DRA/K V
Decision and Risk Analysis
Financial Modelling &
Risk Analysis
Kiriakos Vlahos
Spring 2000
DRA/K V
Session overview
• Why do we need risk analysis?
• Project evaluation
• Risk analysis approaches
– Scenario analysis
– Sensitivity analysis
– Monte-Carlo simulation
• Summary
DRA/K V
Risk management in
business
Corporate
risk
Capital budgeting
and portfolio
evaluation
Project Evaluation
DRA/K V
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.
DRA/K V
Risk analysis
approaches
• Scenario analysis
• Sensitivity analysis
• Monte-Carlo simulation
• Decision Analysis
• Option theory
DRA/K V
Skywalker
Proposal to open and operate a video
store.
“You can expect to make at least
£50,000 in the first year”
Assumptions
Monthly Purchase (no of tapes)
Tape Price
Tape Life (no of plays)
Plays per Mth (per tape)
Rent per Day
Shop Rent p a
Interest p a
50
£30
30
4.33
£3
£6,000
10%
DRA/K V
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
Base case model
DRA/K V
SKYWALKER VIDEO MODEL
in £000
Jan
Feb
Average Stock
1.0
1.1
Mar
1.1
Apr
1.2
May
1.2
Jun
1.3
Jul
1.3
Aug
1.4
Sep
1.4
Oct
1.5
Nov
1.5
Dec
1.6
Opening Cash
Rental recpts
Purchases
Replacements
Rent qtrly
3.0
10.8
-30.0
-4.3
-1.5
-22.2
11.4
-1.5
-4.5
-17.0
11.9
-1.5
-4.8
-11.5
12.4
-1.5
-5.0
-1.5
-7.0
13.0
-1.5
-5.2
-.8
13.5
-1.5
-5.4
5.9
14.1
-1.5
-5.6
-1.5
11.4
14.6
-1.5
-5.8
18.9
15.2
-1.5
-6.1
26.7
15.7
-1.5
-6.3
-1.5
33.4
16.2
-1.5
-6.5
42.0
16.8
-1.5
-6.7
Total
Interest
Closing Cash
-22.0
-.2
-22.2
-16.9
-.1
-17.0
-11.4
-.1
-11.5
-7.0
-.1
-7.0
-.8
.0
-.8
5.9
.0
5.9
11.4
.1
11.4
18.7
.2
18.9
26.5
.2
26.7
33.1
.3
33.4
41.6
.3
42.0
50.5
.4
51.0
SKYWALKER VIDEO
Monthly closing cash for base scenario
60.0
50.0
40.0
30.0
20.0
10.0
.0
-10.0
-20.0
-30.0
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Closing cash exceeds £50000 at the end of the year
DRA/K V
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!
Skywalker Scenarios analysis
DRA/K V
Assumptions
Monthly Purchase
Tape Price
Tape Life
Plays per Mth
Rent per Day
Shop Rent p a
Interest p a
Optimistic
Base
Pessimistic
60
50
40
25
30
35
35
30
25
5.00
4.33
2.50
3.00
2.50
2.00
3,000
6,000
10,000
15
10
7
190,000
Skywalker Final Cash:
Comparison of Scenarios
140,000
90,000
40,000
-10,000 Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
-60,000
Optimistic
Base
Pessimistic
Sep
Oct
Nov
Dec
DRA/K V
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
What-if analysis
DRA/K V
• What-if Tape Price turns out to be 35?
