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Real option valuation: Valuing a nitrogen plant using

Monte Carlo simulation

Master-thesis

to obtain the degree of Master of Science at the University of Groningen, faculty Economics and Business,

on the authority of A.A. Tsvetkov, PhD. Handed in on July 11th, 2018

by

Boudewijn Christiaan Boerema (S2397226)

Born on January 3rd, 1993 in Joure

Abstract: The investment decision to build a nitrogen plant, which adds nitrogen to gas with a high caloric value to make this gas compatible with the Dutch energy market, is evaluated using real options theory. The firm has the possibility to delay their investment for a maximum of five years. This option to delay is then valued by using a Least Squares Monte Carlo simulation and regression. The prices of high caloric and low caloric gas are modeled with mean-reverting stochastic processes where the equilibrium price is also a stochastic process. The price of electricity is modeled with a mean-reverting process with a constant equilibrium price, while the price of emission allowances is modeled with a regular geometric Brownian motion. One interesting result is that an increase in the risk-free interest rate decreases the value of the real option, contrary to what other literature on the subject suggests. This is a result of the risk-free rate only being used to discount the future cash flows, while it does not determine these cash flows. Another result is that increased uncertainty, i.e. volatility, for the equilibrium price level of Dutch natural gas has no influence on the value of the real option, even though the literature suggests that increased uncertainty should increase real option value. A further result is that the value of the real option decreases if uncertainty, i.e. volatility, of the Dutch natural gas price increases, until it reaches a certain point after which it starts to increase again, contrary to what the literature suggests. A possible

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1. Introduction

In response to years of problems with earthquakes and the increased intensity of these

earthquakes caused by gas extraction in Groningen, political decisions are to be made regarding the commercial exploitation of the Groningen gas fields (Rijksoverheid, 2018a). Recent

developments in politics point in the direction of a complete stop of extraction by 2029-2030 (Rijksoverheid, 2018b). However, because the Groningen gas field is the biggest gas field in The Netherlands and accounts for 50% of the natural gas production in The Netherlands, a substitute must be found for this amount (Roggenkamp & Hammer, 2004).

Anyhow, this gas field has some distinctive properties compared to other gas fields in the world, i.e. the gas that is won from Groningen contains a relatively large amount of nitrogen. This large amount of nitrogen has negative consequences for the caloric value, i.e. the amount of energy that one cubic meter contains is much lower (GTS, 2015a). Because of the high nitrogen, the gas from the Groningen field is labeled as low caloric gas, as it has a lower caloric value than for example Russian or Norwegian gas, which is high-caloric gas. The gas from the Groningen field is therefore sometimes also called G-gas, while the high-caloric gas is called H-gas (GTS, 2015a).

Because nearly all Dutch household use gas from the Groningen gas fields, G-gas became the standard for stoves and boilers in The Netherlands. If the extraction of G-gas is halted in 2030, this only leaves twelve years for a complete revamp of the entire country’s energy system. However, there are possibilities to alter the caloric values of natural gas: By adding nitrogen to high-caloric gas it can be made into pseudo G-gas, which can be used for the Dutch energy system. There are already plants in place that can do this, however they are not able to supply the entirety of the Dutch demand for gas. Therefore, a new plant must be built which can at least help close the gap. Plans for this new plant were unveiled in 2015. However, in 2016 the decision to build the new plant was delayed because the maximum amount of gas that could be extracted was decreased to a level that was, at that time, deemed safe (Tweede Kamer, 2016). This decision to delay is reminiscent of a “real option.” According to Triantis (2000), real options are opportunities to delay and adjust investment and operating decisions over time in response to the resolution of uncertainty. This description of real options fits perfectly with the decisions that were made in 2016: There was uncertainty whether the nitrogen plant was needed, so the investment was delayed.

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real options analysis is able to account for this uncertainty. The real option that is considered in this thesis is the option to defer: The firm has the option to defer the investment for five years, after which it can abandon the investment at no cost. In this thesis the cost for acquiring the option is considered sunk, therefore it has no influence on the valuation of the option.

The plant that is considered here converts H-gas, from Russia, to G-gas by injecting the H-gas with nitrogen. The nitrogen is extracted from the air by cooling down the air by enormous amounts, which costs a lot of electricity to do so. This extracted nitrogen is then added to the Russian gas to make it into Dutch gas, capable of being used by Dutch appliances and industries. The plant itself produces no emissions, but the transport of gas to and from the plant does cause emissions, which have to be paid for with emission allowances.

