DRA/KV

Decision and Risk Analysis

Financial Modelling & Risk Analysis

Kiriakos VlahosSpring 2000

DRA/KVSession overview

• Why do we need risk analysis?

• Project evaluation

• Risk analysis approaches

– Scenario analysis

– Sensitivity analysis

– Monte-Carlo simulation

• Summary

DRA/KV

Risk management in business

Project Evaluation

Capital budgetingand portfolio evaluation

Corporate risk

DRA/KV

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/KV

Risk analysis approaches

• Scenario analysis

• Sensitivity analysis

• Monte-Carlo simulation

• Decision Analysis

• Option theory

DRA/KV

Proposal to open and operate a video store.

“You can expect to make at least £50,000 in the first year”

Skywalker

Monthly Purchase (no of tapes) 50Tape Price £30Tape Life (no of plays) 30Plays per Mth (per tape) 4.33Rent per Day £3Shop Rent p a £6,000Interest p a 10%

Assumptions

DRA/KVProject 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

DRA/KVBase case model

SKYWALKER VIDEOMonthly closing cash for base scenario

-30.0

-20.0

-10.0

.0

10.0

20.0

30.0

40.0

50.0

60.0

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Closing cash exceeds £50000 at the end of the year

SKYWALKER VIDEO MODEL

in £000 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Average Stock 1.0 1.1 1.1 1.2 1.2 1.3 1.3 1.4 1.4 1.5 1.5 1.6

Opening Cash 3.0 -22.2 -17.0 -11.5 -7.0 -.8 5.9 11.4 18.9 26.7 33.4 42.0

Rental recpts 10.8 11.4 11.9 12.4 13.0 13.5 14.1 14.6 15.2 15.7 16.2 16.8

Purchases -30.0 -1.5 -1.5 -1.5 -1.5 -1.5 -1.5 -1.5 -1.5 -1.5 -1.5 -1.5

Replacements -4.3 -4.5 -4.8 -5.0 -5.2 -5.4 -5.6 -5.8 -6.1 -6.3 -6.5 -6.7

Rent qtrly -1.5 -1.5 -1.5 -1.5

Total -22.0 -16.9 -11.4 -7.0 -.8 5.9 11.4 18.7 26.5 33.1 41.6 50.5

Interest -.2 -.1 -.1 -.1 .0 .0 .1 .2 .2 .3 .3 .4

Closing Cash -22.2 -17.0 -11.5 -7.0 -.8 5.9 11.4 18.9 26.7 33.4 42.0 51.0

DRA/KVScenario 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!

DRA/KV

Skywalker - Scenarios analysis

Assumptions Optimistic Base Pessimistic

Monthly Purchase 60 50 40

Tape Price 25 30 35

Tape Life 35 30 25

Plays per Mth 5.00 4.33 2.50

Rent per Day 3.00 2.50 2.00

Shop Rent p a 3,000 6,000 10,000

Interest p a 15 10 7

Skywalker Final Cash:Comparison of Scenarios

-60,000

-10,000

40,000

90,000

140,000

190,000

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Optimistic Base Pessimistic

DRA/KVSensitivity 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

DRA/KVWhat-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

Results Panel:

Monthly Purchase 50 FinalTape Price 35 Cash 30,926Tape Life 30Plays per Mth 4.33Rent per Day 2.50Shop Rent p a 6,000

Interest p a 10

SKYWALKER VIDEO MODELin £000 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov DecAverage Stock 1.0 1.1 1.1 1.2 1.2 1.3 1.3 1.4 1.4 1.5 1.5 1.6

Opening Cash 3.0 -28.0 -23.8 -19.4 -16.1 -11.1 -5.6 -1.4 4.7 11.1 16.4 23.5Rental recpts 10.8 11.4 11.9 12.4 13.0 13.5 14.1 14.6 15.2 15.7 16.2 16.8Purchases -35.0 -1.8 -1.8 -1.8 -1.8 -1.8 -1.8 -1.8 -1.8 -1.8 -1.8 -1.8Replacements -5.1 -5.3 -5.6 -5.8 -6.1 -6.3 -6.6 -6.8 -7.1 -7.3 -7.6 -7.8Rent qtrly -1.5 -1.5 -1.5 -1.5

Total -27.7 -23.6 -19.2 -16.0 -11.0 -5.6 -1.4 4.6 11.0 16.2 23.3 30.7Interest -.2 -.2 -.2 -.1 -.1 .0 .0 .0 .1 .1 .2 .3

