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Preface
When it comes to the process of writing, many thoughts cross my mind. One of my favourites is, “Of making many books there is no end, and much study wearies the body (Ecl. 12:12b NIV).” Though this biblical citation seems to indicate that there is no virtue in writing, I think there is a bottom line that is truly applicable to my master’s thesis. During the process of writing, I felt my mind captured and my body worn out. Yet, ending the writing process is a great relief.
It pleases me to invite you to read my master’s thesis. I gave my utmost for it and I hope you will see a glance of my academic capabilities, which I consciously used to conduct a real options valuation of the Dutch Maglev project. The Dutch Maglev project is a loved and hatred infrastructure project that interested me for years during my youth. It was a great experience to revisit this youth interest with the perspective of a master’s student in finance. I hope academic research will never end, but at the same time, I made a substantial contribution with my master’s thesis to the evaluation of infrastructure projects.
At this place, I want to thank all the people who assisted me with my master’s thesis. First and for all, I want to thank my supervisor dr.ing. N. Brunia who assisted me in a challenging way. Second, I am thankful for the data that dr. J.P. Elhorst provided me. Next, I want to thank my friends for all the good time I spend with them. I also want to thank my parents who raised me in a loving and caring way. They made it possible for me to study. Finally yet importantly, I am grateful to my girlfriend Marije. Your continuous love and encouragement kept me going on with my master’s thesis.
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I. Introduction
In 2004, a Dutch parliamentary commission on infrastructure projects examined the valuation process of infrastructure projects after misinformation from the government about the Betuweroute and the Amsterdam‐Brussels high‐speed train (Tijdelijke Commissie Infrastructuurprojecten 2004). Both projects experienced severe cost overruns and had lower traffic demand and a longer transition period than expected. At the same time, the government was examining the Dutch Maglev project, a magnetic levitation project connecting Groningen and Amsterdam. The project’s aim was to stimulate the lagging Northern economy and to relieve the capacity constraints of the Randstad with respect to transport, land, and labour markets (Elhorst and Oosterhaven 2008). After several social cost benefit analyses (NEI 2001; RUG 2001; Nyfer 2000), the government rejected the Dutch Maglev project in 2007 because they considered the profitability not proven.
This parliamentary examination followed a tradition of official reports that are written on the valuation of infrastructure projects, such as the CPB/NEI (2000) and SACTRA (1999). These reports contain dozens of requirements on forecasts and profitability of infrastructure projects. Like most large engineering projects, infrastructure projects are characterized by heavy, fixed, and normally irreversible investments (Zhao & Tseng 2003). Moreover, infrastructure projects have a high level of uncertaintyii and are subdue government regulation. Flyvbjerg (2007) finds that traffic demand and construction costs are uncertain and thereby difficult to forecast. The government regulation consists of, among others, strict rules on setting prices, which limits managerial freedom on infrastructure projects. Hence, the valuation of infrastructure projects is difficult. As a result, there is an ongoing debate between policy makers and advisors on the proper valuation of infrastructure projects.
This debate is not constrained to policy makers and advisors in the Netherlands. In two seminal studies, Flyvbjerg (2006, 2007) finds cross‐country empirical evidence of highly inaccurate traffic demand and construction costs forecasts of infrastructure projects. For rail projects, 72 percent of them had traffic forecasts that were overestimated by more than 67 percent. The average cost escalation of rail projects was 45 percent. For high‐speed rail projects, the average cost escalation was even 52 percent. The evidence is similar for other types of infrastructure projects. Hence, this empirical evidence shows the weakness of the traditional valuation of infrastructure projects.
Traditionally, practitioners use a social cost benefit analysis to evaluate infrastructure projects. They account for the underlying project risk by using a risk‐adjusted discount rate. The concept of such a risk‐adjusted discount rate, however, is commonly misunderstood by engineers and politicians (Garvin and Cheah 2004). Often, the firm’s cost of capital is incorrectly used to adjust for the riskiness of the infrastructure project. The empirical evidence of the weakness of traditional valuation of infrastructure projects together with a shift to private provision of infrastructure, for instance by Build‐Operate‐Transfer (BOT) arrangements, has led to a stream of literature on the proper valuation of infrastructure projects. This literature reports severe shortcomings of the traditional valuation techniques, which are based on the discounted cash flow approach. De Neufville (2003) summarizes them into three major shortcomings. First, practitioners that use
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traditional valuation techniques neglect market and technological uncertainties. Second, practitioners do not account for asymmetric payoffs. Finally, they use incorrect risk‐adjusted discount rates when risk levels are not stable. Consequently, practitioners incorrectly assume that management is passive and does not react on market and technological uncertainties, asymmetric payoffs, and unstable risk levels. Ignoring this managerial flexibility results in too low valuations because the value of flexibility is not taken into account (Amram and Kulatilaka 1999; Trigeorgis 1999).
Real options valuation is widely proposed as a better valuation technique to evaluate infrastructure projects (Garvin and Cheah 2004; Ho and Liang 2002). The real options valuation approach identifies and models uncertainties in infrastructure projects, such as traffic demand. Consequently, managerial flexibility is taken into account. This managerial flexibility consists of real options. For example, if expected traffic demand is low the government can defer construction of the infrastructure project and wait until expected traffic demand is higher. Although the real options valuation approach is widely proposed in the literature, real options valuations of infrastructure projects based on real and high‐detailed data are scarce. Most authors use simulated data because they have limited data available. Moreover, the applied real options valuations are mostly illustrative and low‐detailed. Flyvbjerg (2006) proposes in‐depth case study research with real and high‐detailed data to verify the appropriateness of valuation approaches. Therefore, there are now too few real options valuations of infrastructure projects based on real and high‐detailed data to verify the appropriateness of the real options valuation approach to evaluate infrastructure projects. In addition, the ability of the government to make correct forecasts of infrastructure projects, which Flyvbjerg (2007) demonstrates to be weak, and real options valuation is hardly examined.
