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. â€¢

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