Risk Management & Real Options
VII. The Value of Information
Stefan ScholtesJudge Institute of Management
University of Cambridge
MPhil Course 2004-05
2 September 2004 © Scholtes 2004 Page 2
Course content
I. IntroductionII. The forecast is always wrong
I. The industry valuation standard: Net Present Value
II. Sensitivity analysisIII. The system value is a shape
I. Value profiles and value-at-risk charts
II. SKILL: Using a shape calculatorIII. CASE: Overbooking at EasyBeds
IV. Developing valuation modelsI. Easybeds revisited
V. Designing a system means sculpting its value shapeI. CASE: Designing a Parking Garage
III. The flaw of averages: Effects of
system constraintsVI. Coping with uncertainty I:
DiversificationI. The central limit theoremII. The effect of statistical
dependenceIII. Optimising a portfolio
VII. Coping with uncertainty II: The value of information
I. SKILL: Decision Tree Analysis
II. CASE: Market Research at E-Phone
2 September 2004 © Scholtes 2004
Decision Trees
Graphical tool for analysing decisions under risk• Helps to structure the decisions to be made• Shows the dependency of the decisions on uncertain events
Useful when • a sequence of decisions has to be made• the result of each decision is influenced by uncertain events• we have some information about the probability of each event
Cash flowCash flow
Cash flowCash flow
Cash flowCash flow
ProbabilityProbability
ProbabilityProbability
Cash flowCash flow
Cash flowCash flow
TimeTime
2 September 2004 © Scholtes 2004 Page 4
0 0
Bid?
30.0%
$20,000 15000
Competing Bid?
0
80.0%
$20,000 15000
70.0% Win bid?
0
20.0%
0 -5000
How much?
-$5,000
30.0%
$25,000 20000
Competing Bid?
0
40.0%
$25,000 20000
70.0% Win bid?
0
60.0%
0 -5000
30.0%
$30,000 25000
Competing Bid?
0
10.0%
$30,000 25000
70.0% Win bid?
0
90.0%
0 -5000
SciTools Bidding
No
Yes
$115K
$120K
$125K
No
Yes
No
Yes
No
Yes
Yes
No
Yes
No
Yes
No
A small but realistic exampleA small but realistic example
2 September 2004 © Scholtes 2004 Page 5
Product development (pharmaceutical industry) Marketing (introducing a new product) Oil exploration Bidding for contracts Medical diagnosis ETC.
Prevalent application areas
2 September 2004 © Scholtes 2004 Page 6
SciTools Case (W/A)
SciTools Inc. specialises in scientific instruments Invited to bid for government contract
• Deliver a specific number of instruments• Sealed bid auction, lowest bid wins
$5,000 to prepare bid Cost of instruments to be delivered: $95,000 SciTools estimates a 30% chance of no competing bid If there is a competing bid, past contract data suggests the
following ranges and probabilities
Lowest competing bid Probability
below $115,000 20%
$115,000 - $120,000 40%
$120,000 - $125,000 30%
above $125,000 10%
2 September 2004 © Scholtes 2004 Page 7
Payoff table
Lists payoff for each possible scenario and each possible decision
Lowest competing bid
no bid below 115,000
115,000 –120,000
120,000 – 125,000
above 125,000
SciToolBid
No bid 0 0 0 0 0
115,000 15,000 - 5,000 15,000 15,000 15,000
120,000 20,000 - 5,000 - 5,000 20,000 20,000
125,000 25,000 - 5,000 - 5,000 - 5,000 25,000
Probability
30% 14% 28% 21% 7%
2 September 2004 © Scholtes 2004 Page 8
Time line of decisions and events
Bid? How much? Competing bid? Win bid? Payoff
ActionsActions(under our control)(under our control)
EventsEvents(not under our control)(not under our control)
ResultResult(function of actions(function of actions
and events)and events)
2 September 2004 © Scholtes 2004 Page 9
Bid?
Competing Bid?
Win bid?
How much?
Competing Bid?
Win bid?
Competing Bid?
Win bid?
SciTools Bidding
No
Yes
$115K
$120K
$125K
No
Yes
No
Yes
No
Yes
Yes
No
Yes
No
Yes
No
2 September 2004 © Scholtes 2004 Page 10
0
Bid?
