Decision Making Under Uncertainty

Extracted from: ICSE’ 2002 Tutorial on Software Economics

Hakan Erdogmus

Warren Harrison

2

Economic Analysis and Decision Making

• Economic Analysis of Software Engineering is driven by the need to make decisions

• Common problems encountered by decision-makers include:– decision deferral– inability to defend the decision– inconsistent judgement

• Traditional software engineering decision-making is based on technical outcomes

3

Components of a Decision

• Choice involves selecting the “best” alternative under consideration

• A decision has four components:– Actions– States of Nature– Outcomes– Choice Criterion

4

Components of a Decision: Actions

• Actions are alternative things you can do in response to the decision

• Properties of candidate actions:– mutually exclusive– enumerable– initial level of objectivity need not be great, but must

come to pass eventually – start out with subjective description, refine later

5

Components of a Decision:States of Nature

• External events that can affect the efficacy of the alternatives – we can’t control them!

• Events that will certainly occur or events that have no impact on the alternatives should not be considered.

• States of nature are mutually exclusive.• Initial level of objectivity need not be great, but

must come to pass eventually.

6

An Example

• A new income tax package is being planned.• The product needs an installation feature.• We can either license a commercial installation

package or we can build our own.• To develop our own will cost $10,000.• To license a commercial package will entail a

$1.00/unit royalty,but no up front costs.

7

Technical Evaluation

• The effort required to develop the interface software versus the effort required to custom develop all the code

• The maintainability of the COTS software• The reliability of the COTS software• The quality and reliability of vendor support

from NASA Software Management

Guidebook, NASA-GB-001-96More on COTS in Segment 5!

8

Economic Evaluation

• Breakeven Analysis• Expected Cost to Build• Expected Cost to License• Discounted Cash Flow• Buying Options

9

Breakeven Analysis

010000200003000040000

050

00

1000

0

1500

0

2000

0

2500

0

3000

0

3500

0

Sales in Units

Co

st o

f L

icen

se

Dec

isio

n

Build

License

• $10,000 fixed cost vs. $1/unit variable cost• at 10,000 units Building breaks even

10

Outcomes

• For each action, what will the outcome be for each state of nature?– Action: License– Action: Build Our Own– State of Nature: We sell less than 10,000 units– State of Nature: We sell more than 10,000 units– Outcomes: ...

11

Outcome Basis

• The outcome is based on the cost of the action and the benefit of the action– Costs

• Build our own – cost of development• License commercial package – royalty

– Benefits• Product gets installed – does not matter which choice

12

The Decision Matrix

Sales Build License 1,000 units 10,000 1,000 5,000 units 10,000 5,000 10,000 units 10,000 10,000 20,000 units 10,000 20,000 25,000 units 10,000 25,000 30,000 units 10,000 30,000 50,000 units 10,000 50,000 75,000 units 10,000 75,000 100,000 units 10,000 100,000

13

The Decision Matrix

Sales Build License 1,000 units 30% 10,000 1,000 5,000 units 25% 10,000 5,000 10,000 units 20% 10,000 10,000 20,000 units 10% 10,000 20,000 25,000 units 10% 10,000 25,000 30,000 units 2% 10,000 30,000 50,000 units 1% 10,000 50,000 75,000 units 1% 10,000 75,000 100,000 units 1% 10,000 100,000

14

The Decision Matrix

Sales Build License 1,000 units 30% 10,000 1,000/300 5,000 units 25% 10,000 5,000/1,250 10,000 units 20% 10,000 10,000/2,000 20,000 units 10% 10,000 20,000/2,000 25,000 units 10% 10,000 25,000/2,500 30,000 units 2% 10,000 30,000/600 50,000 units 1% 10,000 50,000/500 75,000 units 1% 10,000 75,000/750 100,000 units 1% 10,000 100,000/1,000 Expected Cost $10,000 $10,900

15

Choice Criterion

• Rules we might use to decide which action to choose:– pick the action with the lowest cost for the most likely

state of nature– pick the action that never results in the highest cost– pick the action with the lowest expected cost

16

Expected Cost

• Viability of expected cost is dependent on the assessment of the likelihood of each state of nature

• Garbage-in Garbage-out!• Information is not free – how much is it worth?• How can we measure the worth of more accurate

information?

