research Centre of the Netherlands:
The value of a real options approach
Petten, the Netherlands, December 2007
Technology valuation at the Energy
research Centre of the Netherlands:
The value of a real options approach
MSc Thesis
Jasper Leijsten
Jasper@Leijsten.nl
Rijksuniversiteit Groningen
MSc International Business and Management
Specialization: International Financial Management
&
Uppsala Universitet
MSc Economics and Business
ABSTRACT
High uncertainty about future prospects of patents and technology early in their lives complicates the valuation process significantly. Traditional NPV methods have difficulties in dealing with operational and strategic flexibility that is embedded in
technology projects. Extending the NPV analysis with real option valuation can provide a useful solution. This thesis discusses the traditional approaches as well as a
real option approach to valuation. It explores the research portfolio of ECN and applies real option valuation to a practical example of ECN technology: the thermo
acoustic heat pump project. These results are tested on their robustness to different assumptions in the valuation. It concludes by proposing option based valuation as a useful and potentially powerful tool for valuation of patents and technology for ECN.
KEYWORDS
Valuation, Patents, Technology, Traditional NPV, Real option theory, Flexibility, Time-to-build option, Growth option, ECN.
JEL CODES
PREFACE
Completing this thesis marks the end of my studies in International Financial Management (IFM), a joint Master of Science program of the University of Groningen and the Uppsala University.
During the last seven months I have had the wonderful opportunity to combine the process of writing this thesis with an interesting internship at the Energy research Centre of the Netherlands (ECN). For a business and economics student, the environment of a high level technology research institute is truly an adventure.
From ECN I would like to thank Albert Fischer and Marco Pieterse for their support, supervision and out-of-the-box thinking. I would like to thank Ton Hoff and Kees van der Klein for the possibility to conduct this research. The openness with which ECN welcomes their employees is a very motivating and valuable contribution in creating a successful research environment. I like to thank Janny Minheere who made my life so much easier and provided me with all the practical and cheery support thinkable. From the university of Groningen I would like to thank dr. P.P.M Smid for his comments and reflections during his direct academic supervision on this research. and dr. C.L.M. Hermes for all his efforts in setting-up and coordinating the joint IFM program together with the Uppsala University, which I really enjoyed.
Finally, I would like to thank my family for their strong support during my entire educational epoch, and my father in particular for the safeguard of being able to make my own choices and pursue my ambitions. I guess, to have the incredible patience this young academic mind has needed, should be called quite an achievement in itself. I hope that reading this thesis will be a pleasant and interesting experience and that it may provide you with useful information.
INDEX
Abstract... 2 Preface ... 3 Index ... 4 1. Introduction ... 6 1.1 Background ... 61.2 Patents and underlying inventions ... 8
1.3 Why value patents... 9
1.4 Problem Statement...10
1.5 Structure of the report ...11
2. Patent Valuation models ...12
2.1 Patent Valuation Models ...12
3. Traditional income based methods...15
3.1 Static NPV model ...15
3.2 Sensitivity analysis ...16
3.3 Traditional Simulation (ECNs Strategic Decision Analysis) ...16
3.4 Decision Tree Analysis (DTA)...18
4. Real Options theory...20
4.1 Basic idea ...20
4.2 Financial options analogy ...21
4.3 Concepts of Real Options theory...23
4.4 Real options in Projects...27
4.5 Interactions among real options...31
5. R&D at ECN ...32
5.1 R&D in general...32
5.2 The R&D process at ECN ...32
6. ECN Real Case...35
6.1 The thermo acoustic heat pump project ...35
6.2 Embedded options ...36
6.3 Option interactions...39
7. Framework for valuation...40
7.1 Assumptions ...40
7.3 Valuation method for ENPV ...42
7.5 The ENPV including real options...45
8. Valuation results of the TAHP project ...46
8.1 Static NPV...46
8.2 ENPV including real options...46
9. Sensitivity analysis ...51
9.1 Gross present value sensitivity ...51
9.2 Volatility sensitivity...52
9.3 Abandonment value sensitivity ...53
9.4 Follow-on project size sensitivity...54
10. Conclusion...56
Literature:...60
INTRODUCTION
This thesis is about the valuation of technology at the Energy research Centre of the Netherlands (ECN). It explores different approaches to the valuation of technology and determines which approach is most suitable for ECN: a real options approach. Subsequently this finding is extended with the building of a concrete valuation framework for a real ECN technology: the Thermo Acoustic Heat Pump (TAHP). The TAHP project will be used to test and demonstrate the working of a real option approach for ECN and determine the value of this project for ECN.
This introductory chapter will provide background on ECN and the environment it operates in. Subsequently it will make a distinction between patents and their underlying inventions. Finally the chapter will explain what it means to value a patent and for what reasons patents are being valued.
1.1 Background
In today’s increasingly globalized knowledge-based world the push for innovation and economical progress is evident. It is not only the Western world that develops primary technologies and drives growth anymore. Every day, increasing pressure is felt from China, India, and other Asian economies, not only on the matter of labour but increasingly also competition is felt on the level of inventing state-of-the-art technology. The goal of Europe that was set in the Lisbon accords to be back in the world’s top in the field of research and innovation in 2010 is ambitious. At the moment Japan and the US invest higher percentages of their GDP on academic research, whereas China will be spending the same as Europe from 2008 on [World energy Outlook, 2007]. In short: the pressure is on and the need for high level academic research is clear.
their knowledge into potential fruits: economic and employment growth [Australian Centre for Innovation, 2002].
Being the largest research centre in the Netherlands in the area of fuel cells, biomass, wind and solar energy, the Energy research Centre of the Netherlands (ECN) is rethinking its strategic position as well. Its long-term goal of developing high-level knowledge and technology for the transition to a sustainable energy system will remain unchanged and authority in project selection and decision-making should remain independent. Moreover, ECN has taken on the challenge to accept a larger responsibility in getting their inventions implemented in the market place.
On a regular basis ECN researchers patent their newly found technologies to protect them, as a first step to commercial exploitation. However, only a small proportion of patents turn out to be of extra-ordinary value in the long run. Considering the fact that intellectual property (IP) budgets are limited, it is essential to know the value of patents sufficiently to make well-founded decisions about their management [Hoogwijk, 2004]. Management in this sense could be the decision to pay the fees of extending a patent, but it could also imply strategically important decisions. E.g. in what way a patent can be, or should be commercialized, or the decision what would be a reasonable price for the sale of a patent, or a license on technology.