30.0%
$20,000
Competing Bid?
0
80.0%
$20,000
70.0% Win bid?
0
20.0%
0
How much?
-$5,000
30.0%
$25,000
Competing Bid?
0
40.0%
$25,000
70.0% Win bid?
0
60.0%
0
30.0%
$30,000
Competing Bid?
0
10.0%
$30,000
70.0% Win bid?
0
90.0%
0
SciTools Bidding
No
Yes
$115K
$120K
$125K
No
Yes
No
Yes
No
Yes
Yes
No
Yes
No
Yes
No
DiscountedDiscountedCash flowsCash flows
Probabilities of Probabilities of eventsevents
2 September 2004 © Scholtes 2004 Page 11
0 0
Bid?
30.0%
$20,000 15000
Competing Bid?
0
80.0%
$20,000 15000
70.0% Win bid?
0
20.0%
0 -5000
How much?
-$5,000
30.0%
$25,000 20000
Competing Bid?
0
40.0%
$25,000 20000
70.0% Win bid?
0
60.0%
0 -5000
30.0%
$30,000 25000
Competing Bid?
0
10.0%
$30,000 25000
70.0% Win bid?
0
90.0%
0 -5000
SciTools Bidding
No
Yes
$115K
$120K
$125K
No
Yes
No
Yes
No
Yes
Yes
No
Yes
No
Yes
No
Scenario values = Scenario values = sum of dcf’s sum of dcf’s along path in treealong path in tree
2 September 2004 © Scholtes 2004 Page 12
Valuing a tree
Each path through the tree has a value - but which path will the project take?
• Control at decision nodes• Chance at chance nodes
Want to optimise decision: Choose the decision that maximises the value of the project
• Value at decision point depends on the future• But value at a point in the future does not depend on how I reached
this point• Sunk cost argument – think forward, not backwards
Key idea: When valuing the nodes, start in the future, not in the past!
• We know the value of the project at all possible final states• Go backwards in time, valuing nodes successively
2 September 2004 © Scholtes 2004 Page 13
Valuing decision nodes
£ 3,000£ 3,000
£ 1,200£ 1,200
Which action would you choose?Which action would you choose?
ExpandExpand
Don’t expandDon’t expand
2 September 2004 © Scholtes 2004 Page 14
Valuing event nodes
£ 3,000£ 3,000
- £ 1,200- £ 1,200
What’s the value of this gamble? What’s the value of this gamble?
R&D successR&D success
R&D failureR&D failure
2 September 2004 © Scholtes 2004 Page 15
Valuing event nodes
£ 3,000£ 3,000
- £ 1,200- £ 1,200
Expected value = 0.4* £ 3,000-0.6* £ 1,200 = £480Expected value = 0.4* £ 3,000-0.6* £ 1,200 = £480
R&D successR&D success
R&D failureR&D failure
40%40%
60%60%
2 September 2004 © Scholtes 2004 Page 16
Valuing event nodes
£ 3,000,000£ 3,000,000
- £ 1,999,200- £ 1,999,200
Expected value = 0.4* £ 3,000,000-0.6* £ 1,999,200 = £480Expected value = 0.4* £ 3,000,000-0.6* £ 1,999,200 = £480
R&D successR&D success
R&D failureR&D failure
40%40%
60%60%
2 September 2004 © Scholtes 2004 Page 17
Risk aversion
KEY PROBLEM: If you want to “optimise” your actions you must put a “price-tag” on the chance nodes
• How else would you know how to choose the “best” action?
People are risk-averse and want to be rewarded for risk taking• Simple solution: use risk-premium to discount expected values
Value = Expected Value / (1 + Risk Premium)• But: What’s the “correct” risk premium?
The subject of decision analysis, as an academic discipline, is largely concerned with “how to put a price tag on a chance node”
• Utility theory, real options, etc.
For the sake of this course we assume that decision makers work with expectations, possibly adjusted by risk-premium discounting
2 September 2004 © Scholtes 2004 Page 18
0 0
Bid?
30.0%
$20,000 15000
Competing Bid?
0
80.0%
$20,000 15000
70.0% Win bid?
0
20.0%
0 -5000
How much?
-$5,000
30.0%
$25,000 20000
Competing Bid?
0
40.0%
$25,000 20000
70.0% Win bid?