17

Time Value of MoneyMoney Received or Spent in the Future

• We must spend the money now to build• Royalties are paid out in the future • If we invest the $10,000 rather than spending it

on creating an installation feature at 10%:– 2003: $1,000 interest $11,000– 2004: $1,100 interest $12,100– 2005: $1,210 interest $13,310– 2006: $1,331 interest $14,641

18

A Dollar in the Future is Not Equalto a Dollar Today

Foregone interest: $10,000 today, in a year at 10% interest is $11,000

Risk: the longer before an investment starts paying off, the more likely conditions can change

Liquidity: people value the flexibility to use their funds whenever they want – the longer funds are tied up, the less utility a person receives

Time Value of Money =Opportunity Cost (foregone benefits)+ Risk+ Inflation + Liquidity

19

Present Value and Discounting

• Today’s value of a sum of N periods in the future:

Present Value = (Future Value) / (1 + k)N

Where– k: discount rate per period– N: number of periods

• To fairly compare $10,000 spent today against royalties to be paid out in one year we must discount the cost of the royalties

• Apply to benefits in a similar fashion

20

Net Present Value

• Evaluating Investment Opportunities:

• NPV = Investment – PV(income stream)• Use “cost of capital” as the discount rate• NPV Decision Rule: If NPV > 0 then invest

• Internal Rate of Return (IRR) – the discount rate that drives the NPV to zero …

21

Build vs. License ExampleThe Decision Matrix Revisited

Sales Build PV(License) 1,000 units 30% 10,000 909/272 5,000 units 25% 10,000 4,545/1,136 10,000 units 20% 10,000 9,090/1,818 20,000 units 10% 10,000 18,181/1,818 25,000 units 10% 10,000 22,727/2,272 30,000 units 2% 10,000 27,272/545 50,000 units 1% 10,000 45,454/454 75,000 units 1% 10,000 68,181/682 100,000 units 1% 10,000 90,909/909 Expected Cost $10,000 $9,906

22

Keeping Our Options Open

• It is financially desirable to build our own installation feature if sales rise above 10,000 units

• We can insert “hooks” into the application that will allow us to quickly add our own installation feature if sales turn out to be high.

• Should we invest in adding “hooks”? How much can we afford to invest?

23

Handling Uncertainty

• Models for evaluating process and project management choices under uncertainty:– Should we buy or build?

…Decision Tree Analysis illustrated

– Why are iterative processes viable?… Real Options Analysis illustrated

– Should we implement this feature now?… More options thinking

– Should we develop a prototype?– Should we invest in infrastructure (product line,

framework, component libraries)?

24

Sales Build License 1,000 units 30% 10,000 1,000 5,000 units 25% 10,000 5,000 10,000 units 20% 10,000 10,000 20,000 units 10% 10,000 20,000 25,000 units 10% 10,000 25,000 30,000 units 2% 10,000 30,000 50,000 units 1% 10,000 50,000 75,000 units 1% 10,000 75,000 100,000 units 1% 10,000 100,000

Build vs. License Example RevisitedHow Much to Invest to Add the “Hooks”?

LOW = .75

MED = .22

HIGH = .03

• ½ of projected sales in Q2; rest in Q4

• Decision to build taken at Q2 after based upon Q2 sales figures

25

Build vs. License Example RevisitedConditional Sales Projections and Probabilities

Sales E[Q2 sales] E[Q4 sales] 1,000 units 30% 500 ( = 40%) 5,000 units 25% 2,367 ( = 75%) 2,500 ( = 33%) 10,000 units 20% 5,000 ( = 27%) 20,000 units 10% 10,000 ( = 45%) 25,000 units 10% 11,591 ( = 22%) 12,500 ( = 45%) 30,000 units 2% 15,000 ( = 10%) 50,000 units 1% 25,000 ( = 33%) 75,000 units 1% 37,500 ( = 3%) 37,500 ( = 33%) 100,000 units 1% 50,000 ( = 33%)

