Base Case and Sensitivity Analysis – “Waterfall and Tornadoes”

Base Case and Sensitivity Analysis – “Waterfall and Tornadoes”

22.05-I • Deterministic & Sensitivity Analysis

We create a model to evaluate alternatives and test the importance of uncertainties.

Strategy Table

DecisionStructure

DeterministicAnalysis

ProbabilisticAnalysis

AppraisalInitial

Situation

Iteration

InfluenceDiagram

1

2

3

4

5

DeterministicModelA B C

DeterministicSensitivity

DecisionTree

ProbabilityDistributions

Value ofInformation

Decision Quality


We will discuss using spreadsheets for deterministic (base case) analysis and sensitivity analysis.

• Base Case Analysis and Waterfall Diagrams

• Sensitivity Analysis and Tornado Diagrams

• Using Sensitivity Results for Insight


Base case* analysis gives an initial comparison of each alternative.

1

2

3

4

5

A B C

Spread

sheet

Model

Base CaseInputs

¥

1 2 3 4

Base CaseOutput

s

The important question is “Why is #3 best?”

* All variables set at their “base case” values


Another base case output—the cash flow plot—illustrates cash needs and yields from each alternative under consideration.

–60

–50

–40

–30

–20

–10

0

10

20

30

1 2 3 4 5 6 7 8 9 10

Year

AnnualCash Flow ($ millions)

Run Out

Moderate Investment

Aggressive Investment

The plot shows how moderate or aggressive investment extends mature product life, with economic break-even in 3–5 years.


Initial evaluation with the model also yields important insights into sources of value and risk.

1

2

3

4

5

A B C

Spread

sheet

Model

Base Case

Waterfall of Value

Sources of Value

Uncertainty Range

TornadoDiagram

Sources of Risk


Base case evaluation shows the net value of each alternative, in this case dealing with mature products investment alternatives.

Net Present Value($ millions)

50 100 150 2000 300250

“Run Out” 71

ModerateInvestment

291

AggressiveInvestment

280

Why is the value of the aggressive investment less than the moderate investment?


This horizontal “waterfall chart” shows incremental sources of value and cost for each strategy.

Net Present Value ($ millions)

0 200 400 600 800 1,000

71

291

280

Run Out

ModerateInvestment

AggressiveInvestment

Halo Revenues

Product Revenues

Key

Added Value

Promotion

SF

Reduced Value

Product Revenues

Halo Revenues

SFPr.

Although typically drawn vertically, this orientation simplifies labeling.


The waterfall chart can “break out” the base case value added or lost from each major source.

Required Investment

Net Present Value

Market Growth

New Products

Fixed Costs

Value from FutureSale

Base Case NPV

Business context: Purchase an existing business, add value, then sell.

Current Contributi

on

Contributions

to Profit

0


The elements of a waterfall correspond to the “value centers” of the influence diagram.

Licensing

Licensing

Contribution

Licensing

Revenues

Commission

Costs

Service

Consulting

Revenues

Service

Contribution

Installation

Costs

FixedOverhead

Fixed

Overhead

Base Case NPV

It’s best to “sketch” the waterfall in parallel with developing the influence diagram.

Required Investmen

t

Net Present Value

NPV

Waterfall of Value

Corresponding Influence Diagram0


The choice of “value centers” depends on the business context and the strategic decisions.

Retail chain

• Existing stores

• New locations

Biotech product company

• Product #1

• Product #2

• Upcoming product launch

• Research pipeline

Global expansion opportunity• North American contribution• Europe• Asia/Pacific• Other regions

Business portfolio• Business unit, group, or sector #1• Business unit, group, or sector #2

Think of value centers as primary market segments or business centers or components of value, not cost centers.


The waterfall is a good way to reconcile changes in a strategy’s valuation over time.

InitialValuation

Data Revisions

Revised Valuation May 27

Revised Valuation June 15

Competitor Exits

Increase Fixed

Overhead

0

NetPresentValue


Create the waterfall by working “backwards,” incrementally turning off sources of value.

Contributions to Profit

NPV

Base Case Value

1

Value from Future Sale

2Overhead

3

Product C

4

Product B

4

Product A

Step 1 Record base case NPV.Step 2 Change future sales value to zero; record

NPV.Step 3 Set fixed and overhead costs to zero;

record NPV.Step 4 Switch off product contributions one by

one; record each NPV.Step 5 With all products switched off, NPV should

equal the required investment.

