1. Decision and Risk Analysis
Financial Modelling &
Risk Analysis
Kiriakos Vlahos
Spring 2000

2. Session overview Why do we need risk analysis? Project evaluation
Risk analysis approaches
Scenario analysis
Sensitivity analysis
Monte-Carlo simulation
Summary

3. Risk management in business
Corporate
risk
Capital budgeting
and portfolio
evaluation
Project Evaluation

4. Why do we need risk analysis?
Single point forecasts are dangerous!
Derive bounds for the range of possible outcomes
Sensitivity testing of the assumptions
Better perception of risks and their interaction
Anticipation and contingency planning
Overall reduction of risk exposure through hedging
Risk analysis helps you develop insights, knowledge and confidence for better decision making and risk management.

5. Risk analysis approaches
Scenario analysis
Sensitivity analysis
Monte-Carlo simulation
Decision Analysis
Option theory

6. Skywalker Proposal to open and operate a video store.
“You can expect to make at least £50,000 in the first year”

7. Project Evaluation Evaluating a business proposition
Does it make sense overall?
Market conditions
Trust issues
What is the outlook under a basic set of assumptions? (Base Case)
What are the risks involved?
Writing a business plan

8. Base case model
Closing cash exceeds £50000 at the end of the year

9. Scenario analysis
“Scenarios are discrete internally consistent views of how the world will look in the future, which can be selected to bound the possible range of outcomes that might occur.”
Michael Porter in “Competitive Strategy”
“Shell flavour” of scenarios
Scenarios should present testing conditions for the business. The future will of course be different from all of these views/scenarios, but if the company is prepared to cope with any of them, it will be able to cope with the real world.
Do not assign probabilities to scenarios!

10. Skywalker - Scenarios analysis

11. Sensitivity analysis
Explore robustness of results to variations in model parameters
Understand and challenge assumptions
Methodology
Identify variables to which results are particularly sensitive and those to which they are relatively insensitive
Gain an indication into range over which results might vary, thus assessing the risks
Tools
What-if questions
One-way sensitivity analysis
Two-way sensitivity analysis
Tornado diagrams
Spider plots

12. What-if analysis What-if Tape Price turns out to be 35?
Changing Tape Price to 35, and leaving all other planning values at their base value, we get a December Closing Cash of £30,926
If Tape Price is 25, December Closing Cash is £70,982

13. One-way sensitivity analsysis
e.g. Sensitivity of closing cash to Rent per day

14. Two-way sensitivity analysis
Two-variable data table can be applied to a
single cell such as December Closing Cash cell:

15. 3-D plot of two-way sensitivity analysis
Skywalker: Sensitivity of closing cash to
to Rental & Plays per month
Tutorial on data tables in Datatables.xls

16. Tornado diagrams
Helps us determine visually the main uncertainty drivers.
Around base case.
Only one variable changes at a time. All other stay at base case values.
Does not take into account of interactions between uncertain variables.
Tutorial on Tornado diagrams in Tornado.xls

17. Constructing spider plots

18. Skywalker: Spider plot

19. Price/Demand Relationship
Price is a decision variable and demand
should depend on price, e.g.
Regression equation:
PlaysperMonth = RentperDay
One-way sensitivity analysis to Rent per day
Which price maximises closing cash?

20. Monte-Carlo simulation
Uncertain variables
Base Case Model
Uncertain Parameters
Base Value
Hours Flown
800
Charter Price/Hour
700
Ticket Price/Hour 90
Capacity of Sch. flights
60%
Ratio of charter flights
40%
Operating Cost/hour
445
Profit & Loss
Income from Scheduled
£259,200
Income from Chartered
£224,000
Operating costs
(£356,000)
Fixed Costs
(£60,000)
Taxable profit
£67,200
Tax
(£22,176)
Profit after tax
£45,024
Simulate
Output distribution

21. Merck’s Research Planning Model
Scientific,
Medical
Monte-Carlo
constraints
Simulation
R&D
variables
Technological
constraints
Manufacturing
variables
Economic
relationships
Probability
distributions
for cash-flow
Marketing
Projections
ROI, NPV
variables
of variables
Macro-
economic
assumptions

22. @RISK - How it works Single simulation trial
INPUTS
MODEL
CALCULATIONS
RESULT
= Profit
= $62
Sales * Price - Cost
211 $5
$993
Multiple simulation trials
INPUTS
MODEL
CALCULATIONS
RESULT
Profit
Trial 1: 211 * =
$62
Trial 1: 193 * =
$884
Trial 1: 219 * =
$315
...
Trial N: 233 * =
$423

23. Novaduct case

24. Novaduct - Uncertainty
“Market share increase is equally likely to be
any value between -0.2% and 0.8%”
-0.2
0.8
“Market growth is most likely to be a 2%
increase but could range from a 10%
decrease to an 8% increase” 90
102
108

25. Using @RISK 1. Introduce uncertainty into base model
eg =RiskUniform(min, max)
=RiskTriang(min, most likely, max)
=RiskNormal(mean, std.dev.)
2. Select output cells
(Cells for which we want simulation results)
3. Select simulation settings
Number of iterations, random number seed
4. Execute simulation
5. View results
Graphs, summary statistics
6. Return to spreadsheet and possibly repeat previous steps

26. Novaduct using @RISK @Risk Toolbar =RiskUniform(-0.2%,0.8%)
ASSUMPTIONS
Discount Rate
15%
Prod Cost 5
103.0%
Price 7
106.0%
Market Share
MS Incr
0.3%
MktGrowth
102.0%
=RiskUniform(-0.2%,0.8%)
=RiskTriang(0.9,1.02,1.08)
@Risk Toolbar
Simulation
settings
Specify
output cells
Simulate
Open & Save
Simulation
Results
View input
& output cells
Window

27. Simulation settings

28. @RISK Window

29. Simulation results NPV IRR Mean 914 Mean 25% Max 3174 Max 45%
Min Min -14%
P(NPV<0) = P(IRR<15%) = 0.15
P(NPV<1,000) = P(IRR<35%) = 0.85

30. Cashflow Summary Graph
Central line connects mean values
First band is 1 std.dev.
Second band is interval between 5% and 95% percentiles

31. Summary Single point forecasts are dangerous! Challenge assumptions
Scenario Planning
Sensitivity analysis
Data tables
Tornado diagrams
Monte-Carlo simulation
Preparation for Workshop
Datatables.xls and Tornado.xls
@RISK tutorial
Exercises