LOW

MED

HIGH

Q4 sales projections based on Q2 sales

26

Q0

Build vs. License Decision

Decision Tree for Option to Build

Q2 Q4Build

License

Add Hooks;Start withLicensing

License

License

Build

Build

High:25K < units

Med:10K < units 25K

Low:units 10K

High: . 50K units

Med: 37.5 units

Low: . 25K units

High: 15K units

Med: 12.5K units

Low: 10K units

High: 5K units

Med: 2.5K units

Low: .5K units

.33

.33

.33

.1

.45

.45

.27

.33

.40

.03

.22

.75State Node

Prob.of State

Action Node

Descriptionof State

ActionTime

27

Decision Tree AnalysisCaluculating Cost of Option to Build

B: $10K

L: $37.5K

L: $35.6KPV

B: $10K

L: $11.6K

L: $11KPV

B: $10K

L: $2.4K

L: 2.3KPV

+ $37.5K

+ $11.6K

+ $2.4K

$9.6K

.33

.33

.33

.27

.33

.40

.03

.22

.75

.1

.45

.45

50K

37.5K

25K

15K

12.5K

10K

5K

2.5K

.5K

Q2Q4

PV$9.2K

Q0

E[license cost for Q2]

Fold back DT using dynamic programming

28

Decision Tree AnalysisDT for Cost of “Licensing All the Way”

L: $37.5K

L: $35.6KPV

L: $11.6K

L: $11KPV

L: $2.4K

L: 2.3KPV

+ $37.5K

+ $11.6K

+ $2.4K

$10.6K

.33

.33

.33

.27

.33

.40

.03

.22

.75

.1

.45

.45

50K

37.5K

25K

15K

12.5K

10K

5K

2.5K

.5K

Q4

PV$10.2K

Q0

Q2

E[license cost for Q2]

29

Build vs. Buy DecisionHow Much to Invest to Add the “Hooks”?

Up to this amount can be invested now to add the hooks to match the min cost alternative; otherwise build now!

Alternative E(Cost) Min Cost Difference

A. Build now 10 0B. License all the way 10.2 -0.2C. Option to build 9.2 0.8

10

$K

30

Build vs. Buy Decision… from an Options Perspective

Small investment:Add hooks toacquire the optionto build installationfeature later

Large investment:Build feature

Uncertainty partiallyresolved

High sales:Build feature

Low sales: Continue licensing

Receive benefit:Cost savingsNo license cost

Q4

Q0 Q2

A Real Option

ExpirationDate

Exercise Price

UnderlyingAsset

(uncertain)

OptionValue

31

What is an Option?

• An option is a future discretionary action with an uncertain benefit.

• Financial Options– option contracts written on financial

securities (stocks, commodity prices, exchange rates)

• Real Options– options defined on uncertain benefits

of a real asset, for example future cash flows of a project

CALL OPTION

This contractgives you theright to buyone unit ofXYZ stock

for $15on or beforeJan 5, 2000.

32

Options in Software Development

• Developing a prototype before the full application to resolve technical and user uncertainty.

• Development of a framework for a future product line to allow cost-efficient generation of multiple applications.

• Development of a flexible architecture that accepts components for future extensibility and easy replacement of functionality.

• Waiting to see whether Java gains acceptance before migrating a stable application to Java.

Reusable, flexible architectures:See also Segment IV

33

Why Are Options Valuable?Call Option

Exercise price = $45Current Price = $50

75

35

6 months to expiration

If stock falls to $35

$35 – $45 = –$10 Payoffs atexpiration

Option valueat expiration

If stock rises to $75

$75 – $45 = $30

$30.00Option Exercised

$0.00Option Forgone

Option Pricing: How much should I pay to acquire this option now?

Rational

Exercise

34

Value of an Option Dependson Five Factors

InterestRates

1

Volatility ofUnderlying Asset

2 Time toExpiration

3

4

The exercise price is not paid until expiration. Until then, that money can be earning interest!

The larger the difference between the exercise price and current asset value, the more the asset value has to move to surpass it.

The more time passes, the more chance for the asset value to wander up or down.

The more volatile the asset is, the more likely its value to move up or down over time.

Present Valueof Underlying

Asset

ExercisePrice

RationalExerciseRegion

5

inversely proportionalto factor

proportional to factor

35

Flexibility, Value & Iterative Processes

Why tighter iterations and frequent releases?