In this master’s thesis, I will add to the debate on the valuation of infrastructure projects by conducting a real options valuation of the Dutch Maglev project between Groningen and Amsterdam. This valuation is based on real and high‐detailed data. It examines the relationship between the project forecasts on the one hand and the project valuation on the other hand. The research question is, “What is the value of flexibility of the Dutch Maglev project?”
The real options valuation is conducted on real data of the Dutch Maglev project by Elhorst and Oosterhaven (2008). Underlying uncertainties are identified and modelled explicitly in Crystal Ball®iii. A Monte Carlo simulation of 10,000 runs estimates the average project value and volatility. Real options are modelled with a binomial option‐pricing model, following Copeland and Antikarov (2001). More specific, the government has the option to defer construction, abandon the project during the operation period, and postpone part of the train investment by considering it an expansion option. The net present value with flexibility will be compared with the net present value without flexibility, which is computed by a traditional discounted cash flow approach, to obtain the value of flexibility. At the end, the implication of the results of my real options valuation for the debate is discussed.
Three social cost benefit analyses of the Dutch Maglev project have been conducted, respectively by the NEI (2000, 2001), RUG (2001) and Nyfer (2000). All of them use the traditional discounted cash flow approach. Despite the agreement of the studies on an overall negative net present value, a lot of discussion arose between the practitioners about the methodology, cash flow forecasts and the implication of the results for the decision making process. Ultimately, the discussion was ended by the decision of the government to
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II. Literature
The literature on real options valuation can be clearly divided into theoretical and applied literature. The theoretical literature is abundant and well developed. Amram and Kulatilaka (1999) and Trigeorgis (1999) both provide excellent introductions on real options. Below is a brief overview of the main aspects of the real options valuation approach. The applied literature, however, is for certain application areas limited. Real options valuations of high‐speed rail projects, which comes as close as it gets to my case of the Dutch Maglev project, are scarce. Therefore, an overview of comparable real option valuations is given too. This section ends with the contributions of my master’s thesis to the literature.
A. Theoretical literature
Real options valuation became increasingly popular after the shortcomings of traditional valuation techniques were widely recognized. Based on the discounted cash flow approach, the traditional valuation techniques have both conceptual and mechanical shortcomings (de Neufville 2003). First, practitioners that apply the traditional discounted cash flow approach ignore technological and market uncertainties. That is, they fail to recognize that management can react actively on changing technological and market circumstances. Second, a mechanical shortcoming is that the discounted cash flow approach neglects the usual asymmetric payoff structure of projects. For example, the occurrence of a construction cost overrun is more realistic than lower construction costs than expected (Flyvbjerg 2007). Incorrectly assuming that payoffs are symmetric leads to the flaw of averages, also known as Jensen’s inequality. It says that the expected project value with average uncertainty is not equal to the average of the expected project values. Third, the use of a risk‐adjusted discount rate is only appropriate with stable levels of risk. In reality, risk levels are changing, among others due to technological and market uncertainties. Therefore, the discounted cash flow approach lacks a proper risk‐adjustment method over time. If management takes these market and technology uncertainties, asymmetric payoffs, and unstable risk levels into account, the traditional valuation techniques result in too low values. Indeed, practitioners do not include the value of flexibility because they ignore managerial flexibility (Trigeorgis 1996). The real options valuation approach identifies the underlying uncertainties, addresses for asymmetric payoffs, and accounts for unstable risk levels. As a result, managerial flexibility is taken into account. Therefore, the real options valuation approach reveals the hidden value of flexibility (Trigeorgis 1999). The real options valuation approach provides a number of different modelling approaches. Miller and Park (2002) give an overview of the various models. In short, real options valuations can be divided in discrete‐ time and continuous‐time. The most common discrete‐time method is the binomial option‐pricing model by Cox et al. (1979). Continuous‐time models range from closed‐form models, stochastic differential equations, to simulation models. The various models of real options valuation differ with respect to their applicability, complexity and accurateness.
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of inputs or outputs in the project. Sixth, staged investments can be seen as time to build options. Finally, multiple interaction options are combinations of the real options above.
Hence, both the modelling approach as well as the type of real options is varied in the literature. The last aspect of the real options valuation approach is the modelling of the underlying uncertainties. The identification of uncertainties as well as managerial flexibility is crucial for valuing real options and thereby the value of flexibility (Greden et al. 2005). Miller and Lessard (2001) identify three broad categories of risk with respect to infrastructure projects, namely market‐related risks, completion risks, and institutional risks. Market‐related risks consist of demand forecasts inaccuracy, financial risk, and supply risk. Completion risk addresses the technical, construction and operation risks of the infrastructure project. Finally, institutional risks deal with the political situation, for example regulations concerning pricing and entry. These risks can either be modelled by using analyst forecasts, historical data or a Monte Carlo simulation. Copeland and Antikarov (2001) recommend the third possibility. That is, to model the underlying uncertainties in Crystal Ball® and estimate the average and standard deviation of the project value with a Monte Carlo simulation. The average and standard deviation are used to build the binomial option‐pricing model. The Monte Carlo simulation in Crystal Ball® allows for the inclusion of multiple uncertainties but generates a single volatility estimate so that a simple and intuitive binomial option‐pricing model can still be used. Uncertainties allow for managerial flexibility if management is able to take an active stance towards them. An important distinction is whether this managerial flexibility represents a real option ‘on’ the project that management considers a black box, or a real option ‘in’ the project, which changes the actual design of the project (Wang and de Neufville 2004). In fact, real options ‘in’ the project require a deeper understanding of the project because the properties of the option, such as the exercise price and exercise date are hard to observe. In contrast, real options ‘on’ the project are comparable to financial options and can be valued easily.