The model that is used in this paper is based on the models that Schwartz and Smith (2001) and Abadie and Chamorro (2009) use. The prices of Russian and Dutch gas are modeled with mean-reverting stochastic processes, where the equilibrium price that the gas prices revert to are also modeled with mean-reverting stochastic processes. The price of electricity is modeled with a simple mean-reverting stochastic process where the equilibrium price is constant. The price of emission allowances is modeled with a regular geometric Brownian motion. These stochastic processes are used to simulate years into the future. By using a Least Squares Monte Carlo approach the value of the real option is calculated. The sensitivity of the value of the real option is then evaluated for a different time to maturity of the real option, the volatility of the Dutch natural gas price, the equilibrium price level of Dutch natural gas, the risk-free interest rate and the cost of investment.

This thesis can be interesting for the firm that currently hold the option to build the plant or another investor that is interested in building this plant. If this other investor is interested in this plant, they could use this thesis to assess the value of entering the project, in particular because there are always some initial costs with securing the option. This investor should make

arrangements to secure the funding of the project if the project will be realized in the next five years.

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scenarios for the value of the real option. Section 6 concludes and gives pointers for future research.

2. Literature review

2.1 Basic principles of real options

The traditional methods used for evaluating investments in projects are the net present value (NPV) and discounted cash flows (DCF) (Graham & Harvey, 2002; Ryan & Ryan, 2002). Dixit and Pindyck (1994) mention that there are implicit assumptions that are often overlooked when using these methods: irreversibility, uncertainty and timing. The most important is the

irreversibility of an investment. If an irreversible investment is made, the cost is immediately considered sunk. For example, in the case of worse market conditions than initially expected, you cannot recover the, often large, initial cost. A second characteristic to consider is the uncertainty of the future value of the project. Changing economic conditions that affect the perceived riskiness of future cash flows can have a large impact on investment spending, more so than interest rates for example. The last characteristic is the timing of the investment. The option to postpone an investment can add value to the investment. Postponement can lead to better information about the market, or more favorable prices. The possibility to delay an investment can therefore be seen as an option due to the fact that the firm has the opportunity to invest, but not the obligation to invest, which is similar to a financial call option (Dixit and Pindyck, 1994). Traditional methods, such as the DCF, do not consider the value of active management. The implication of this is that all future investment decisions are taken in present time, and that afterwards management is seen as unable to alter its decisions while the project is going on. If they would have had the ability, management could limit potential losses or increase the cash flows based on changes in the circumstances surrounding the project. Real options theory centers on the valuation of managerial flexibility to be able to respond to different scenarios with high levels of uncertainty. Trigeorgis (1999) stated this as follows: “an options approach to capital budgeting has the potential to conceptualize, and even quantify, the value of options from active management. This value is manifest as a collection of corporate real options embedded in capital investments opportunities…”

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time.” There are two types of basic options, a call and put option. A call option gives the holder the right to buy an asset at a pre-specified price, the exercise price, in a pre-specified time. A put option gives the holder the right to sell an asset for its exercise price in a pre-specified time. An option is “in the money” if the exercise price is below the current price of the specified asset in the case of a call option. For a put option, it is considered “in the money” if the exercise price is above the current price of the underlying asset. Otherwise, the option is “out of the money”. The most common options are American and European options. The difference between these options comes from the possibility of exercising. An American option can be exercised at any point until it has reached expiration, which is the last date at which an option can be exercised. European options can only be exercised on its expiration. There are other types of options, but they are less widely used.

Myers (1977) was the first to use the term “real option”, describing it as the opportunity, but not the obligation to purchase a real asset. Copeland and Antikarov (2001) defined real options as “the right, but not the obligation, to take an action (e.g., deferring, expanding, contracting or abandoning) at a predetermined cost, called exercise price, for a predetermined period of time – the life of the option.” Kogut and Kulatilaka (2001) defined real options as “an investment decision that is characterized by uncertainty, the provision of future managerial discretion to exercise at the appropriate time, and irreversibility.” An opportunity to invest (real option) is therefore comparable to a financial call option as described by Black and Scholes (1973). If a firm with an opportunity to invest has the option to spend money (exercise price) now or in the future, in return for an asset (e.g., project) of some value, it would invest if the option is “in the money” and receive a positive net payoff. Otherwise, the firm would not invest if the option is “out of the money”, to avoid a negative net payoff.

2.2 Types of real options

There are several types of real options. Table 1 shows the types of real options and their descriptions, as summarized by Trigeorgis (1996). The rest of this section contains a more elaborate explanation of these types of real options.

