The value of flexibility

The value of flexibility

Risk Management & Real Options VII. The Value of Information Stefan Scholtes Judge Institute of Management University of Cambridge MPhil Course 2004-05 Course content I. II. III. IV. V. VI. Introduction The forecast is always wrong I. The industry valuation standard: Net Present Value II. Sensitivity analysis 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 Developing valuation models I. Easybeds revisited Designing a system means sculpting its value shape I. CASE: Designing a Parking Garage I II. The flaw of averages: Effects of system constraints Coping with uncertainty I: Diversification I. The central limit theorem II.

The effect of statistical dependence III. Optimising a portfolio 2 September 2004 VII. Scholtes 2004 Coping with uncertainty II: The value of information I. II. SKILL: Decision Tree Analysis CASE: Market Research at EPhone Page 2 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 Cash flow Cash flow Probability Cash flow 2 September 2004 Scholtes 2004 Cash flow Time No 0 0 A small but realistic example Bid? SciTools Bidding No $115K 30.0% $20,000 15000 Com peting Bid? 0 Yes Yes 70.0% 80.0% $20,000 Win bid? 0 20.0% No

Yes 0 -5000 How m uch? -$5,000 No $120K 30.0% $25,000 20000 Com peting Bid? 0 Yes Yes 70.0% 40.0% $25,000 No $125K 20000 Win bid? 0 60.0% No 0 -5000 30.0% $30,000 25000 Com peting Bid? 0 Yes

Yes 2 September 2004 15000 Scholtes 2004 70.0% 10.0% $30,000 25000 Win bid? 0 No 90.0% 0 Page 4 -5000 Prevalent application areas Product development (pharmaceutical industry) Marketing (introducing a new product) Oil exploration Bidding for contracts Medical diagnosis ETC. 2 September 2004 Scholtes 2004 Page 5 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 6 Payoff table

Lists payoff for each possible scenario and each possible decision Lowest competing bid SciTo ol Bid no bid below 115,000 115,000 120,000 120,000 125,000 above 125,000 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 14% 28% 21% 7% Probabilit 30% y 2 September 2004 Scholtes 2004 Page 7 Time line of decisions and events Bid? How much? Competing bid? Win bid? Payoff Actions (under our control) 2 September 2004 Events (not under our control) Scholtes 2004

Result (function of actions and events) Page 8 No Bid? SciTools Bidding No $115K Com peting Bid? Yes Yes Win bid? No Yes How m uch? No $120K Com peting Bid? Yes Yes Win bid? No No $125K Com peting Bid? Yes Yes 2 September 2004 Scholtes 2004 Win bid? No Page 9

No 0 Bid? SciTools Bidding Probabilities of events Discounted Cash flows $115K No 30.0% $20,000 Com peting Bid? 0 Yes Yes Yes 70.0% 80.0% $20,000 Win bid? 0 No 20.0% Yes 40.0% 0 How m uch? -$5,000 No $120K

30.0% $25,000 Com peting Bid? 0 Yes 70.0% $25,000 Win bid? 0 60.0% No No $125K 30.0% $30,000 Com peting Bid? 0 Yes Yes 2 September 2004 0 Scholtes 2004 70.0% 10.0% $30,000 Win bid? 0 No 90.0% 0 Page 10

No 0 0 Scenario values = sum of dcfs along path in tree Bid? SciTools Bidding No $115K 30.0% $20,000 15000 Com peting Bid? 0 Yes Yes 70.0% 80.0% $20,000 Win bid? 0 20.0% No Yes 0 -5000 How m uch? -$5,000 No $120K 30.0%

$25,000 20000 Com peting Bid? 0 Yes Yes 70.0% 40.0% $25,000 No $125K 20000 Win bid? 0 60.0% No 0 -5000 30.0% $30,000 25000 Com peting Bid? 0 Yes Yes 2 September 2004 15000 Scholtes 2004 70.0% 10.0% $30,000

25000 Win bid? 0 No 90.0% 0 Page 11 -5000 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 12 Valuing decision nodes 3,000 Expand Dont expand 1,200 Which action would you choose? 2 September 2004 Scholtes 2004 Page 13 Valuing event nodes 3,000 R&D success R&D failure - 1,200 Whats the value of this gamble? 2 September 2004 Scholtes 2004 Page 14 Valuing event nodes 3,000 R&D success 40% 60%

R&D failure - 1,200 Expected value = 0.4* 3,000-0.6* 1,200 = 480 2 September 2004 Scholtes 2004 Page 15 Valuing event nodes 3,000,000 R&D success 40% 60% R&D failure - 1,999,200 Expected value = 0.4* 3,000,000-0.6* 1,999,200 = 480 2 September 2004 Scholtes 2004 Page 16 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)

The subject of decision analysis, as an academic discipline, is largely concerned with how to put a price tag on a chance node But: Whats the correct risk premium? 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 17 No 0 0 Bid? SciTools Bidding No $115K 30.0% $20,000 15000 Com peting Bid? 0 Yes Yes 70.0% 80.0% $20,000 Win bid?