Several authors have constructed a framework for real options valuation. These frameworks combine uncertainty modelling, modelling approaches, and real options types. All frameworks for real options valuation are based on the traditional discounted cash flow approach. The net present value without flexibility is the reference value. The framework of Copeland and Antikarov (2001) combines a Monte Carlo simulation of modelled uncertainties with the intuitive binomial option‐pricing model by Cox et al. (1979). Dixit and Pindyck (1994) and Trigeorgis (1996) constructed frameworks with more complex modelling approaches. De Neufville (2000), however, proposes a more descriptive framework of real options valuation. Essentially, each real options valuation is a trade‐off between mathematical elegance on the one hand and intuitive interpretation on the other hand (Garvin and Cheah 2004).
B. Applied literature
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on the value of flexibility. Pimentel et al. (2008) develop a mathematical complex model but fail to show convincing results for their real options valuation of the Portuguese high‐speed rail project. In short, the number of real options valuations of high‐speed rail projects is small and inconclusive about the value of flexibility.
Table 1
Overview of real options valuations of high‐speed rail projects Articles Bowe & Lee (2004) Huang & Chou
(2006) Petkova (2007) Pimentel et al. (2008) Case Taiwan High‐ speed rail Taiwan High‐ speed rail Dutch Maglev project Portuguese High‐speed rail
Data Real* Real* Simulated Simulated
Uncertainty Operating cash flows
Revenues Traffic demand Traffic demand, investment, benefits Real option Deferment, expansion, contract Abandonment, MRG** Deferment, abandonment Deferment NPV*** ‐€ 28,280mln € 138,510mln ‐€ 180mln ‐€ 276mln % of NPV**** 201 9.67 107 1,365
Model Closed‐form Closed‐form Simulation Stochastic differential
equations * Taiwan High‐Speed Rail Consortium ** Minimum government guarantee *** Net present value without flexibility **** Option value as a percentage of the net present value without flexibility The first real options valuation of a high‐speed rail project is by Bowe and Lee (2004). They examined the Taiwan high‐speed rail project with real data from the Taiwan High‐Speed Rail Consortium. They identified operating cash flows as the uncertainty and modelled it in continuous time with a Geometric Brownian motioniv. The consortium possesses the real options to defer, expand, and contract the project. Bowe and Lee (2004) use a modified version of the Black‐Scholes model, which belongs to the closed‐form approach, to compute the combined value of flexibility. The value of flexibility is approximately 201 percent of the project value without managerial flexibility. The net present value without flexibility of the high‐speed rail project is negative and equal to ‐€ 28,280mln. The real options are all valuable, ranging from € 12,920mln for the contraction option to € 15,200mln for the deferment option. The combined option value, however, equals € 56,380mln so there is a negative interaction effect of ‐€ 13,730mln. Hence, the option values are non‐additive. In short, Bowe and Lee (2004) show that flexibility is a major determinant of the economic viability of the Taiwanese high‐speed rail project.
The article by Bowe and Lee (2004) provides substantial evidence for the value of flexibility of infrastructure projects. However, the analysis has three shortcomings. First, they modelled uncertainty as operation cash flows, which is a rough measure that includes multiple costs and benefits. The variance is computed on basis of the distribution of cash flows, which is influenced by operating and financial decisions. Therefore, the valuation results are potentially biased. Second, Bowe and Lee (2004) examine managerial flexibility from the perspective of the consortium. The effect on society, however, is unclear. Taxpayers could pay the
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burden. Finally, Bowe and Lee (2004) do not discuss the information on which management bases its flexibility decisions.
Huang and Chou (2006) also conducted a real options valuation of the Taiwan high‐speed rail case but without referring to the article by Bowe and Lee (2004). Huang and Chou (2006) used the same data of the Taiwan High‐Speed Rail Consortium. Instead, they model revenues as the underlying uncertainty with a Geometric Brownian motion process. Huang and Chou (2006) then derive complex closed‐form equations. They examine both the real option to abandon the project during the pre‐construction phase and the minimum revenue guarantee (MRG). The consortium has the right to forgo the commencement of the construction process if the project seems to exceed budgetary constraints. The MRG can be regarded as a European put option granted by the government to stimulate the execution of the high‐speed rail project. The net present value of the project without flexibility is € 138,510mln, which clearly differs from the negative net present value of Bowe and Lee (2004). The abandonment option equals € 7,440mln and the minimum revenue guarantee is approximately € 7,720mln. The combined option values equals € 13,390mln so there is a small interaction effect. The value of flexibility is approximately 9.67 percent of the net present value without flexibility. Reviewing the article of Huang and Chou (2006) with respect to the previous study by Bowe and Lee (2004) shows that a real options valuation with identical data is not a guarantee of comparable results. Not only is the value of flexibility different, but also the underlying net present value. Hence, one has to be very careful with making statements on basis of these real options valuations of the Taiwan high‐speed rail case. Moreover, the study by Huang and Chou (2006) has two shortcomings. First, they do not model the underlying uncertainty precisely. Revenues are subject to numerous factors, including traffic demand, cost of capital, and financing decisions. In fact, the authors use the volatility of the Taiwan’s stock market to estimate the variance of the high‐speed rail project’s variance. Second, the real options have weak assumptions. The private consortium can abandon during the pre‐construction phase without incurring a penalty. Likewise, the effect of the minimum government guarantee on society is unclear. Presumably, when revenues are lower than expected the taxpayer pays the burden.
Petkova (2007) wrote her master thesis on the rail system planning for the Portuguese high‐speed rail project. She examined the benefit of a real options valuation for this high‐speed rail project. For she did not have data on the Portuguese project, Petkova (2007) used simulated data of the Dutch Maglev project. Her data consists only of revenues, time savings, and investment costs. Traffic demand is identified as the underlying uncertainty and modelled with a Geometric Brownian motion. The government has the flexibility to defer construction of the project and abandon during the operation phase. The net present value without flexibility equals ‐€ 180mln. The deferment option is worth € 273mln, which represents 107 percent of the NPV without flexibility. Remarkably, the abandonment option value is not reported. On basis of this illustrative real options valuation with simulated data, Petkova (2007) concludes that the real options valuation approach is not yet suitable for high‐speed rail projects.