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Type of option Description

Option to defer Gives the holder the opportunity to wait to invest in the project. Time-to-build or staged

investment option

This allows for the holder to evaluate the project at different stages and make investment decisions at these stages.

Option to alter operating scale

This option allows the holder to increase or decrease their operating scale, based on market conditions

Option to abandon This option gives the holder the ability to abandon an investment permanently, and if possible, sell capital equipment and other assets. Option to switch This option gives the holder the ability to switch inputs and outputs,

based on changes in prices or market demand.

Growth option An early investment gives the option holder the ability to take better advantage of future growth opportunities compared to their competitors. Compound options Combinations of real options

Source: Trigeorgis (1996)

The time-to-build, or staged investment, option allows for staging investment. Each stage can be viewed as another option on the value of the following stages and is valued as a compound option (Trigeorgis, 1996). Many projects have stages that do not allow for any return, such as construction or start-up time. Until the project is completed these projects do not make any profits. By evaluating the project at different stages, the option gives the holder the possibility to abandon the project if unfavorable events occur or market conditions worsen during an earlier stage of the investment (Majd & Pindyck, 1987). These options are important in all R&D-intensive industries, such as pharmaceuticals, as well as long-development capital-R&D-intensive projects, such as construction or energy-generating plants, and in start-ups (Trigeorgis, 1996). The option to alter operating scale provides the option holder with the possibility to react to different market conditions. For example, if market conditions turn out more favorable than initially expected, the firm can expand its scale of production. Vice versa, if market conditions are worse than initially expected, the firm can reduce the scale of operation. The firm can also choose to shut down production and wait for more favorable market conditions to restart production (Trigeorgis, 1996). These options are important in natural-resource industries,

facilities planning and construction in cyclical industries, fashion industries, consumer goods and commercial real estate.

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level where continuing investment has adverse effects, this option can be extremely important (Trigeorgis, 1996). The resale of capital equipment and other assets allows for the firm to not lose the entire investment; the option to abandon allows for this opportunity to sell (Myers & Majd, 2001).

The option to switch allows the option holder to evaluate the possibility to switch its firm’s inputs or outputs. Based on changes in prices or market demand, the firm can change its output, giving product flexibility. Alternatively, the same outputs can be produced using different types of inputs, giving process flexibility (Trigeorgis, 1996). Kulitaka and Trigeorgis (2004) show that there is added value because of this flexibility, even though it may come with additional costs. Growth options are an early investment in a capability that allows the firm to take better advantage of future growth opportunities compared to its competitors that did not make this initial investment (Kulatilaka & Perotti, 1998). These options are important in all infrastructure-based or strategic industries, especially in high tech industries, R&D and industries with multiple product generation or applications, such as computers and pharmaceuticals, as well as in

multinational operations and strategic acquisitions (Trigeorgis, 1996).

Real-life projects are often a combination of the aforementioned options. Firms often protect themselves against worsening market conditions, while at the same time they are also ready for more favorable market conditions. The combined value of these options may be different from the sum of their individual value. This is a result of the interaction between the options

(Trigeorgis, 1996).

2.3 Valuation of real options

The value of a real option depends on multiple variables. Copeland and Antikarov (2001) explain these variables and how they influence the value of a real option. Table 2 shows the effect that an increase in one of these variables has on the value of the real option.

Table 2. Influence of an increase in variable on the value of a real option Increase in variable Effect on real option

Value of the underlying asset Increase

Exercise price Decrease

Time to maturity Increase

Uncertainty Increase

Risk-free interest rate Increase

Dividends Increase

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The first is the value of the underlying asset; in the case of real options is an investment,

acquisition or project. An increase in the value of the underlying asset increases the value of the real option.

The second variable is the exercise price. An increase of the exercise price causes the value of the real option to decrease. For real options, the exercise price is usually the cost of

implementing the next phase of a project or the revenue received in the case of an abandonment option.

Third, if the time to expiration of the option increases, the value of the real option increases as well. In real options, the time to maturity is maximum period that an investment can be made without losing its flexibility. The value increases with a longer expiration as there are more opportunities to gather information.

Fourth, the uncertainty about the present value. If there is managerial flexibility the value of the real option will increase if uncertainty increases. An option is a right, but not an obligation to take an action. Therefore, an increase in uncertainty improves the upside potential while downside losses are limited.

The fifth variable is the risk-free rate of interest over the life of the option. An increase of the risk-free rate increases the value of the real option. According to Keith and Michaels (1997) “an increase in interest rates increases the option’s value, in spite of its negative effect on the net present value, because it reduces the present value of the exercise price”.

