"Economics defines investment as the act of incurring an immediate
cost in the expectation of future rewards"
(Dixit & Pindyck, 1994, p.3)
Three important investment decision characteristics are relevant in Real Options Approach:
Most investments are like a call option on a
common stock, that gives the holder the right to make an investment and
receive a project (see the call option
analogy). The project value fluctuates stochastically and most
investments options (or investment opportunities) are not a "now or
never" opportunity. There is a value of waiting to invest. You will
exercise the option (not the obligation) of investment only if the project
is sufficiently "deep in the money". In others words, if the
project's output price and/or the dividend yield of the project
are sufficiently high.
Some financial options solutions may be useful in the real investments
context (with some relevant adaptations and parameters interpretations)
using analogies like the dividend yield
analogy.
The return of an investment, like the return of a stock, comprises the addition of two parcels: the capital gain and the dividends. Over the time, the expected rate of return from a real investment is equal the sum of the expected growth rate (capital gain rate) plus the dividend yield (net cash flow distribution rate or the convenience yield of the underlying commodity, depending of context), see the next equation:
The expected rate of return corresponds to the "risk-adjusted"
discounting rate, from a financial market models like the CAPM
(Capital Asset Pricing Model). In presence of managerial flexibility the
discounting rate changes over time, and the DCF approach becomes quite
complex and inadequate.
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Investments in productive capacity are, in general, irreversible: you
cannot recover all the money, if the business doesn't become prosperous.
The cost of investment is partially or completely sunk.
Petroleum examples:
But even in the partially sunk examples, there is a alternative value
for the second-hand material only if the problem is technical (a well with
low productivity or an exhausted short-lived reserve, for example). If the
problem is economic (a depressing oil's price affecting the industry as a
whole), the recovered material value is reduced to a little more than the
scrap value (the "little" is because the option value of the
material to be valuable again in next future).
There are others equipment that are valuable (much more than scrap
value) even in large industry specific crisis. Examples are electric
generators, computers, trucks, and so on, but the "market for lemons"
effect lowers the real value of the equipments. If the industry crisis is
not specific ( is a consequence from a world's recession), even these less
specific equipments values are affected (depressed) by the lower demand.
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Some few concepts:
Certainty : "refers to situations when the investor
knows with probability 1 what the return on his investment is going to be
in the future" (Levy & Sarnat, 1984,
p.77). So uncertainty is when a collection of values
(associated with respective uncertain "states of nature") can
happen, with strictly positive probabilities for, at least, two different
possible values.
Investors are assumed to have rational expectations in
that they agree on the mappings of the assets values (for all
states-of-nature along the time). See for example
Huang & Litzemberger (1988,
p.188). In others words, they have rational expectations about the
underlying stochastic processes of the assets. This is an equilibrium
model under uncertainty. See also the source
Lucas & Prescott (1971) and Muth (1961)
This concept is more powerful than the adaptive expectations from
past prices or the static expectations concept that underlies the
traditional Marshallian's microeconomic theory. For this last point and
for an example of the rational expectations at work, see
(Dixit & Pindyck, 1994, pp.219-221).
The problem is to maximize the firm's wealth, supposing as given the
assets' stochastic processes, that all the investors with rational
expectations agree when reaching the prices equilibrium.
Although some authors make a theoretic
distinction between risk and uncertainty, in finance practice these
terms are used with the same meaning. From a practical point of view, I
prefer the term uncertainty because its neutral connotation is
more appropriated for a scientific economic study (risk has
frequently a negative connotation, or emphasizes the "bad side"
of the uncertainty). The term "risk" is usual (and useful) in
financial markets and financial operations (hedging, dividend and debt
policy) in corporations, not in economic decisions.
The Two Sides of the
Uncertainty and the Asymmetry Effects:
Uncertainty means for example, that the future price of oil's barrel
will be up or down, in relation to the forecasted price. So
uncertainty has two sides: the "good" side and the "bad"
one. (See also in "Real Options by Slides" page, the picture
"The Two Sides of the Uncertainty").
