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‘REAL OPTIONS’ FRAMEWORK
TO
ASSESS RESEARCH INVESTMENTS
AT
THE U.S. DEPARTMENT OF ENERGY
Nicholas S. Vonortas*
Center for International Science and Technology Policy
&
Department of Economics
The George Washington University
Chintal Desai*
Department of Finance
The George Washington University
Submitted to the U.S. Department of Energy
March 20, 2008
Mailing address: Center for International Science and Technology Policy, The
George Washington University, 1957 E Street, N.W., Suite 403,
Washington, D.C., 20052.
Tel.: (202) 994-6458
Fax: (202) 994-1639
E-mail: [email protected]
Web: http://gwu.edu/~cistp
1
1. Introduction
This Report presents the results of an exploratory study to appraise the feasibility of the
‘real options’ analytical methodology for justifying public research programs. This
innovative methodology has been investigated in order to support investment portfolio
analysis in systematic priority-setting processes aimed at long-term, highly uncertain
research programs. The study falls within the realm of on-going efforts by the Office of
Science, US Department of Energy (DOE), to characterize its portfolio of sponsored
research programs.
Evaluation has become a core tool of strategic planning and management of public
programmes to support research and development (R&D). During the past several years
governments all over the world have made sustained efforts to more systematically
evaluate their R&D programmes. Evaluation refers to both ex-ante programme appraisal
and ex-post evaluation and includes all three building blocks of the evaluation properly
shown on Figure 1:
Priority setting
Monitoring
Impact assessment
Figure 1. A Framework for Public Research Evaluation
Ex-Ante Ex-Post
Priority
Setting
Impact
Appraisal
Monitoring
Evaluation
Innovation System (Features, Institutions, etc)
2
Such evaluative activities have been promoted in the effort to enhance accountability and
transparency, initiate systematic ex-ante appraisals of proposed programmes, further
extend programme monitoring and ex-post impact assessment, and improve the
communication of program activities and outcomes to policy decision makers and
sponsors.
The report deals with the first building block of evaluation (priority setting). It argues that
significant advances in economics and finance theory of pricing derivatives and in
computing power at our disposal over the last 20 years make it feasible now to introduce
strategic capital budgeting methodologies which, for the first time, allow capturing in
financial terms the flexibility inherent in active strategy and management of R&D
resources. Business strategies can now be analyzed as chains of “real options”.
The report argues that the usefulness of this methodology is not limited to the private
sector. While the appraisal of R&D differs in terms of beneficiaries, the fundamentals of
ex ante appraisal remain in the public sector. This includes the research and the
technologies of interest to the Department of Energy. We argue that the real options
methodology can be very useful in justifying investments in long-term research by the
Department’s Office of Science. And provide detailed examples of the way this can be
accomplished.
The remainder of the report is organized as follows. Section 2 introduces the concept of
‘Strategic Capital Budgeting’, followed by R&D Options in Section 3. As a prelude to the
introduction of the R&D project appraisal models, Section 4 summarizes the old debate
regarding whether long tern research can be analyzed quantitatively. Section 5 presents
the core material of the report, summarizing the literature and the modeling examples for
application of the real options methodology to justify research programs of the Office of
Science. Section 6 underlines the automation of two real options models which makes the
appraisal and sensitivity analysis fairly routine. Concluding remarks are provided in
Section 7.
2. Strategic Capital Budgeting
Strategic, long-term research and development (R&D) projects have been typically
justified in the past on the basis of qualitative arguments and expert opinions regarding
windows of opportunity such R&D opens in new technological areas. A case in point is
all major federal agencies in the United States funding non-defense research at a
considerable scale. Such research has been justified on the basis of peer review
arguments focusing on research quality and expert panel opinions regarding potential
future benefits. Conventional capital budgeting methods such as net present value (NPV)
and return on investment (ROI) have been circumvented under the argument that they do
not capture the full value of an investment opportunity, often unduly penalizing
investments with expected payoffs further out in the future.
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An important underlying reason for this attitude is that strategic planning and capital
budgeting have historically been treated as two distinct domains for resource allocation.
Strategic planning projects an organization into the future, creating a path from the
present to where the organization should be some years later. Starting down the path,
however, the organization is supposed to begin learning – about business conditions,
competitors’ actions, the quality of own operations, and so on – and must be able to
respond flexibly as a result. Capital budgeting has traditionally followed as a separate
step dealing with measurable returns (profits/cash flows) of a programme while
abstracting from more intangible strategic benefits associated with the programme. The
result has always been an alleged chronic deficit between the calculated value of
strategic, long-term programmes and their “true” value. The deficit is due to the oversight
by the conventional NPV model of the inherent strategic value of the programme and the
flexibility associated with active management to alter the programme's trajectory once
undertaken. Several factors are inadequately treated in the traditional approaches,
including:
Uncertainty of the outcome
Timing of the investment
Irreversibility of committed resources
Inaccurate use of the discount rate
Given that the above-mentioned are major characteristics of strategic long-term R&D,
inadequate accounting for them may seriously distort decision-making based on the
potential benefits of investments in government sponsored R&D programmes.
Conventional methods for assessing long-term R&D investments are also criticized for
using inappropriate discount rates which: (i) blend time discount and risk adjustment
factors thus creating the false impression that project risk follows a time path with no
predictable pattern; (ii) do not account for the fact that the product of R&D is often better
information which will decrease uncertainty (and risk) over time. ‘Official’ discount rates
required by the U.S. government for analysis of federal programs, for example, disregard
the significant differences among R&D programmes, technologies, and industries.
There is scope for significant improvement. A growing number of economists and
business analysts have advocated the use of the option-pricing method to appraise future
R&D investments. It is argued that the theory of options on financial securities can be
applied to non-financial investments, resulting in a ‘real options’ analytical framework
that also allows placing a valuation on the flexibility and strategic characteristics of long-
term investments. That is to say, real options can formally address not only the
measurable returns but also the intricacies of market and technological uncertainty,
timing, irreversibility, and the discount factor associated with strategic, long-term
investments.
Real investment opportunities typically involve multiple options whose individual values
most often will interact and may be valued together (Trigeorgis, 1996). This feature
should make them unsuitable for conventional discount cash flow methods that approach
capitalized budgeting from a decentralized point-of-view, valuing projects on a stand-
alone basis. Which is probably why R&D managers in the private and public, having long
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recognized that projects can have intangible strategic benefits that may lead to
competitive advantage, have not trusted such methods in the past. The options approach
is an attempt to capture these benefits in the valuation analysis. It is imperative that one
accounts for all options in order to attain the best estimation of valuation.
The ‘real options’ methodology has, then, significant strengths for the ex ante appraisal
of R&D investments. It holds promise for convincingly unifying the processes of
strategic planning and capital budgeting into an active process of ‘Strategic Capital
Budgeting’.1
It should be noted here that the ‘real options’ methodology draws heavily upon the
fundamentals of risk neutrality.2 There are three advantages in using this risk-neutral
environment. First, it allows incorporating into the analysis the various flexibilities
(options) available in a typical investment project to be incorporated in the analysis. Such
options include the optimal time to invest, options to stop and restart, the option to
abandon the project, the option to expand, etc. Second, it uses all the information
contained in market prices (e.g., futures prices) when such prices exist. Third, it allows
using the powerful analytical tools developed in contingent claims analysis to determine
the value of the investment project and the optimal operating policy (exercise of real
options). (Schwartz and Trigeorgis, 2001)
By explicitly incorporating in the valuation both the inherent uncertainties (market,
technology) and the active decision making required for a strategy to succeed, the options
methodology purports to systematize quantitatively what managers have yearned for
always. It would help executives think strategically and capturing the value of doing that
– of managing actively rather than passively (Luehrman, 2001). The creative activity of
strategy formulation can be informed by valuation analyses sooner rather than later.
Financial insight may actually contribute to shaping strategy, rather than being relegated
to an after-the-fact exercise of ‘checking the numbers’. ‘Strategic capital budgeting’, in
other words, starts becoming reality.