And finally, the dividends that may be paid out by the underlying asset. An increase of the dividends paid out will increase the value of the real option. Real options dividends, for example a project’s free cash outflows, can be attributed to the project value loss during the time that the option is alive (Brealey, Myers Allen & Mohanty, 2012).

2.5 Valuation methods

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The dynamic programming approach optimizes the decision that influences future payoffs. Dynamic programming makes intermediate values and decisions visible, which provides the user with information about the option and how to deal with complex decision structures (Amram & Kutilaka, 1998). Dynamic programming can be solved by using a binominal option valuation model. Examples of dynamic programming can be found in Moreira, Rocha and David (2004), Madlener, Kumbaroğlu and Ediger (2005), van Benthem, Kramer and Ramer (2006), and Chorn and Shokhor (2006).

However, when a project is more complex a numerical method has to be used to solve it. This is often done by simulation. Simulation techniques, such as Monte Carlo simulation, simulate thousands of possible paths that the underlying asset can take in a risk-neutral world, based on its stochastic process. The optimal investment strategy at the end of each path is determined and the payoff is calculated (Hull, 1999). Examples of simulation techniques being used can be found in Fuss, Szolgayova, Obersteiner and Gusti (2008), Szolgayova, Fuss and Obersteiner (2008), Fuss, Johansson, Szolgayova and Obersteiner (2009), Deng and Xia (2006), and Abadie and Chamorro (2009).

2.6 Contribution to research

A real options analysis for this type of plant has not been done before. Most real options analyses focus on power generating plants. For example, Fuss et al. (2008) and Szolgayova et al. (2008) looked at coal-fired power plants, while Abadie and Chamorro (2009) look at a gas-fired power plant. A nitrogen producing plant that converts high caloric gas to low caloric gas has not been researched yet.

Previous research concerning real options in the energy sector often only use one or two stochastic processes. For example, Fuss et al. (2008) considered a similar problem where they did a real options analysis on a coal-fired power plant, modeling the price of electricity and CO2

with stochastic processes while keeping coal prices, operations and maintenance cost and the cost of switching between technologies constant. Szolgayova et al. (2008) also look at a coal-fired power plant where only the price of electricity and CO2 are modeled with stochastic

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While Abadie and Chamorro (2009) look at an option to expand, in this thesis the option to defer investment is considered. The sensitivity of the value of the real option is considered for several variables that are likely to change value in the future. These variables are the volatility of the Dutch natural gas price, the long-term equilibrium price of Dutch natural gas, the risk-free interest rate and the value of the investment cost.

3. Methodology

3.1 Goal of this paper

The goal of this paper is to find the value of a real option which gives the firm the option the build the plant at any moment within a five-year period. After this five-year period the firm has no obligation to build the plant. There are no costs associated with having the option and no possibilities to sell capital equipment and other assets. The type of real option is therefore an option to defer combined with an option to abandon. Normally, there are costs considered with obtaining the option to build the plant. However, in this thesis it is assumed that the firm has already paid these costs, which are therefore considered sunk.

The value of the plant itself is a function of the Russian natural gas price, the Dutch natural gas price, the electricity price, emission allowances price and operating costs. By using Monte Carlo simulation, the paths over the lifetime of the plant can be simulated to find the cash flows over that period. At time t = 0 the present value of the plant when it’s operating is a function of R0, LR0, N0, LN0, E0, C0:

𝑉(𝑅0, 𝐿𝑅0, 𝑁0, 𝐿𝑁0, 𝐸0, 𝐶0) = 𝑃𝑉𝑁 − 𝑃𝑉𝑅 − 𝑃𝑉𝐸 − 𝑃𝑉𝐶 − 𝑃𝑉𝑂, (1) Where PVN is the present value of Dutch gas revenues, PVR is the present value of Russian gas costs, PVE is the present value of electricity costs, PVC is the present value of emission costs and PVO is the present value of operating costs. The NPV is then:

𝑁𝑃𝑉 = 𝑉(𝑅0, 𝐿𝑅0, 𝑁0, 𝐿𝑁 0, 𝐸0, 𝐶0) − 𝐼 = 𝑃𝑉𝑁 − 𝑃𝑉𝑅 − 𝑃𝑉𝐸 − 𝑃𝑉𝐶 − 𝑃𝑉𝑂 − 𝐼, (2) Where I is the initial investment necessary for the project.

