|The New Website
There is a new website devoted to the academic
activities of Investment Science at Stanford University. The
website is appropriately titled "Real Options and Beyond". It can
be found at http://www.stanford.edu/
~luen/RealOptions. The other site http://www.investmentscience.com is still of great importance for
general and applied aspects of investment science. You will find
copies of past issues of this Newsletter at both sites. Your
comments on these sites are welcome.
Short Course News
Investment Science for Industry was given at
Stanford last April. Several recent participants were referred to
the course by past members. It is heartening to see the chain build
in this way.
Enormous investment levels are associated with
most infrastructure projects-projects such as the building of dams,
gas or oil pipelines, power plants, semiconductor fabs,
petrochemical plants, bridges, highways, or tracks for fast trains.
These projects are also extremely complex, and subject to special
risks, often including a large degree of political risk. The
success of such projects can hinge on the careful crafting and
analysis of a financially-driven management and planning process.
Investment Science provides a rich and rigorous framework for the
development of such processes.
Standard financial methods (especially
traditional discounted cash flow methods) have three major
shortcomings when applied to infrastructure problems. The first is
that ordinary discounting does not properly value projects that
have embedded options, limits, or timing variations; and most
infrastructure projects do have these characteristics. The second
difficulty is that risks associated with infrastructure problems
are long-term risks, for which there are usually no direct markets.
The ultimate financial return of an oil pipeline project, for
example, depends on the price of oil over a span of a few decades
and current oil futures markets do not extend nearly that far.
The third shortcoming of discounting methods is
that the large scale of infrastructure projects often takes them
out of the realm of "small to medium" projects for the investing
party. A typical project is so large that its private risk (the
risk that cannot be hedged through market action) is not
diversified within a larger portfolio of projects. Hence, investors
want to employ risk-averse criteria for purposes of valuation and
decision making. Again, this cannot be properly achieved by
standard discounting within a complex project consisting of several
stages and containing options and other on-going decisions.
Fortunately, Investment Science principles can
overcome all three difficulties in ways that are easy to understand
The first difficulty, that of treating options
and other decisions, can be addressed in exactly the same way as
for other projects; specifically, by laying out possibilities and
decisions in a tree structure. Proper evaluation and decision
making can then be carried out either by simulation or by a
backward moving evaluation.
The second difficulty, namely the lack of
long-term futures markets can be overcome by generating artificial
(or proxy) markets based on the observed behavior of large firms in
the field. For example, large oil companies make capital investment
decisions on the basis of a view of long-term oil prices, these
decisions together with spot price characteristics can be used to
generate a synthetic futures market for purposes of evaluation and
hedging of oil infrastructure projects such as pipelines. How this
is done is a possible topic for a future newsletter.
We shall concentrate here on the third
difficulty, namely, the large size of typical infrastructure
problems. This large size, itself, invalidates normal discounting
methods, which are inherently linear. Consider a bet on the flip of
a coin. Heads you win X one year from now, tails you get nothing
(as shown in the diagram). How much is that worth? That is, how
much would you pay to take those chances of payoff?
The expected value of the bet is
X/2. However, the value to an investor is less
than that for two reasons: the time delay and the risk of the
payoff. In terms of time delay the value is reduced to
[X/2]/Rf , where
Rf is the risk free return (say
Rf = 1.06). If X is small, like a
few dollars, most people would be happy to pay close to V =
However, if X is large compared to a person's net worth, that
person would most likely not be willing to gamble nearly
X/2 for a 50-50 chance to win X. He or she would
discount the value quite heavily. In fact, the degree of discount
will increase with X. This means that there can be no one, fixed,
discount rate that works for all X's. But given a specific X, an
investor would settle on a rate characterized by a return
R1, so that the coin flip was
worth V = [X/2
For instance, if X were $10 billion, investors
might set a value (the amount they are willing to invest) at $2
billion rather than the expected value of $5 billion. This would
amount to setting R1 = 5/2= 2.5
which is equivalent to discounting at a rate of 150%.
Things gets more complex in a project that has
structure. For example, consider the situation below, on the
This is a two-year tree with each branch
being taken with a probability of 1/2. Notice that if we were to
reach point A, we have the same coin flip situation as before.
Hence, from above, we know the value from there is
[X/2]/ R1. The
same applies to point B, and the value is the same as at A. Hence,
the first year appears to be completely risk-free, for the project
will go to A or to B and the value is the same at each of these.
Hence we should discount the first year at the risk-free rate. This
means that, overall, V = [X/2
The graph on the left is
actually equivalent to the one on the right, when the two years are
considered together. In two years there is a 50-50 chance of
getting X or 0. This is the original coin flip
but delayed two years instead of one. If we were to use a constant
discount rate of R1 each year, we
would value this as
R1) which is much more severe
discounting than we obtained by considering the situation on the
left. The method on the left is actually the correct one, if we are
to be consistent with the simple coin flip. Notice that in the
correct method the discount factor varies in different parts of the
project, and this is typical of proper valuation.
For the numbers we used
for the coin flip, the two valuation methods produce values of $2
billion and $800 million, respectively, for this more complex
example. This is an enormous difference, entirely due to the
difference in discounting.
Contradictions such as
this arise frequently in complex projects, but there is a
methodology for getting everything right. Technically, the method
is that of "certainty equivalence" which means that we keep track
of how much each portion of the project is worth.
Proper valuation is
important, not simply because we want a realistic assessment of a
project. It is also essential for proper design and on-going
decision making. If valuation is too conservative (because high
discount rates are used throughout) then decisions will be too
conservative. Conversely, if discount rates are too low,
unwarranted risks will be taken. In practical terms for an oil
pipeline, decisions made regarding materials, routing, timing,
maintenance plans, and so forth may be not be consistent with the
risks involved. Decisions based on proper valuation methods can
account for a significant fraction (often 30% or more) of the total
value of the project. Indeed, infrastructure projects are projects
where Investment Science has tremendous potential, for it can save
the equivalent of billions of dollars in a single large