In concluding this Section a caveat must be mentioned. Strategic capital budgeting will
need to draw upon the accumulated experience with investment appraisal. The real
options methodology for assessing R&D investments can not, and should not, be viewed
in isolation of the traditional science and technology assessment tools utilized by
government agencies. In particular, it is imperative to understand that the methodology
will depend on expert reviews for critical pieces of information about the nature of the
project, the technology, the timing and magnitude of the benefits, and so forth. Expert
reviews and options appraisals of R&D programs should complement, leverage, and
enhance each other.
1 The term ‘Strategic Capital Budgeting’ is coined here to describe this concept. 2 Risk neutral environment allows discounting using return on risk free asset, i.e., the return with the least
amount of risk, e.g. return on US Treasury bills.
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3. In Search of R&D Options3
The decision to invest initially in an R&D project with a highly uncertain outcome is
conditional on revisiting the decision sometime in the future. This is similar in its
implications to buying a financial call option: this will permit (but not oblige) the owner
to purchase stock at a specified price (exercise price) before or on the expiration date of
the option. Similarly, an initial R&D investment will permit (but not oblige) the investor
to commit to a particular technological area – thereby, buying the entitlement of the
future stream of profits – sometime until the predetermined date for revisiting the initial
investment decision.
The analogy between the R&D option and the stock option can be summarized as
follows:
The cost of the initial R&D project is analogous to the price of a financial call
option.
The cost of the follow-up investment needed to capitalize on the results of the
initial R&D project is analogous to the exercise price of a financial call option.
The stream of returns to this follow-up investment is analogous to the value of the
underlying stock for a financial call option.
The downside risk of the initial R&D investment is that the invested resources
will be lost if, for whatever reason, the follow-up investment is not made. This is
analogous to the downside risk of a financial call option which, in case that the
option is not exercised, will be the price of the option.
Increased volatility (uncertainty) decreases the value of an investment for risk-
averse investors. It, consequently, increases the value of an option to this
investment. Similarly, increased uncertainty (for the whole required R&D
investment) raises the value of an initial R&D project if it is considered an option
to a potentially valuable technology.
A longer time framework decreases the present discounted value of an
investment. It, consequently, increases the value of an option to that investment.
Similarly, time length may well increase the value of an initial R&D project if it is
considered an option to longer-term, high-opportunity investments.
It has, thus, been argued that when an investor commits to an irreversible investment the
investor essentially exercises his call option. In other words, the investor ‘… gives up the
possibility of waiting for new information to arrive that might affect the desirability or
timing of the expenditure; [the investor] cannot disinvest should market conditions
change adversely.’ (Dixit and Pindyck, 1994, p. 6).
On the other hand, for most investments there exists some abandonment value in terms of
a salvage value or the opportunity to simply shut down should the project become
unprofitable. The abandonment option is parallel to a financial put option – where a price
is paid for the opportunity to sell a security at a favorable price should the security
3 This section draws on Vonortas and Lackey (2003) among others. For extensive reviews of the real
options literature see Schwartz and Trigeorgis (2001, various chapters) and Vonortas and Desai (2004).
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decline in value. Thus in each R&D investment there is an inherent value in the ability to
stop investment or redirect resources to another project.
The important implication is that the question of how to go about exploiting future
opportunities reverts to a question of how to exercise the corresponding call options
optimally. Academics and financial practitioners have studied this problem in (financial)
stock option pricing theory where the value of a stock option has been formally expressed
as a function of the underlying parameters. The basic principles arising from this work
can be transferred to the arena of ‘real’ that is, non-financial investments.
The real options method seems, then, well suited to deal with uncertainty and flexibility
related to an R&D investment project. The various decisions are often grouped into
category types. For example, Brigham and Ehrhart (2002) distinguish between four
categories:
Investment timing option;
Growth option;
Abandonment option;
Flexibility option.
The first category involves an option concerning the placement of an investment. The
second concerns options for growth in the future if expansion was desired. The third
concerns the choice to abandon a given investment. In a R&D environment the option to
abandon is always present since, at any point in time, previous R&D activities can be
considered sunk costs. Finally, the fourth category concerns options that allow changes to
the current situation in a relatively short-term time frame. In an R&D environment most
option value occurs due to growth and flexibility options.
R&D projects generally involve multiple phases with or without overlapping. If the
investment is made in a phased manner, with the commencement of a subsequent phase
being dependent on the successful completion of the preceding phase, it is known as
sequential investment.
Each stage provides information for the next thus creating an opportunity (option) for
subsequent investment in a new technological area. Such projects can be valued using the
techniques of ‘Compound Options’, also known as ‘Option on Options’.
By explicitly recognizing the choice-to-invest aspect of earlier-stage R&D projects, this
mechanism greatly enhances the ability of decision-makers to justify long-term R&D
investments made by the public sector. For example, an early R&D investment by the
public sector in an emerging technological area may be considered the mechanism for
enabling (establishing the option for) the private sector to undertake the follow-up
investment required to innovate in that area. Moreover, by differentiating among the
various stages in an R&D program, this mechanism allows the better evaluation of both
technological and market risk, principally because it allows frequent adaptation to the
new knowledge obtained in the previous stages.
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Of course, the methodology still has limitations. At the theoretical level, the reviewed
models which treat R&D investment as a sequential compound option, where investments
take place in a phased manner, impose a ‘linearity’ which has been shown in the
innovation systems literature to be useful as a first approximation but less so as an end in
itself because:
i. R&D phases very often take place in parallel or, at least, overlap significantly;
ii. There are significant feedback loops between research stages (learning).
In order to address issue (i) one needs to solve simultaneous compound options. This has
only been achieved through the binomial approach until now. Continuous time ‘real
option’ models remain on the future research agenda. In order to address issue (ii) one
will need to introduce significant complication to existing models. Efforts to overcome
this problem include a paper by Berk, Green and Naik (2004) that uses Bayesian
approach to represent learning.
At the more practical level, the ‘real options’ valuation methodology is still under
development – i.e., it remains ‘fluid’ – adding to its natural complication. Nevertheless,
there has been progress in applying these concepts in practice, as shown and explained in
the core Section dealing with the OS study (Section 5).
Before we turn to the analytical part, Section 4 below treats a generic measurement issue
that has caused some confusion among policy decision makers.
4. Generic Measurement Issues
The cost-benefit analysis of a future investment depends on the availability of reasonable
estimates for the anticipated costs and benefits. In contrast to most other investments, a
major concern in the case of R&D projects relates to the uncertainty regarding the use of
the results. The closest the project is to the D, the more accurate the definition of the
expected outcome and its projected use is and the easiest the estimation of both costs and
benefits. The reverse also holds: the closer projects are to the R, the further away and less
well defined the anticipated benefits are and the trickier the estimation of the costs and
benefits.
Moreover, the closer the project is to the research end of the spectrum (R) the higher the
possibility of knowledge spillovers, meaning that the benefits spread out into direct
benefits accruing to the individual/organization that undertakes the project and indirect
benefits accruing to all others who eventually access the produced knowledge.4 Finally,
research projects can have tangible and intangible benefits.
This has created anxiety in the public sector with widespread arguments that, because
they tend to be more long-term, end up having unintended spillovers, and earn benefits in
the longer term, public investments in research cannot be analyzed with methodologies
4 Direct benefits are also called private returns. Social returns include both direct and indirect benefits.
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similar to those in the private sector. We tend to disagree, while we recognize the need
for adapting the methodologies accordingly.
The only projects that can be evaluated with a formal method are, of course, those with at
least one anticipated line of direct, tangible benefits. This group includes the vast
majority of projects. Blue-sky research, in the true sense of the term, is rare even for the
Office of Science.
Good project appraisal practice suggests that one uses the high-end estimate of cost and
the low-end estimate of benefits. We argue that any R&D project – other than the few,
truly blue-sky explorations – has an anticipated core application (or a set of core
applications) whose critical features can be articulated by experts fairly accurately. In the
least, experts should be able to help create reasonable scenaria or provide the boundaries
for sensitivity analysis. Costs and benefits are, then, evaluated in reference to that core
application(s) only. In other words, we use a conservative estimate of benefits. To the
extent that they materialize, further benefits – both direct and indirect, tangible and
intangible – will be a “bonus”.
In other words, we argue that even basic research can, most of the time, be appraised ex
ante with quantitative methodologies that use market variables such as monetary returns.
