Riding the - - PDF document

• S. Scholtes

Judge Institute of Management University of Cambridge 30/10/2003 1

• Riding the waves of change:

Simulating Risky Investments

• S. Scholtes

Judge Institute of Management

• Speaker: Karl Rose

(Strategic Intelligence, Shell) Topic: Managing in Darkness Time: Thursday 30 October 4.30 pm Venue: LT2

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Judge Institute of Management University of Cambridge 30/10/2003 2

• Danny and I will prepare a mock exam before the weekend. We will

let you know by email

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Judge Institute of Management University of Cambridge 30/10/2003 3

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• Projection based

techniques are too simplistic in their treatment of risk

• Cumulated project value

Time

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• Cumulated project value

Time Strategic phase: Are we doing the right thing?

• Cumulated project value

Time Strategic phase: Are we doing the right thing? Opportunity gains

• ideas matter
• period cash flows increase

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• Cumulated project value

Time Strategic phase: Are we doing the right thing? Operational phase: Are we doing things right? Opportunity gains

• ideas matter
• period cash flows increase
• Cumulated project value

Time Strategic phase: Are we doing the right thing? Operational phase: Are we doing things right? Opportunity gains

• ideas matter
• period cash flows increase

Efficiency gains

• fighting the cost battle
• cash flows positive but decreasing

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Judge Institute of Management University of Cambridge 30/10/2003 7

• Cumulated project value

Time Strategic phase: Are we doing the right thing? Operational phase: Are we doing things right? Opportunity gains

• ideas matter
• period cash flows increase

Efficiency gains

• fighting the cost battle
• cash flows positive but decreasing

Uncertainty

• Power plant investment

– Fuel price, electricity price, demand, regulation…???

• Bidding for resources (e.g. 3G bandwidth)

– Production capacity, market price, market demand, competition, political issues??

• R&D

– Technical success, market demand, regulation, …

• New product launch

– Demand-price curve, competition, production quality, brand,…

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!"

“Are you sure that we got the forecasts right?” “You can never be 100% sure with forecasts but I am fairly confident that the forecast is right.”

Source: U.S. Department of Energy, 1998

12 10 80 60 40 20 1975 1980 1985 1990 1995 2000 2005

Year

1982 Trend predicted 1981 1984 1985 1986 1987 1991 1995 Actual

Dollars per Barrel

#$$

US DEO oil price forecasts

1983

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#$$

• In the early 1980's McKinsey were hired by AT&T to forecast the growth

in the mobile phone market until the end of the millennium.

• They projected a world market of 900,000.
• Today, 900,000 handsets are sold every three days

!

• Lesson: The forecast is always wrong
• But: such projections are part of every NPV analysis
• Ergo: NPV analyses are always wrong
• Obvious fact that needs to be recognized:

– After the fact, the NPV of a project is well defined if the realised cash flows have been recorded – Before the fact, i.e. NOW, the cash flows are uncertain and hence the NPV itself is an uncertain quantity

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%$ !$&

• NPV is expected NPV

– Beware the flaw of averages

• Adjust discount rate for risky projects

Discount rate = time value of money + risk premium

• BUT: Conceptually difficult to mingle time value of money with risk

premium in one figure – If risk premium is applied to costs (negative cash flow) then the expected cost is reduced rather than increased – Global risk adjustment (at cash flow level) versus local risk adjustment (at level of input uncertainties - to account for different risk profiles of different inputs)

• '"
• Traditional NPV analysis
• Risk-enhanced NPV analysis (Monte Carlo simulation)

Inputs: Projections

• f uncertain

values Output: NPV projection Inputs: Shapes

• f uncertain

values Output: Shape of NPV

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(&

• Discount rates reflect

– Macro-economic trend: Time value of money

• “risk-free” rate, e.g. long-term government bonds

– Debt risk: Bankruptcy

• corporate bond spread - difference between corporate and

government bond rate – Equity risk: Uncertain cash flows

• risk-adjusted discount rates, CAPM-betas
• Avoid double-counting for risk!

– Sensible to discount at the corporate debt rate since MCS takes risk of cash flow fluctuation into account – Can estimate the distribution of the equity premium of the project by simulating NPV at debt rate / investment

#$

• The flaw of averages: NPV based on average inputs is NOT the

average NPV

• Flaw of averages lurks everywhere, where numbers are used to

replace uncertain quantities!

