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2005) and illustrates the approach with several
examples.
While many of these ideas are relatively straightforward
and build on concepts suggested by Nau
and McCardle (1991) and Smith and Nau (1995), we
hope to make this material more accessible to decision
analysts and to encourage additional work on the
relationship between decision analysis and finance.
Triantis and Borison (2001) provide an assessment of
the use of options-based project valuation methods
in practice and conclude that a modest evolution is
occurring within some companies to support their
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Brandão et al.: Using Binomial Decision Trees to Solve Real-Option Valuation Problems
70 Decision Analysis 2(2), pp. 69–88, ©2005 INFORMS
adoption. In particular, Triantis and Borison anticipate
increasing convergence among the various realoption
approaches, particularly the decision-analytic
and option-pricing approaches. In that spirit we also
review some basic option-pricing concepts that will
be familiar to many readers but that are nonetheless
included as a useful reference in the context
of this discussion. We will also take care to discuss
the underlying assumptions and limitations of these
methods and to suggest when they might be a valuable
addition to the decision-analysis tool kit when
used appropriately.
The remainder of the article is organized as follows.
Section 2 reviews the traditional approaches to project
valuation. Section 3 outlines a decision tree approach
to the real-option problem discussed by Copeland and
Tufano (2004). Section 4 provides an extension of this
approach to problems in which project cash flows
over time are explicitly modeled and used as the basis
for valuing real options. This approach is illustrated
in §5 with a numerical example. In §6 we conclude
with a discussion of the limitations of this approach
and identify some areas for further research.
2. Background on Project Valuation
With the DCF approach to valuation, the net present
value of a project is calculated by discounting the
future expected cash flows at a discount rate that
takes into account the risk of the project. In practice,
this discount rate is often the weighted average cost
of capital (WACC) for the firm, based on the assumption
that both the firm and the project share identical
market risks. While this assumption may be valid for
projects that mimic the risks associated with the firm
as a whole, it may not be appropriate for unusual
or innovative investment projects. In such cases, the
practitioner must exercise judgment in choosing an
appropriate discount rate for the project. For a discussion
of the issues associated with the selection of a
project discount rate and the calculation of theWACC,
see Grinblatt and Titman (1998, Chapters 10 and 12).
A major criticism of DCF is the implicit assumption
that the project’s outcome will be unaffected by
future decisions of the firm, thereby ignoring any
value that comes from managerial flexibility. Management
flexibility is the ability to make decisions during
the execution of a project so that expected returns
are maximized or expected losses are minimized.
Examples of project flexibilities include expanding
operations in response to positive market conditions,
abandoning a project that is underperforming, deferring
investme