

Cash outflow 900

Net Cash Flow 300



Wages per unit 4.00

X

-0.8

Y

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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.

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Set correlation conditionsSimulation model

$ Risk variables

Sales price 12 V1


Cash inflow 1,200

Materials 300

Wages 400

Expenses 200

Cash outflow 900

Net Cash Flow 300



Wages per unit 4.00

X

-0.8

Y

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Correlated variables – Generating Relationship Data

Correlated Variables(r = 0.8), 200 runs

8 9 10 11 12 13 14 15 16

Sales price (independent variable)

70

80

90

100

110

120

130

Vo

lum

e o

f sa

les

(dep

end

ent

vari

able

)

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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.


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Simulation Runs

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Distribution of results (net cash flow)

pn

1 where: p = probability weight for a single run

n = sample size

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Net present value distribution (different project perspectives)

0.00

0.20

0.40

0.60

0.80

1.00

-300000 -200000 -100000 0 100000 200000 300000

Banker's view Ow ner's view Economy's view

Cumulative probability

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Time

Mastering Cash Flow - What lies beneath the projections?CashFlow

Base-Case Cash flow

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Time

The impact of uncertainty on the projected cash flowThe impact of uncertainty on the projected cash flow

Debt Service

CashFlow

Downside Cash flow

Upside Cash flow

NET CASH FLOW

Base-Case Cash flow

Key Benefits • Risk Measurement• Risk Mitigation• Risk Management

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Interpretation of Risk Analysis Results

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Case 1: Probability of negative NPV=0

+- 0NPV

+- 0NPV

ProbabilityCumulative probability

DECISION : ACCEPT

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Case 2: Probability of positive NPV=0

+- 0NPV

+- 0NPV


DECISION : REJECT

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Case 3: Probability of zero NPV greater than 0 and less than 1

+- 0NPV

+- 0NPV


DECISION : INDETERMINATE

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Case 4: Mutually exclusive projects(given the same probability, one project always shows a

higher return)

+-

Project A Project B

NPV+-

NPV


DECISION : CHOOSE PROJECT B

Project A Project B

Case 4: Non‑intersecting cumulative probability distributions of project return for mutually exclusive projects

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Case 5: Mutually exclusive projects (high return vs. low loss)

Case 5: Intersecting cumulative probability distributions of project return for mutually exclusive projects

+-

Project A Project B

NPV+-

NPV


DECISION : INDETERMINATE

Project A Project B

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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 2.0

Expected value of losses

Expected value of gains

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Expected Loss Ratios

+- 0 NPV

Probability

-3.5Expected value

of loss

+5.5Expected value

of gain

Loss ExpectedGain Expected

Loss Expected

el

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Risk under conditions of limited liability

+- Ev(1)Ev(0)0 NPV

Probability

EquityLiabilityLimit

Expected valueincreases

Adjusted probabilitydistribution to reflectliability limits

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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.

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• 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.

Advantages of risk analysis (cont.)

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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.

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Lecture on Crystal Ball

FINA 522: Project Finance and Risk Management

INTRODUCTION TO RISK ANALYSIS PROGRAM

MICROSOFT EXCEL& CRYSTAL BALL

INTRODUCTION TO RISK ANALYSIS PROGRAM

MICROSOFT EXCEL& CRYSTAL BALL

June 2006

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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.

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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.

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Methods

• Sensitivity Analysis

• Monte Carlo Risk Analysis (or Simulation

Analysis) using Crystal Ball Software

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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

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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.