5

Required Investmen

t

0


One note about style: use short phrases on a “vertical bar” waterfall.

Short

sometimes.phrases

cantell

a

powerful

story

NetPresentValue

You might be tempted to rotate text to add more words.

0


Vertical text is OK in books and handouts, but it’s not effective in presentations.

unless lying down!

your

audience happens

to

be

Sideways text is not

effective,


The horizontal waterfall format accommodates many bars and lots of text.

Net Present Value

Look at all arrows & neat stuff you can write on

this waterfall chart now that it’s oriented the “other” way.

You run the risk of boring your audience of course,

but if you write like Charles Dickens, you might

consider this form of waterfall.

You can also write in the arrow, or use text to help

emphasize direction: Left!

Right!

And your audience doesn’t have to lie down!

In here!


The waterfall shows only base case values—it is equally important to understand which factors drive value higher or lower.

RequiredInvestmen

t

Contributions to ProfitValue from

FutureSale

Base Case Value

NPV

Product A

Product B

Product C

Overhead

Uncertainties that Increase Value

Uncertainties that Decrease Value

0







What do analysts in companies typically do when they encounter uncertainties?

• Ignore them

• Run three cases: base case, best case, worst case− How good is “best?”

− How bad is “worst?”

• Make an “assumption” and proceed.− The “easy way out”

− Are these justified?

A “tornado” analysis provides the justification you need for leaving variables at their base values versus including their uncertainty explicitly in your analysis.


Sensitivity (“tornado”) analysis identifies the primary sources of risk, which are then analyzed using probabilistic analysis.

DecisionStructure

DeterministicAnalysis

ProbabilisticAnalysis

Appraisal

Iteration

Many Uncertainti

es

Tornado

Primary Sources of

Risk

Initial Situation

We also typically reassess ranges for the top bars in the tornado.


Single-variable sensitivity analysis determines the change in model output when one input changes.

Spreadsheet Model

NPV ($ MM) 75

OUTPUT43

44

Low Case8%

-6

High Case28%

134

Swing140

Market Share 20%

INPUT Base Case

A B

1

2


A “tornado diagram” graphically depicts the variables’ contributions to uncertainty in NPV.


-50 0 50 100 150 200

Base Value = 75

Price per dose

Market Share

Doses per Day

Prevalence Rate

Compliance

Treatment Rate

Development Cost

COGS (%Rev)

Uptake curve lengthAnnual Price change

$1.50 $6.00

8% 28%

1 3

1.5% 3.0%

30.0% 70.0%

30.0% 60.0%

140.0 60.0

30% 15%

7 3

-2% 1%


The tornado diagram is generated by reevaluating NPV using low and high values for each variable separately.

Base Case NPV = $75 MM

Variable

Variable Values

Base10% Low

90% High

Price per Dose $3.50 $1.50 $6.00

Market Share 20% 8% 28%

Doses per Day 2 1 3

Prevalence Rate 2.0% 1.5% 3.0%

Compliance 55% 30% 70%

Treatment Rate 50% 30% 60%

Development Cost 100 60 140

COGS 25% 15% 30%

Uptake curve length 5 3 7

Annual Price Change 0% -2% 1%

Results

“Low” “High” Swing

-2 171 173

-6 134 140

7 142 135

41 142 101

14 112 98

22 101 79

99 51 48

100 62 37

91 56 35

55 86 31


Uncertain inputs can have a large effect on the output for two reasons.

The input may be highly uncertain.

Range of Input

Range of Output

Range of Input

The output variable may be highly sensitive to small changes in an input.

Range of Output{


Three of the variables are “coupled” or “dependent.” They tend to vary together.

• We should determine the sensitivity of NPV to joint changes in these variables.

• Note: These scenarios are obtained by assessing a combination of events that would lead to a low (10th percentile) and a high (90th percentile) outlook.

