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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

mailto:[email protected]

http://gwu.edu/~cistp

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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)

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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

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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







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.


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.


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.


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


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.


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.


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.


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.


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.


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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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


4

Table 4. Value of compound option on marketed product, assuming no technical risk

Today


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


5

Table 5. Value of compound option on marketed product, assuming technical risk

Today


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


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


7

Table 7. Value with no flexibility

Today


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


8

Table 8. Option value

Today


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


9

Table 9. Value with no flexibility

Today


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


10

Table 10. Option value assuming the value follows a random walk with drift

Today


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


‘REAL OPTIONS’ FRAMEWORK - Unicamp · The ‘real options’ methodology has, then, significant...

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