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deferment option while she announced to examine also the option to abandon the Dutch Maglev project. Finally, Petkova (2007) does not explain how the government is able to make the decision on the real options. That is, the information on which the government is able to defer the investment is not discussed. Pimentel et al. (2008) examine the Portuguese high‐speed rail project too. Similar to Petkova (2007), there is no data available so they use a simple self‐constructed dataset. Pimentel et al. (2008) are the only authors that identify multiple uncertainties in their real options valuation of a high‐speed rail project. Namely, they model traffic demand, investment costs, and revenues by a Geometric Brownian motion process. The net present value without flexibility equals approximately ‐€ 276.2mln. Only the deferment option is examined, which has a value of € 3,492mln. The real option represents 1,365 percent of the NPV without flexibility. Pimentel et al. (2008) conclude that they developed a sophisticated real options valuation model with stochastic differential equations, which needs to be tested with real data.
The article by Pimentel et al. (2008) provides a sophisticated but complex model. The preliminary results on basis of a simulated dataset are, however, unconvincing. The value of flexibility equals 1,365 percent of the net present value without flexibility whereas the average percentage ranges from zero to approximately 200 percent in other studies. Outliers like these can probably be attributed to parameter estimation. Furthermore, Pimentel et al. (2008) report little on the estimation of these input parameters, which are detrimental to the valuation results. For example, the validity of a standard deviation of 32.5 percent of the benefits is not demonstrated. Therefore, the stochastic model by Pimentel et al. (2008) is not useful yet to evaluate the value of flexibility.
Hence, the limited number of real options valuations of high‐speed rail project fails to present conclusive evidence on the value of flexibility. Moreover, there is no preferred modelling approach in the applied literature. Nonetheless, in the applied literature there are numerous real options valuations in other application areas, which are comparable to infrastructure projects. These application areas also have heavy, fixed, and normally irreversible investments. Table 2 summarizes these comparable real options valuations. I selected real options valuations on mines, oil and gas projects, public parking garages, toll roads, and a number of miscellaneous projects.
11 Table 2
Overview of real options valuations in other application areas
Application area Articles Data Real option* NPV** % of NPV*** Model
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Similar to the real options valuations of toll roads, real options valuations of mines, oil and gas projects, public parking garages, and miscellaneous projects do not provide conclusive evidence of the value of flexibility either. The value of flexibility ranges from 3 percent to as high as 1,981 percent. In addition, the modelling approaches differ between the studies. The examined real options are, in order of most studied, the option to defer, abandon, expand, and switch. Less than 50 percent of the real options valuations use real data. Hence, these comparable real options valuations focus on the methodology.
In short, both the real options valuations of high‐speed rail projects and comparable projects provide no conclusive evidence of the value of flexibility. Most valuations are based on simulated and low‐detailed data because the authors focus on the methodology. There is no preferred modelling approach, however. Moreover, the underlying assumptions are not discussed thoroughly. For example, the crucial assumption of information to have managerial flexibility is hardly examined. Finally, the results of the real options valuations are mixed and incomparable.
C. Contribution to literature
In conclusion, the theoretical literature on real options valuations offers a wide variety of modelling approaches, types of real options, and uncertainty modelling. Yet, the applied literature fails to present conclusive evidence on the value of flexibility of infrastructure projects. The real options valuations also differ with respect to their methodology. It is difficult to find a set of best practices. With this master’s thesis, I will make three contributions to the literature. First, I conduct a real options valuation of the Dutch Maglev project based on real data, which stems from an existing social cost benefit analysis by Elhorst and Oosterhaven (2008). Second, this valuation is highly‐ detailed. Flyvbjerg (2006) requires such real and high‐detailed data to conduct a proper case‐study. Finally, I will discuss the important concept of information in the real options valuation.
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III. Methodology
I use the dataset of Elhorst and Oosterhaven (2008) of the Dutch Maglev project for my real options valuation. This dataset contains yearly estimates for costs and benefits for the period 2011‐2060. I construct a cash flow statement from this dataset. I adopt the framework for real options valuation by Copeland and Antikarov (2001) because it allows for the modelling of multiple uncertainties in continuous time but uses the intuitive binomial option‐pricing model of Cox et al. (1979). First, a net present value analysis is conducted on basis of the cash flow statement. Second, uncertainties are identified and modelled in Crystal Ball®. Third, a Monte Carlo simulation is used to estimate the average and standard deviation of the Dutch Maglev project value. Fourth, real options are modelled with a binomial‐option pricing model following Cox et al. (1979). Finally, the value of flexibility is computed by taking the difference between the NPV with flexibility and the NPV without flexibility. I present a sensitivity analysis to check the robustness of my results.A. Net present value
I use the social cost benefit analysis of Elhorst and Oosterhaven (2008) as a starting point for the real options valuation. A cash flow statement is constructed after conducting a number of rearrangements. First, the discount ratev and the growth rate are separated to show their individual effects. Then, a sensitivity analysis on the discount rate is more precise. Second, indirect economic effects are aggregated and categorized by type of effect. These indirect economic effects have no effect on the real options valuation. Third, the construction costs are divided into yearly estimates following the investment schedule by PWC (2000). Construction costs can now be modelled as an uncertainty. Finally, exploitation costs incorrectly contain train investment. This train investment is reported separately. Construction costs and train investment together constitute the investment costs of the Dutch Maglev project.
Table 3 shows the condensed cash flow statementvi for the first 15 years. Direct benefits consist of exploitation revenues and time savings. Additional indirect benefits and costs contain additional consumer benefits and labour market effects. External effects, such as noise and pollution, are reported too. The costs of the Dutch Maglev project consist of construction costs, train investment, and exploitation costs. Following Elhorst and Oosterhaven (2008), a social discount rate of 4 percent is used to compute discounted cash flows at 2010 value. A detailed explanation of the cost and benefit items is provided in appendix B.