The boundary condition when valuing the real option is:

𝐵𝑜𝑢𝑛𝑑𝑎𝑟𝑦 𝑐𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛: [𝑉(𝑅0, 𝐿𝑅0, 𝑁0, 𝐿𝑁0, 𝐸0, 𝐶0) ≥ 𝐼, 0], (3) That is, the value of the plant must be higher than the investment necessary.

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option to defer investment. Second, an evaluation of the value of the real option is made for different maturities of the real option. Third, the effect on the value of the real option for various levels of uncertainty are considered, both for the volatility of the Dutch natural gas price and the long-term equilibrium price for Dutch natural gas. Fourth, a change in the equilibrium price level is considered for Dutch natural gas. Fifth, the effects of the risk-free rate on the value of the real option is examined. And finally, the effect on the value of the real option of a change in the cost of investment is evaluated.

3.2 Least Square Monte Carlo

To determine the value of the real option the Least Square Monte Carlo (LSM) method is used. In this thesis the Monte Carlo simulation method is used, as both the PDE and dynamic

programming approach would be very complex. The LSM method was designed by Longstaff and Schwartz (2001) to determine the value of American options. A real option is comparable to an American option; both options can be exercised at any moment until maturity. The LSM is an algorithm that uses backward induction to estimate the option price. The optimal exercise

strategy is obtained by using Monte Carlo simulation with least squares regression.

First, the desired amount of sample paths is simulated. The time steps are assumed to be discrete which allows for early exercise. At each time step, a least squares regression takes place

according to the no-arbitrage valuation theory. The discounted optimal payoffs from continuation of the next time step are regressed on the set of basis functions towards underlying asset prices. Longstaff and Schwartz (2001) use only the in the money paths, which reduces the

computational time and gives an estimate of the option value with lower standard errors.

At the final date, the option holder exercises the option when it is in-the-money and lets it expire when it is out-of-the-money. At every other time step, the fitted value of the regression is

compared to the expected payoff from immediate exercise. If this fitted value is larger than the payoff from immediate exercise, the optimal strategy is to keep the option alive for at least one more time step. If the values are equal, the option holder should immediately exercise the option to benefit from the instant payoff.

When these steps are completed, a matrix of the optimal exercise strategy and of the optimal cash flows at every time step is constructed. Every optimal payoff is then discounted to time zero and the average of all these payoffs is the value of the option.

3.3 Commodity prices

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& McCardle, 1998). In these models, commodity prices are assumed to grow at a constant rate with the variance in future spot prices increasing in proportion to time. If prices increase, or decrease, more than anticipated in one time-period, all future forecasts are increased, or

decreased, proportionally. However, in the 90s authors started to argue that mean-reverting price models were a more appropriate model for many commodities, examples of this can be found in Laughton and Jacoby (1993, 1995), Cortazar and Schwartz (1992), Dixit and Pindyck (1994) and Smith and McCardle (1999). According to Schwartz and Smith (2000) the intuition behind this is as follows: “when the price of a commodity is higher than some long-run mean or equilibrium price level, the supply will increase because higher cost producers of the commodity will enter the market—new production comes on line, older production expected to go off line stays on line—thereby putting downward pressure on prices. Conversely, when prices are relatively low, supply will decrease since some of the high-cost producers will exit, putting upward pressure on prices. When these entries and exits are not instantaneous, prices may be temporarily high or low but will tend to revert toward the equilibrium level.”

Schwartz and Smith (2000) mention that the short-term deviations can occur as a result of different weather conditions or seasonality, disruptions in supply, stochastic volatility or discrete jumps. However, in the model a mean-reverting process is used, therefore these short-term deviations are expected to revert toward zero. The long-term equilibrium price level moves according to a geometric Brownian motion with drift. This drift is a catch-all variable that Schwartz and Smith (2000) say reflects the expectations of the exhaustion of existing supplies, improving technology for the production and discovery of the commodity, inflation, as well as political and regulatory effects.

3.4 Technical specifications of the nitrogen plant

The quality of natural gas is expressed as the Wobbe-index: the energy per cubic meter of gas (MJ/m3). There are essentially two types of gas: gas with a Wobbe-index lower than 46.5 MJ/m3, which is called low caloric gas (L-gas), and gas with a higher Wobbe-index, which is called high caloric gas (H-gas). Groningen gas (G-gas) has a Wobbe-index of 43.8 MJ/m3 and is the standard

for low caloric gas. This lower value is a result of a comparatively higher amount of nitrogen compared to H-gas (GTS, 2015a).

To convert H-gas with a Wobbe-index of 53 MJ/m3 to G-gas 11.1% nitrogen has to be added.