However, regardless of the motivation for valuing a patent, the value cannot be determined by regarding the patent as an ordinary investment project. A patent should be seen as a complex series of possibilities, each involving costs and actual benefits or potential future benefits that unfold over time under conditions of often considerable uncertainty and with a considerable variety of courses of action [Pitkethly, 2002]. This is due to the highly uncertain outcomes of the patent application process, the technical success of the underlying invention, and in the end, the commercial viability of the invention.
efficient markets, would according to Kamiyaka et al. [2006, p. 6], be able to: “improve innovations processes by facilitating exchanges of patented inventions (via sale or licensing) among private and public sector actors that can put inventions in the hands of those most able to commercialize them.” When stating this, Kamiyaka et al. touch upon an essential point: that most value from technology may be extracted when it is commercialized by a party that is able to do so in an effective manner. This does not necessarily mean that commercialization has to be outsourced completely, nor does it have to be done fully in-house. It can be done in partnerships, joint ventures or any hybrid structure that would be most suitable.
For ECN to find suitable and successful modes of commercializing their knowledge and technology appears to be an interesting and challenging task. Moreover, it could undoubtedly be a very rewarding one, both in terms of earnings and the success in bringing technology to the market.
1.2 Patents and underlying inventions
There are different ways to look at the value of a patent or a technology. First of all one should decide what one wants to look at exactly: the patent itself as being a grant of legal protection against infringers, the underlying invention or the complete development and commercialization project of the technology [Pitkethly, 2002]. When this is clear, there are several approaches to value technology, each with its own concrete valuation models.
Looking at the value of the patent itself, separated from the underlying invention, Pitkethly [2002, p. 2] defines the patents value as follows: “The value of the potential extra profits obtainable from fully exploiting the invention defined by the patent’s claims in the patent’s presence compared with those obtainable without patent protection.”
however, the interest will be on the matter of the complete project, and the value of the patent in combination with the commercialization of the underlying project.
1.3 Why value patents
Organizations shift more and more to open models of innovation based on collaboration and external sourcing of knowledge. They are exploiting their IP, notably patents, not only by incorporating their products into new products, processes and services, but also by licensing them among other firms or research institutes. More and more IP is used as bargaining chips in negotiations and as a means of attracting external financing from venture capitalists, banks and other sources [Kamiyama et al., 2006]. Patent values could be needed internally to determine royalty rates for patent licensing contracts, for possible mergers or acquisitions, or when estimating the corporate value of the organization. Financial analysts value patents to assess the value of organizations as a basis for investment decisions and recommendations [Kamiyama et al., 2006].
The valuation of a technology can form a starting point for negotiations between buyer and seller. A more objective valuation would be able to serve as a better reference price in the negotiations and consequently promote technology transfer. [Boer, 2004]. Therefore, to effectively trade patents and IP there is a need for effective IP valuation methods.
93
Fig. 1.1: Source: Otsuyama [2003, p. 106]
1.4 Problem Statement
This research is done in the light of the cooperation between ECN and Planet Capital. Planet Capital is a venture development and venture capital firm, with a focus on sustainable technology and services. It is hired by ECN to help the institute exploring the opportunities for commercialization of innovative technologies, defining future commercialization strategies and to assess the commercial values of its technologies and patents. Furthermore Planet Capital assists ECN in entrepreneurial projects, for example the formation of new start-up companies and advises on deal structures in licensing negotiations.
ECN has been approached by a large investment group that wants to make an offer for a large package of IP with the prospects of commercializing the technology. ECN has to make a choice in its commercialization strategy and decide whether it would be more interesting for them to monetize their technology and knowledge in one package (outsourcing the commercialization process to a large player), or whether it is more interesting for ECN to commercialize its technology and patents one by one and extract the real underlying value themselves on a project-to-project basis.
To decide on the issue above, ECN needs to value its IP portfolio. The purpose of this thesis is to advice on how to value ECNs technology to later on provide valuable
IP valuation becomes essential IP valuation becomes important Value of IP is recognized independently Value of IP gradually becomes important Need for IP valuation is low
IP exploitation as financial assets
- Financing method for IP holding firms - Investing assets for financial institutions
IP exploitation as management strategy
- Securing ideal patent portfolio - Use actively as business assets
IP exploitation as business strategy
- Realization patents as legal “weapon” - Use as “source of profits”
IP exploitation for securing superiority
- Expansion of alternative product designs - Enforcement against infringer
IP exploitation for defense
- Prevention of operation of other firms - Defense against attack from other firms
insights into the commercialization of ECN technology. In order to reach this goal a main research question is formulated:
How can ECN value its intellectual property base?
To answer this question, the following sub-questions have been formulated: What valuation methods currently exist to value patents?
What does the intellectual property portfolio of ECN look like? How can a concrete ECN case be valued?
What can be learned concerning the valuation of ECN technology, from a real ECN case?
1.5 Structure of the report
The thesis is structured in two main parts: a theoretical part and a case study of ECN. The first part consists of a literature review and focuses on the fundamentals of valuation and real option theory. It includes valuation techniques for real options as well as the underlying building blocks of traditional capital budgeting and financial option theory. The theoretical section aims to provide a good understanding of the valuation of patents and technology and how to deal with uncertainty and the operational and strategic options that can play an important role in this type of valuation processes.
2. PATENT VALUATION MODELS
2.1 Patent Valuation Models
To create an overview of possible valuation methods, following Parr and Smith [1994], they can be classified into: cost based methods, market based methods and income based methods. This classification will be used to discuss which general method is best suited to ECN. Subsequently, the individual valuation methods and their characteristics will be discussed in the next chapter.
2.1.1 Cost based methods
Cost based methods estimate the cost of recreating the future utility of the technology being valued, and assume this value to be the future returns from the technology [Smith and Parr, 2000]. This is incorrect, since a historical investment does not guarantee a certain pay-off. As cost based methods do not have anything to do with future benefits that could accrue from the patent, it can be concluded that these methods are inappropriate for realistic patent valuation.
2.1.2 Market based methods
To conclude, market based methods do not provide accurate valuations for patents or technology. It is not clear what the value actually represents and if the underlying asset is really comparable to the proprietary asset.
2.1.3 Income based methods
Income based methods consider the present value of all future cashflows of the (underlying) technology as the value of the technology. This concept, disregarding the costs of technology development, determines the value of the technology according to its feasibility of creating expected profits [Boer, 1999].
