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The Actuary The magazine of the Institute & Faculty of Actuaries
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Real options a practitioner’s guide

THE AUTHORS OF THIS GUIDE claim that within ten years, real
option analysis (ROA) will supersede standard net present
value (NPV) techniques in the valuation of capital projects,
ie those where an initial investment is made to generate
uncertain future cashflows. They go further, and state that
NPV consistently underestimates the value of projects. What is the
basis of their claim?
First, I should clarify what they are talking about. The standard
NPV method (with which all actuaries are familiar) discounts the
expected future cashflows (positive and negative) to the present and
subtracts from the net total the investment required the project
goes ahead if the answer is positive and bigger than alternative projects.
The discount rate usually reflects the opportunity cost of capital,
eg the weighted average cost of capital (WACC) based on the
returns required by the company’s bondholders and shareholders.
The NPV method came to be widely accepted by firms during the
1960s and 1970s, helped by the growing power of computers.
Real and financial options
From the outset, and during the life of a project, management has
considerable flexibility, for instance, to defer, expand, contract,
extend the life of, or abandon the project. These are real options
where management has the right, but not the obligation, to take a
course of action at some cost (the exercise price) for a period of time
(the life of the option). Options to defer, expand, and extend are like
American calls, options to contract or abandon like American puts.
Like financial options, the value of real options depends on parameters
such as the value and riskiness (volatility) of the underlying
project, the exercise price, time to expiry, risk-free rate of interest
and any cash outflows (dividends). Unlike financial options the
underlying project is not an asset traded in the market which cannot
be influenced by the option holder. This makes the parameters
more difficult to estimate.
In reality more complex options are encountered, eg compound
and switching options. Compound options occur where a second
option becomes live, depending on the outcome of a first option,
for instance where the investment is phased. Switching options
occur when (at a cost) you can switch from one mode to another,
eg closing or reopening a mine starting up another power generator
to cope with peak loads.
Who uses real option analysis?
The book mentions industries where the initial (and contingent)
capital investments required are on a massive scale, eg aircraft and
car manufacturing, oil and mineral extraction, or pharmaceutical
research and development. Clearly, one must attach proper values
to the real options held by management or offered to customers.
(ROA not only provides values, but also the rules to choose between
courses of action). Interestingly, there is an example of a real option
taken from the US life insurance industry. During the late 1960s
policyholders were given lifelong options to borrow against the policy
value at 9%, interest rates having been low for some time. In the
early 1980s, Treasury Bills were yielding 17% and millions of policyholders
decided to take loans, leading to insolvent insurers.
Valuing real options
In order to illustrate the authors’ argument, it is helpful
to consider a simple example, of my own construction,
of valuing a deferral option using ROA. It
also shows how NPV and DTA (decision tree analysis
a more sophisticated form of NPV) fail to calculate
the value of flexibility correctly.
You have the choice between investing 100 now to
produce an uncertain cashflow in one year of 120 or
80 with equal chance; or waiting a year when the outcome
will be certain but the investment required then
will be 110. The risk-free rate is 5%, WACC is 15%.
What should you do?
The standard NPV method assumes you pre-commit
now, so the value of the alternatives are:
NPV (invest now)
= -100 + [(0.5°â€”120) + (0.5 °â€” 80)”/1.15
= -100 + 86.96
= -13.04
NPV (defer)
= [(0.5 °â€”120) + (0.5 °â€” 80) ”/1.15 110/1.05
= -17.80
So the NPV value of the option is -17.80 minus
(-13.04) which equals -4.76. According to this, one
should not invest now, and deferring is even worse.
DTA attempts to be more rational by anticipating
that, on deferral, the investment would only take
place if the known outcome is 120, ie DTA attempts to
incorporate flexibility.
DTA (defer)
= (0.5 °â€”(120 -110))/1.15
= 4.35
So the DTA value of the option is 4.35 minus (-13.04)
which equals 17.39. According to this, flexibility has
positive value and one should invest in a year.
ROA says that although this looks reasonable, it violates
the principle of ‘no arbitrage’, or law of one price.
Another way of saying this is that while the 15% discount
rate is appropriate for uncertain cashflows of
120 or 80, it is not correct when the cashflows are
affected by the option. In this case one must find a
portfolio which replicates the cashflows of the project
with flexibility to value it correctly (or equivalently,
use the mathematical device of ‘risk-neutrality’). But
how to find a traded security on which to base this
portfolio?
The authors regard this search as futile and instead
make the crucial assumption that the NPV without
flexibility can be used as a substitute security. So if we
have m units of risky security and B units of bond,
then the replicating portfolio would
produce the following pay-offs after
one year:
(m °â€”120)+(B °â€” 1.05)=120 11=10
(m °â€” 80)+(B °â€”1.05)=0
Implying m = 0.25 and B = -19.05
so that the current value is
(0.25 °â€” 86.96) minus 19.05 which is
equal to 2.69. So ROA value of option
is 2.69 minus (-13.04) which equals
15.73.
The book gives worked examples
of all types of simple, compound,
and switching options. Readers may
be relieved to know that stochastic calculus (often
used for financial options) is avoided in favour of
binomial (and quadranomial) lattices, which are
essentially tree diagrams with simple arithmetic functions
with which spreadsheets can cope quite easily.
This has a theoretical basis as well as a practical
motive, eg the impact of regulatory decisions is a discontinuous
process.
When is ROA most useful?
ROA is most valuable at the conjunction of three
events:
°ª when the NPV is close to zero or small relative to
the size of investment;
°ª when there is great uncertainty about the future (eg
when significant new information is likely to arise);
°ª when management has a lot of flexibility in
responding.
Note that by increasing the value of projects, ROA is
not just a method of accepting projects that would
have been rejected by NPV the cost of the option
may exceed its value.
Clear style
I have not compared this book to others, but I found
the style clear and the workings easy to follow. I was
impressed by how much theory and practice was covered
in a relatively short book without the content
becoming ‘dense’.
ROA is still being developed but does seem to be a
logical progression from standard NPV techniques for
evaluating diverse types of capital projects. For ROA to
be widely accepted, management would have to feel
comfortable with the additional complexity, and feel
that it is justified by the benefit of attaching explicit
values and decision rules to flexibility. •

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