This assumes an upper limit of a Wobbe-index of 45.3 MJ/m3 for G-gas. This increases the

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convert H-gas to G-gas. To go from a Wobbe-index of 48 MJ/m3 to 55 MJ/m3 increases the amount of nitrogen necessary with around a factor of 3 (GTS, 2015a).

To acquire the nitrogen necessary for the conversion a nitrogen plant is built. A nitrogen plant produces nitrogen by extracting nitrogen from the air at around 180 degrees Celsius below zero. This nitrogen is then used for converting the H-gas into G-gas. The nitrogen plant used in this paper has a maximum capacity of 120.000 m3/h to produce nitrogen, with a reserve capacity of

60.000 m3/h (GTS, 2015a). Research by DNV GL (2015a, 2015b) showed that there is enough

H-gas available to produce at maximum capacity. However, it is not possible for the plant to function at 100% capacity as it then becomes impossible for Gasunie Transport Services (GTS, the administrator of the national gas transport system and the nitrogen installations) to let the gas market function without a loss of quality (GTS, 2015b).

To extract nitrogen the air has to be cooled down considerably, which requires a large amount of electricity. At 100% capacity the amount of energy required is 520 GWh annually (Ministry of Economic Affairs, 2017). At 85% capacity this becomes 442 GWh annually. The maximum production of G-gas at 85% capacity is 4 bcm with a Wobbe-index of 53 MJ/m3 and 7 bcm with

a Wobbe of 51.8 MJ/m3 (GTS, 2015b). The production of nitrogen is the limiting factor, which

causes the large difference in the output of gas. As a lower Wobbe-index means that less

nitrogen has to be added, more gas can be processed per hour, increasing the total volume of gas that can be processed.

The building time for the plant is 36 months. After it is built, the plant can be used for a further 30 years. The total timespan from the moment the investment decision is made is therefore 32.5 years.

3.5 Model

The model used in this thesis in an adaptation of the models used by Schwartz and Smith (2000) and Abadie and Chamorro (2009). It utilizes the short-term mean reversion by using a mean-reverting process and uses an equilibrium price level to denote the price level that the price should revert to. The Russian natural gas price is therefore modeled as follows:

𝑑𝑅𝑡= 𝑘𝑅(𝐿𝑅− 𝑅𝑇)𝑑𝑡 + 𝜎𝑅𝑅𝑡𝑑𝑊𝑡𝑅, (4) 𝑑𝐿𝑅 = 𝜇𝑅(𝐿𝑋− 𝐿𝑅)𝑑𝑡 + 𝜉𝑅𝐿𝑅𝑑𝑊𝑡

𝐿𝑅, (5)

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natural gas, µR is the rate at which LR returns to its long-term equilibrium price level LX and ξR is the volatility of the Russian natural gas equilibrium price level.

The Dutch natural gas price follows the same principles as the Russian gas prices. It is also modeled with a mean-reverting process and uses an equilibrium price level:

𝑑𝑁𝑡 = 𝑘𝑁(𝐿𝑁− 𝑁𝑇)𝑑𝑡 + 𝜎𝑁𝑁𝑡𝑑𝑊𝑡𝑁, (6) 𝑑𝐿𝑁 = 𝜇𝑁(𝐿𝑌− 𝐿𝑁)𝑑𝑡 + 𝜉𝑁𝐿𝑁𝑑𝑊𝑡

𝐿𝑁, (7)

where Nt denotes the time-t price of Dutch natural gas, LN is the equilibrium price level of Dutch natural gas, which moves in accordance with equation (4). kN is the speed of reversion of the Dutch natural gas price towards its equilibrium price level. σN is the volatility of Dutch natural gas, µN is the rate at which LN returns to its long-term equilibrium price level LY and ξN is the volatility of the Dutch natural gas equilibrium price level. dWR

t, dWLtR, dWNt, and dWLtN are

increments to standard Wiener processes. They are assumed to have a normal distribution with a mean of zero and a variance of dt.

Following the model by Abadie and Chamorro (2009), the electricity price’s long-term equilibrium price level is not subject to change, it is therefore modeled as a simple, mean reverting equation:

𝑑𝐸𝑡 = 𝑘𝑒(𝐿𝑒− 𝐸𝑡)𝑑𝑡 + 𝜎𝑒𝐸𝑡𝑑𝑊𝑡𝐸, (8) where Et is the price of electricity at time t, kE is the speed of reversion towards its long-term equilibrium price level Le and σE is the volatility of the electricity price.