Pitkethly [2002] also emphasizes the importance of the forecast of future income for the appreciation of the value of a patent or technology. He indicates that the key issue on the appropriateness of these methods is in how to arrive at the forecast of these cashflows. Baek et al. [2007], subdivides income based methods according to which elements one encounters when assessing future expected cashflows. These elements include the estimation of the income generation period, the estimation of future income itself, assessing project risks and converting future earnings into present values. Pitkethly [2002] states that only when the elements of time and uncertainty in future cashflows are accounted for properly, does one come to valuation methods that have sound theoretical foundations.
When one considers the issues discussed above in the valuation of a patent or technology, traditional Net Present Value (NPV) based methods can go a long way in providing a suitable valuation method. However on top of the elements time, uncertainty and risk, another dimension that has not been discussed so far has to be added. Next to the high amount of uncertainty in expected future cashflows that long term R&D projects and in general all patents and technology bring about, the dimension of flexibility needs to be considered.
can interpret the newly arrived information and recognize the operational and strategic options to increase the value of the project. During the course of a project, its management has the opportunity to alter decisions that were made earlier. This dimension of flexibility and strategic options can be assessed by extending traditional NPV methods by using ‘real options theory’.
To summarize the different income based methods, a classification from Pitkethly [2002] is given in fig 2.1. This classification of Pitkethly [2002] is not comprehensive, as more detailed adjustments could be made to this overview.
Fig. 2.1: Valuation methods in order of increasing sophistication. Source: Pitkethly [2002, p. 6]
From the above it can be concluded that income based methods provide a more appropriate method for valuation of technology than cost based or market based methods. However, income based methods also differ in complexity and sophistication. In the next chapter the most common traditional income based methods will be described in more detail. The subsequent chapter will explain income based valuation using ‘real option’ theory and includes the binomial option pricing model.
Increasing sophistication
Methods based on projected cashflows Market based methods
Cost based methods - Market conditions
E.g. Black-Scholes option pricing model
b.) Continuous time
E.g. Binomial option pricing model
a.) Discrete time
Option Pricing Theory based methods
4.) Changing Risk
NPV based Decision Tree Analysis method
3.) Flexibility
NPV Methods allowing for the riskiness of cashflows
2.) Uncertainty
NPV Methods allowing for the time value of money
1.) Time
3. TRADITIONAL INCOME BASED METHODS
The traditional approach to valuing investment projects, based on net present value (NPV), essentially involves discounting the expected net cash flows from a project at a discount rate that reflects the risk of those cashflows (the “risk-adjusted” discount rate) [Trigeorgis and Schwartz, 2001]. These traditional NPV based models are still the most common models that are used in organizations [Trigeorgis, 1996].
Most common is the static NPV model, which can be made more complex by extending it with decision trees to incorporate a small amount of flexibility in the model, or with simulation (Monte Carlo) analysis. Within ECN the NPV model extended with Monte Carlo analysis sometimes is applied, under the name Strategic Decision Analysis (SDA). In this chapter each model will be discussed. As mentioned, the extension of the NPV model with Real Options theory will be discussed in next chapter.
3.1 Static NPV model
The static NPV model is often criticized by underlining the “now or never” approach to investment decisions. The model calculates an NPV for a project assuming ‘passive’ management. This means that either a project is accepted and fully executed, or a project is rejected from its beginning.
Static NPV model
0 1 1 I k c E NPV T t t t
ct E k 0 I T tExpected cash flow
Risk adjusted discount rate Investment at time 0
Number of years in project’s life Year
Table 3.1: Static Net Present Value formula, Source: Trigeorgis [1996, p. 51]
3.2 Sensitivity analysis
Basic sensitivity analysis is often called a “what if” approach. It uses a base scenario (usually the expected scenario) and consequently changes each separate variable into a best and a worst estimated value, holding all other variables constant, to see what the impact is on the NPV calculation [Ross, Westerfield and Jaffe, 2005].
Sensitivity analysis can be used to identify the crucial variables that might contribute the most to the riskiness of an investment [Trigeorgis, 1996]. Some variables might be very risky in the sense that they cannot be estimated easily and might vary a lot; however, these variables might have only small influences on the NPV. Knowing which variables have a significant impact on the NPV can be very useful. Extra time and resources can then be invested to reduce the uncertainty of the estimate of the relevant variables.
However, one should be careful when using sensitivity analysis because it has important limitations. As it can consider only one variable at the time, interdependencies of the variables are not taken into account [Trigeorgis, 1996]. Therefore sensitivity analysis can be inappropriate. An improvement to sensitivity analysis can be Monte Carlo simulation.
3.3 Traditional Simulation (ECNs Strategic Decision Analysis)
distribution of the NPV outcome of the project. The probability distribution is also called the risk profile.
The simulation attempts to imitate a real world decision setting. A Monte Carlo simulation usually follows three steps [Trigeorgis, 1996]. First a mathematical model is created by specifying all variables and their probability distributions, including a description of their interdependencies. Next, the computer picks a random sample from the probability distribution of each of the uncertain variables and calculates the associated NPV. In the final step the process described in step 1 and 2 will be repeated 500 – 1000 times, resulting in the probability distribution of the NPV, including the expected NPV and the standard deviation.
Monte Carlo simulation can handle uncertainty better than static NPV, even when it is extended by a sensitivity analysis. However, it has important limitations as well, that should be taken into consideration. First of all the estimation of the probability distributions of the variables is not an easy task, but even if this would work, it will be a very complex process to capture the correct interdependencies.
Second, when the outcome of the simulation is a distribution of the NPV, the meaning of the probability distribution is not clear, since it is still unknown what discount rate should be used for the project. It seems incorrect to use a risk-adjusted discount rate, as any other adjustment for risk on top hereof would be double counting [Myers, 1976]. A risk-free interest rate as discount rate is also incorrect as the uncertainty in the cashflow distribution is not resolved by giving a probability distribution. Assuming the project has many possible present values, there is no way to see the present value as the value the project would have in competitive markets [Trigeorgis, 1996].
Third, even if management would choose to use the resulting probability distribution of the NPV as a basis for decision-making, there is only an expected NPV available discounted at the risk-free rate. There is no rule to judge the available measure of variance, and there is certainly no rule available to translate this distribution into any manageable actions.
strategy [Trigeorgis, 1996]. The model cannot cope with the options for management to use their flexibility to revise their strategy once uncertainty resolves during the project and cashflows appear to be different from the expected scenario. However, the simulation model is the most practical approach to valuation when it is difficult to make use of a dynamic model [Trigeorgis, 1996].
