Risk Management & Real Options

II. The forecast is always wrong

Stefan ScholtesJudge Institute of Management

University of Cambridge

MPhil Course 2004-05

2 September 2004 © Scholtes 2004 Page 2

NPV – the industry standard

Aim: Value a project that requires an investment now and generates future cash flows over several periods, say several years

Naïve: Value = sum of cash inflows – cash outflows• Treat initial investment as cash outflow in period zero

But: $ 1 today is worth more than $ 1 in a year’s time• Inflation – time value of money• Could invest $1 elsewhere – opportunity cost of capital

Opportunity cost of capital: “Best” rate of return on alternative investment

What does “best” mean? • Bank account 2% p.a.• Government bond 5% p.a.• Stock market 15% p.a.• Venture capital 25% p.a.

2 September 2004 © Scholtes 2004 Page 3

Rewards for risk taking

Three main risks involved in investment

Macro-economic risk (exchange rates, GDP growth, oil price, etc.)• Shared throughout the economy

Default risk• Risk to debt holders: Company defaults

Equity risk• Risk to equity holders: Future cash flows are uncertain

Want reward for taking risk

Taking macro-economic risk is rewarded by government bond rate

Taking default risk is rewarded by corporate spread = corporate debt rate – government bond rate

Equity risk is reflected in company’s “beta” (CAPM Finance textbook)

2 September 2004 © Scholtes 2004 Page 4

Discounted cash flow models

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years in received flowcash of valuesToday'nd

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Value of $1 to be received in the future

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0.2

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Time of payment

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sen

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5%

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Annual compounding Continuous compounding

2 September 2004 © Scholtes 2004 Page 5

Discounted cash flow models

Discount rate d reflects the annual opportunity cost of capital for a project with a similar “level of risk” (whatever that means…)

• The higher the discount rate, the lower the present value of a future cash outflow (positive cash flow)

• The higher the discount rate, the lower the present value of a future cash inflow (negative cash flow)

Present value (PV) of a project: sum of all discounted future cash flows

Net present value (NPV) = PV minus today’s investment

See Parking Garage.xls for an example of an NPV sheet (without tax considerations)

2 September 2004 © Scholtes 2004 Page 6

How is NPV used?

Is this project economically sensible? • “YES if NPV>0”• Advise changes with discount rate

Which of several projects should we do?• “Choose the ones with larger NPV first, until budget is exhausted”• Ranking changes with discount rate

2 September 2004 © Scholtes 2004 Page 7

What discount rate?

Practice: Discount rate is the return expectation of the capital owners, debtors and equity investors (“weighted average cost of capital”)

BUT:

Cambridge Antibody Technology (or the likes) : “…We know as a relatively young biotech company we should have a discount rate of 20%+. But if we were applying discount rates of this order, we wouldn’t do a single project…”

BP (or the likes): “…We don’t discuss discount rates. We apply a 10% hurdle rate to all our projects…”

Boeing (or the likes): “…Any sensible discount rate would wipe out all our returns beyond a 15 year time horizon – but our aircraft projects have a product life of 30+ years…”

2 September 2004 © Scholtes 2004 Page 8

NPV: Plus and minus

Plus: Setting up an NPV model forces you to think about the logic of

a system’s value generation• What are the key ingredients: costs, revenues• What are the key drivers: demand, prices, unit costs, fixed costs,

etc.• What are the major tax implications: depreciation, etc.

Minus: Which discount rate? Even more important: NPV calculation is based on projections

of uncertain future demand, prices, unit costs, fixed costs, etc., and

THE FORECAST IS ALWAYS WRONG

Secondly, NPV is based on a fixed plan of action• Does not account of deviating from plan if uncertainties unfold

different from expectations (come to this later)

2 September 2004 © Scholtes 2004 Page 9

Cost forecast

0.5 1.0 1.5 2.0 2.5 3.0

15

10

5

Percent of

Occurrences

Median 1.25

Real/Estimated Cost Ratio

Ratio of actual to estimated costs for routine airport resurfacing of runways

Source: R. de Neufville, MIT

2 September 2004 © Scholtes 2004 Page 10

Source: U.S. Department of Energy, 1998Source: U.S. Department of Energy, 1998

121200

101000

8080

6060

4040

2020

0019751975 19801980 19851985 19901990 19951995 20002000 20052005

YearYear

1982

Trend predicted 1981

1984

1985

1986 1987

1991

1995

ActualDo

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Do

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arr

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Oil price forecast

US DEO oil price forecastsUS DEO oil price forecasts

1983

2 September 2004 © Scholtes 2004 Page 11

Demand forecasts

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 global market of 900,000 handsets

Today, 900,000 handsets are sold every three days

2 September 2004 © Scholtes 2004 Page 12

A first cure: Sensitivity analysis

Simplest model: Numbers-in-numbers-out• Need number calculator

Sensitivity analysis = what-if analysis

Improved model: Range-in-range-out• Calculate the range of output values corresponding to a range of

input values of one uncertain variable• Vary one variable at a time

Easily done in a spreadsheet

2 September 2004 © Scholtes 2004 Page 13

Typical graphical output

Sensitivity Chart

-$15,000,000

-$10,000,000

-$5,000,000

$0

$5,000,000

$10,000,000

$15,000,000

$24.00 $29.00 $34.00 $39.00 $44.00

Oil Price

NP

V

2 September 2004 © Scholtes 2004 Page 14

Tornado diagrams

Input ranges typically specified by • Base value (“most likely”)• Pessimistic value • Optimistic value

Base-case: Calculate base value for the output measure (e.g. NPV) on the basis of base values for inputs

Tornado bar: For each input variable• Determine the highest and lowest value of the output measure as

the input variable varies over its rangeR̵ Extremes of output measure typically achieved at either end of the input

range• Determine the range of percentage deviations of the output from its

base value as input varies over its range

Rank the input variables by their impact on percentage deviation of the output variable from the base value

2 September 2004 © Scholtes 2004 Page 15

Tornado Diagram

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

Illustrates the effect of a RANGE of values of one input variable on the performance measure

E.g.: The “variable cost range” can change the performance measure by more than 100% to either side of its base value

2 September 2004 © Scholtes 2004 Page 16

Problems with sensitivity analysis

Vary uncertainties one-by-one

Varying many inputs simultaneously over their ranges and recording the highest and lowest value of the output measure leads to a huge range of the output measure

• “End-range” scenarios are overly pessimistic or overly optimistic• Difficult to incorporate dependencies of variables (e.g. dependence

of price on demand)

Scenarios are played out for us but we don’t know how likely they are!

Need to enter the world of probability to understand the notion of “likelihood”

2 September 2004 © Scholtes 2004 Page 17

Where are we going?

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…