The price of emission allowances follows a regular geometric Brownian motion and is taken from Insley (2003). It is modeled as follows:

𝑑𝐶𝑡 = 𝛼𝐶𝐶𝑡𝑑𝑡 + 𝜎𝐶𝐶𝑡𝑑𝑊𝑡𝐶, (9) where Ct is the price of an emission allowance at time t, αc is the constant drift rate and σc is the volatility of the emission allowances. dWEt and dWCt are assumed to have a normal distribution with a mean of zero and a variance of dt.

Due to the way this model is set up, the values of Rt, Nt, Et and Ct are not able to reach negative values. The correlations are assumed to be ρWR,WLR =ρWR,WLN = ρWN,WLR = ρWN,WLN = ρWE,WLR =

ρWE,WLN = ρWC,WLR = ρWC,WLN = 0, and ρWR,WN, ρWR,WE, , ρWR,WC, ρWN,WE, ρWN,WC, ρWE,WC are all

assumed to have a correlation different from zero.

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14 3.6 Risk-neutral version

Schwartz and Smith (2000) develop a risk-neutral version of their model to value futures contracts, options on these futures contracts and other commodity related investments. In this risk-neutral model risk-neutral stochastic processes are used to describe the dynamics of the underlying state variables and discounts all cash flows at a risk-free rate. The risk-neutral version of the model introduces an additional parameter for every process: λ. This parameter specifies constant reductions in the drift rate for the processes. The equations in the model therefore become: 𝑑𝑅̂𝑡 = [𝑘𝑅(𝐿̂𝑅− 𝑅̂𝑇) − 𝜆𝑅𝜎𝑅𝑅̂𝑡]𝑑𝑡 + 𝜎𝑅𝑅̂𝑡𝑑𝑊𝑡𝑅, (10) 𝑑𝐿̂𝑅 = [𝜇𝑅(𝐿̂𝑋− 𝐿̂𝑅) − 𝜆𝐿𝑅𝜉𝑅𝐿̂𝑅]𝑑𝑡 + 𝜉𝑅𝐿̂𝑅𝑑𝑊𝑡𝐿𝑅, (11) 𝑑𝑁̂𝑡 = [𝑘𝑁(𝐿̂𝑁− 𝑁̂𝑇) − 𝜆𝑁𝜎𝑁𝑁̂𝑡]𝑑𝑡 + 𝜎𝑁𝑁̂𝑡𝑑𝑊𝑡𝑁, (12) 𝑑𝐿̂𝑁= [𝜇𝑁(𝐿̂𝑌− 𝐿̂𝑁) − 𝜆𝐿𝑁𝜉𝑁𝐿̂𝑁]𝑑𝑡 + 𝜉𝑁𝐿̂𝑁𝑑𝑊𝑡𝐿𝑁, (13) 𝑑𝐸̂𝑡 = [𝑘𝑒(𝐿𝑒− 𝐸̂𝑡) − 𝜆𝐸𝜎𝐸𝐸̂𝑡]𝑑𝑡 + 𝜎𝑒𝐸̂𝑡𝑑𝑊𝑡𝐸, (14) 𝑑𝐶̂𝑡 = (𝛼𝑐 − 𝜆𝑐) 𝐶̂𝑡𝑑𝑡 + 𝜎𝐶𝐶̂𝑡𝑑𝑊𝑡𝐶, (15)

where λR denotes the market price of risk from current Russian natural gas price, λLR is the market price of equilibrium Russian gas price risk, λN is the market price of risk from the current Dutch natural gas price, λLN is the market price of equilibrium Dutch gas risk, λE is the current market price of electricity risk, λC is the current market price of emission allowances risk.

The discretized equations are:

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15

where ϵRt, ϵLtR,ϵNt,ϵLtN,ϵEt, and ϵCt are standard normal variates, and Δt is measured in yearly terms. ϵRt and ϵL

tR, ϵNt andϵLtN, ϵtR and ϵLtN, ϵNt and ϵLtR are assumed to be independent, so their correlation coefficient is zero. ϵE

t and ϵLtR, ϵEt and ϵLtN, ϵCt and ϵLtR, ϵCt and ϵLtN, are also assumed to be independent; their correlation coefficients are zero as well. However, ϵR

t,ϵNt, ϵEt, and ϵCt are not assumed to be independent, therefore there can be non-zero correlation.

The model Schwartz and Smith (2000) use allows for the use of Kalman filtering techniques to estimate the state variables. The Kalman filter is a recursive procedure for computing estimates of unobserved state variables based on observations that depend on these state variables. However, to be able to use the Kalman filter the data has to consist of futures or forwards with different terms of maturities.