3.4 Decision Tree Analysis (DTA)
Decision Tree Analysis (DTA) has the ability to incorporate some management flexibility into the analysis of a project. The model maps out the possible alternative managerial actions dependent on chance events in a hierarchical manner [Trigeorgis, 1996]. It is mainly useful to structure projects of sequential nature, where uncertainty is resolved not continuously, but at clear discrete points in time, which are known up front.
An important improvement of DTA compared to the static NPV model is that it does not focus only on the initial decision of accepting or rejecting a project, but forces management to expose the implied operating strategy and be aware of the interdependency between initial and future decisions in the project. This means that some value of management flexibility can be incorporated in the analysis, stemming e.g. from the possibility to abandon a project at prespecified discrete points in time and based on probabilities that need to be estimated at the time of the initial decision [Trigeorgis, 1996].
There are some practical limitations to DTA that should be considered. The most important problem recurs: the determination of an appropriate discount rate. It would be hard to determine even if one constant rate would be used, however one can imagine that earlier in the process the risk is often higher than at a later stage [Trigeorgis, 1996].
are not two or three outcomes, or a high and a low outcome scenario, but all outcomes in between could be possible.
In summary the DTA contains some flaws, considering the discount rate problem and the fact that the uncertainty might not be reduced at known discrete points in time as in the model, but more continuously over time.
4.
REAL OPTIONS THEORY
4.1 Basic idea
The term ‘real options’ stems from the use of financial option theory to value real assets. Option Pricing Theory is primarily developed by Fischer Black and Myron Scholes [1973], who presented the first satisfactory arbitrage-free option pricing model. Afterwards important extensions have been made by Merton [1973]. The papers by Black and Scholes and Merton have formed the basis for many following academic studies. The mathematical tools used by Merton and Black and Scholes are quite advanced and it is the contribution of Cox, Ross and Rubinstein [1979] to introduce a discrete binomial option pricing model which is able to derive the same results using more elementary mathematics. Furthermore, in the binomial model there is more freedom to adjust it for different assumptions. The model can deal with different stochastic processes and it is more suitable for coping with American style options, which can be exercised at any date before maturity.
Real option theory is one of the more recent major contributions to the field of finance. It has brought important new insights in the way of looking at investments and can be seen as the successor of the traditional NPV methods. The method is used more and more as a valuation and strategic decision-making tool in private companies and increasingly also in public organizations. It provides a model that comes closer to the reality of today’s business situations. Traditional valuation methods ignore the flexibility of management to alter decisions as new information becomes available. Real option theory extends the traditional NPV decision tree analysis because it incorporates managerial flexibility and strategic options into the analysis.
Fig. 4.1: Project value, excl. flexibility value Source: Flatto [1996]
Fig. 4.2: Project value, incl. flexibility value Source: Flatto [1996]
The traditional NPV models value a project based on a number of assumptions made up front. However, in reality when operating a project one doesn’t find the limitations of the assumptions of the model. There are always the options to alter the course of a project when new information comes on hand during a project. When the conditions point to a more favourable scenario than expected up front, management can for example try to accelerate development or expand the project. Alternatively, management can choose to postpone a project or abandon it completely. In summary this means that the real options model enhances potential upsides of projects, while limiting the potential downside losses.
4.2 Financial options analogy
Real Options theory is derived from the symmetry between options in real business projects and financial options. Finance theory is advanced in explaining how capital markets work and how to value risky financial assets. This section will discuss the valuation of options and present the binomial model.
4.2.1 Financial options
obligation, at or before some specified time, to purchase or sell an underlying asset whose price is subject to some form of random variation [Brealey, Myers and Allen, 2006]. An important distinction arises between European options, which can only be exercised at a fixed future date, and American options, which may be exercised at any date before maturity [Cox and Ross, 1976].
4.2.2 Risk Neutrality
The binomial approach to option valuation makes use of a riskless hedging portfolio. Because this portfolio is riskless, there is no need for a risk premium for investors to hold it. The hedge will have the same value to risk-averse, risk-neutral or risk-loving investors. As such also the option will have an equal value to all investors, independent of their risk-preference [Kemna, 1987]. For convenience reasons, options are therefore valued in a risk-neutral environment [Cox, Ross and Rubinstein, 1979]. In the risk-neutral environment, all options have an expected rate of return equal to the risk-free rate. As a result there is no need to find a suitable (variable) discount rate reflecting the risk. The downside however is, that one has to work also with risk neutral probabilities, which have to be calculated.
4.2.3 Binomial Option formula
Binomial model of Cox, Ross and Rubinstein
a n p
Xr
a n p
S C , , ' n , , 0 d u d r p (1 ) p r u p' If a > n then C0 C X r n a p 0 S
Call option price Exercise price
Risk-free interest rate
Number of periods until maturity
Minimal number of upward moves that the share must make over the next n
periods for a call to finish in-the-money Risk-neutral probability
Current share price
Complementary binomial distribution Table 4.3: The binomial option pricing model of Cox, Ross and Rubinstein [1979]
4.3 Concepts of Real Options theory
In this section the analogy of financial options and real options will be discussed, as well as some concepts that are important for understanding real options theory. Technical and economic uncertainty will be separated, which is important for real options pricing. Subsequently, different types of real options that can be embedded in a project will be explained.
4.3.1 Financial and real options analogy
The Black-Scholes model created the foundation for considering securities of a firm as an ‘option on firm value’. However, the application of real option theory just starts here. The next step is to consider a business as a package of embedded corporate real options. Most firms for example have real options to later expand production, defer investments, or abandon R&D projects half way for salvage value [Smit and Trigeorgis, 2001].
strategy; the portfolio consists of a position in the underlying asset, partly financed with a risk-free loan. It can be constructed such that each future state over the next period delivers an equal payoff as the option, meaning it would also have the same current value as the option [Trigeorgis, 1996]. By pretending these projects are executed in a risk-neutral environment, where all assets are expected to return the risk-free rate, the risk-adjusted expected cashflows can be discounted appropriately by the risk-free rate.
Table 4.3 shows the direct analogy of the different input variables which are needed to calculate the option value.
Table 4.3 Analogy between financial options and real options. Source: [Trigeorgis, 1996]
When each of these inputs is known, the value of real options can be calculated. For correctness a complete definition of all the parameters and their similarity to financial option parameters will be given. These parameters are inputs for the discrete binomial model.