0
60.0%
0 -5000
30.0%
$30,000 25000
Competing Bid?
0
10.0%
$30,000 25000
70.0% Win bid?
0
90.0%
0 -5000
SciTools Bidding
No
Yes
$115K
$120K
$125K
No
Yes
No
Yes
No
Yes
Yes
No
Yes
No
Yes
No
2 September 2004 © Scholtes 2004 Page 19
FALSE 0
0 0
Bid?
12200
30.0% 0.3
$20,000 15000
TRUE Competing Bid?
0 12200
80.0% 0.56
$20,000 15000
70.0% Win bid?
0 11000
20.0% 0.14
0 -5000
TRUE How much?
-$5,000 12200
30.0% 0
$25,000 20000
FALSE Competing Bid?
0 9500
40.0% 0
$25,000 20000
70.0% Win bid?
0 5000
60.0% 0
0 -5000
30.0% 0
$30,000 25000
FALSE Competing Bid?
0 6100
10.0% 0
$30,000 25000
70.0% Win bid?
0 -2000
90.0% 0
0 -5000
SciTools Bidding
No
Yes
$115K
$120K
$125K
No
Yes
No
Yes
No
Yes
Yes
No
Yes
No
Yes
No
AverageAverageProfitProfit
2 September 2004 © Scholtes 2004 Page 20
Risk Profile For SciTools Bidding of SciTools.xls
0
0.2
0.4
0.6
0.8
1
-10000 -5000 0 5000 10000 15000 20000
Value
Prob
abili
ty
Don’t forget: The value is a shape!
This is the value shape corresponding to the decision rule that we determined when we “optimized” the project by backwards induction (maximise expected value)
2 September 2004 © Scholtes 2004 Page 21
Sensitivity analysis
Managerial analyses are based on projections and subjective judgement
• Even if past data is used extensively, why should the future be similar to the past?
“Shake the ladder before you climb it”: Test how robust your conclusions are w.r.t. your input assumptions
• Probabilities on branches• Costs• Demand• Market prices• Etc.
2 September 2004 © Scholtes 2004 Page 22
Expected Profit vs. Bid Costs
11600
11800
12000
12200
12400
12600
12800
4400 4600 4800 5000 5200 5400 5600
Bid Costs
Pro
fit
E
2 September 2004 © Scholtes 2004 Page 23
Expected Profit vs. Production Costs
400060008000
10000120001400016000180002000022000
84000 86000 88000 90000 92000 94000 96000 98000 100000 102000 104000 106000
Production costs
Pro
fit
2 September 2004 © Scholtes 2004 Page 24
Expected Profit vs. Probability of competing bid
120001205012100121501220012250123001235012400
0.24 0.26 0.28 0.3 0.32 0.34 0.36
Probability of competing bid
Pro
fit
2 September 2004 © Scholtes 2004 Page 25
Tornado Diagram for Profit
-80.0% -60.0% -40.0% -20.0% 0.0% 20.0% 40.0% 60.0% 80.0%
Probability of competingbid
Bid Costs
Production costs
% Change from Base Value
2 September 2004 © Scholtes 2004 Page 27
ePhone product launch
Fixed cost of 5 Mio units production facility = $60 Mio Unit margin = $20 Mio Cost of test market = $ 5 Mio Demand scenarios
Test effectiveness
Success Survival Failure
Global 5 Mio 2 Mio 0.8 Mio
Test market 150,00 60,000 24,000
Probability of test market outcome
40% 50% 10%
Test Global -> Success Survival Failure
Success 60% 30% 10%
Survival 15% 70% 15%
Failure 10% 30% 60%
2 September 2004 © Scholtes 2004 Page 28
Value of (imperfect) information
Test provides information by changing probabilities of market scenarios
• This is called imperfect (or “sample”) information
Expected value of information• = expected value with information – expected value w/o information
Example:• Expected value with information = Test “yes” branch w/o cost of test• = $ 2,288+5,000=$7,288• Expected value w/o information = Test “no” branch• = $ 0 (no launch)
Expected value of imperfect information = $ 7,288,000• Maximal price that the company might be willing to pay for the test
2 September 2004 © Scholtes 2004 Page 29
Value of perfect information
Thought experiment: • What would we be willing to pay for an oracle that could tell us the
state of the market in advance?
