1. Risk Management & Real Options VII. The Value of Information Stefan Scholtes Judge Institute of Management University of Cambridge MPhil Course 2004-05

2. 2 September 2004 © Scholtes 2004Page 2 Course content I. Introduction II. The forecast is always wrong I. The industry valuation standard: Net Present Value II. Sensitivity analysis III. The system value is a shape I. Value profiles and value-at-risk charts II. SKILL: Using a shape calculator III. CASE: Overbooking at EasyBeds IV. Developing valuation models I. Easybeds revisited V. Designing a system means sculpting its value shape I. CASE: Designing a Parking Garage I II. The flaw of averages: Effects of system constraints VI. Coping with uncertainty I: Diversification I. The central limit theorem II. The effect of statistical dependence III. Optimising a portfolio VII. Coping with uncertainty II: The value of information I. SKILL: Decision Tree Analysis II. CASE: Market Research at E-Phone

3. 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 flow Probability Probability Time

4. 2 September 2004 © Scholtes 2004Page 4 A small but realistic example

5. 2 September 2004 © Scholtes 2004Page 5 Product development (pharmaceutical industry) Marketing (introducing a new product) Oil exploration Bidding for contracts Medical diagnosis ETC. Prevalent application areas

6. 2 September 2004 © Scholtes 2004Page 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 bidProbability below $115,00020% $115,000 - $120,00040% $120,000 - $125,00030% above $125,00010%

7. 2 September 2004 © Scholtes 2004Page 7 Payoff table Lists payoff for each possible scenario and each possible decision Lowest competing bid no bidbelow 115,000 115,000 – 120,000 120,000 – 125,000 above 125,000 SciTool Bid No bid00000 115,00015,000- 5,00015,000 120,00020,000- 5,000 20,000 125,00025,000- 5,000 25,000 Probability30%14%28%21%7%

8. 2 September 2004 © Scholtes 2004Page 8 Time line of decisions and events Bid?  How much?  Competing bid?  Win bid?  Payoff Actions (under our control) Events (not under our control) Result (function of actions and events)

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10. 2 September 2004 © Scholtes 2004Page 10 Discounted Cash flows Probabilities of events

11. 2 September 2004 © Scholtes 2004Page 11 Scenario values = sum of dcf’s along path in tree

12. 2 September 2004 © Scholtes 2004Page 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

13. 2 September 2004 © Scholtes 2004Page 13 Valuing decision nodes £ 3,000 £ 1,200 Which action would you choose? Expand Don’t expand

14. 2 September 2004 © Scholtes 2004Page 14 Valuing event nodes £ 3,000 - £ 1,200 What’s the value of this gamble? R&D success R&D failure

15. 2 September 2004 © Scholtes 2004Page 15 Valuing event nodes £ 3,000 - £ 1,200 Expected value = 0.4* £ 3,000-0.6* £ 1,200 = £480 R&D success R&D failure 40% 60%

16. 2 September 2004 © Scholtes 2004Page 16 Valuing event nodes £ 3,000,000 - £ 1,999,200 Expected value = 0.4* £ 3,000,000-0.6* £ 1,999,200 = £480 R&D success R&D failure 40% 60%

17. 2 September 2004 © Scholtes 2004Page 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

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19. 2 September 2004 © Scholtes 2004Page 19 AverageProfit

20. 2 September 2004 © Scholtes 2004Page 20 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)

21. 2 September 2004 © Scholtes 2004Page 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.

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26. 2 September 2004 © Scholtes 2004Page 26 Group-work: E-Phone case

27. 2 September 2004 © Scholtes 2004Page 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 SuccessSurvivalFailure Global5 Mio2 Mio0.8 Mio Test market150,0060,00024,000 Probability of test market outcome 40%50%10% Test Global ->SuccessSurvivalFailure Success60%30%10% Survival15%70%15% Failure10%30%60%

28. 2 September 2004 © Scholtes 2004Page 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

29. 2 September 2004 © Scholtes 2004Page 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

30. 2 September 2004 © Scholtes 2004Page 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

31. 2 September 2004 © Scholtes 2004Page 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 ̵ second stage expansion will only face 90% of demand Miss out on economies of scale: ̵ 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?

32. 2 September 2004 © Scholtes 2004Page 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

33. 2 September 2004 © Scholtes 2004Page 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?

34. 2 September 2004 © Scholtes 2004Page 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

35. 2 September 2004 © Scholtes 2004Page 35 Course content I. Introduction II. The forecast is always wrong I. The industry valuation standard: Net Present Value II. Sensitivity analysis III. The system value is a shape I. Value profiles and value-at-risk charts II. SKILL: Using a shape calculator III. CASE: Overbooking at EasyBeds IV. Developing valuation models I. Easybeds revisited V. Designing a system means sculpting its value shape I. CASE: Designing a Parking Garage I II. The flaw of averages: Effects of system constraints VI. Coping with uncertainty I: Diversification I. The central limit theorem II. The effect of statistical dependence III. 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