Closing Cash -28.0 -23.8 -19.4 -16.1 -11.1 -5.6 -1.4 4.7 11.1 16.4 23.5 30.9

Assumptions

DRA/KV

One-way sensitivity analsysis

e.g. Sensitivity of closing cash to Rent per day

Dec Closing Cash

=M26

2.00 10.8

Rent 2.25 26.4

per 2.50 42.0

Day 2.75 57.6

3.00 73.2

.010.020.030.040.050.060.070.080.0

2.00 2.25 2.50 2.75 3.00

Rent Per Day (£)

Dec

Clo

sing

Cas

h £0

00

DRA/KV

Two-way sensitivity analysis

Plays per Month

50,954 2.00 3.50 4.33 5.00

2 -21,379 2,758 16,115 26,896

Rent 2.25 -13,333 16,839 33,534 47,011

per 2.5 -5,287 30,919 50,954 67,126

Day 2.75 2,758 45,000 68,373 87,241

3 10,804 59,080 85,793 107,356

Skywalker: December Closing Cashfor different Rental & Plays per Month

-40,000

-20,000

0

20,000

40,000

60,000

80,000

100,000

120,000

1 2 3 4 5 6

Plays per Month

Rental

2

2.25

2.5

2.75

3

Two-variable data table can be applied to a single cell such as December Closing Cash cell:

DRA/KV

3-D plot of two-way sensitivity analysis

2.02.5

3.03.5

4.04.5

5.02.00

2.25

2.50

2.75

3.00

-40

-20

20

40

60

80

100

120

Clo

sin

g c

ash

£00

0

Plays per Month

Rent per Day

Skywalker: Sensitivity of closing cash to to Rental & Plays per month

Tutorial on data tables in Datatables.xls

DRA/KVTornado diagrams

20 40 60 80 100

Interest p a

Monthly Purchase

Shop Rent p a

Tape Life

Tape Price

Plays per Mth

Rent per Day

Closing cash in £000

Tutorial on Tornado diagrams in Tornado.xls

Assumptions Optimistic Pessimistic Optimistic PessimisticMonthly Purchase 60 40 51.9 50.0

Tape Price 25 35 71.0 30.9

Tape Life 35 25 60.9 37.0

Plays per Mth 5.00 2.50 67.1 6.8

Rent per Day 3.00 2.00 85.8 16.1

Shop Rent p a 3,000 10,000 54.1 46.7

Interest p a 15 7 51.5 50.6

Assumptions Impact on closing cash

Helps us determine visually the main uncertainty drivers.

DRA/KV

Constructing spider plots

AssumptionsOptimistic Base Pessimistic

MonthlyPurchase 60 55 50 45 40Tape Price 20 25 30 35 40Tape Life 35 32.5 30 27.5 25Plays per Mth 5 4.665 4.33 3.165 2Rent per Day 3 2.75 2.5 2.25 2Shop Rent p a 3000 4500 6000 8000 10000Interest p a 7 9 10 13 15

% change from baseOptimistic Base Pessimistic

MonthlyPurchase 120 110 100 90 80Tape Price 67 83 100 117 133Tape Life 117 108 100 92 83Plays per Mth 115 108 100 73 46Rent per Day 120 110 100 90 80Shop Rent p a 50 75 100 133 167Interest p a 70 85 100 125 150

Closing cash resultsOptimistic Base Pessimistic

MonthlyPurchase 51.9 51.4 51.0 50.5 50.0Tape Price 91.0 71.0 51.0 30.9 10.9Tape Life 60.9 56.3 51.0 44.6 37.0Plays per Mth 67.1 59.0 51.0 22.8 -5.3Rent per Day 85.8 68.4 51.0 33.5 16.1Shop Rent p a 54.1 52.6 51.0 48.8 46.7Interest p a 50.6 50.8 51.0 51.2 51.5

DRA/KV

Skywalker: Spider plot

-20.0

.0

20.0

40.0

60.0

80.0

100.0

% 50% 100% 150% 200%

% change from base

Clo

sin

g c

as

h £

00

0

Tape Price Tape Life Plays per Mth

Rent per Day Shop Rent p a Interest p a

MonthlyPurchase

DRA/KV

Price/Demand Relationship

Price is a decision variable and demand should depend on price, e.g.

Plays per Month v Rental per Day

0

1

2

3

4

5

6

7

1.5 2.0 2.5 3.0 3.5Rent pe r Da y

Pla

ys p

er M

onth

Regression equation:PlaysperMonth = 13.13 - 3.80RentperDay

-60

-40

-20

20

40

60

1.00 1.50 2.00 2.50 3.00 3.50

Rent per day (£)

Clo

sin

g c

ash

£00

0

One-way sensitivity analysis to Rent per day

Which price maximises closing cash?