5. Office of Science Study
An exploratory study was initiated three years ago by the Office of Science of the US
Department of Energy to appraise the feasibility of the ‘real options’ analytical
methodology for supporting investment portfolio analysis in systematic priority-setting
processes aimed at long-term, highly uncertain research programs. The study falls within
the realm of DOE’s on-going efforts to characterize its portfolio of sponsored research
programs. The study purported to address two overall objectives:
To determine the feasibility of developing a succinct compound options model to
support systematic priority-setting systems for DOE-sponsored research
programs.
To develop a methodology for undertaking investment portfolio analysis using the
‘real options’ approach.
5.1 Literature Review
In its earlier stage, the study reviewed the already extensive real options literature to
determine the best modeling approach to follow in the case of appraising longer-term
research investments in energy-related fields.
The options are broadly classified according to the timing of decision-making, the
obtained solution and the addressed uncertainties. Based on the timing of decision-
making, these models can be classified into discrete time and continuous time models. In
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the discrete time models, prices are assumed to change at some fixed interval of time, say
daily, monthly or semi-annually, whereas in the continuous time models prices change
continuously. Different models address different types of uncertainties relating to cost,
asset price, technology, etc. Figure 2 illustrates the primary models in the various
categories we have considered.
Binomial Model
Discrete Time
Geske (1979) Margrabe (1978)
Carr (1988)
Pindyck (1993)
Ott and Thompson (1996)
Schwartz and Moon (2000)
Berk, Green, Naik (2004)
Continuous Time
Compound Option Models
Figure 2. Main option models under consideration.
In the discrete time model category, we have considered binomial and quadranomial
models. In the binomial model, the project value are assumed to take two distinct values
in the next time period, whereas the quadranomial model assumes that it can take four
possible values. This number of values reflects the type of assumed uncertainty and, in
particular, the existence of technological uncertainty only (binomial) or the co-existence
of technological and market uncertainty (quadranomial). Assuming complete markets and
risk neutral valuation allows computing an option value under the binomial framework
(Cox, Ross and Rubinstein, 1979). Only two available securities are required: the risk
10
free asset and the underlying security.5 The risk neutral valuation of the Cox-Ross-
Rubinstein binomial option valuation model is based on the same assumption of risk
indifference as the Black-Scholes model (Black and Scholes, 1973): the expected return
on the underlying asset is the risk-free interest rate. When the application is more
complex and includes particular features of a real asset, such as multiple sources of
uncertainty or many decision dates, analytical solutions cannot typically be obtained.
Numerical methods are required in such applications.
The binomial option valuation model has three advantages: (a) it can be utilized to value
any type of real option; (b) it retains some feature of discounted cash flow valuation; and
(c) uncertainty and consequences of contingent decisions are easily demonstrable.
(Amram and Kutilaka, 2002). Moreover, binomial discrete time models are easy to
understand and involve basic mathematics, thus making them very convenient for
practitioners (Benninga and Tolkowsky, 2002; Copeland and Antikarov, 2002; Perlitz,
Peske and Schrank, 1999; Shockley, Curtis, Jafari, Tibbs, 2003).
Discrete time models, however, can only provide an approximation of the optimal time to
abandon the project since they use discrete time. This limitation can be overcome by
using continuous time models. The simplest of these is the Black and Scholes (1973)
model which computes the value of European call and put options (previous Section).
Cox, Ross and Rubinstein (1979) prove that in the limit – i.e., if we allow the number of
steps to approach infinity, thus making the price jump to be close to zero – then the
binomial model converges to the Black-Scholes model.
Pindyck (1993), one of the cornerstone publications in the continuous time literature,
described two forms of cost uncertainty that are of relevance to our analysis:
Technical uncertainty which refers to the typical limitations in carrying out an
R&D project successfully such as skill shortages, lack of adequate knowledge,
and limited resources of all kinds. This uncertainty can only be resolved by
investment.
Input cost uncertainty which is external to the firm and includes things such as the
increase in the price of raw materials.
These two kinds of uncertainty can be described as the diversifiable and non-diversifiable
risks of the portfolio management. In a narrow sense, R&D projects involve diversifiable
risks. However, their complete evaluation, also including the market exploitation of the
resulting opportunities, will also involve non-diversifiable risks.
In long-term R&D projects, cost uncertainty matters and could interact with asset value
uncertainty. Higher uncertainty raises the value of the option. By referring to the example
of a fusion energy project at NASA, Ott and Thompson (1996) show that cost uncertainty
is equally important to the asset value uncertainty in valuing long-term R&D projects.
Cost uncertainty is found to increase not only the active investment region but also the
project value. Compared to the case when there is a no cost uncertainty, its presence
raises the expected discounted value of the completed project and lowers the expected
5 The asset whose value determines the price of an option or another derivative.
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discounted value of the expenditures. The overall effect is an increase in the active
investment region.
The advent of the work by Schwartz and Moon (2000) gave a major push forward to the
possibilities of using real options analytical methodologies in valuing longer-term R&D
projects. Building on Pindyck (1993), Schwartz and Moon (2000) consider three
uncertainties associated with an R&D project:
Cost uncertainty which pertains to the expected cost of completion of the project
and is assumed to follow the controlled diffusion process introduced by Pindyck
(1993).
Asset value uncertainty which reflects the risk associated with the resulting cash
flow (revenue) after the successful launch of the product made possible by the
R&D project under investigation. Asset value uncertainty follows a Geometric
Brownian motion.
Possibility of a catastrophic event which considers the situation when the project
halts unexpectedly due to external factors and its value reduces to zero. For
example, if a competitor successfully develops a product before the completion of
the R&D stage of a given firm, then the firm may abandon the project.
Using the contingent claim analysis with two state variables (asset value at successful
completion of the R&D project; expected cost to completion), Schwartz and Moon
(2000) find the value of the project as well as determine the optimum investment rule. In
other words they determine the value of the state variables inducing the optimal
investment.
In an important applied work, Davis and Owens (2003) have used the Schwartz and
Moon (2000) and Ott and Thompson (1996) analytical approach to evaluate R&D
investments in renewable energy sources. The major conclusion of the paper is that
renewable energy technologies hold a significant amount of option value that cannot be
captured by using traditional valuation techniques such as NPV. In order to derive the
benefits of continued R&D spending a more advanced valuation perspective such as real
option analysis is needed.
Last, the theoretical article by Berk et al. (2004) modifies Schwartz and Moon (2000) by
incorporating revisions in the probability of successful R&D using the Bayesian
framework. Technical cost uncertainty is described as purely idiosyncratic risk that can
be diversified, whereas the asset value uncertainty is systematic in nature (non-
diversifiable). During the R&D stage, the arrival of new information on the expected
asset value changes the systematic risk of the project and results in revisions in the
project’s value at successful completion. Thus, ‘learning by doing’, a big absent in
Schwartz and Moon (2000), impacts both the project value and the investment cost. Four
state variables are used – number of stages to completion, level of future cash flows,
occurrence of obsolescence (catastrophic event), and project history – to determine the
value of the R&D project, the optimal investment policy, and the risk premium. The risk
premium is higher during the initial stage of R&D and reduces as the project approaches
completion. Closed form solutions for the R&D project value and for the risk-premium
are possible, even for the multi-stage R&D project, when no learning is involved. When
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there is ‘learning by doing’, numerical methods are used for finding the optimal
investment rule and the value of the project.
The continuous-time modeling technique of Pindyck (1993), Ott and Thompson (1996),
Schwartz and Moon (2000), and Berk et al. (2004) encapsulates some of the most
important concepts regarding our objective (Figure 2). It incorporates all relevant
uncertainties of long-term R&D. It provides not only the value of the project but also the
optimum investment rule. The model is sufficiently developed already for R&D
applications. Agreeing with Davies and Owens (2003), we believe that it is currently the
most promising for the task in hand. It was proposed as such to the Office of Science.