“Once a day”

1

70%

$6.00

“bid”*

2

55%

$3.50

“tid”*

3

30%

$1.50

Number of Doses

Compliance

Price per Dose

Price/Dosing Scenario

*tid: ter in die – three times a day

bid: bis in die – twice a day


Joint sensitivity analysis determines the sensitivity of NPV to simultaneous changes in coupled* variables

Variable Values

Variable

Doses per Day

Compliance

Price per Dose

Low

3

30%

$ 1.50

BaseCase

High

2

55%

$ 3.50

1

70%

$ 6.00

Base Case NPV = $75 MM

Results

“Low” “High” Swing

- 13 87 100

* Coupled, or dependent, uncertainties are likely to vary together—either positively or negatively correlated.


The updated tornado diagram focuses our attention on the most significant sources of risk.


-50 0 50 100 150 200

Base Value = 75

Market Share 8% 28%

Prevalence Rate 1.5% 3.0%

Treatment Rate 30.0% 60.0%

Development Cost 140.0 60.0

COGS (%Rev) 30% 15%

Uptake curve length 7 3

Annual Price change -2% 1%

TID BIDDose/Pricing Scenario

Sensitive

Insensitive

We suggest re-assessing the uncertainty in the most sensitive uncertain variables and including them in probabilistic analysis.


Uncertainties with the greatest “swing” are crucial to capturing the uncertainty in overall value.

*The uncertainty in the model output (e.g., NPV) is proportional to the sum of the squares of individual input variable swings, if the variables are independent.

31Price Change

TOTAL

35Uptake Curve

37COGS

48Dev Costs

79Treatment Rate

100Dose/Pricing Scen

101Prevalence Rate

140Market Share

Individual Swing

Uncertainty

961

50526

1225

1369

2304

6241

10000

10201

18225

Variance (swing)2

100%2%

98%2%

96%3%

93%4%

89%12%

77%19%

58%20%

38%38%

Cumulative Contribution

Contribution to Total

Uncertainty*







The tornado diagram helps identify potential problems with the assessments and the model.

Net Present Value

Are these really the most sensitive, or are the ranges too wide?

Too symmetric? Are experts biased?

Low cost, high NPV!

Cost:

High Low

“Floating” bar—are the values

right?Are these really low/zero swings, or is there a mistake?

Does the base case match the waterfall (and spreadsheet) base

case?


Waterfall and tornado analyses provide tools to “mine” for NPV insights.

• Which risk factors might we be able to control?

• Is any strategy clearly most attractive?- How can we revise the strategy to capture more value?- How can we help focus the attention of company management?

• Where should the analysis be refined?

• What are the primary sources of value?

• What drives the uncertainty in net present value?

• What uncertainties have the greatest effect on decisions?

• Which variables are dependent?


Appendix


There is another form of sensitivity—decision sensitivity; it identifies uncertainties that affect decision-making.

How important is each uncertainty—enough to change our decision?

Example: A Drug Development investment decision

Invest

Don’t Invest$ 0

Market Share

Uncertainties

PrevalencePrice/dosingscenario


The tornado identifies uncertainties that affect our choice between investing or not; this is called “decision sensitivity.”

Variable

Net Present Value

Base Value: 75

Don’t Invest

Invest

Invest

Don’t Invest

Invest Invest

Invest Invest

Invest Invest

Best Decision, Given:

Low Input High Input

We could change our decision based on the outcome Market Share and Dose/Pricing Scenario alone. These two are “decision sensitive.”

0 50 100 150

Market Share

Prevalence Rate

Treatment Rate

Development Cost

COGS (%Rev)

Dose/Pricing Scan

8% 28%

1.5% 3.0%

30.0% 60.0%

140 60

30% 15%

TID BID


Judge the quality of available information before plunging into evaluation.

4Clear

Values andTrade-offs

5LogicallyCorrectReasoning

6Commitmentto Action

0% 100%

Decision

Quality

1Appropriate

Frame

2

Creative,

Doable

Alternatives

3Meaningful, Reliable

Information

3Meaningful, Reliable

Information

Meaningful, Reliable Information:

0% “Blissful ignorance”• Don’t know how much we know• Ignoring uncertainty• Ignoring “intangibles”

50% “Informed about uncertainty”• Know information gaps• Know what’s important• Quantified uncertainty• Interdependence not explored

100% “Knowledgeable and ready” • Information correct and explicit• Important gaps filled• Know limits of knowledge

Documents

Base Case and Sensitivity Analysis – “Waterfall and Tornadoes”