Less focus on planningTighter iterations

More frequent releasesScrumDSDM

Crystal Extreme Programming

Feature-Driven DevelopmentAdaptive Software Development

Agile Modeling

Spiral

36

Waterfall: Delivers complete system. Realizes value late.

Value Realization Models:Waterfall vs. Iterative

Develop Rework

End Deploy

Deploy DeployDeployDeploy DeployDeploy Deploy

Iterative: Delivers incomplete system. Maximizes value by delivering early and frequently.

PV =

PV = + + + + +$ $ $ $ $ $

$

$ =

Late Benefit

Sum of Incremental Benefits

37

Black Hole:Large Investment, Single Release

Largeinvestment

Receivebenefit(uncertain)

Release

• Uncertainty resolved at the end• No learning

Projectcancelled!

38

Small Investments, Small Releases

Smallinvestment

Release

Receivebenefit

• Uncertainty resolved gradually in multiple stages• Learning benefits

Multiple options: stop, continue, modify?

Stop => preserve value from previous stages

Each subsequentrelease is anoption on the previous release!

Release

Release

Release

39

Value in the Black Hole

• No schedule slips

• Benefit is uncertain

• Cost and Expected Benefit already in PV terms (already discounted with a risk- adjusted discount rate)

Net Present Value rule says: Don’t do it!

Benefit is uncertain because business, technology, customer/user requirements, or market may change!

Single-State ProjectCost 110Expected Benefit 100NPV –10

40

Alternative:Two-Stage Project with Learning

  Release 1 (R1) Release 2 (R2) Overall

FlexibilityPurpose

Uncertainty

Mandatory Learning

More uncertain

OptionalCompletion

Less uncertain

 

Cost 55 55 110

Benefit(uncertain)

 

50 R1outcome

?

Volatility(per release)

40% ? ?

Duration(months)

2 2 

4

Risk-free rate(per month)

.8% .8% .8%

Same as before

Half the benefit

Same as before

High; same as before

41

What is Volatility?

• Planned Features (PF): features to be included in the next release

• Feature Backlog (FB): extra features yet to be implemented in future releases

• Realized Features: RF PF FB– Feature implemented during the release– Customer still wants and values the feature

P: Customer’s assessment of a feature’s value at planning time

R: Customer’s assessment of a feature’s value after release relative its planned value

• Total Planned Value (TPV) = f PF P(f)

• Total Realized Value (TRV) = f RF R(f)

• ROI = (TRV – TPV) TPV

• Volatility = StDev(ROI)

Release ROI

1 35%2 10%3 -55%4 -65%5 -20%6 -25%7 -15%8 -10%9 25%

10 85%11 50%12 -45%13 -25%14 -5%15 -5%16 55%17 -15%18 25%

Mean 0%StDev 40%

42

Value of Two-Stage Project

ExpectedR1

Benefit

50 50

88

67

38

28

50

88

28

50

122

28

93

41

71 -55 16

R1Outcome

ExpectedR2

Benefit

PayoffAfterR2

PV ofPayoff

NPV +OptionValue

R1Cost

R1 Outcome

X Stop

X Stop

Cont

Discrete model of uncertaintyas a Binomial DT:

Use volatility of benefit to generate a set of possible outcomes

Fold back decision tree using risk-free rate& risk-adjusted probabilities

(R1 Outcome) + E[R2 Benefit] – (R2 Cost)

43

Valuation Using a Replication Strategy

• The valuation method used in the previous example is called risk-neutral valuation.

• The valuation assumes that the payoffs the DT can be replicated by a trading strategy involving an imaginary asset whose uncertainty is correlated with that of the strategy being valued.

• The trading strategy represents the opportunity cost of the strategy being valued => they must have the same present value.