15 B. Uncertainties
I have identified three uncertainties in the Dutch Maglev project: traffic demand, construction costs, and transition period. They are reported in table 4. Traffic demand and transition period are market‐ related risks whereas construction costs is a completion risk (Miller and Lessard 2001). In the applied literature, traffic demand and construction costs are common as uncertainties in infrastructure projects (e.g. Pimentel et al. 2007; Petkova 2007). Moreover, Flyvbjerg (2006, 2007) gives empirical evidence on the incorrect forecasts of traffic demand and construction costs. Therefore, I include both uncertainties in my real options valuation. The third uncertainty, transition period, is less common. Most authors make an assumption on the time it takes an infrastructure project to reach full capacityvii but they do not recognize the underlying uncertainty. I follow Cheah and Liu (2006) by modelling this transition period uncertainty. It differs from traffic demand because transition period uncertainty influences all cost and benefit items, except noise. Although a longer transition period will decrease traffic demand during the start‐up phase, I assume there is no lasting effect on traffic demand. The uncertainties are independent so there is no correlation between them. Table 4 Modelled uncertainties in the Dutch Maglev project.
Uncertainty Type of risk* Modelling Range
Traffic demand** Market‐related Geometric Brownian motion +/‐20% Construction costs Completion Poisson jump process 10‐20% Transition period Market‐related Lognormal distribution 3‐9 years***
* Type of risk according to the classification by Miller and Lessard (2001) ** Exploitation revenues, time savings, and exploitation costs are modelled as indirect uncertainty items. *** Transition period average is 5 years.
I model these uncertainties by selecting specific cost and benefit items and assigning stochastic processes to them, following Zhao and Tseng (2004). This approach is until now restricted to real options valuations with simulated data because the approach requires high‐detailed data. This high‐ detailed data requirement is met by the data of Elhorst and Oosterhaven (2008). My uncertainty modelling approach is as explicit as possible. Alternative approaches to model uncertainties are the modelling of the project value as an uncertainty (e.g. Ho and Liu 2002; Bowe and Lee 2004) or to model factors within costs and benefit items, such as traffic demand being a function parameter of revenues (e.g. Pimentel et al. 2007; Mayer and Kazakidis 2007). The first alternative is too rough whereas the second has not yet been applied to real data because it requires too detailed data. The dataset by Elhorst and Oosterhaven (2008) does not contain underlying parameters, such as tariff and traffic demand. Therefore, I prefer the approach by Zhao and Tseng (2004). Traffic demand Traffic demand is not directly observable in the data by Elhorst and Oosterhaven so specific cost and benefit items that are related to traffic demand are selected. First, exploitation revenues are directly vii
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related to traffic demand. Second, time savings of commuting and other trips are related to traffic demand. Finally, exploitation costs are related to traffic demand. Exploitation costs consist of approximately 20 percent infrastructure and 80 percent transport exploitation costs (PWC 2000). I assume only transport exploitation costs are variable. Therefore, 80 percent of the exploitation costs are modelled in relation to traffic demand. The remainder of 20 percent is kept constant.
These cost and benefit items related to traffic demand will be modelled by a Geometric Brownian motion process, following Petkova (2007) and Pimentel et al. (2007). Marathe and Ryan (2005) demonstrate empirically that the Geometric Brownian motion process is accurate in forecasting traffic demand. The Geometric Brownian motion is presented in equation (1) following Charnes (2007), with Vt the value at time t, μ is the annual growth rate, σ the standard deviation and Z the normally distributed residual with zero mean and a standard deviation of 1. σZ 2 σ μ 1 t t 2 e V V ⎟⎠+ ⎞ ⎜ ⎝ ⎛ − − = (1)
I assume traffic demand has a zero growth rate by setting the growth rate μ equal to half the variance in equation (2). This assures that there is no automatic upward bias so the modelling of traffic demand uncertainty is consistent with the social cost benefit analysis by Elhorst and Oosterhaven (2008). In their social cost benefit analysis, only time savings for commuting trips grows at the real wage growth rate of 1.11 percent (CPB 1997) to account for higher wages in the future. With a zero growth rate for traffic demand, the arithmetic average of the Monte Carlo simulation of the selected cost and benefit items will give zero growth but individual simulation runs do have small positive or negative trends. 2 σ μ= 2 (2)
The standard deviation σ is assumed 20 percent, which is commonly used in the literature (e.g. Pimentel et al. 2007). An alternative would be to use expert estimates but these are unavailable for the Dutch Maglev project. The lower bound of the Geometric Brownian motion is zero but there is no upper bound. I will conduct a sensitivity analysis by setting an upper bound for traffic demand uncertainty.
In Crystal Ball®, the Monte Carlo simulation of the Geometric Brownian process takes residuals from the normal distribution (0,1) for each run. Then, it computes the estimate on basis of this residual Z and the input parameters μ and σ. Finally, the arithmetic average of the estimates is calculated to obtain the average and standard deviation of the project value. This arithmetic average of the estimates differs from the expectation of the average parameter inputs that is equal to Vt. Equation
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evidence shows that on average there is a large cost escalation while few projects have lower construction costs than initially forecasted (Flyvbjerg 2006). Including cost overruns as Poisson jumps results in a logarithm distribution of the aggregate construction costs. Chou et al. (2009) empirically verify such a logarithmic distribution of Poisson jumps. t t t t I I q I = + (4)
The Poisson process shown in equation (4) is in discrete time because I assume cost overruns can occur only once a year. The jumps are mutually independent so there is no correlation between a jump occurring in a particular year and following years. The probabilities in (5) are modelled by a binomial probability distribution. The jump qt in (4) has a random size of φ, which ranges from 10
until 20 percent, given in equation (6). A random jump size is more realistic because cost overruns are not identical. Moreover, a random jump size accounts for the range of volatility inputs for construction costs in the literature (e.g. Ho & Liu 2001; Pimentel et al. 2007). This random size φ is modelled by a uniform distribution. λ 1 λ y probabilit y probabilit with with 0 φ qt − ⎩ ⎨ ⎧ (5) 0.10≤φ≤0.20 (6)
The probability λ that a cost overrun will happen follows the Poisson distribution in (7) with x
representing the number of cost overruns per year. Cost overruns are limited to occur only once a year so x is equal to one. The equations beneath are derived from Dixit and Pindyck (1994).