Gross present value of project (V )
The gross present value of the project is the underlying asset of the real option, defined by the gross present value of the expected cashflows that will be received from the project, when it is fully commercialized. The investment should not be included in this value as it is a separate parameter in the calculation of the option value.
Financial call option on share Real option on project Current value of share
Exercise price Time to maturity
Share value uncertainty (volatility) Risk-free interest rate
Dividends S X T r D = = = = = = V I T r C
Gross Present value of the project Investment cost
Time until opportunity disappears Project value uncertainty (volatility) Risk-free interest rate
Investment (I )
The investment is analogous to the exercise price of a financial option. It is the amount that has to be spent in order to receive the full benefit of the underlying asset (V ).
Project value uncertainty ( )
Under uncertainty the value of the underlying project cannot be expressed by one number. The project value uncertainty is measured by the annual standard deviation of the project’s returns. For a financial option the standard deviation is easy to determine, as it can be approached by using the available historic volatility of the underlying asset. However for real assets the volatility might be slightly more complex to determine. Trigeorgis [1996] states that the volatility of a “twin security” that highly correlates with the project, or the underlying commodity price volatility can be used as a proxy. A final alternative could be to make a subjective estimation of the volatility.
Time until opportunity disappears (T)
The time until the opportunity disappears is analogous to the time to maturity of a financial option. For financial options the maturity date is fixed, while for the real option calculation a best estimate has to be made of the time that is left until an opportunity disappears. However, for a patent the time to maturity is obviously the length of time that is left until the patent expires and the opportunity to gain a competitive advantage is lost [Dixit and Pindyck, 1994].
Risk-free interest rate (r )
The risk-free interest rate is equal for both financial and real options. A good estimate is the yield of a government bond with the same time to maturity as the project.
Cash inflows (C)
4.3.2 Uncertainty
Throughout this thesis the concept of uncertainty concerning the future of projects is a central issue. Especially in R&D environments many factors in the future development of a technology and the resulting cashflows of its commercialization are unknown due to the early stage the project is often in. However for any industry, uncertainty of a project comes from different angles. There can be uncertainty about the project outcome because of uncertainty that is endogenous to the project and uncertainty that comes from the outside (the market). For the purpose of this thesis it is useful to make a classification in two categories: economic uncertainty and technical uncertainty. Most R&D project uncertainty is a combination of both.
Economic uncertainty
Economic uncertainty stems from the uncertainty that exists in the market. An important characteristic of economic risk is that it cannot be influenced by the organization itself. However, management can react to these changes by adjusting decisions and investments to the market situation. During the course of the project more information on the economic situation will become available. As a result, economic uncertainty can be reduced by waiting to invest. Value can then be created by using the extra information that is gained, to make better decisions and consequently maximize value.
Technical uncertainty
Technical uncertainty does not correlate with general economic movements or industries. It is an inherent part of the project and depends on actions of the organization itself. Hence, there is no incentive to wait to invest as no new information will be gained by waiting. Dixit and Pindyck [1994] explain technical uncertainty as being the physical difficulty of completing a project. In staged R&D projects, the technical uncertainty is reflected by the probabilities of success or failure to move from one development stage to the next. This implies that pure technical uncertainty can only reduce the value of options.
on the future and can reduce technical uncertainty. The actual uncertainty can only be resolved by taking on and completing the project.
4.4 Real options in Projects
Depending on the nature of a project, different types of options can be embedded. Some of these options occur naturally and some options can be build-in strategically for the purpose of flexibility. To determine which options to include in the valuation of a project, different types of real options will be discussed as well as the concept of option interactions.
4.4.1 Types of real options
Trigeorgis [1996] divides real options in two groups: ‘growth options’ and ‘flexibility options’. Growth options enable the organization to undertake profitable investments down the line as follow-on investments, whereas flexibility options make use of the investments in projects that are already in place. In the next sections the different growth and flexibility options will be described.
4.4.2 Growth option
4.4.3 Flexibility Options
The’ time-to-build option’ for staged investments
Many investment projects, but especially R&D projects can be considered as time-to-build options [Trigeorgis, 1996; Dixit and Pindyck, 1994; Alvarez and Stenbacka, 2001; Kemna, 1987]. Majd and Pindyck [1987] characterize these projects by distinguishing three elements: (1) the investment decisions and associated cash outlays occur sequentially over time, (2) there is a maximum rate at which outlays and construction can proceed (it takes time to build) and (3) the project yields no cash return until it is completed.
R&D projects fit these characteristics well as they can often be divided in several stages of development that an invention has to pass through. Fundamental to these type of projects is the fact that each stage of investment yields information that reduces the uncertainty over the value of the completed project [Majd and Pindyck, 1987; Trigeorgis, 1996]. The sequential staged investments provide the ability to temporarily or permanently stop investing when the forecasted value of the completed project falls, or if the expected cost of the investment increases. [Dixit and Pindyck, 1994]. As such valuable options to default are embedded in the project. As already shortly mentioned the possibility of stopping at some point in the process makes these projects analogous to compound options: each stage that is completed gives the organization a call option to complete the next stage. There is a right, but not an obligation to continue with the next stage [Trigeorgis, 1996].
The option to defer
reduction in costs [Kemna, 1987]. The downside however, is the missing of cashflows to be received during the waiting time.
The option to defer is included in many projects, but it has often been explained in the context of the oil industry. Boer [2004] provides a good example on the exploration and exploitation of an oil reserve. The oil company finds oil in a certain area they have only leased for exploration for a limited amount of time. In option terms, after discovery they own a call option on the development of the oil reserve. The exercise price is the investment to get the oil out of the reserve. The question is when exactly to extract the oil. Should the company do it right away, or does deferring the investment create more value because of the ability to profit from a higher oil price. Also for long term R&D the option to defer can be relevant, although the situation differs slightly from the oil exploration example. In the R&D process patents are often obtained early in the process and the development of the technology relatively takes a long time. This means that waiting to invest in developing the technology further, at the end often results in a shorter period that is available to exploit the asset. Because when the patent lasts a shorter period, the number of years in which license income can be earned, or the time that a start-up company can profit from its ‘monopoly’ position decreases as well. However, when there is very large economic uncertainty, the value of the option to defer might exceed the value that is lost by being able to exploit the technology for a shorter period.