Managers and policy decision makers, however, get cold feet when confronted with
complicated theoretical analyses. For this reason, a subsequent phase of the project
concentrated on establishing the validity of an alternative technique that would maintain
the main characteristics of the specific continuous-time model above but would be
simpler, more user-friendly, and closer to the concepts that prospective users in the public
sector are familiar with. We have found it in the seminal discrete time model of Cox,
Ross and Rubinstein (1979), as applied by Shockley et al. (2003). The strengths of the
model include:
1. Relatively straightforward, easy to understand
2. Relatively easy to calculate
3. Provides back-of-the-envelope calculation
4. Gives fairly reasonable approximation
5. Extensively used by practitioners
A second relevant model in the discrete time tradition has been developed by Copeland
and Antikarov (2001) and by Shockley (2007). The basic difference with the previous
model is the number of uncertainties that are operational at any point in time. Shockley et
al. (2003) only deal with technical uncertainty. The expected cash flow (revenue)
resulting from the application of the R&D results in the economy is known. Copeland
and Antikarov (2001) add market uncertainty and revert to a quadranomial model.
Shockley (2007) also treats both technical and market uncertainty with a somewhat
different model.
Both the binomial and the quadranomial have been adapted to our environment and the
technique is reported in a subsequent section. Before that, we turn to the core role of
uncertainty (volatility) in these analytical techniques.
5.2 Volatility (Uncertainty)
Volatility is a core input parameter in the pricing of financial options such as options on
stocks, bonds, index, currency, futures etc. It is a measure of how much the value of the
underlying asset can vary between the initiation and the expiration of the option. In real
options contexts – e.g., R&D project – the underlying asset is the (expected) output of the
R&D project in question. This can include a new or improved product, service, or
production process.
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It is important to notice that the analogy of real options to financial options is not perfect:
there is uncertainty not only about the value of the underlying asset but also about the
successful completion of the R&D project itself (i.e., about the “options vehicle”).
Volatility in R&D projects can, then, be interpreted as the combination of two different
types of uncertainty:
• Technical uncertainty reflecting the chances of successfully completing the
research project
• Market uncertainty reflecting the fluctuation in the value stream of the underlying
asset – i.e., the fluctuation in the stream of returns to the output of the research
There are various ways of estimating technical uncertainty – e.g., the binomial example
mentioned above – and market uncertainty – e.g., forecasting econometric models,
Monte-Carlo simulations.
Technical and market uncertainty seem unrelated at the first look. In reality, they interact
and may be strongly correlated. Differences in the degree of interaction between
applications has serious analytical implications.
For simplicity, it can be argued that there are important differences between research
aiming at “process” technologies and research aiming at “product” technologies. In the
former case, the product sold in the market is well understood. In the latter case, it is not.
Combined Technical and Market Uncertainties: New Process
Consider the example of developing technology for building a new type of power plant to
generate electricity. In this example, R&D related risks can be termed as technical
uncertainty. The price of electricity, the demand for electricity and the variable costs of
electricity generation depend on market-wide factors. During the R&D stage, information
becomes available not only about the likelihood of successful completion of the R&D
project but also about the market uncertainty parameters. While technical uncertainty is
not affected by the improved understanding of the market, the obtained information could
well lead to a revision of previous estimates of the future value stream of the R&D output
which, in turn, can affect the decision to continue or abandon the R&D project. This is a
case of uncorrelated, but interacting, technical and market uncertainties.
Combined Technical and Market Uncertainties: New Product
Now consider the example of early-stage biotech research to identify a new
pharmaceutical compound for a yet imperfectly understood viral disease. Again, R&D
related risks can be termed as technical uncertainty. The expected price of the new drug,
the demand for the drug, and the variable costs of producing the drug depend on market-
wide factors. During the R&D stage information becomes available not only about the
likelihood of successful completion of the R&D project as originally defined. New
information will probably relate to better understanding of the target virus itself. It may,
for example, indicate new mutations of the virus which require modifications in the R&D
program, in turn, affecting technical uncertainty. Moreover, such information also affects
the market uncertainty parameters. The obtained information will lead to a revision of
both the previous estimates of the chances of success of the R&D program and of the
14
future value stream of the R&D output. These two together will affect the decision to
continue or abandon the R&D project. This is a case of correlated technical and market
uncertainties.
For our purposes, we have hypothesized that the target technologies of DOE non-defense
research are of the former kind (new process): the final product (energy) is well
understood. The search is for alternative ways of producing it cheaper and cleaner. The
quadranomial model of Copeland and Antikarov (2001) and the combined uncertainty
model of Shockley (2007) are applicable and have been adapted.
5.3 Data Requirements
Real options calculations for R&D projects require a certain amount of information
which is not distinctly different from other methodologies. More specifically, the
variables required for such an application include:
Number of investment phases in the R&D project.
Expected cost of investment for each phase.
Time to completion for each phase.
Probability of success in each phase.
Value of technological advancement: This is the so-called value of the underlying
asset. Assuming that the research is successful and one (or more) marketable
technological advancement has been created, the requested information is for the
expected cash flows (revenue) generated during commercialization. In the case of
public R&D investments, economists would call here for the sum of private and
social returns from it.
Price of capital investment necessary for the economic application of the specific
technological advancement(s). Economists typically use the interest rate as the
cost of capital. The Office of Management and Budget also determines a discount
rate for public investments.
Investment required for commercialization (capital cost such as plant, etc.)
Obviously, for long-term research, precise values of these core variables are impossible.
Reasonable estimates, however, should be obtainable. The source of the basic
information for the first four variables listed above would be research program managers
and the expert scientific panels advising R&D-intensive public agencies. Processed
appropriately (sensitivity analysis, scenarios, simulation), expert opinions can be used to
obtain the required estimates. The remaining three variables are market related. Estimates
could be obtained from economic models and simulation models.
15
5.4 Real Option Value with Only Technical Uncertainty: Binomial
This example follows the method of Shockley, Curtis, Jafari, Tibbs (2003) who explain
the valuation of a compound option for an R&D investment involving four stages before
commercialization. For simplicity, an R&D project with two stages is considered. The
example illustrates how the real option framework can be useful vis-à-vis traditional
discounted cash flow (net present value) methodology. It uses the binomial model that is
simple and can be used as a back-of-the-envelope calculation.
Consider an R&D investment that consists of two phases:
Phase I Phase II
Investment Required $ 2 million $ 5 million
Probability of Success 5% 50%
Time period of completion 2 years 2 years
Further investment of $10 million is required after the successful completion of the R&D.
This capital investment is mainly to build the plant and establish selling and distribution
channel. It is expected that the project will generate net cash flows worth $20 million
after the successful completion of the R&D. All these amounts are in real dollar terms.
The discount rate is the inflation-adjusted cost of capital, taken as 10%. The risk free rate
is assumed 5%, and the volatility in the asset value is assumed 100% to reflect highly
uncertain cash flows and high probability of failure in the R&D project.
The objective is to calculate the value of the R&D project (option) at time 0. The decision
rule is simple: if this net value is positive, then invest.
Time line:
t=0 t=1 t=2
Phase 1- Invest $2 m Phase 2- Invest $5 m
Success, p=5%
Success, p=50%
Abandon
Abandon
16
At time t=1 the firm is at node B and has to make a decision whether to invest $5 million
for Phase 2. The firm knows that it can learn about the success of Phase 2 only through
this investment. Based on the success of Phase 2 and on the prevailing market condition,
the firm can then decide whether to spend a further $10 million on capital investment at
point t=2.
The investment problem of the firm at t=1 can be considered as an investment in a
European call option. Here, the underlying is the expected net cash flow of the project,
which we have assumed $20 million, and the exercise price is the investment of $10
million. Further, the maturity period is two years. So, we can say that the firm is holding
a call option at point t=1. If the value of this call option is higher than $5 million then,
firm should invest further otherwise it should stop.
Moving backwards in time to t=0 we see that the firm now has to make a decision
whether to invest $2 million in Phase 1. This can be considered yet another European
option. For this option, the underlying is the payoff of the call option at t=1 discussed
above which, in turn, provides the firm the right (not the obligation) to have the
underlying asset of the expected cash flow, which in our case is $20 million. In other
words, at point t=0 we can say that the firm is holding an option on the option or, better, a
compound option.
We summarize below the technique to value such a compound option using the binomial
tree. The details of the application of binomial model for option valuation are given in
Cox, Ross and Rubinstein (1979).
Step 1: Compute the value of the underlying asset (R&D project output) at time 2, given
success in producing a technological advancement X. This value is here given to
be $20 million.