0 20.0% No Yes 0 -5000 How m uch? -$5,000 No $120K 30.0% $25,000 20000 Com peting Bid? 0 Yes Yes 70.0% 40.0% $25,000 No $125K 20000 Win bid? 0 60.0% No 0 -5000 30.0% $30,000 25000

Com peting Bid? 0 Yes Yes 2 September 2004 15000 Scholtes 2004 70.0% 10.0% $30,000 25000 Win bid? 0 No 90.0% 0 Page 18 -5000 No FALSE 0 0 0 Bid? SciTools Bidding 12200 30.0% No $115K

TRUE 0 $20,000 0.3 15000 Com peting Bid? 12200 80.0% Yes Yes Average Profit 70.0% 0 $20,000 TRUE -$5,000 11000 20.0% 0 0.14 -5000 How m uch? 12200 30.0% No $120K FALSE $25,000 0 20000 Com peting Bid?

0 9500 40.0% Yes Yes 70.0% $25,000 $125K FALSE 0 $30,000 20000 5000 30.0% No 0 Win bid? 0 60.0% No 0 0 -5000 0 25000 Com peting Bid? 6100 Yes Yes

2 September 2004 15000 Win bid? No Yes 0.56 Scholtes 2004 70.0% 0 10.0% $30,000 0 25000 Win bid? -2000 No 90.0% 0 0Page 19 -5000 Dont forget: The value is a shape! Risk Profile For SciTools Bidding of SciTools.xls 1 Probability 0.8 0.6 0.4 0.2 0 -10000 -5000 0 5000

10000 15000 20000 Value This is the value shape corresponding to the decision rule that we determined when we optimized the project by backwards induction (maximise expected 2 September 2004 Scholtes 2004 Page 20 value) 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 21 Expected Profit vs. Bid Costs 12800 Profit 12600 12400 12200 12000 E 11800 11600 4400 4600 4800 5000 5200 5400 5600 Bid Costs 2 September 2004 Scholtes 2004 Page 22 Profit Expected Profit vs. Production Costs 22000 20000

18000 16000 14000 12000 10000 8000 6000 4000 84000 86000 88000 90000 92000 94000 96000 98000 100000 102000 104000 106000 Production costs 2 September 2004 Scholtes 2004 Page 23 Profit Expected Profit vs. Probability of competing bid 12400 12350 12300 12250 12200 12150 12100 12050 12000 0.24 0.26

0.28 0.3 0.32 0.34 0.36 Probability of competing bid 2 September 2004 Scholtes 2004 Page 24 Tornado Diagram for Profit Production costs Bid Costs Probability of competing bid -80.0% -60.0% -40.0% -20.0% 0.0% 20.0% 40.0% 60.0% 80.0% % Change from Base Value 2 September 2004 Scholtes 2004 Page 25

Group-work: E-Phone case 2 September 2004 Scholtes 2004 Page 26 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 Success Survival Failure 5 Mio 2 Mio 0.8 Mio Test market 150,00 60,000 24,000 Probability of test market outcome 40% 50% 10%

Global Test effectiveness Test Success Survival Failure Success 60% 30% 10% Survival 15% 70% 15% Failure 10% 30% 60% 2 September 2004 Global -> Scholtes 2004 Page 27 Value of (imperfect) information Test provides information by changing probabilities of market scenarios

Expected value of information This is called imperfect (or sample) 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 28 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 29 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 30 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 T Miss out on economies of scale: T second stage expansion will only face 90% of demand 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 31 The value of flexibility KEY LESSON: In the presence of uncertainty managerial flexibility has considerable value But: Managerial flexibility also costs money 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 E.g. buying a larger parcel of land suitable for possible later expansion 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 32 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 33 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 34 Course content I. II. III. IV. V. VI. Introduction The forecast is always wrong I. The industry valuation standard: Net Present Value II. Sensitivity analysis 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 Developing valuation models

I. Easybeds revisited Designing a system means sculpting its value shape I. CASE: Designing a Parking Garage I II. The flaw of averages: Effects of system constraints Coping with uncertainty I: Diversification I. The central limit theorem II. The effect of statistical dependence III. Optimising a portfolio 2 September 2004 VII. Coping with uncertainty II: The value of information I. SKILL: Decision Tree Analysis CASE: Market Research at EPhone Coping with uncertainty III: The value of flexibility II. VIII. Scholtes 2004 Page 35

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