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#$

• Example: Depreciation over an uncertain lifetime (Savage 2002)
• If a piece of equipment lasts N years, then the linear depreciation

rate is 1/N per year

• Suppose a piece of equipment is equally likely to last 2,3,4,…,10

years – Average lifetime: 6 years – Flaw of averages: Average depreciation rate is 1/6=16.7%?

#$

Lifetime Depreciation rate 2 50% 3 33% 4 25% 5 20% 6 17% 7 14% 8 13% 9 11% 10 10% Average 6 21%

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#

• Simplistic example:

– Demand for a new product is highly uncertain Marketing estimates it to be anywhere between 600 and 1400 units with equal likelihood for all these demands – Unit margin is £1000 – Fixed cost for 1000 units capacity is £900,000

• What’s the profit if the mean demand is realised?
• What is the shape of profits?
• What is the expected profit?
• Managers should base their decisions on shapes of uncertain

quantities NOT on projections

• Calculated risk-taking requires that the decision makers are

INFORMED about the amount of risk they take – NPV histograms are one way of visualising risk – Value-at-risk charts are another

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• Value at Risk Chart

0.0% 10.0% 20.0% 30.0% 40.0% 50.0% 60.0% 70.0% 80.0% 90.0% 100.0%

• £5,000
• £4,000
• £3,000
• £2,000
• £1,000

£0 £1,000 £2,000 £3,000 £4,000 £5,000 Thousands

NPV target value % sampled NPVs below target

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• At Risk provides

– Fitting input distributions to data – Various random number generators – A simulation “engine” – Graphical output – Simple optimisation potential

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(*

• Start from projection-based model (number-in-number-out model)

– Identify uncertainties (colour these cells) – Identify sensible distributions for these uncertainties

• Add suitable random number generators in uncertain input cells

– Use @Risk generators if you work with @Risk – @Risk does not automatically sample but produces, on default, the mean of the generated uncertainty – This is good since you are forced to remain consistent with the projection-based model

• Mark performance measures by clicking “Add output” button
• Choose # iterations by clicking Simulation Settings button (5,000 is fine for

most purposes)

• Click Run Simulation button

#*

• Generate triangular demand between 5000 and 12,000 with peak at

10,000 – What is the mean?

• Generate uniform costs between £200 and £250
• Take price as £300
• Fix production at 10,000 with fixed costs of £ 600,000

– Cost of capacity: £100,000 fixed cost, £50 per unit capacity

• What is the profit based on projections (i.e. average inputs) ?
• What’s the expected profit?
• Produce a risk profile and copy it into an Excel spreadsheet

– Why is it not normal?

• Perform a simulation without capacity constraints (i.e. fixed cost of

production = £600,000)

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• Start from an NPV spreadsheet
• Do a sensitivity analysis

– Ask for ranges of inputs – Identify the key uncertainties in a Tornado diagram

• Do a Monte Carlo analysis on the key uncertainties

– Ask for distributions of key uncertainties

• Analyse the “tails” of the NPV distribution

– What causes the tails? – How can we re-design the project to avoid losses (left tail) and to amplify gains (right tail)? – Have we overlooked flexibility? Should we add flexibility?

""+,

• Robber plc. (Mini case from finance class)
• What are the uncertain inputs?
• Which ones are important?
• Begin by estimating ranges and do a sensitivity analysis

– Use tornado diagram button in PrecisionTree

Costs Initial investment £1,000,000 +/- 10% Annual maintenance £200,000 +/- 15% Variable costs between £12 and £16 Revenues Wholesale price £25 +/- £2 Sale of plant after 5 yrs between £100,000 and £200,000 Sales 50,000 +/- 50%

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#-

What are the key uncertainties?