Step 2: Find the present value (PV) of the underlying asset (R&D output) at t=0
assuming that the R&D project is successful. In our case it is:
PV of the underlying = $20 million * exp (-0.1*2) = $ 16.375 million
Step 3: Using the subjective probabilities of success (expert opinion) compute technical
uncertainty (volatility). Using the Black-Scholes formula:
T
TZSZdN
)5.0()/ln()(
2
2
17
Where,
N (d2 / Z) = Joint subjective probability of success of the R&D project
= 5% * 50% = 2.5%
Z = Investment required for the commercialization stage = $10 million
S = Discounted value of X = $16.375 m
T = Total time to complete R&D project = 2 years
= Technical uncertainty of the R&D project (need to compute)
= Cost of capital (e.g., interest rate) = 10%
By solving the above for formula for technical uncertainty = 82%.
Although of key importance, the subjective probability information above does not allow
us to compute the value of the R&D investment and make a decision. At this point, we
transition to the option model.
Step 4: Using the outcomes of Step 2 and Step 3 (discounted value and technical
uncertainty), we compute all possible end values of X (all scenarios).
u2 V0
u V0
V0 ud V0 = du V0 = V0
d V0
d2 V0
t=0 t=1 t=2
Find the value of the up step (u) and the down step (d), assuming time duration between
successive binomial jumps to be one year. Up (down) step refers to the value of $1 if we
are at the upper (lower) node of the binomial tree at the end of the time interval of a step
(in our case two years).
teu
182.0 e = 2.26
ted
182.0 e = 0.442
18
Based on the PV of the underlying asset as calculated in step 2 and the value of up and
down steps above, we can complete the binomial tree of the PV of the underlying (of the
value of X), moving forward.
D 83.638
B 37.007
A 16.376 E 16.375
C 7.245
F 3.206
t=0 t=1 t=2
Step 5: Using the end values obtained in Step 4, the available information on necessary
investments at each stage of the project, and the options model we compute the
optimal R&D investment at each stage and for each scenario. This set also
includes the initial optimal R&D investment at time 0.
We are now moving from the end of the tree to the beginning. We use the principle that
the option value can never be negative.
At time t = 2 years
Value at node D: max (83.64–10, 0) = 73.64
Value at node E: max (16.37–10, 0) = 6.37
Value at node F: max (3.21–10, 0) = 0
Vd = 73.64
Vb
Va Ve = 6.375
Vc
Vf = 0
t=0 t=1 t=2
At time t = 1 years
Our next objective is to calculate bV and cV . Start from bV . We use the two pieces of
available information:
1) The availability of the risk-free investment at the rate 5%.
19
2) The possibility of investing $37.007 and receiving $83.64 in the good state of the
world or $16.37 in the bad state of the world.
We will create a combination of these two investments that will allow us to obtain the
given payoffs $73.64 and $6.37.
73.64
V'b
6.37
Investment A Investment B (Risk free) 83.64
37
16.37
10.5
10
10.5
Lets take x units of investment A and y units of investment B.
64.735.1064.83 yx
37.65.1037.16 yx
Solving the above two simultaneous equations will give, x = 1 and y= - 0.9524 '
bV = 37 * 1 + 10* (-0.9524) = $27.476
However, at node B, we have to make an investment of $5 million in order to move to
Phase II of the R&D. Thus,
476.220,476.22max0,5max * bb VV
Similarly we calculate for cV , and then at time 0, aV .
Vd = 73.64
Vb =22.476
Va = 5.167 Ve = 6.375
Vc = 0
Vf = 0
t=0 t=1 t=2
Step 6: The value of R&D investment as per the real option framework is $ 5.167
million. According to the decision rule, positive value at t=0 means that the
project moves forward.
20
This value is significantly different from that calculated using the traditional net present
value valuation method which does not take in to account the managerial flexibility.
Using Traditional NPV approach:
Description Probability
of success. Joint
Probability Investment Joint prob. X
Investment Discounted
value
(1) (2) (3) (4) (5) =(3) x (4) (6)
t=0 Beginning 100% 100.00% -2 -2.00 -2.00
t=1 Phase I 5% 5.00% -5 -0.25 -0.23
t=2 Phase II 50% 2.50% 10* 0.25 0.20
* Value of Asset X $20 – Investment $10 NPV -2.022
The project is rejected.
5.5 Real Option Value with Technical and Market Uncertainty
In this section we apply the real option framework to evaluate the R&D investment in a
second numerical example. The example was first presented in Shockley (2007). We
proceed as follows. We first set up the problem. Second, we compute the option value of
the R&D project assuming that we face both technical and market uncertainties. Here,
there are two approaches to compute the option value as given in Copeland and
Antikarov (2001) and Shockley (2007). Finally, we attempt to link the assumptions on
the value of underlying with the theory given in Schwartz and Mark (2000).
A caveat is appropriate here. The language of the original pharmaceutical example has
been maintained as our main objective was to compare the two analytical methodologies.
This can be easily modified to Office of Science projects with no changes in the results.
Moreover, the process has been fully automated as will be mentioned in a later section
and the values of the variables can be readily varied for sensitivity analysis.
5.5.1 Problem Definition
The examined R&D project consists of five stages, with the investment, probability of
success, and time to completion for each stage is given below.
21
During the R&D phase
Number of years of R&D phase 8 years
Total number of stages 5
Stages
Investment (in
millions)
Probability
of Success
Duration in
year
Preclinical development $6.0 75% 1
Phase I $15.0 50% 1.5
Phase II $25.0 66.67% 2
Phase III $150.0 50% 2.5
NDA filing $15.0 95% 1
Launch $50.00
The management needs to make a decision at time 0, which we assume as 12/31/2003,
whether to make an investment of $6 million on the preclinical development.
The timeline of the problem is given in Table 1.
[TABLE 1 ABOUT HERE]
Assuming R&D success, the future cash flow (net revenue) generated by the marketed
drug is as follows:
Assumptions about Cash flows on Marketed DrugTime period Sales revenue (mm)
January - June 2012 20
July - December 2012 60
January - June 2013 125
July - December 2013 200
January - June 2014 250
July - December 2014 250
January - June 2014 275
July - December 2015 275
Percentage growth every six months through june 2018 -10%
Perpetual growth every year after June 2018 -20%
Direct expenses of making and selling drug as a % of revenues 20%
Marginal tax rate 18%
Hurdle rate for marketed drug 14%
Step 1. Based on the above-given information, we can compute the discounted cash flow
valuation of the R&D project at the end date of the research. The value of the R&D
project X on 12/31/2011 (eight years after 2003) is $1,101.10 million.
Step 2. We further discount this value at the given discount rate of 14% to time 0 (today).
22
million386$%141
10.11018
The detailed computation is given in Table 2.
[TABLE 2 ABOUT HERE]
The above calculation is useful in both methods used to compute the option value.
5.5.2 Shockley (2007) Method
Shockley follows a two-step procedure. He incorporates first the market uncertainty and
then the technical uncertainty.
Step 3. We assume volatility to be 50% corresponding to the market uncertainty.
Step 4. We prepare the binomial tree of all possible outcomes of the underlying asset
(outcome of the R&D project).
We start from the computed discounted value of X today ($386 million) to calculate the
tree for the eight years of the research projects as in Table 3.
[TABLE 3 ABOUT HERE]
Step 5. We compute the value of compound option assuming there is no technical risk.
We move backwards starting from the end values. We compute the value of risk neutral
probability and utilize the fact that the option value cannot be negative: we will undertake
the investment only if the net value is greater than zero. The detailed tree is shown in
Table 4.
[TABLE 4 ABOUT HERE]
Up to this point, the procedure is basically the same as in the example of technical only
uncertainty in Section 4.4, even though we were dealing with market uncertainty. We
now move to incorporate technical uncertainty.
Step 6. We modify our values obtained in Step 5 to incorporate the technical probability
of success. The detailed tree is given in Table 5.
23
[TABLE 5 ABOUT HERE]
As an illustration of the calculations in this step we use the example of how we arrived at
value $73,660 million shown in the first row of NDA stage on Jun-11 column.
Jun-11 Dec-11
73,660 104,919
51,708
We use the values obtained in Step 5 on Dec-11. They are:
Dec-11
110,442
54,430
The probability of launch is given as 95%. We will multiply the above given value with
95% and move backwards using the risk neutral probabilities and risk free rate. The risk
free rate has been given at 5%. The risk neutral probabilities are
Where, fr risk-free rate
teu = .......... = 0.4476
ted = ........... = 0.5524
Substituting the values, we get q = , and 1-q = .