Rational managers are not passive: management can revise investment and
operating decisions in response to market conditions, in order to maximize
the firm's wealth. They act to take advantage in "good times"
(market's upside) and mitigate losses in "bad times" (market's
downside). So, in presence of economic uncertainty, active management adds
value to investment opportunity, which is not captured by the traditional
use of discounted cash flows (DCF) method. See for example
Trigeorgis & Mason (1987, p.15)
For example, the ability to wait permits that the manager "see"
the evolution of the oil prices, before takes an irreversible decision to
invest in a new oilfield or abandon an old oilfield: if the oil's price
increases to a sufficiently high level (the good side of uncertainty), the
manager makes the investment in the new oilfield (in better conditions or
with less probability of losses) or reopen the old oilfield. However, if
the oil's price decreases (the bad side of uncertainty), the manager
doesn't invest in the new oilfield and can abandon the old oilfield (at a
sufficiently low price).
If the uncertainty is technical, for example a R&D investment, again
the uncertainty adds value to this opportunity: a step by step investment
reveals informations. So, a rational manager will stop the project (or
reduce the investment) if the information is unfavorable (bad side), and
continue the investment (or even speed it up) if is a favorable one (good
side).
So, an increase of uncertainty, increases the investment opportunity
value ( the opposite that tells the traditional DCF) in view of the
asymmetric manager's action in response to uncertainty. This is the
asymmetry on the value of the opportunity to invest in a project (or
option to invest), the first asymmetric effect of the uncertainty.
However, increasing the value of the option to invest doesn't mean
increasing the willingness to invest: an increase of economic
uncertainty reduces the willingness to invest (or delays the investment
decision), because the increment in the investment opportunity value is
due to the waiting value.
What side of uncertainty is more important for decisions? The
answer is: depends on the kind of decision to be taken (see, in the "Real
Options by Slides" page, the picture "The
Managerial Decisions"). If the decision is to invest or
wait, the bad side is the relevant one, and the decision is governed
by the "bad news principle"
(or fear/caution principle).
If the decision is to abandon or wait, the good side is the
relevant one, and the decision is governed by the "good news
principle" (or the hope principle). See for example
Dixit & Pindyck, 1994 , pp.18 and
40-41.
These different roles played by the two sides of the uncertainty is the
asymmetry on the decision rule, the second asymmetric effect of
the uncertainty.
Economic Uncertainty and Technical Uncertainty
There are two types of uncertainty which has different (opposite) effects
on investment decision rule:
The economic uncertainty is correlated with the general
movements of the economy (industry's prices/costs movements). So the oil
price (or the reserve price, or the rig rental rates, etc.) is an example
of variable with economic uncertainty. This uncertainty is exogenous
to the decision process: the oil price (or its variance) doesn't change
because you go ahead with the oilfield development or not
(supposing a decision from a price taker firm, not an OPEC
decision). The economic uncertainty incentives the waiting (for better
conditions) to invest, leading to postpone investments. A project with a
considerable positive Net Present Value (NPV) can be insufficient
to immediate investment: it is necessary that the project to be "deep
in the money".
The technical uncertainty is NOT correlated with the
general movements of the economy/industry. This uncertainty is endogenous
to the decision process. An example is a non-delimited new oilfield: the
oil-in-place volume (or the gas, or the water-in-place, or the average
permeability, etc.) is a variable with technical uncertainty. In this
case, waiting doesn't change the variable value. Only with a step-by-step
investment strategy (3D-seismic, drilling some wells, pilot production,
etc.) is possible to reduce this kind of uncertainty. So investing
(step-by-step) provides valuable information (reduce the variance of the
uncertainty and revise the expected value). This additional value is
called a shadow value, because it is not a directly measurable
cash flow (traditional DCF doesn't "see" this). The technical
uncertainty, on the contrary of the economic uncertainty, incentives the
starting of the investments (but its necessary to be staged investments).
In presence of relevant technical uncertainty, a project with negative
NPV, can be economically optimal to begin investing. For each new relevant
information is necessary to revise the investment decision: go ahead (or
even speed it up) if the true value is on the "good side" of
uncertainty, or stop if the "bad side" is the true one.