Assumptions
Monthly Purchase
50
Tape Price
35
Tape Life
30
Plays per Mth
4.33
Rent per Day
2.50
Shop Rent p a
6,000
Interest p a
10
Results Panel:
Final
Cash
30,926
SKYWALKER VIDEO MODEL
in £000
Jan
Feb
Average Stock
1.0
1.1
Mar
1.1
Apr
1.2
May
1.2
Jun
1.3
Jul
1.3
Aug
1.4
Sep
1.4
Oct
1.5
Nov
1.5
Dec
1.6
Opening Cash
Rental recpts
Purchases
Replacements
Rent qtrly
3.0
10.8
-35.0
-5.1
-1.5
-28.0
11.4
-1.8
-5.3
-23.8
11.9
-1.8
-5.6
-19.4
12.4
-1.8
-5.8
-1.5
-16.1
13.0
-1.8
-6.1
-11.1
13.5
-1.8
-6.3
-5.6
14.1
-1.8
-6.6
-1.5
-1.4
14.6
-1.8
-6.8
4.7
15.2
-1.8
-7.1
11.1
15.7
-1.8
-7.3
-1.5
16.4
16.2
-1.8
-7.6
23.5
16.8
-1.8
-7.8
Total
Interest
Closing Cash
-27.7
-.2
-28.0
-23.6
-.2
-23.8
-19.2
-.2
-19.4
-16.0
-.1
-16.1
-11.0
-.1
-11.1
-5.6
.0
-5.6
-1.4
.0
-1.4
4.6
.0
4.7
11.0
.1
11.1
16.2
.1
16.4
23.3
.2
23.5
30.7
.3
30.9
• 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
One-way sensitivity
analsysis
DRA/K V
e.g. Sensitivity of closing cash to Rent per day
Dec Closing Cash
Dec Closing Cash £000
=M26
2.00
10.8
Rent
2.25
26.4
per
2.50
42.0
Day
2.75
57.6
3.00
73.2
80.0
70.0
60.0
50.0
40.0
30.0
20.0
10.0
.0
2.00
2.25
2.50
Rent Per Day (£)
2.75
3.00
Two-way sensitivity
analysis
DRA/K V
Two-variable data table can be applied to a
single cell such as December Closing Cash cell:
Plays per Month
Rent
per
Day
50,954
2.00
3.50
4.33
5.00
2
2.25
2.5
2.75
3
-21,379
2,758
16,115
26,896
-13,333
16,839
33,534
47,011
-5,287
30,919
50,954
67,126
2,758
45,000
68,373
87,241
10,804
59,080
85,793
107,356
Skywalker: December Closing Cash
for different Rental & Plays per Month
120,000
100,000
Rental
80,000
2
60,000
2.25
40,000
2.5
20,000
2.75
3
0
1
2
3
4
-20,000
-40,000
Plays per Month
5
6
3-D plot of two-way
sensitivity analysis
DRA/K V
Skywalker: Sensitivity of closing cash to
to Rental & Plays per month
120
100
Closing cash £000
80
60
40
20
-20
3.00
2.75
-40
2.0
2.50
2.5
3.0
Rent per Day
2.25
3.5
Plays per Month
4.0
4.5
2.00
5.0
Tutorial on data tables in Datatables.xls
Tornado diagrams
DRA/K V
Helps us determine visually the main uncertainty
drivers.
Assumptions
Optimistic Pessimistic
Assumptions
Monthly Purchase
Tape Price
Tape Life
Plays per Mth
Rent per Day
Shop Rent p a
Interest p a
60
25
35
5.00
3.00
3,000
15
Impact on closing cash
Optimistic Pessimistic
40
35
25
2.50
2.00
10,000
7
51.9
71.0
60.9
67.1
85.8
54.1
51.5
50.0
30.9
37.0
6.8
16.1
46.7
50.6
Rent per Day
Plays per Mth
Tape Price
Tape Life
Shop Rent p a
Monthly Purchase
Interest p a
20
40
60
80
100
Closing cash in £000
Tutorial on Tornado diagrams in Tornado.xls
Constructing
spider plots
DRA/K V
Assumptions
MonthlyPurchase
Tape Price
Tape Life
Plays per Mth
Rent per Day
Shop Rent p a
Interest p a
Optimistic
60
20
35
5
3
3000
7
55
25
32.5
4.665
2.75
4500
9
Base
50
30
30
4.33
2.5
6000
10
Pessimistic
45
40
35
40
27.5
25
3.165
2
2.25
2
8000 10000
13
15
110
83
108
108
110
75
85
Base
100
100
100
100
100
100
100
Pessimistic
90
80
117
133
92
83
73
46
90
80
133
167
125
150
51.4
71.0
56.3
59.0
68.4
52.6
50.8
Base
51.0
51.0
51.0
51.0
51.0
51.0
51.0
Pessimistic
50.5
50.0
30.9
10.9
44.6
37.0
22.8
-5.3
33.5
16.1
48.8
46.7
51.2
51.5
% change from base
MonthlyPurchase
Tape Price
Tape Life
Plays per Mth
Rent per Day
Shop Rent p a
Interest p a
Optimistic
120
67
117
115
120
50
70
Closing cash results
MonthlyPurchase
Tape Price
Tape Life
Plays per Mth
Rent per Day
Shop Rent p a
Interest p a
Optimistic
51.9
91.0
60.9
67.1
85.8
54.1
50.6
Skywalker: Spider plot
DRA/K V
100.0
Closing cash £000
80.0
60.0
40.0
20.0
.0
%
50%
100%
150%
-20.0
% change from base
Tape Price
Tape Life
Plays per Mth
Rent per Day
Shop Rent p a
Interest p a
MonthlyPurchase
200%
Price/Demand
Relationship
DRA/K V
Price is a decision variable and demand
should depend on price, e.g.