The option to change scale
The option to change the scale of operations includes the option to expand and the option to contract (scale down). The option to expand can be considered as a call option to obtain an expansion on the project as it currently exists. The exercise price is the cost to create the expansion. The flexibility that is embedded in the project has a value. There is an option to create value from the extra capacity when market circumstances are favorable but not the obligation to do so when market circumstances are less favorable.
be scaled down to fit the demand and reduce excess capacity and the costs of planned future investments. In option terms, the option to contract can be considered as a put option on the excess capacity of the initial project with an exercise price equal to the cost savings [Trigeorgis, 1996]. The option to contract can be relevant for R&D projects as the high uncertainty of new technology and product introductions make it hard to estimate the right size or capacity at the start of a project. The flexibility to change the scale of the project can often be build in at an early stage of the project to reduce the costs of rescaling a project [Trigeorgis, 1996].
The option to abandon
The option to abandon can be valuable when market conditions become so unattractive that the salvage value of the project is higher than the present value of the project. The option to abandon can be valued as an American put option on the project’s current value. The exercise price is then the salvage value of the project or the value of its best alternative use [Trigeorgis, 1996]. The American option can be exercised at any time during the project and as such provides a constant limited insurance against project failure.
For R&D projects the salvage value is usually lower than salvage values in traditional industries with many tangible capital-intensive assets. However, knowledge also often can be used alternatively making the efforts and costs incurred not worthless. A partially developed technology might also still provide value for another market party.
The option to switch
4.5 Interactions among real options
As mentioned, more than one type of real option might be relevant for a project and needs to be considered [Flatto, 1996]. However, what is important to note is that options may have interactions and cannot always be looked at separately [Trigeorgis, 1996]. Trigeorgis shows that the effective value of an additional option is generally less than the value of the option as if it had occurred in isolation. The severity of the option interactions generally depends on the type, separation, degree of being "in the money," and the order of the options involved [Trigeorgis, 1993]. Trigeorgis [1993, p.2] states: “The incremental value of an additional option often tends to be lower the greater the number of other options already present. Neglecting a particular option while including others may not necessarily cause significant valuation errors. However, valuing each option individually and summing these separate option values can substantially overstate the value of a project.” Options may interact for various reasons and to varying degrees, depending on the probability of their joint exercise during the investments life [Trigeorgis, 1996]. Proper options analysis should consider possible interactions among multiple options and the extent to which option values are not strictly additive.
5. R&D AT ECN
This chapter first looks at R&D within ECN from a general viewpoint. Subsequently, a classification is provided describing the different development stages ECN has identified within their projects. This classification is then used to create an overview of the state of the portfolio of ECN.
5.1 R&D in general
Academic research often explains R&D as a process with a number of sequential stages. According to Contractor & Narayanan [1990] scholars may differ in the terms and specifics they use, but generally tend to describe the process in two general phases. One phase describing the early stages where organizations are involved in attempting to innovate and finding technical solutions to problems and a second phase in which organizations are involved in trying to generate benefits from the produced innovation. According to Kelm et al. [1995] the events preceding a new product launch, such as project initiation, progress, and other events that imply a project has not yet reached a successful outcome, represent the ‘innovation stage’, whereas a new product introduction marks the beginning of the ‘commercialization stage’ of the R&D project. Morris et al. [1991] emphasizes the decision that needs to be taken after the innovation stage is finished: is the outcome of the research going to be commercialized or not. In option terms: the innovation stage is a kind of call option to start the commercialization phase.
5.2 The R&D process at ECN
Table 5.1: Different stages of project development at ECN
The classification of table 5.1 creates the possibility to provide insight in what the portfolio of ECN looks like. Without going into the details of all the projects, technologies can be assessed on general criteria, how far they have been developed on their way towards a commercially viable end product. In figure 5.1 can be found how many of the technologies are in each stage of development.
N=49 0 5 10 15 20 25 30
PoP PoC PoF PoM
Development stage N u m b er o f pr o je ct s
Figure 5.1: Number of projects in each stage of development
Stage Characteristics
Proof of Principle PoP
-Confirmation of the working of the principle idea Low external involvement in development Low external financing
Cooperation with universities
Proof of Concept PoC
-Confirmation of the application of the idea on a larger scale Increasing financial and some technological support from industry ECN contributes most effort to the development and strives to build out their intellectual property position
Proof of Feasibility PoF
-Confirmation if the idea is suited for application on commercial scale Industry offers support with market knowledge
Stronger involvement of industry in the development, as well as in financing
Proof of Manufacturing
PoM
-Confirmation of possibility of manufacturing the technology on a commercial scale
Apart from the fact that this stage approach provides important insight in the research portfolio of ECN, there is another advantage. The stage approach can provide milestones for each project and an estimation of the probability of success to advance through the stage. Targets can be set for the development and the project can be evaluated at the end of each stage. The evaluation should also include the possibility to defer or abandon a project that is not performing as expected. A project can be abandoned for reasons concerning the progress of the project, or not living up to the technical criteria that are set for a project. However abandonment can also be the best option when future market expectations for the envisioned innovation become less positive. This could for example be because a competitor has entered the market earlier with a similar product or because price levels are decreasing. In the second case, apart from abandonment also deferral could be an option to wait until market expectations might turn more favorably. Furthermore it could be a consideration to scale down a project when it is expected to generate less future benefits.
Though it is not in favor of the comparability amongst different projects in the portfolio of ECN, researchers have the authority to create their own stage model, which is specifically tied to their project. This makes sense because of the distinct characteristics of some projects. The general categorization above can then form a starting point or guideline to adapt to the specifics of their project.
Both the general ECN stage approach to the research projects and a specific stage model can be looked at as ’time-to-build options’ for staged investments. The cash outlays occur sequentially over time, the project demands sequential investments and the project yields no cash return until it is completed. So each stage that is finished provides an option to continue the next stage, which is an option in itself. Options on options are similar to compound options [Trigeorgis, 1996].
6. ECN REAL CASE
In this chapter a specific project will be described that will be valued using the framework that will be build in chapter 7. The project that will be described is the Thermo Acoustic Heat Pump project and can be classified as being in the proof of concept phase.
6.1 The thermo acoustic heat pump project
The thermo acoustic heat pump (TAHP) is a technology that can be used to upgrade industrial waste heat. The acoustic energy is created using industrial waste heat in a thermo acoustic-engine. In a TAHP this acoustic energy is used to upgrade the same waste heat to a useful temperature level. In figure 6.1 an 6.2 an illustration of the thermo acoustic system is shown.