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Steps in Building a Monte Carlo Simulation

1. Mathematical model: project evaluation spreadsheet2. Identify variables which are sensitive and uncertain3. Define uncertainty• Establish a range of options (minimum and maximum)• Allocate probability distribution

– Normal distribution– Triangular distribution– Uniform distribution– Step distribution

4. Identify and define correlated variables• Positive or negative correlation• Strength of correlation5. Simulate model6. Analysis of results• Statistics• Distributions

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ORGANIZATION CHART FOR CASH-FLOW MODEL

TABLE OFPARAMETERS

CASHFLOWS

SENSITIVITYANALYSIS

LINK

LINK

LINK

RISK ANALYSIS

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DETERMINISTIC ANALYSIS(Unit Price of Goods)

$250 $350$150

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SENSITIVITY ANALYSIS(Unit Price of Goods)

$250 $350$150

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MONTE CARLO RISK ANALYSIS(Unit Price of Goods)

$250 $350$150

Upgrading a Gravel Road to Tar

Risk Analysis

Guidelines for Crystal Ball©

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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

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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

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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

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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

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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…

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• 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.

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• Insert the distribution as given.• For example: Traffic Growth Rate Cell E8 (Triangular)

Assumption Name

Mean(Likeliest)

Minimum Value Maximum Value

• Insert the distribution as given Minimum 0.00 Likeliest 0.04 Maximum 0.08

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• For triangular distribution, fill-in:

– Assumption Name– Minimum and Maximum Values– Press “Enter” to update display

• Press “OK” (risk assumption is defined)

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• Investment Cost-over run has step distribution• Fill-in the following fields in the box:

Minimum and Maximum Values

for Each Step

Assumption Name

Probability of Occurrence for Each Step

Custom DistributionsMinimum Maximum Probability -0.20 -0.10 19% -0.10 0.00 24% 0.00 0.10 44% 0.10 0.20 13%

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• 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”.

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• Maintenance Costs Savings Factor has triangular• Continue with ALL other assumptions• For example: Maintenance Costs Savings Factor (Triangular)

Assumption Name

Mean

Minimum Value

Maximum Value

Minimum -0.10 Likeliest 0.00 Maximum 0.10

Triangular Distribution

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• 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

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• After click on the correlation, the following screen appears.

Correlation Coefficient

Assumption Name

• 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.

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• VOC Savings Factor has normal distribution• Continue with ALL other assumptions• For example: VOC Savings Factor Cell: F22 (Normal)

Assumption Name

Standard Deviation

Deterministic Value

Normal Distribution

Mean 0.00 Standard Dev. 0.12

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• 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)

Assumption Name

Minimum Value

Maximum Value

Minimum -0.12 Maximum 0.12

Uniform Distribution

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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…

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• 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

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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

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Step 6: Configure Risk Simulation

• Any risk simulation must be properly configured BEFORE running it

• In RUN menu choose: Run Preferences…

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• 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

• Press “>>” to go to next stage …

Set Number of Trials

Switch OFF

Got to NEXT stage

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• Choose Sampling Method:– Monte Carlo (most often used)– Latin Hypercube (computer memory intensive)

• Do NOT change any other parameters here

• Press “>>” to go to next stage …

Sampling Method

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• 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

• Press “OK” (configuration is complete)

Speed Options

Switch ON

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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…)

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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

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• In the forecast window, choose PREFERENCES menu and select CHART…

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• Make sure you select the following options:

• When done, press “APPLY TO ALL”

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• 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

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• Create an Overlay Chart, in RUN menu choose: Open Overlay Chart

Press Choose Forecasts…

Choose NPV Forecasts

Press OK

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• Overlay chart should be also formatted for better visual presentation, as shown below:

Press Chart Prefs…

Press OK

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• 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

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• To generate a Report, in RUN menu choose: Create Report…

Choose Assumptions

NO Percentiles

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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

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• Summary Statistics for a risk forecast:

Co

mm

on

ly u

sed

an

d w

idel

y u

nd

erst

oo

d d

escr

ipto

rs

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• What do we need to do to manage risks?

• Is risk management proposal effective? – Need to test contracts.

0 Lecture Nine FINA 522: Project Finance and Risk Management Updated: 29 April, 2007.

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Transcript of 0 Lecture Nine FINA 522: Project Finance and Risk Management Updated: 29 April, 2007.