Rewriting equation (7) to express expected time until a cost overrun occurs leads to equation (8). Hence, the expected time until a cost overrun occurs is equal to one divided by the probability λ.
( )
x! e λ x f λ x − = (7)( )
λ 1 dT λTe T E 0 λT = =∫
∞ − (8) The construction period ranges from 2011 to 2015, being five years. The expected time T until a cost overrun occurs is, however, unknown. Flyvbjerg (2006) finds that nine out of ten projects have cost overruns so there is a high probability that construction costs will be higher than forecasted. Therefore, I assume that at least one cost overrun occurs in every construction period. The expected time T now equals the construction period length of five years. Then, the probability λ of a costoverrun becomes 0.2.
Transition period
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I apply a modified version of the approach by Cheah and Liu (2006) who assume that the growth rate during the transition period follows a lognormal distribution. Whereas they model the transition growth rate as an uncertainty, the length of their transition period is still fixed. I model the length of the transition period as the underlying uncertainty by assuming it follows a lognormal distribution. The annual proportion of full capacity is computed by dividing 100 percent by the transition period length and multiplying it with the number of years after construction, shown in equation (9). St is the annual proportion, t the number of years, and T the transition period length. St =
( )
100T ×t (9)A lognormal distribution is appropriate because the number of years cannot be negative and the lognormal distribution is positively skewed. This positive skewness corresponds with the direct and indirect benefits that take time to evolve, which is likely to be longer instead of shorter than the originally estimated five years. The mean of the lognormal distribution is 5 years and the standard deviation equals one. As a result, the transition period ranges from approximately three to nine years. There is no effect of the transition period uncertainty after the project reached full capacity. C. Real options
I have identified three real options for the Dutch Maglev project. They are reported in table 5. First, the option to defer construction. Next, the option to abandon the project during operation phase. Finally, the option to expand capacity by investing in additional trains. These real options are common in the real options literature (Amram and Kulatilaka 1999). Besides the calculation of the value of the real options individually, I compute combinations of these options. In total, I report seven option values.
Table 5
Real options in the Dutch Maglev project
Real option Variable Exercise price Length Volatility Risk‐free rate
Deferment Total inv. € 6,597mln* 5 years 23.1%** 4%*** Abandonment Salvage value € 692mln** 25 years 23.1%** 4%*** Expansion Train inv. € 125mln**** 10 years 23.1%** 4%***
* Estimated average of project value during construction period, 2011‐2016. ** Estimated standard deviation of project value during operation period, 2016‐2040. *** Harmonised long‐term interest rate (ECB 2009). **** Estimated at € 692mln (NEI 2001). ***** Train investment is € 125mln, 20 percent of the initial estimate (NEI 2000).
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the operation period. I estimate the project value for the two periods separately because investments become sunk costs after they are made. Therefore, they do not affect the project value for the remaining operation period. Moreover, investments costs are the exercise price of the deferment option so including the construction period to compute the average project value leads to incorrect double counting of investment costs. That is, they are the exercise price of the deferment option and part of the underlying project value. In summary, the Monte Carlo simulation gives an average and standard deviation for the construction period 2011‐2015 and an average and standard deviation for the operation period 2016‐2040.
The binomial option‐pricing model also requires the exercise price, the lifetime in years, and the annual risk‐free rate. With these inputs, I compute risk‐neutral probabilities of upward and downward movements in the project value, which is the underlying asset of the real option. The following equations are derived from Copeland and Antikarov (2001). I use equation (10) and (11) to compute the upward movement u and downward movement d in the project value. These
movements are inputs for equation (12) and (13) to compute the risk‐neutral probability upward πu
and the risk‐neutral probability downward πd. The risk‐neutral probabilities are adjusted for the
underlying risk, so I use the annual risk‐free rate as the appropriate discount rate. σ e u = (10) u 1 d = (11) d u d r 1 πu f − − + = (12) u d 1 π π = − (13)
The binomial option‐pricing model consists of an event tree and a decision tree. The event tree represents the net present value without flexibility, where upward and downward movements are computed with the risk‐neutral probabilities. The decision tree includes managerial flexibility by computing the outcomes of the marginal decision rules of the real options. The real option values are obtained by solving the binomial option‐pricing model for each node of the decision tree, working backward from right to left. All real option values are discounted back to 2010. I compute also the probability that the government invests in the Dutch Maglev project. Following Pimentel et al. (2007), this probability is obtained by multiplying the nodes of the decision tree where the government exercises the deferment option.
Deferment
The deferment option is an Americanviii call‐optionix on the Dutch Maglev project to invest. It is an option “on” the project because the characteristics of the Dutch Maglev project are unchanged (Wang and de Neufville 2004). The government can invest immediately in 2011 but has the option to
viii
American options can be exercised before the real option expires. The alternative, European options can only be exercised at the end of the lifetime of the real option.
ix
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wait‐to‐invest until prospects are more favourable. The decision on deferment is made by comparing the present project value, V – E, with V the project value and E the exercise price, and the expected
project value, given in equation (14). The expected project value is the discounted product of the upward project value Vu and the downward project value Vd times the corresponding risk‐neutral
probabilities πu and πd (Copeland and Antikarov 2001). If there is an upward movement of volatility,
the project value is higher. Similarly, a downward movement reduces project value. The volatility is computed from the standard deviation of the project value during the operation period, 2016‐2040, and the risk‐free rate. Therefore, an upward volatility movement represents higher traffic demand or a shorter transition period. The deferment option is valuable when the government can obtain a higher project value by postponing investment. When the deferment option expires, the government only invests if the present project value, V – E, exceeds zero, shown in equation (15).
