Transcript The value of flexibility - Department of Engineering

Risk Management & Real Options
II. The forecast is always wrong
Stefan Scholtes
Judge Institute of Management
University of Cambridge
MPhil Course 2004-05
NPV – the industry standard
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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
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Treat initial investment as cash outflow in period zero
But: $ 1 today is worth more than $ 1 in a year’s time
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Inflation – time value of money
Could invest $1 elsewhere – opportunity cost of capital
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Opportunity cost of capital: “Best” rate of return on alternative investment
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What does “best” mean?
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Bank account 2% p.a.
Government bond 5% p.a.
Stock market 15% p.a.
Venture capital 25% p.a.
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Rewards for risk taking
Three main risks involved in investment
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Macro-economic risk (exchange rates, GDP growth, oil price, etc.)
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Default risk
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Shared throughout the economy
Risk to debt holders: Company defaults
Equity risk
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Risk to equity holders: Future cash flows are uncertain
Want reward for taking risk
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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)
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Discounted cash flow models
Annual compounding
T oday's value of cash flow x receivedin n years
Continuous compounding
x
x
(

)
(1  d ) n
exp(nd )
Value of $1 to be received in the future
1
0.9
0.8
Present value
0.7
0.6
5%
0.5
10%
0.4
15%
0.3
0.2
0.1
0
0
5
10
15
20
25
30
Time of payment
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Discounted cash flow models
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Discount rate d reflects the annual opportunity cost of capital for a
project with a similar “level of risk” (whatever that means…)
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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)
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Present value (PV) of a project: sum of all discounted future cash flows
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Net present value (NPV) = PV minus today’s investment
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See Parking Garage.xls for an example of an NPV sheet (without tax
considerations)
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How is NPV used?
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Is this project economically sensible?
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“YES if NPV>0”
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Advise changes with discount rate
Which of several projects should we do?
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“Choose the ones with larger NPV first, until budget is exhausted”
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Ranking changes with discount rate
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What discount rate?
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Practice: Discount rate is the return expectation of the capital owners,
debtors and equity investors (“weighted average cost of capital”)
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BUT:
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Cambridge Antibody Technology (or the likes) : “…We know as a
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BP (or the likes): “…We don’t discuss discount rates. We apply a 10%
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Boeing (or the likes): “…Any sensible discount rate would wipe out all
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…”
hurdle rate to all our projects…”
our returns beyond a 15 year time horizon – but our aircraft projects
have a product life of 30+ years…”
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NPV: Plus and minus
Plus:
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Setting up an NPV model forces you to think about the logic of a
system’s value generation
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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:
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Which discount rate?
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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
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Secondly, NPV is based on a fixed plan of action
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Does not account of deviating from plan if uncertainties unfold different from
expectations (come to this later)
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Cost forecast
Ratio of actual to estimated costs for routine
airport resurfacing of runways
15
10
Per cent
of
Occur rences
5
Me dian  1.25
0.5
1.0
1.5
2.0
2.5
3.0
Re al/Es tim ate d Cos t Ratio
Source: R. de Neufville, MIT
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Oil price forecast
Source: U.S. Department of Energy, 1998
Dollars per Barrel
12
0
US DEO oil price forecasts
1982
Trend predicted
1981
10
0
80
1984
1983
1985
60
1986
1987
40 Actual
1991
20
0
1975
1995
1980
1985
1990
1995
2000
2005
Year
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Demand forecasts
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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 global market of 900,000
handsets
Today, 900,000 handsets are sold every three
days
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A first cure: Sensitivity analysis
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Simplest model: Numbers-in-numbers-out
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Need number calculator
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Sensitivity analysis = what-if analysis
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Improved model: Range-in-range-out
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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
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Typical graphical output
Sensitivity Chart
$15,000,000
$10,000,000
NPV
$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
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Tornado diagrams
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Input ranges typically specified by
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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
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Determine the highest and lowest value of the output measure as the input
variable varies over its range
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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
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Tornado Diagram
Tornado Diagram for NPV
Sales
Price
Variable costs
Maintenance
Investment costs
Plant sales
-200.0%
-150.0%
-100.0%
-50.0%
0.0%
50.0%
100.0%
150.0%
200.0%
% 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
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Problems with sensitivity analysis
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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
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“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”
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Where are we going?
I.
Introduction
II.
The forecast is always wrong
I.
II.
III.
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The industry valuation standard: Net
Present Value
Sensitivity analysis
The system value is a shape…
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