Plays per Month v Rental per Day
7
6
Plays per Month
5
4
3
2
1
0
1.5
2.0
2.5
Rent pe r Da y
3.0
3.5
Regression equation:
PlaysperMonth = 13.13 - 3.80RentperDay
One-way sensitivity analysis to Rent per day
60
Closing cash £000
40
20
1.00
1.50
2.00
2.50
3.00
-20
-40
-60
Rent per day (£)
Which price maximises closing cash?
3.50
DRA/K V
Monte-Carlo simulation
Base Case Model
Uncertain Parameters
Hours Flown
Charter Price/Hour
Ticket Price/Hour
Capacity of Sch. flights
Ratio of charter flights
Operating Cost/hour
Uncertain variables
Base Value
800
700
90
60%
40%
445
Profit & Loss
Income from Scheduled
Income from Chartered
Operating costs
Fixed Costs
£259,200
£224,000
(£356,000)
(£60,000)
Taxable profit
Tax
£67,200
(£22,176)
Profit after tax
£45,024
Simulate
Output distribution
DRA/K V
Merck’s Research
Planning Model
Scientific,
Medical
constraints
R&D
variables
Manufacturing
variables
Marketing
variables
Monte-Carlo
Simulation
Technological
constraints
Economic
relationships
Projections
of variables
Macroeconomic
assumptions
Probability
distributions
for cash-flow
ROI, NPV
@RISK - How it works
DRA/K V
Single simulation trial
INPUTS
MODEL
CALCULATIONS
RESULT
Sales * Price - Cost
= Profit
= $62
211
$5
$993
Multiple simulation trials
INPUTS
MODEL
CALCULATIONS
RESULT
Profit
Trial 1: 211 * 5 - 993 =
$62
Trial 1: 193 * 8 - 700 =
$884
Trial 1: 219 * 6 - 999 =
$315
...
Trial N: 233 * 6 - 975 =
$423
Novaduct case
DRA/K V
NOVADUCT SPREADSHEET FOR FIVE YEARS
1
2
MARKET
8000
8160
PRICE
7.0
7.4
V COST
5.0
5.2
SALES (MS)
1200
1248
NET REVENUE
2400
2834
FIXED COSTS
-2000
-2060
CASHFLOW
-2500
400
774
ASSUMPTIONS
Discount Rate
Prod Cost
Price
Market Share
MS Incr
MktGrowth
15%
5
7
15%
0.3%
102.0%
103.0%
106.0%
(cashflow in thousands)
3
4
5
8323
8490
8659
7.9
8.3
8.8
5.3
5.5
5.6
1298
1350
1403
3325
3879
4503
-2122
-2185
-2251
1203
1693
2252
RESULTS
NPV
IRR
1312
30%
Novaduct - Uncertainty
DRA/K V
“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
DRA/K V
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
Novaduct using @RISK
DRA/K V
ASSUMPTIONS
Discount Rate
Prod Cost
Price
Market Share
MS Incr
MktGrowth
15%
5
7
15%
0.3%
102.0%
103.0%
106.0%
=RiskUniform(-0.2%,0.8%)
=RiskTriang(0.9,1.02,1.08)
@Risk Toolbar
Simulation
settings
Open & Save
Simulation
Results
Specify
output cells
View input
& output cells
Simulate
View @RISK
Window
DRA/K V
Simulation settings
DRA/K V
@RISK Window
Simulation results
DRA/K V
Distribution for NPV/F13
Distribution for IRR/F14
0.18
0.16
1.4E-01
0
50
0
10
00
15
00
20
00
25
00
30
00
0
NPV
Mean
914
Max
3174
Min
-1360
P(NPV<0) =
0.17
P(NPV<1,000) = 0.52
0.
4
0.
4
0.
3
0.4
0.2
0
IRR
Mean
Max
Min
P(IRR<15%) =
P(IRR<35%) =
0.
4
0.2
0.6
0.
4
0.4
0.8
0.
3
0.6
1
0.
2
0.8
1.2
-0
.2
-0
.1
-0
.1
1
-1
50
0
-1
00
0
-5
00
Distribution for IRR/F14
Prob of Value <= X-axis
Value
Prob of Value <= X-axis
Value
1.2
0.
2
-0
.2
-0
.1
-0
.1
Distribution for NPV/F13
0.
2
00
00
00
00
00
0
0.02
0
30
25
20
15
10
0
50
0
00
-5
00
-1
-1
50
0
0.0E+00
0.06
0.04
0.
2
2.0E-02
0.
1
4.0E-02
0.1
0.08
0.
1
6.0E-02
0.
0
8.0E-02
0.14
0.12
0.
0
1.0E-01
PROBABILITY
PROBABILITY
1.2E-01
25%
45%
-14%
0.15
0.85
DRA/K V
Cashflow Summary
Graph
• Central line connects mean values
• First band is 1 std.dev.
• Second band is interval between 5%
and 95% percentiles
DRA/K V
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