Thus,
%)5*5.0exp(
5524.0*95.0*430,544476.0*95.0*442,110 = 73,660
Step 7. If the option value is more than the initial investment, then, undertake the project.
In our example (Figure 5), the value at time 0 is $8.96 million which is more than the $6
million of required initial investment. The management should pursue R&D investment.
du
dequpprobNeutralRisk
tr f
*
)(.
24
5.5.3 Copeland and Antikarov (2001) Method: Quadranomial
It is assumed that the price of the product generated from the R&D project is known at
time 0 and that it follows a random walk, i.e., the expected future price is the same as the
current price. They also assume the quantity sold fixed. On this basis, it can be assumed
that the value of the project also follows a random walk. The value of the R&D project is,
as always, the net revenue from selling the resulting product (revenue minus costs).
5.5.3.1 R&D project value follows a random walk without drift
Step 3. Volatility equals 50%.
Step 4. We prepare the binomial tree of all possible outcomes of the underlying value of
the R&D project.
This is similar to step 4 of Shockley (2007). However, in this case, we assume the value
of the project to be the same at the beginning as the value of the project upon successful
completion of the research eight years later. This value was found to be $1,101 million in
Step 1. Table 6 presents the detailed computations.
[TABLE 6 ABOUT HERE]
Step 5. We compute the value without considering any flexibility.
Essentially, we will compute the net present value with out using the option pricing
theory. That is, without using the information that we can abandon the project if the value
is negative. Here also, we will move backwards with the starting point equal to all the
values in the last scenario from the Step 1 above. Then, we move backwards using the
risk neutral probabilities, risk free rate, and the technical success on the nodes wherever it
is applicable. The details are given in Table 7.
[TABLE 7 ABOUT HERE]
Without considering any flexibility, the value of the R&D project is found to be $24.52
million, which is well above the initial required investment of $6 million. The project is
justified.
Step 6. We now incorporate the flexibility in the computation of the option value.
25
Using the information about the end-values obtained in Step 5 above, and the flexibility
that the management can abandon the project if the value is negative, we obtain the
option value as given in Table 8.
[TABLE 8 ABOUT HERE]
The value of the option at t=0 equals $79.92 million, an even cleaner sweep above the $6
million of the initial investment. The R&D investment is justified.
One can try to compare this option value with the option value that can be obtained with
the Shockley method (Section 4.5.2). Under the assumption of random walk, the resulting
option values are only marginally different, $81.43 million versus $79.92 million.
5.5.3.2 R&D project value follows a random walk with drift
Step 4. We prepare the binomial tree of all possible outcomes of the underlying value of
the project.
We use the initial value of $386 million. Volatility equals 50%. Following the procedure
explained in Step 4 of Section 4.5.2 and obtain the same values as given in Figure 3.
Step 5. We compute the value without considering any flexibility.
We follow the procedure similar to that in Step 5 of Section 4.5.3.1 to obtain the values
shown in Table 9.
[TABLE 9 ABOUT HERE]
Step 6. We now incorporate the flexibility in the computation of the option value.
Here also, we follow the procedure similar to that as shown in Step 6 of Section 4.5.3.1.
See Table 10 for details.
[TABLE 10 ABOUT HERE]
We obtain the value of option at time $8.96 million. Notice that this value is similar to
that of the Shockley (2007) method in Section 4.5.2.
26
5.5.4 Concluding Remarks
The methods of Shockley (2007) and Coperland and Antikarov (2001) in determining the
compound option value of an R&D investment in the presence of both technical and
market uncertainty have been found to be essentially equivalent. Their results are
identical when the R&D project value is assumed to follow a random walk with a drift.
Finally, it is important to draw the link with the continuous time models and, especially,
the model by Schwartz and Moon (2000) that was identified earlier as the one with the
most attractive features to the typical situation of R&D projects and programs of the
Office of Science. In Schwartz and Moon (2000) the asset value uncertainty is assumed
to follow the following stochastic process:
dwVdtVdV
Where, V Value of asset upon successful completion of the project
Drift rate
dw Increment to Gauss-Wiener process
Instantaneous standard deviation of the proportional changes in the asset value
received upon successful completion of R&D
It can be observed that the discrete time methods of Shockley (2007) and Copeland and
Antikarov (2001) use this theoretical background to calculate the R&D project option
value with the drift rate equal to the cost of capital.
6. Model Automation
Section 5 showed stylized models for three analytical methods with different assumptions
about the existence and the role of uncertainty. We have spent significant time and
resources in this research effort to ‘automate’ the Excel spreadsheets on which the
models have been set up and work on the underlying software so that the method is fully
flexible. This has been achieved with both the binomial model (only technical
uncertainty) and the quadronomial model (technical and market uncertainties).
In other words, we have built a process through which it takes no more than a few
seconds to calculate the option value of any R&D project at time t=0 when one or more
of variables or of the fundamentals of the model are modified. This includes all of the
important information listed in Section 5.3 including the number of investment phases,
any of the costs, time to completion, probability of success of each phase, value of the
underlying asset, price of capital, ad investment for commercialization.
The results are impressive, allowing for instant and full sensitivity analysis of either the
binomial or quadranomial model. We have made several presentations of the automated
model to DOE officials over the later phases of the project.
27
7. Conclusion
Almost a decade after Vonortas and Hertzfeld (1998) called for adaptation and use of the
real options methodology in ex ante appraisals of public R&D programmes, the follow-
up has been light relatively to much more extensive application in the private sector.
Some public agencies have, indeed, moved to study the methodology and its adaptability
to their needs: they have included agencies like the Department of Energy in the United
States which deal with technologies and markets in which the methodology found its
earliest applications in the private sector.6 The energy field is related to the area of natural
resource investments where the methodology was applied first due to the availability of
traded resource or commodity prices, high volatilities (uncertainties), and long duration
(Myers, 1977). Pharmaceuticals and biotechnology have been another large area of
application. By now, the use of options methodologies in the private sector is extensive as
it is obvious that a very significant part of the market valuation of both large and small
knowledge-based companies reflects the technology options they hold.
We have aligned with the reviewed literature to argue that the ‘real options’ methodology
has a lot of strengths and should be considered seriously. In particular, we believe that
this method has significant potential for creating a complementary, rigorous mechanism
to the established expert review procedures for research priority setting and evaluation
across federal agencies in general, and the Department of Energy in particular. Expert
reviews and options appraisals of R&D programs should complement, leverage, and
enhance each other. A host of recent methodological improvements in assessing both
event probabilities and the risks involved in uncertain non-financial investments have
become available during the past couple of decades and can now be exploited to greatly
enhance formal assessments of strategic, long-term research programs.
This project has made significant progress in streamlining the real options methodology
by focusing on its application for the justification of research programs by the Office of
Science. In particular, we have:
(a) Identified the background theoretical real options model which better applies to the
needs of the Office of Science;
(b) Translated complicated notions of the theoretical real options model, especially with
respect to the core concept of uncertainty, into structures much more straightforward and
better understood by the average research program manager;
(c) Identified the necessary variables for R&D program appraisal and argued that they are
quite feasible to produce and that they critically depend on the technical knowledge of the
research project in question as produced by the consultative procedures of the Office of
Science already in place;
(d) Built realistic examples and worked them out fully in order to indicate how these
simplified models account for the important considerations that the Office of Science
cares about;
6 See, for example, Davies and Owens (2003) and Vonortas and Desai (2004).
28
(e) Built two versions of the application model (binomial, quadranomial) to handle the
different types of uncertainty that are prevalent during the life time of the examined
research project and beyond (technical and market uncertainty);
(f) Showed that, by capturing the value of flexibility in managerial decision-making,
these models produce much more value that can be utilized to justify research programs
more and beyond the traditional quantitative approached such as net present value and
return on investment;
(g) Fully automated both application models (binomial, quadranomial) so that their
application by non-experts is a simple matter.