44

Risk-Neutral Valuation

50 50

88

67

38

28

50

122

28

93

41

71

3 Construct a Binomial Tree using u & d factors

5 Fold back Binomial Tree using risk-adjusted probabilities & discounting back at the risk-free rate

…u = 1.33

d = .75

1 Choose granularity: N = 3 states

p = .6

1 – p = .4

3 Calculate optimal payoffs @ decision points

50(.75)

50(1.33)

50(.6) + 28(.4)–––––––––-–- 1 + .008

2 Calculate up & down factors using volatility estimate

4 Calculate risk-adjusted probabilities from u & d

45

Valuation Using a Replication Strategy Constructing the Binomial Tree

Inputs• : estimated volatility per release• N: desired granularity

• number of different states representing possible benefits of a release

• rf: risk-free rate • for 1/(N – 1)th of the duration of a release• observed in the markets or can be set to 0

Outputs• u: upward factor = exp(sqrt(1/(N – 1)))• d: downward factor = 1/u

46

Valuation Using a Replication Strategy Folding Back the Decision Tree

Inputs• u: upward factor• d: downward factor

• rf: risk-free rate

Output• risk-adjusted probabilities to calculate expected values• risk-adjusted probability for an upward move:

p = (1 + rf – d)/(u – d)

• risk-adjusted probability for downward move:1 – p

47

Valuation Using a Replicating StrategyParameters for Build-Buy Example

Inputs• = 40% per release

• N = 3

• rf = 0.8% per month

Outputs• u = exp(0.4 sqrt(1/(3 – 1))) = 1.33• d = 1/u = .75

• p = (1 + rf – d)/(u – d) = (1 + .008 – .75)/(1.33 – .75) = .6

• 1 – p = 1 – .6 = .4

48

DTA vs. Risk-Neutral Valuation

DTA• Needs probability

estimates for each state• Discount rates should

reflect changing risk• No traded twin asset

• More flexible

Risk-Neutral Valuation• Needs only a volatility

estimate• Can use risk-free rate

throughout• Assumes traded twin

asset• Less flexible

The two techniques are fully compatible andcan easily be combined (Smith & Nau, 1995).

49

The more uncertain the benefits are, the more valuable staging is…

Expanded NPV (with option)

0

5

10

15

20

25

30

10

%

20

%

30

%

40

%

50

%

60

%

70

%

80

%

90

%

10

0%

11

0%

Uncertainty (volatility)

Net Present Value + Option Value

50

Value of Delaying Decisions

Time

Reqt’s Design Coding Test Production

Cost of Change?Traditional Assumption

But, what if it were flat?

51

Constant Cost of Change

You could implement the feature today, at a cost of $10

You think it might be worth $15 in benefits... We’ll know in a year!

Great uncertainty

Upside scenario: Customer is grateful

Downside scenario: Customer couldn’t care less––you wasted time and money

You are thinking of implementing a new feature*…

*Source: Beck, Extreme Programming Explained (2000)

52

Option Value of Waiting

$15.00 PV of deferrable feature’s expected benefits$10.00 Cost of implementation

$5.00 Net Present Value of immediate implementation

5% The risk-free interest rate1.0 Years until implementation decision must be taken100% Volatility of feature’s benefit

$7.5* Option value of deferred implementation

*Option value calculated using the standard formula for the price of a call option (Black & Scholes, 1973).

53

Option Value of Waiting Under DifferentChange Cost Models

Cost of Change

0

20

40

60

80

100

120

0 2 4 6 8 10 12 14 16 18 20 22 24

Time (months)

$

Traditional

Flattened

Two different Cost of Change curves

54

To Wait or Not to Wait?

Value of Waiting

0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14 16 18 20 22 24

Time (months)

$

Traditional

Flattened

Traditional: Do it now

Flattened: If it will take more than 9 months for uncertainty to resolve, wait; otherwise do it now

Benchmark NPV

55

Rules of Thumb for Delay Decisions

Traditional Flattened Constant

Un

cert

ain

ty /

Tim

e H

ori

zon

Cost of Change

Sooner Sooner

Sooner Later

Later

Later

Hig

h /

Lo

ng

Lo

w /

Sh

ort

56

SummaryHow Economic Value is Created?

Flexible Practices

Strategic Management

EconomicValue

… increase ability to respond to changing

conditions… encourage learning…support incremental

development…help manage risk

… give rise to options

… makes options valuable

… increases value of options

Uncertainty

BusinessTechnology

RequirementsMarket

… is created & increased by• early value realization

• deferral of large commitments when warranted

• rational exercise of underlying options

IterativeApproaches

… realize value early… creates incentive to earn

early and spend late

Time Valueof Money