Figure 6.1: Helmholtz resonator Figure 6.2: Thermo acoustic heat exchanger
It is assumed by ECN that for this technology the commercialization will be done by the partners who will be responsible for the production and installation of the products. The profit for ECN stems from the license income that will be generated based on the sales of the TAHP. The different stages of the project, the time planning and the technical uncertainty can be found in table 6.1. The probabilities for the technical success are estimated by the researchers involved in the project. They have identified and assessed all the factors of influence on the technical success per stage. Hence, these probabilities are conditional: the preceding stage needs to be successfully completed first.
Stage Start Completed Prob. technical success
R&D up till 2006 ? 12-2006 100%
Basic Research 01-2007 06-2008 50%
Research critical components 07-2008 12-2008 60%
Bench scale 10kW 01-2009 12-2009 75%
Pilot 100 kW 01-2010 12-2010 85%
Demo 1MW 01-2011 12-2012 95%
Full commercialization 01-2013 12-2026 100%
Table 6.1: TAHP Project Source: ECN
If the research proofs successful and leads to commercialization and application of the technology several possible new project opportunities open up. An important strength of real option theory is that it can include these growth options in the valuation of the technology. This will also be done for this project, however one should be careful estimating the size of these follow-on projects, as they are relatively far away in time, and as such sensitive to erroneous estimations.
6.2 Embedded options
The analysis of embedded options will be done below, followed by a discussion on the interactions between the selected embedded options.
The’ time-to-build option’ for staged investments
It was discussed that the nature of the R&D projects at ECN implies sequential investments. During the project, there is the option for ECN to abandon the project when information comes to ECN that indicate unfavorable conditions for the project. When these conditions lead to a salvage value that is higher than the value of the project, it can be abandoned. Considering the TAHP project, there are not many specific machines or other capital intensive assets involved early in the project that lead to a high salvage value. However, there could be salvage value in the knowledge on the partially developed technology. At clear intervals between development stages, the results of the R&D could be sold to external parties, depending on the utility of these results to others. Hence, the time-to-build option is very relevant for this project and should be included in the analysis of the project.
The option to defer
The option to defer can be embedded in a R&D project. It would be of value when economic uncertainty would be leading and deferring the project would lead to an increase in possession of information. However technical uncertainty plays a large role in the research, hence deferral of the project will not resolve this type of uncertainty.
Furthermore ECN has the advantage of possessing the patents for the technology. This way it can prevent competitors from entering their market with a competitive product based on similar technology. The patents however last only a limited number of years, meaning that deferring the project would reduce the number of years in which value can be extracted from the invention in the commercialization process. Therefore it is expected that this option only has limited value for ECN and is not included in the analysis.
The option to change scale
will take on the production and install the technology. It is assumed that there will be enough partners with production capacity available to suffice market demand. As such the option to change scale is not relevant for ECN, since it is assumed there is no limit to their production capacity.
Growth option
The growth option represents the possibilities that will open up only when the current project is executed and successfully completed. The TAHP project is a prerequisite for the follow-on investments. As ECN is active in R&D, learning is a very important element. According to management of the TAHP project, there is common recognition that the possession of a working thermo acoustic technology would open up possibilities for a new R&D project, as there would be possibilities to use the technology for other applications than only upgrading industrial waste heat. The growth option is therefore considered to be very relevant for ECN.
However, it is difficult to collect exact data on the exact size and details of a follow-on project, as ECN currently does not include these possibilities in the evaluatifollow-on of their projects. To illustrate the importance of the growth option, it is assumed that the follow-on project will be of the same size as the original project. It is likely that the follow-on project will have a similar cost-benefit structure as the original project as well as a similar timescale. It is assumed to start in January 2013, when the original project reaches the stage of full commercialization and the research is finished. However, since there is significant uncertainty considering the size of the follow-on project, sensitivity analyses are essential and can be found in chapter 9.
6.3 Option interactions
As mentioned in section 4.5, in situations where multiple options are embedded in the same asset, options can interact. They may interact for various reasons and to varying degrees, depending on the probability of their joint exercise during the investments life. According to Trigeorgis [1996] options are approximately additive, when they are of opposite type and have a different exercise region. Furthermore a higher probability of joint exercise of the embedded options reduces their value.
7. FRAMEWORK FOR VALUATION
This chapter will construct and explain the framework for the valuation of the TAHP project and discusses the assumptions that are made in order to do the valuation including the value of the flexibility in the project and the strategic options that the project provides. The result will lead to the extended net present value (ENPV) of the TAHP project.
7.1 Assumptions
The framework is build upon the theory of Trigeorgis [1996] and uses the binomial method of Cox, Ross and Rubinstein [1979]. A number of assumptions are made which will be discussed below.
7.1.1 Risk neutral valuation
The valuation will assume risk-neutrality as explained in section 4.2.2. This implies that no riskless profitable arbitrage will be possible, assets can be bought and sold without transaction costs being incurred and there is no limit on short selling assets. These assumptions are needed for the binomial model that will be used to calculate the option values. The model makes use of the replicating portfolio approach.
7.1.2 Data from ECN
It is assumed that all the data regarding the project that were received from ECN are correct. This includes the estimation of the underlying cashflows, the technical uncertainty and the estimates of the future investments that are needed.
7.1.3 Economic uncertainty
application on other processes than the stock market, mainly in real option analyses. They concluded that historical time series for usage of established industries, among which they tested the electric power consumption, meet the criteria for a geometric Brownian motion. However, the data for the growth of emergent industries did not meet the criteria in all cases. Since the TAHP project is related to the consumption of gas, an already established industry, the assumption of the geometric Brownian motion is assumed to hold for this project.
7.1.4 Technical uncertainty
The estimates of technical uncertainty are extracted from ECNs own analysis. Technical uncertainty is not correlated with the market and it is verified with management of ECN that the estimates of technical uncertainty are their best estimate at this point in time and do not incorporate any market or economic uncertainty factors. It is assumed that extra efforts to decrease these uncertainties up front by gaining extra information is impossible. So as explained in section 4.3.2 pure technical uncertainty can only decrease project values.
7.1.5 Volatility
It is hard to estimate a volatility for ECN considering it is a non-public organization. Furthermore the diversity of the projects and the specific details of each project would make it hard to use an average project volatility. For as far as a comparable project could be found within ECN, the lack of data make this approach impossible.