Key: which probabilities should we assign to the outcome of the oracle?
• Probabilities should be our best estimates of probabilities without doing a test
• Success probability for the oracle will be 100%
Can update decision tree to obtain value of perfect information = $13,000,000
Effectiveness of the test market: • Value of imperfect information (test market) is roughly 56% of the
value of perfect information
2 September 2004 © Scholtes 2004 Page 30
Capacity optimization
Sales projection of 5 Mio units for success scenario is due to capacity constraint
Demand for success scenario is projected to be 7 Mio units
$ 60 Mio fixed cost of production facility= $ 10 Mio fixed cost, independent of capacity+ $ 50 Mio for capacity of 5 Mio units
Variable cost of capacity is $ 10 per unit
2 September 2004 © Scholtes 2004 Page 31
Staged project
Alternative: Start small and expand if and when the market is good enough
Company needs to pay for this flexibility up-front (before exercising it)
• Buy a suitably large parcel of land now for $ 5 Mio
Further costs• Potential loss of sales in high market scenario due to low initial
capacity T̵ second stage expansion will only face 90% of demand
• Miss out on economies of scale: T̵ Pay fixed costs of $10 Mio again if flexibility is exercised
Is the staged project preferable to large capacity up-front?• Value of the single stage project with higher capacity is only $ 3,8 Mio• How can the staging possibly play in the extra $15 Mio of fixed costs
plus the potential loss in demand?
2 September 2004 © Scholtes 2004 Page 32
The value of flexibility
KEY LESSON: In the presence of uncertainty managerial flexibility has considerable value
But: Managerial flexibility also costs money• E.g. buying a larger parcel of land suitable for possible later expansion
Need to trade off cost of flexibility against value of flexibility One way to quantify the value of managerial flexibility is to
compare the “value” of the “passive” project with that of the “flexible project”
• Expected value of flexibility = expected value of flexible project w/o cost of flexibility MINUS expected value of passive project
In our case: value of the passive project (with optimized capacity) = $ 4.030 M, value of the flexible project = $ 4.915 M, cost of flexibility = $ 1.000 M
Value of flexible project w/o cost of flexibility = $ 4.915M +$1.000M = $5.915 M
Value of flexibility = $5.915M - $4.030M= $1.885 M is larger than the cost of flexibility of $1.000 M
2 September 2004 © Scholtes 2004 Page 33
Recap Decision Analysis
MOST IMPORTANT ASPECT: DECISION TREES GIVE YOU A MODELLING TEMPLATE TO UNDERSTAND AND COMMUNICATE A DECISION PROBLEM
• Structure problem as a sequence of decisions and events
SECONDARY ASPECT: Can “optimise” decisions and value the project through “Roll-back” or “Fold-back” of the tree
KEY PROBLEM: HOW DO YOU PUT A PRICE TAG ON CHANCE NODES?
2 September 2004 © Scholtes 2004 Page 34
Recap Decision Analysis
Risk Profiles• Decision tree valuation using expected values assume risk
neutrality• Risk profiles provide useful additional information
Sensitivity Analysis• Probabilities and other inputs represent judgement, which includes
experience and information• Any single number is likely to be wrong
Expected value of information• The economic value of gathering more information can be
calculated before making a decision Expected value of flexibility
• The economic value of additional managerial flexibility can be incorporated into your analysis
2 September 2004 © Scholtes 2004 Page 35
Course content
I. IntroductionII. The forecast is always wrong
I. The industry valuation standard: Net Present Value
II. Sensitivity analysisIII. The system value is a shape
I. Value profiles and value-at-risk charts
II. SKILL: Using a shape calculatorIII. CASE: Overbooking at EasyBeds
IV. Developing valuation modelsI. Easybeds revisited
V. Designing a system means sculpting its value shapeI. CASE: Designing a Parking Garage
III. The flaw of averages: Effects of
system constraintsVI. Coping with uncertainty I:
DiversificationI. The central limit theoremII. The effect of statistical
dependenceIII. Optimising a portfolio
VII. Coping with uncertainty II: The value of information
I. SKILL: Decision Tree Analysis
II. CASE: Market Research at E-Phone
VIII. Coping with uncertainty III: The value of flexibility