(
)
⎟⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + + − f d d u u r 1 V π V π E; V max (14) max(
V−E;0)
(15) The deferment option has the following assumptions, based on the literature (e.g. Garvin and Cheah 2004; Woolridge et al. 2002). The option to defer has a lifetime of five years. The length of the operation period remains 25 years. There are no costs associated with waiting, except for heavier discounting. The exercise price, which is investment costs, is the average of the project value during the construction period similar to Pimentel et al (2007). The Monte Carlo simulation of 10,000 runs in Crystal Ball® reports an average of ‐€ 6,597mln for the construction period 2011‐2015, which is slightly lower than the static discounted cash flow value of € 6,391mln by Elhorst and Oosterhaven (2008). The difference stems from the modelled uncertainty of cost overruns.Abandonment
The abandonment option is an American put‐option on the Dutch Maglev project to abandon operations. It is an option “on” the project because the characteristics of the Dutch Maglev project are unchanged (Wang and de Neufville 2004). The government can continue operations but has the option to cancel all future operations and obtain the salvage value. The decision on abandonment is made by comparing the salvage value, E, and the expected project value, given in equation (16). The
expected project value is the discounted product of the upward project value Vu and the downward
project value Vd times the corresponding risk‐neutral probabilities πu and πd (Copeland and Antikarov
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( )
E;V (17) The abandonment option has the following assumptions, based on the literature (e.g. Petkova 2007; Rose 1998). The option exists for the entire operation period that is from 2016 to 2040. The exercise price is the salvage value, estimated by NEI (2001) at € 692mln. NEI (2001) estimated this value on basis of 35 percent of the investment costs and discounted it back to 2010. I assume that the salvage value decreases over time due to deterioration of the Maglev infrastructure. Therefore, I do not compensate for the heavier discounting of the salvage value after 2015.Expansion
The expansion option is an American call‐option on the Dutch Maglev project to make an additional train investment. It is an option “in” the project because the characteristics of the Dutch Maglev project are changed (Wang and de Neufville 2004).The government does not make the full train investment in 2015 but postpones 20 percentx of it and regards this train investment as an expansion option. Therefore, the train investment in 2015 drops from € 628mln to € 503mln. The remaining train investment, worth € 125mln, is optional for the government. Therefore, the full capacity decreases from 100 percent to 80 percent. There are fewer trains to transport passengers. Exercising the expansion option increases the full capacity to 100 percent and, thereby, project value, at the cost of € 125mln. The decision on expansion is made by comparing the present project value with expansion, V – E, with V the project value and E the exercise price, and the expected
project value without expansion, given in equation (18). The expected project value is the discounted product of the upward project value Vu and the downward project value Vd times the
corresponding risk‐neutral probabilities πu and πd (Copeland and Antikarov 2001). The volatility is
22 D. Sensitivity analysis
The results of real options valuation depend for a large extent on the underlying assumptions. For example, Bowe and Lee (2004) and Huang and Chou (2006) use the same data but arrive at very different results. Therefore, a sensitivity analysis on the underlying assumptions in my real options valuation is required. These underlying assumptions can be classified in three groups. First, the assumptions of the net present value analysis. Second, the assumptions underlying the modelled uncertainties. Third, the assumptions of the input parameters of my real options valuation. For each group of assumptions I conduct sensitivity analyses to check whether my results are robust.
Net present value analysis
My net present value analysis has two strong underlying assumptions. Namely, the discount rate and the length of the operation period. These two issues have also led to much debate between practitioners of the social cost benefit analyses (Elhorst and Oosterhaven 2008). For the discount rate, I conduct a sensitivity analysis on the discount rate by computing the net present value effect of a one percent negative and a one percent positive change in the discount rate. Moreover, I compute the net present value by using a market return instead of the social discount rate. For the length of the operation period, I compute the net present value for the longer period, 2011 until 2060, and compare it to the normal period length of 2011‐2040. Furthermore, I discuss the salvage value as a compensation measure for this operation period difference that is 2040‐2060.
Uncertainties assumptions
I model three uncertainties in my real options valuation, traffic demand, construction costs, and transition period. Constructions costs uncertainty drives the volatility of the construction period, 2011 to 2015. Similarly, traffic demand and transition period uncertainty drive the volatility of the operation period, 2016 to 2040. In Crystal Ball®, I compute the relative contribution of the uncertainties to the construction period, the operation period, and the total period of 2011 to 2040. The relative contribution to volatility identifies the largest determinant of the standard deviation of the project value, which is an input parameter to the binomial option‐pricing model. I conduct a sensitivity analysis on the largest relative volatility contributor.
Next, traffic demand uncertainty will be restricted to an upper bound. Originally, the Geometric Brownian motion process has a lower bound of zero but no upper bound. Therefore, traffic demand could double within a couple of years. As a sensitivity analysis, I assume full capacity equals 80 percent of maximum capacity. Therefore, traffic demand uncertainty has an upper bound of 125 percent of full capacity, which is the original estimate in the data by Elhorst and Oosterhaven (2008).
Input parameters
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IV. Data
A. Introduction
There exist three major social cost benefit analyses on the Dutch Maglev project. They are conducted by the NEI (2000, 2001), RUG (2001) and Nyfer (2000). Although all three studies report a negative net present value, there was a lot of discussion about the data and valuation practices. This discussion is summarized in the paragraph on data issues. Most data on the Dutch Maglev project stem from studies of the Ministry of Transport. Yet, the studies differ substantially. I use the dataset by Elhorst and Oosterhaven (2008), who are the main authors of the social cost benefit analysis by the RUG (2001).