Tornado Diagram for NPV

• 200.0%
• 150.0%
• 100.0%
• 50.0%

0.0% 50.0% 100.0% 150.0% 200.0% Plant sales Investment costs Maintenance Variable costs Price Sales % Change from Base Value

• One way to cope with demand uncertainty is by holding inventory
• Needs to be added to the model
• Also: Production capacity and production schedule need to be explicitly

modelled – E.g. Production = min(capacity, last year’s production) – Sales = min(demand, production)

• Finally: Demand in year 2 is not independent of demand in year 1

– We learn about demand over time – Don’t model annual demands independently but model initial demand and then demand growth/decline – Growth / decline factors are random – Distribution of factors change over time (product life cycle)

• Same applies to input prices (e.g. stock prices, oil prices, etc.) and possibly
• ther costs

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• A simple model of a demand curve
• Model: Sample initial demand then growth rates with the distributions of

growth rates changing over time

• Sample appropriate rates from historical growth / decline data
• Work with your marketing people towards a sensible (simple and relevant)

demand model

time

demand growth maturity decline

""+,,

Costs Distribution low most likely high Initial investment £1,000,000 +/- 10% triangular £900,000 £1,000,000 £1,100,000 Annual maintenance £200,000 +/- 15% triangular £170,000 £200,000 £230,000 Variable costs between £12 and £16 uniform £12 £16 Inventory costs between £0.50 and £1.50 uniform £0.50 £1.50 Revenues Wholesale price £25 +/- £2 uniform £23 £27 Sale of plant after 5 yrs between £100,000 and £200,000 uniform £100,000 £200,000 Sale of inventory after 5 yrs £10 +/- 100% triangular £0 £10 £20 Demand 50,000 +/- 50% triangular 25,000 50,000 75,000 Annual demand change between -10% and +10% uniform

• 10%

10%

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,./

• Can now choose project design parameters, e.g. plant capacity, so

that NPV is “maximal “ – Suppose investment cost is 30% fixed cost and 70% linearly dependent on capacity (variable cost of capacity)

• Notice the difference between optimising capacity in a projection-

based model or a Monte-Carlo model

• Capacity has an “option” flavour: You pay for it up-front for the right

but not the obligation to produce if and when demand is high – “Real options” view of capacity

0*

• Analysis is a never-ending journey…
• Risk profile provides you with an idea about the project performance in

– average case (middle part) – worst case (left tail) – best case (right tail)

• Given a performance profile, you can ask yourself

– How can I change the design of the project to

• cut losses (cut down the left tail)?
• amplify gains (enlarge the right tail)?
• MCS is a great vehicle for project design optimisation

– More on this in the Real Options elective

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1

• To cope with the large demand uncertainty, we could build a small

plant, say with 45000 capacity first and then expand it after year 1 if the year 1 demand is sufficiently large, say larger than X

• Expansion decision can be included in the year 2 column of the

simulation model If ( demand in year 1 > X, “Expand”, “Don’t Expand”)

• We can then use if statements to add expansion cost and extra

capacity after year 2 if the decision was to expand

• Decision is invoked by a DECISION RULE (If statement)

If the demand in year 1 is larger than X then expand by Y

#20$

• Start from an NPV spreadsheet
• Do a sensitivity analysis

– Ask for ranges of inputs – Identify the key uncertainties in a Tornado diagram

• Do a Monte Carlo analysis on the key uncertainties

– Ask for distributions of key uncertainties

• Analyse the “tails” of the NPV distribution

– What causes the tails? – How can we re-design the project to avoid losses (left tail) and to amplify gains (right tail)? – Have we overlooked flexibility? Should we add flexibility?

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(*

The Key Lessons of the course:

• Management Analysis is not a destination but an exploratory journey

– Building a computer model forces you to communicate your understanding of the business process in unambiguous terms to the computer – This helps you clarify your understanding of the business process

• Management Analysis is useless if it cannot be communicated broadly

– Find a sensible trade-off between simplicity and relevance – Use the tools sensibly, always backed up by intuition

• Management Analysis is not a contrast to good business intuition but a

complement to it – Forces you to formulate how your intuition translates into profit

**

• Please use your modelling skills in other courses (core or elective)

during the programme

• Core course material will be further expanded in two electives

(provided there is sufficient demand) – Risk Analysis and Real Options Valuation (tbc) – Revenue Management (tbc) – Same workshop-type style as the core course

• Typical set-up for an elective is a two-day workshop,

followed by a group project and an individual project report

• We are happy to supervise Individual Research Projects with a

quantitative business analysis angle