The TAHP upgrades industrial waste heat to redistribute this heat back into the industrial process. Without the invention, this heat would have to be created by burning gas. For this reason the gas price influences the economic value of the TAHP and the volatility of the gas price will be used to determine the volatility parameter.
7.1.6 The strategic growth option
assumed that there will be a follow-on of the same size and profitability as the original project. However, the only difference will be that the follow-on project is assumed to have no further strategic options. As such, no further growth possibilities after the follow-on project are taken into account.
7.2 Valuation with static NPV method
To calculate the static NPV, the information given by ECN is used. The cashflow forecast has been taken from their calculations. The discount rate is set to 10% to reflect the risk of the project. The reason the static NPV is calculated, is that it can be subtracted from the Extended NPV (ENPV), in order to gain insight in the exact added value of the real options to abandon the project in the research phase and to do a follow-on project when the original project is completed.
7.3 Valuation method for ENPV
The staged investments provide the option to abandon the project when information arrives that is unfavorable to the project. The option value will be calculated working backward through the binomial tree, which will be explained step-by-step below. 1. All the inputs are collected: the gross present value of the underlying cashflows, the annual volatility of the returns of the project, the time to maturity, the investments and the riskfree interest rate.
2. The standard deviation will be used to determine the ratio for moving up (u ) and
down (d) in the binomial tree. From Cox, Ross and Rubinstein [1979] we know that these ratios can be defined by:
n t
e
u / d e t/n
Where:
= The standard definition of the projects returns on a yearly basis
t = The time to maturity of the option, measured in years
The resulting ratios can be used to determine the present value of the project in the nodes of the binomial tree by multiplying the up- or down-ratio by the project value (V) in the preceding node. This way the value at all the end nodes can be calculated.
3. The next step is to extend the binomial tree with the investments that will need to be done over the time span of the project. A condition is that the binomial tree at least has nodes at the intervals when the investments will be done. When for example an investment will be done at t=2 in the example then the investment needs to be included in all the nodes that exist at that time period: uuV, udV and ddV.
4. The framework uses risk-neutral valuation, therefore the risk-neutral probabilities for the up-branches p, and the down-branches (1 p)need to be calculated (see section 4.2.3) . When the risk-neutral probabilities are found they can be entered into the up- and down-braches of the binomial tree.
5. Having calculated the risk-neutral probability, all the project values in the nodes can be calculated working backward through the binomial tree. Therefore the binomial formula is used. The investments need to be entered at all the right intervals as well and than subtracted from the value stemming from applying the binomial formula. When the project value is smaller than the investment, the project should be abandoned. In that case the option is out of the money and as such looses its value.
When this is the case, the value of the project is set to its salvage value. In the expected scenario it is assumed that this will be zero, implying that the costs of abandoning the project and the benefits of selling off project specific assets or the research results obtained so far even out.
6. The gross present value that is used as the input for the model has not been corrected for technical uncertainty at this point. Therefore, when working backward through the tree, the project values need to be multiplied by the technical success probabilities at the corresponding time points in the tree. As for the TAHP project two months periods are used, each stage typically consists out of more periods. The technical uncertainty needs to be entered only at the first period of each stage. The other periods are set to success probabilities of 100%, as the uncertainty is already taken into consideration and does not need to be double counted.
7. The project value now can be calculated by continuing going backwards until the present time is reached. The present value that stems from the calculation includes all the flexibility options to abandon the project and the technical uncertainty during the research stages. The resulting value is an ENPV of the project, but yet only includes the time-to-build option and the options to abandon the project and not the strategic growth option.
the value to be added to the end node is set to zero because the growth option would not be exercised in that case. This way the growth option can be integrated in the binomial tree. The growth option value as such, does not consider any growth possibilities after the follow-on project.
9. When one is interested in what the exact value of the real options in the project is, the static NPV can be subtracted from the calculated ENPV [Trigeorgis, 1996].
7.5 The ENPV including real options
The static NPV of the project together with the calculated option values make up the final result: the ENPV. The ENPV = NPV + time-to-build option value + growth option value.
8. VALUATION RESULTS OF THE TAHP PROJECT
This chapter will show the actual calculation of the option values using the framework and steps that have been described in the earlier chapters. First the static NPV and the option values will be calculated and subsequently the resulting ENPV will be given.
8.1 Static NPV
The results of the static NPV calculation can be found in table 8.1. The gross present value of the project follows from the cashflows of the commercialization of the TAHP project. The gross present value still incorporates the investments that have to be made to commercialize the invention and they need to be subtracted. However, the gross present value first needs to be corrected for technical uncertainty, which amounts to 18.17% for the total project. The number obtained is the gross present value adjusted for technical uncertainty. From this number the present value of the certainty equivalent investments, also corrected for technical uncertainty, is subtracted to calculate the static NPV of the total project. A spreadsheet illustrating this more extensively is included as appendix A.
Discount rate 10.00%
Risk-free rate 4.30%
Scenario GPV
Expected value € 10,304,137
Gross present value € 10,304,137
Technical uncertainty 18.17%
Gross present value adjusted for techn.uncertainty € 1,872,133 PV of CEI adjusted for techn. uncertainty € 1,304,315 (CEI = Certainty equivalent investments)
NPV € 567,818
Table 8.1: Static NPV calculation
8.2 ENPV including real options
invention and includes the value of the option to do a follow-on project when the original project proves successful.
8.2.1 Collection of input parameters
Below the collection of input parameters will be done in the same order as is done in section 4.3.1.
Gross present value (PV) of project (V)
The gross present value can be determined by taking the cashflows before consideration of technical uncertainty and the investments. It is calculated from the data obtained from ECN on the project, see also table 8.1. The estimated gross present value by ECN of the TAHP project is € 10.304.137.
Investment cost (I)
The investment outlay is analogous to the exercise price of a financial option. It is the amount that has to be spent in order to receive the full benefit of the underlying asset (V).
Year 2007 2008 2009 2010 2011 2012 2013
Certainty eq. Investment (CEI) € 1,459,000 € 363,636 € 471,074 € 1,953,418 € 68,301 € 62,092 € 169,342
Table 8.2: Certainty equivalent investments
Project value uncertainty (σ)
The project value uncertainty is defined by the annual standard definition of the return on the project. The underlying price determining factor has been defined as the natural gas price. In a recent paper on real options the International Energy Agency [2007] has calculated an annual volatility of 30% for natural gas. This volatility will also be used for the option calculations on the TAHP project. As such it is assumed that σ =30%.
Time until opportunity disappears (T)