Of course, any model is as good as the assumptions built into it. That is why we advocate
a good understanding of the situation for analysis before structuring the model. Early in
the impact assessment process, the nature, scope, and roles of the relevant technology
must be mapped out and related to the relevant industries and the competitive dynamics
of the associated markets. Such background and economic context analysis requires an
applied microeconomic and industrial organization approach so that technology trends,
corporate strategies, and any external influences such as regulations can be combined into
a context for understanding the role of the R&D programme being studied. Identifying
the “relevant” industries is particularly important because the selection will determine the
population to be analyzed. Public research support will have direct impacts on the
industries that develop the technology and on those industries that buy the technology.
This is the relevant set of players to be analyzed. Economic impacts will naturally extend
to other industries and eventually to the final users in the relevant supply chains.
However, the relationships between the original R&D investment and its impacts in these
downstream industries and users become increasingly blurred due to the classic problem
of attribution: too many diverse influences creating noise in the calculations (Tassey,
2003).
The next step should involve the application of a better understood and fairly simple
options approach, known as the binomial model and/or the quadranomial model
(depending on the uncertainties to be treated). Such estimation has been shown to provide
a fairly good approximation to estimation through more formal ‘real options’ models.
Enhanced through sensitivity analysis, scenario analysis and, perhaps, simulation to
determine the probabilities associated with different outcomes, binomial and
quadranomial models could be used to build decision trees that can provide fairly
accurate results and are better understood – less intimidating – by practitioners.
In the near future, the Office of Science should proceed with a full experimental
application of the real options models developed herein to one or more of its research
programs. We believe that the theory has been developed sufficiently for such an
application.
29
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Vonortas, N. S. and M. Lackey (2003) “Real options for public sector R&D investment”,
in S. Kuhlmann and P. Shapira (eds.), Learning from Science and Technology Policy
Evaluation: Experiences from the United States and Europe, Edward Elgar.
1
Table 1. Product Development Timeline
Today
12/31/2003 Jun-04 Dec-04 Jun-05 Dec-05 Jun-06 Dec-06 Jun-07 Dec-07 Jun-08 Dec-08 Jun-09 Dec-09 Jun-10 Dec-10 Jun-11 Dec-11
Probability of
success
Already
here 75% 50% 66.667% 50% 95%
Decision given
success
Go to
preclinical?
Go to Phase
I?
Go to
Phase II?
Go to
Phase III?
Go to
NDA?
Go to
launch?
Cost (mm) $6 $15 $25 $150 $15 $50
NDAPreclinical Phase I Phase II Phase III
2
Table 2. Discounted cash flow (net revenue) valuation of new product assuming technical success through launch (in millions)
Annual hurdle rate 14%
6 month hurdle rate 6.77%
Risk free rate 5%
Today Launch
31-Dec-03 31-Dec-11 2012-1 2012-2 2013-1 2013-2 2014-1 2014-2 2015-1 2015-2 2016-1 2016-2 2017-1 2017-2 2018-1
Sales revenue 20.00 60.00 125.00 200.00 250.00 250.00 275.00 275.00 247.50 222.75 200.48 180.43 162.38
Direct expenses 4.00 12.00 25.00 40.00 50.00 50.00 55.00 55.00 49.50 44.55 40.10 36.09 32.48
Gross Margin 16.00 48.00 100.00 160.00 200.00 200.00 220.00 220.00 198.00 178.20 160.38 144.34 129.91
Taxes 2.88 8.64 18.00 28.80 36.00 36.00 39.60 39.60 35.64 32.08 28.87 25.98 23.38
Free cash flow 13.12 39.36 82.00 131.20 164.00 164.00 180.40 180.40 162.36 146.12 131.51 118.36 106.52
Terminal value 250.65
Total FCF 13.12 39.36 82.00 131.20 164.00 164.00 180.40 180.40 162.36 146.12 131.51 118.36 357.17
Expected PV at launch $1,101.10
PV today 386.00
3
Table 3. Binomial Tree of underlying asset (R&D output) values
Today
31-Dec-03 Jun-04 Dec-04 Jun-05 Dec-05 Jun-06 Dec-06 Jun-07 Dec-07 Jun-08 Dec-08 Jun-09 Dec-09 Jun-10 Dec-10 Jun-11 Dec-11
386 550 783 1,115 1,588 2,261 3,220 4,586 6,531 9,300 13,245 18,862 26,862 38,255 54,480 77,586 110,492
271 386 550 783 1,115 1,588 2,261 3,220 4,586 6,531 9,300 13,245 18,862 26,862 38,255 54,480
190 271 386 550 783 1,115 1,588 2,261 3,220 4,586 6,531 9,300 13,245 18,862 26,862
134 190 271 386 550 783 1,115 1,588 2,261 3,220 4,586 6,531 9,300 13,245
Vol. 50% 94 134 190 271 386 550 783 1,115 1,588 2,261 3,220 4,586 6,531
Δt 0.5 66 94 134 190 271 386 550 783 1,115 1,588 2,261 3,220
U 1.424 46 66 94 134 190 271 386 550 783 1,115 1,588
D 0.702 32 46 66 94 134 190 271 386 550 783
23 32 46 66 94 134 190 271 386
16 23 32 46 66 94 134 190
11 16 23 32 46 66 94
8 11 16 23 32 46
6 8 11 16 23
4 6 8 11
3 4 6
2 3
1
NDAPreclinical Phase I Phase II Phase III
4
Table 4. Value of compound option on marketed product, assuming no technical risk
Today
31-Dec-03 Jun-04 Dec-04 Jun-05 Dec-05 Jun-06 Dec-06 Jun-07 Dec-07 Jun-08 Dec-08 Jun-09 Dec-09 Jun-10 Dec-10 Jun-11 Dec-11
217 362 580 916 1,382 2,050 3,030 4,391 6,331 9,095 13,188 18,804 26,803 38,194 54,417 77,537 110,442
111 202 361 581 904 1,397 2,066 3,020 4,381 6,474 9,242 13,185 18,801 26,800 38,206 54,430
42 109 200 345 593 920 1,388 2,056 3,163 4,528 6,471 9,239 13,182 18,814 26,812
18 40 92 207 355 583 910 1,531 2,203 3,161 4,525 6,468 9,252 13,195
0 0 49 97 186 345 726 1,057 1,528 2,200 3,158 4,537 6,481
0 6 13 29 67 329 492 723 1,054 1,525 2,212 3,170
0 0 0 0 135 213 326 489 720 1,066 1,538
0 0 0 45 79 131 210 323 501 733
Risk free 5% 0 0 10 21 40 73 128 222 336
exp(r*Δt) 1.025 0 1 3 6 14 32 85 140
q 0.4476 0 0 0 0 0 19 44
1-q 0.5524 0 0 0 0 0 0
0 0 0 0 0
0 0 0 0
0 0 0
0 0
0
Prob. of
success
Already
here 75% 50% 66.667% 50% 95%
Decision
given
success
Go to
preclinical
?
Go to
Phase I?
Go to
Phase II?
Go to
Phase III?
Go to
NDA?
Go to
launch?
Cost (mm) $6 $15 $25 $150 $15 $50
NDAPreclinical Phase I Phase II Phase III
5
Table 5. Value of compound option on marketed product, assuming technical risk
Today
31-Dec-03 Jun-04 Dec-04 Jun-05 Dec-05 Jun-06 Dec-06 Jun-07 Dec-07 Jun-08 Dec-08 Jun-09 Dec-09 Jun-10 Dec-10 Jun-11 Dec-11
8.96 19 41 117 188 292 910 1,340 1,953 2,827 6,264 8,932 12,731 18,142 25,848 73,660 104,919
1 2 35 64 112 394 604 905 1,334 3,075 4,390 6,263 8,930 12,730 36,296 51,708
0 5 13 29 144 241 388 598 1,502 2,150 3,073 4,388 6,261 17,873 25,472
0 0 0 37 71 133 235 727 1,046 1,501 2,149 3,072 8,789 12,535
0 0 5 11 25 56 345 502 726 1,045 1,499 4,310 6,157
0 0 0 0 0 156 233 343 500 724 2,102 3,012
0 0 0 0 64 101 155 232 342 1,013 1,461
0 0 0 21 37 62 99 153 476 696
Risk free 5% 0 0 5 10 19 34 60 211 319
exp(r*Δt) 1.025 0 1 1 3 7 15 81 133
q 0.4476 0 0 0 0 0 18 42
1-q 0.5524 0 0 0 0 0 0
0 0 0 0 0
0 0 0 0
0 0 0
0 0
0
Prob. of
success
Already
here 75% 50% 66.667% 50% 95%
Decision
given
success
Go to
preclinical
?