Elhorst and Oosterhaven (2008) give their final opinion on the profitability of the Dutch Maglev project by explicitly including market imperfections and cross‐border effects. They use the dataset by NEI (2001) as a starting point but make two major changes. First, Elhorst and Oosterhaven (2008) forecast the induced migration effects of commuters relocating themselves after travel time reductions with the commuter location model. Second, they estimate the spatial distribution of employment and the resulting effects of the Maglev project by an economic geography inter‐ industry model (RAEM). Together with several smaller changes, they report a negative NPV of ‐€ 2,591mln for the period 2011‐2040, which clearly differs from the net present value of ‐€ 3,444mln by NEI (2001). An overview of the social cost benefit analysis by Elhorst and Oosterhaven (2008) is shown in appendix A.
B. Data
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optimistic scenario. Therefore, my real options valuation of the Dutch Maglev project with the ‘European coordination’ scenario approximates the average of the real options valuations for the three scenarios separately. I leave it to further research to examine the effect of long‐term macroeconomic growth scenarios on the results of a real options valuation on infrastructure projects.
The used risk‐free rate in the binomial option‐pricing model is the actual harmonised long‐term interest rate for the Netherlands, equal to 4 percent (ECB 2009). The estimation of this risk‐free rate, based on long‐term government bonds with maturities close to 10 years, follows the guidelines by Koller et al. (2005).
C. Data issues
There has been a lot of debate between practitioners about certain elements of the social cost benefit analyses of the Dutch Maglev project. First, the length of the operation period of the Maglev project differed between the various analyses. Elhorst and Oosterhaven (2008) suggested to calculate the net present value also for a longer operation period, i.e. 2016‐2060, apart from the normal operation period of 2016‐2040. They argued that the Dutch Maglev project still provided benefits after 2040. Second, it was disputed whether there was a salvage value of the project after 2040. The NEI (2001) argued that a salvage value compensated for the relatively short lifetime of the Dutch Maglev project. The final cost benefit analysis of the Ministry of Transport, however, did not include a salvage value (Tijdelijke Commissie Infrastructuurprojecten 2004a). Third, there was a fierce discussion on the size of the labour market effects. Elhorst & Oosterhaven (2008) recalculated the effects with their RAEM model and found substantially larger indirect economic effects. This increased the profitability of the Dutch Maglev project. Finally, the policy implication of the outcomes of the social cost benefit analysis was not clear. Despite the negative net present values, Elhorst and Oosterhaven (2008) suggested to consider also the internal rate of return (IRR). A negative NPV could still have a positive internal rate of return. Although the government obtained a lower rate of return than their cost of capital, the Dutch Maglev project had a positive IRR of approximately 3 percent for the period length 2011‐2060 (Elhorst and Oosterhaven 2008).
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V. Results
A. Net present value analysis The discounted cash flow approach yields a net present value of ‐€ 2,591mln for the Dutch Maglev project. I discounted cash flows for the period 2010‐2040 at a social discount rate of 4 percent, following Elhorst and Oosterhaven (2008). The net present value is the same as Elhorst and Oosterhaven (2008) find. The corresponding internal rate of return is approximately ‐0.6 percent. Hence, the following real options valuation is based on the same net present value analysis. Any difference in valuation results must be attributed to the real options valuation.B. Uncertainties
I modelled three uncertainties of the Dutch Maglev project: traffic demand, construction costs, and transition period. The uncertainties are not correlated. I discuss the modelled uncertainties below.
Traffic demand is modelled by selecting exploitation revenues, time savings of commuting and other trips, and exploitation costs as related cost and benefit items. They follow a Geometric Brownian motion. Exploitation costs consists of only 80 percent variable costs because the remaining 20 percent is infrastructure exploitation costs, which is constant (PWC 2000). In Crystal Ball®, I generated 10,000 values for these related traffic demand items with a Monte Carlo simulation. Figure 1 shows two of such simulated scenarios of exploitation revenues for the period 2016‐2040 and the base scenario of the net present value analysis. The simulated scenarios 2 and 3 show a volatile growth pattern, which is more realistic than the static base scenario.
Figure 1. Two simulated scenarios of exploitation revenues in Crystal Ball®
26 scenarios of construction costs for the construction period 2011‐2015 and the base scenario. Scenario 2 has cost overruns in 2013 and 2015 whereas scenario 3 has a cost overrun in 2011. Figure 2. Two simulated scenarios of construction costs in Crystal Ball® The transition period is modelled by assigning a lognormal distribution with a mean of five years. Each cost and benefit item, except noise, is multiplied by the annual proportion of full capacity. At the end of the transition period, the Dutch Maglev project operates at full capacity, 100 percent. Besides the traffic demand uncertainty, figure 1 also shows the transition period uncertainty. The base case has a transition period of five years whereas scenario 2 has a longer transition period and scenario 3 has a shorter transition period. Although the transition period uncertainty affects traffic demand related items during the transition period, there is no lasting effect. C. Real options The binomial option‐pricing model requires five inputs: the risk‐free rate, the exercise price, the lifetime of the option, the average of the project value, and the standard deviation of the project value. The risk‐free rate is 4 percent, based on the long‐term harmonised interest rate (ECB 2009). The exercise price and lifetime are discussed below. The average and standard deviation of the project value are estimated by a Monte Carlo simulation of 10,000 runs in Crystal Ball®. With the modelled uncertainties of traffic demand, construction costs, and transition period, the average project value of the Dutch Maglev project for the period 2010‐2040 equals ‐€ 2,486mln. The corresponding standard deviation is 38.6 percent. The results are shown in figure 3. This net present value differs slightly from the discounted cash flow value of ‐€ 2,591 by Elhorst and Oosterhaven (2008). The difference is attributable to the modelled uncertainties, which lead to an asymmetric distribution of project values. In the literature, such a value difference is called the flaw of averages.