For a modern technical uncertainty explanation, including a model with
the two types of uncertainty combined into the same variable (cost), see
Dixit & Pindyck, 1994 , pp.11,
47-48, Chapter 10/section 4, and p.397 footnote 2) and also
Pindyck, R.S. (1993)
One last question: What the difference between a investor holding a
common stocks' portfolio, and a manager with a projects' portfolio? In the
first case the investors can't take advantage of the technical uncertainty
(investors can only change the portfolio composition, and eliminate this
kind of uncertainty by diversification, cannot maximize the value of each
stock), but in the second case the managers can take advantage of this,
with optimal management of these projects. Managers don't want eliminates
technical uncertainty by diversification, they want maximize the firm
value by taking advantage of this one.
So technical uncertainty is important only for managers.
Uncertainty and Hedge: It's very known the Modigliani &
Miller (MM) proposition II (see MM's
propositions). There is another example of application for the MM's
theorem, as indicated by Dixit & Pindyck
(1994, p.11), for the investment opportunity (or investment option):
"the option value is not affected if the firm is able to hedge the
risk by trading in forward or futures market. In efficient markets such
risk is fairly priced, so any decrease in risk is offset by the
decrease in return" and the financial operation "has no
effect on firm's real decisions".
For non-perfect markets, in general is possible to say that financial
operations (like hedge) has a secondary (second-order) effect in real
investment of corporations. So first the firm takes an economic
decision about the production project investment (most cases a
preference-free decision). After this, the firm takes the financial
and/or hedging decision (most cases a preference-dependent decision).
Here has NOT been saying the financial decision is unimportant. Only
argues this is a separated/independent decision that takes place after the
investment (economic) decision. Hedging and Capital Structure aren't scope
of this site.
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An irreversible investment opportunity (F) is like a financial
call option: the manager can (but is not obligated)
spend the investment cost (D) to obtain a production asset (V), and
frequently this investment opportunity remains only by a time interval
(T-t).
The financial call option is like F, their exercise price is like D, the
stock (received with the exercise of the option) is like V, and the call's
expiration time is like (T-t). The financial analogy is more adequate with
financial assets paying a continuous dividends (or interest) because the
analogy with cash flows (see below the dividend
yield analogy).
The expiration time in real investment can be the time from a patent's
right, the time from a lease in a offshore tract, or an estimate time
considering the threat of preemption or intense industry rivalry (for this
last point, see Kester, 1984).
However, there are some differences and considerations when performing
this analogy: Sick, 1995 (abstract) gives some
lessons: "the early exercise decision is more important in real
options analysis, greater flexibility in modelling project is needed"
and his instructive practical lesson: "The ability to be able to
build a useful and understandable model, is more important to the analyst
than precise estimates of option value."
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The net cash flows from a production project is analogous to a dividend
from a stock, or a periodic revenue from assets in general.
There is an analogy between the dividend yield from a project and the
dividend yield characterized by the currency interest rate, in the
currency option market, for example, because the dividends are close to
continually distributed over the time. This analogy is more general: the
option in a project paying a continuous net cash flow is analogous with
the options written on commodities and commodity futures contracts. The
underlying commodity varies from a natural resource like petroleum or
silver to a financial issue such as foreign currency or a Treasury bond.
Each case has its particulars adaptations, but the general understanding
is the same
In most cases, is reasonable to consider the dividend yield from
the project as a constant even when the cash flows falls over the time
(like a depletive oil field), because the project value (the oilfield
value) also decreases, so that the percentage variations can be considered
more or less the same (or when using an average value is reasonable). With
a constant dividend yield, a simplified solution could be used, like an
analytic approximation. Some analytic approximation models are available
in the literature on financial options that could be used in the real
options context (see in the bibliographical page). Others approaches
probably just find numerical solutions, such as interesting models that
consider the dividend yield as a function of the underlying project value
or even models considering the dividend yield as stochastic process
itself, correlated with the project's value stochastic process.
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