Go to
Phase I?
Go to
Phase II?
Go to
Phase III?
Go to
NDA?
Go to
launch?
Cost
(mm) $6 $15 $25 $150 $15 $50
NDAPreclinical Phase I Phase II Phase III
6
Table 6. Free cash flow (net revenue) tree, assuming that the underlying value follows a random walk without drift
Today
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8
1,101 1,568 2,233 3,180 4,529 6,450 9,186 13,081 18,629 26,530 37,782 53,807 76,627 109,126 155,409 221,320 315,187
773 1,101 1,568 2,233 3,180 4,529 6,450 9,186 13,081 18,629 26,530 37,782 53,807 76,627 109,126 155,409
543 773 1,101 1,568 2,233 3,180 4,529 6,450 9,186 13,081 18,629 26,530 37,782 53,807 76,627
381 543 773 1,101 1,568 2,233 3,180 4,529 6,450 9,186 13,081 18,629 26,530 37,782
268 381 543 773 1,101 1,568 2,233 3,180 4,529 6,450 9,186 13,081 18,629
188 268 381 543 773 1,101 1,568 2,233 3,180 4,529 6,450 9,186
132 188 268 381 543 773 1,101 1,568 2,233 3,180 4,529
93 132 188 268 381 543 773 1,101 1,568 2,233
65 93 132 188 268 381 543 773 1,101
46 65 93 132 188 268 381 543
32 46 65 93 132 188 268
23 32 46 65 93 132
16 23 32 46 65
11 16 23 32
8 11 16
5 8
4
NDAPreclinical Phase I Phase II Phase III
7
Table 7. Value with no flexibility
Today
31-Dec-03 Jun-04 Dec-04 Jun-05 Dec-05 Jun-06 Dec-06 Jun-07 Dec-07 Jun-08 Dec-08 Jun-09 Dec-09 Jun-10 Dec-10 Jun-11 Dec-11
24.52 47 88 252 717 2,042 2,909 4,142 5,899 12,602 17,947 25,558 36,398 51,835 147,638 210,254 315,187
23 44 124 354 1,007 1,434 2,042 2,909 6,214 8,849 12,602 17,947 25,558 72,796 103,670 155,409
21 61 174 497 707 1,007 1,434 3,064 4,363 6,214 8,849 12,602 35,893 51,116 76,627
30 86 245 349 497 707 1,511 2,151 3,064 4,363 6,214 17,698 25,204 37,782
42 121 172 245 349 745 1,061 1,511 2,151 3,064 8,726 12,427 18,629
60 85 121 172 367 523 745 1,061 1,511 4,303 6,127 9,186
42 60 85 181 258 367 523 745 2,122 3,021 4,529
29 42 89 127 181 258 367 1,046 1,490 2,233
Risk free 5% 21 44 63 89 127 181 516 735 1,101
exp(r*Δt) 1.025 22 31 44 63 89 254 362 543
q 0.4476 15 22 31 44 125 179 268
1-q 0.5524 11 15 22 62 88 132
8 11 30 43 65
5 15 21 32
7 11 16
5 8
4
NDAPreclinical Phase I Phase II Phase III
8
Table 8. Option value
Today
31-Dec-03 Jun-04 Dec-04 Jun-05 Dec-05 Jun-06 Dec-06 Jun-07 Dec-07 Jun-08 Dec-08 Jun-09 Dec-09 Jun-10 Dec-10 Jun-11 Dec-11
79.92 132 278 441 653 1,911 2,800 4,030 5,784 12,425 17,919 25,530 36,369 51,806 147,578 210,208 315,137
42 101 186 289 876 1,325 1,931 2,794 6,037 8,822 12,574 17,918 25,529 72,736 103,624 155,359
21 64 112 365 598 895 1,319 2,887 4,336 6,186 8,820 12,573 35,833 51,070 76,577
14 29 118 239 385 592 1,334 2,124 3,036 4,335 6,184 17,638 25,158 37,732
3 13 72 133 234 568 1,034 1,483 2,123 3,034 8,666 12,381 18,579
0 12 26 57 191 496 717 1,032 1,481 4,242 6,081 9,136
0 1 1 5 231 339 494 715 2,061 2,975 4,479
0 0 0 100 153 229 338 986 1,443 2,183
Risk free 5% 0 0 37 62 99 152 456 688 1,051
exp(r*Δt) 1.025 0 10 19 35 60 194 316 493
q 0.4476 2 4 8 16 65 132 218
1-q 0.5524 0 1 1 7 42 82
0 0 0 6 15
0 0 0 0
0 0 0
0 0
0
Prob. of
success
Already
here 75% 50% 66.667% 50% 95%
Decision
given
success
Go to
preclinical?
Go to
Phase I?
Go to
Phase II?
Go to
Phase III?
Go to
NDA?
Go to
launch?
Cost (mm) $6 $15 $25 $150 $15 $50
NDAPreclinical Phase I Phase II Phase III
9
Table 9. Value with no flexibility
Today
31-Dec-03 Jun-04 Dec-04 Jun-05 Dec-05 Jun-06 Dec-06 Jun-07 Dec-07 Jun-08 Dec-08 Jun-09 Dec-09 Jun-10 Dec-10 Jun-11 Dec-11
8.59 16 31 88 251 716 1,020 1,452 2,068 4,418 6,291 8,960 12,760 18,171 51,756 73,707 110,492
8 15 44 124 353 503 716 1,020 2,178 3,102 4,418 6,291 8,960 25,519 36,342 54,480
8 21 61 174 248 353 503 1,074 1,530 2,178 3,102 4,418 12,583 17,919 26,862
11 30 86 122 174 248 530 754 1,074 1,530 2,178 6,204 8,835 13,245
15 42 60 86 122 261 372 530 754 1,074 3,059 4,356 6,531
21 30 42 60 129 183 261 372 530 1,508 2,148 3,220
15 21 30 63 90 129 183 261 744 1,059 1,588
10 15 31 45 63 90 129 367 522 783
Risk free 5% 7 15 22 31 45 63 181 257 386
exp(r*Δt) 1.025 8 11 15 22 31 89 127 190
q 0.4476 5 8 11 15 44 63 94
1-q 0.5524 4 5 8 22 31 46
3 4 11 15 23
2 5 8 11
3 4 6
2 3
1
NDAPreclinical Phase I Phase II Phase III
10
Table 10. Option value assuming the value follows a random walk with drift
Today
31-Dec-03 Jun-04 Dec-04 Jun-05 Dec-05 Jun-06 Dec-06 Jun-07 Dec-07 Jun-08 Dec-08 Jun-09 Dec-09 Jun-10 Dec-10 Jun-11 Dec-11
8.96 19 55 117 188 585 910 1,340 1,953 4,241 6,264 8,932 12,731 18,142 51,696 73,660 110,442
1 3 35 64 224 394 604 905 2,002 3,075 4,390 6,263 8,930 25,459 36,296 54,430
0 5 13 58 144 241 388 897 1,502 2,150 3,073 4,388 12,523 17,873 26,812
0 0 0 37 71 133 353 727 1,046 1,501 2,149 6,144 8,789 13,195
0 0 5 11 25 85 345 502 726 1,045 2,999 4,310 6,481
0 0 0 0 0 156 233 343 500 1,448 2,102 3,170
0 0 0 0 64 101 155 232 684 1,013 1,538
0 0 0 21 37 62 99 307 476 733
Risk free 5% 0 0 5 10 19 34 121 211 336
exp(r*Δt) 1.025 0 1 1 3 7 30 81 140
q 0.4476 0 0 0 0 0 18 44
1-q 0.5524 0 0 0 0 0 0
0 0 0 0 0
0 0 0 0
0 0 0
0 0
0
Prob. of
success
Already
here 75% 50% 66.667% 50% 95%
Decision
given
success
Go to
preclinical?
Go to
Phase I?
Go to
Phase II?
Go to
Phase III?
Go to
NDA?
Go to
launch?
Cost (mm) $6 $15 $25 $150 $15 $50
NDAPreclinical Phase I Phase II Phase III
1