DRA/KV

Monte-Carlo simulation

Base Case ModelUncertain variables

Output distribution

Uncertain Parameters Base ValueHours Flown 800

Charter Price/Hour 700Ticket Price/Hour 90

Capacity of Sch. flights 60%Ratio of charter flights 40%Operating Cost/hour 445

Profit & Loss

Income from Scheduled £259,200Income from Chartered £224,000

Operating costs (£356,000)Fixed Costs (£60,000)

Taxable profit £67,200Tax (£22,176)

Profit after tax £45,024

Simulate

DRA/KV

Merck’s Research Planning Model

R&Dvariables

Manufacturing

variables

Marketingvariables

Scientific,Medical

constraints

Technologicalconstraints

Economicrelationships

Projectionsof variables

Macro-economic

assumptions

Probabilitydistributionsfor cash-flowROI, NPV

Monte-CarloSimulation

DRA/KV

@RISK - How it works

INPUTSMODEL

CALCULATIONS

Sales * Price - Cost

RESULT

= Profit= $62

211

$5

$993

Single simulation trial

Multiple simulation trials

INPUTSMODEL

CALCULATIONS RESULT

Trial 1: 211 * 5 - 993 =

Trial 1: 193 * 8 - 700 =

Trial 1: 219 * 6 - 999 =

Trial N: 233 * 6 - 975 =

Profit$62

$884

$315

$423

...

DRA/KVNovaduct case

NOVADUCT SPREADSHEET FOR FIVE YEARS (cashflow in thousands)

1 2 3 4 5MARKET 8000 8160 8323 8490 8659PRICE 7.0 7.4 7.9 8.3 8.8V COST 5.0 5.2 5.3 5.5 5.6SALES (MS) 1200 1248 1298 1350 1403NET REVENUE 2400 2834 3325 3879 4503FIXED COSTS -2000 -2060 -2122 -2185 -2251CASHFLOW -2500 400 774 1203 1693 2252

ASSUMPTIONS RESULTS

Discount Rate 15% NPV 1312Prod Cost 5 103.0% IRR 30%

Price 7 106.0%Market Share 15%MS Incr 0.3%MktGrowth 102.0%

DRA/KV

Novaduct - Uncertainty

“Market share increase is equally likely to be any value between -0.2% and 0.8%”

“Market growth is most likely to be a 2% increase but could range from a 10% decrease to an 8% increase”

-0.2 0.8

90 108102

DRA/KVUsing @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

DRA/KV

Novaduct using @RISK

ASSUMPTIONS

Discount Rate 15%Prod Cost 5 103.0%

Price 7 106.0%Market Share 15%MS Incr 0.3%MktGrowth 102.0%

=RiskUniform(-0.2%,0.8%)

=RiskTriang(0.9,1.02,1.08)

@Risk Toolbar

Open & SaveSimulation

Results

Simulationsettings Simulate

View @RISKWindow

Specifyoutput cells

View input& output cells

DRA/KVSimulation settings

DRA/KV@RISK Window

DRA/KVSimulation results

NPV IRR

Mean 914 Mean 25%

Max 3174 Max 45%

Min -1360 Min -14%

P(NPV<0) = 0.17 P(IRR<15%) = 0.15

P(NPV<1,000) = 0.52 P(IRR<35%) = 0.85

Distribution for NPV/F13

0.0E+00

2.0E-02

4.0E-02

6.0E-02

8.0E-02

1.0E-01

1.2E-01

1.4E-01

-1500

-1000

-500 0

500100

0150

0200

0250

0300

0

PR

OB

AB

ILIT

Y

Distribution for NPV/F13

0

0.2

0.4

0.6

0.8

1

1.2

-150

0

-100

0-5

00 050

010

0015

0020

0025

0030

00

Pro

b o

f V

alu

e <

= X

-axi

s

Val

ue

Distribution for IRR/F14

0

0.2

0.4

0.6

0.8

1

1.2

Pro

b o

f V

alu

e <

= X

-axi

s

Val

ue

Distribution for IRR/F14

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

PR

OB

AB

ILIT

Y

DRA/KV

Cashflow Summary Graph

• Central line connects mean values• First band is 1 std.dev.• Second band is interval between 5%

and 95% percentiles

DRA/KVSummary

• 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