By running 100.000 simulations using Matlab, 100.000 different paths are created that each variable can take. By then applying the LSM method, the value of the real option is calculated. The code used can be found in Appendix A.

3.7 Value of annuities

To determine the plant value, the value of an annuity is calculated when the plant is in use. This can be done by using either simulation or analytical formulas. Abadie and Chamorro (2009) use analytical formulas to value these annuities. These formulas can be found in Appendix C. These formulas are used to reduce the computing power that is required to value these annuities if simulation were used. Table 3 compares the results of simulations with the analytical result of these equations. The difference between the average of ten simulations and the analytical value is less than 1%. Using these formulas is therefore an acceptable substitute for simulation.

Table 3. Results of using simulation and analytical method

Annuity Simulation Analytical % difference

PVR 17025 16952 0.43%

PVN 18901 18880 0.11%

PVE 3009 3019 -0.33%

PVC 1 1 0.81%

PVO 160 160 0.00%

The value for simulation is an average of ten simulations of 100.000 paths each. The value for

simulation and analytical are in millions of euros. % difference is the difference in percentage between the values obtained from simulation and from analytical calculation. PVR is the present value of the annuity of Russian natural gas, PVN is the present value of the annuity of Dutch natural gas, PVE is the present value of the annuity of electricity, PVC is the present value of the annuity of emission

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4. Data and descriptive statistics

4.1 Descriptive statistics

Table 4 contains the descriptive statistics of the variables used in the model. It shows the descriptive statistics of the price of Russian natural gas, Dutch natural gas, electricity in The Netherlands and emission allowances.

Table 4. Descriptive statistics

Mean SD Median Minimum Maximum N

Russian natural gas 19.41 7.44 19.38 5.92 42.23 235

Dutch natural gas 20.49 4.56 20.75 10.77 29.35 2986

Electricity 44.48 9.76 44.99 15.37 98.98 2586

Emission allowance 6.66 1.69 6.28 3.28 11.39 1432

Russian natural gas, Dutch natural gas and electricity are measured in EUR/MWh. Emission allowances are measured in EUR/metric tonne.

The data for Russian natural gas comes from Index Mundi (2018). It is the average price of natural gas imported from Russia by pipeline into Germany, at the German border. The data is recorded monthly from October 1998 up to and including February 2018. The original data is measured in EUR/MMBTU, which stands for Million Metric British Thermal Unit. To convert this to EUR/MWh, the values are multiplied by 0.0034. The sample used in this paper is from January 2010 to February 2018, to have the same time period as the other variables used. Table 5 shows the descriptive statistics of these two sub-samples.

Table 5. Descriptive statistics for the periods 1998-2010 and 2010-2018 for Russian natural gas

Year Mean SD Median Minimum Maximum N

1998-2010 16.62 7.37 15.10 5.92 42.23 135

2010-2018 23.21 5.70 23.32 12.14 33.63 99

Source: Bloomberg Finance L.P. (2018).

The data for Dutch natural gas prices, Dutch electricity prices, and emission allowances all come from Bloomberg Finance L.P. (2018). They were obtained with a library request to the

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To start with, the Dutch natural gas price is TTF natural gas one-month forward data. This sample was chosen as it was the most complete data set available. The sample consists of daily data from 01-01-2010 to 01-03-2018. The sample contains 2986 days of data. The price is measured in EUR/MWh.

Next, the data for the Dutch electricity prices is the day ahead 24-hour electricity time average spot price of the APX. The sample is measured daily from 01-01-2010 to 29-01-2017, after which there was no more data available. The electricity price is measured in EUR/MWh. The entire sample consists of 2586 observations. Over this period, the price has not fluctuated much, starting and stopping at nearly the same level. The price in the sample does not contain the value added tax of 21% and the energy tax. The value tax differs for various levels of usage, in this case the energy tax would be 0.00116 EUR/kWh.

Lastly, the data for the emission allowances comes from emission allowances traded on the ICE Futures Europe. Emission allowances are measured in EUR/metric tonne. The complete sample consists of daily data from 8-8-2010 to 08-11-2017, for a total of 1876 trading days. There are two sub-samples: the first is the period from 8-8-2010 to 31-12-2012 and the second is from 2013 to 8-11-2017. The split at 2-1-2013 is a result of the initiation of Phase III of the EU ETS, which started in 2013 and will last until 2020. The

changes from Phase II to Phase III resulted in a lower price of emission allowances. Table 6 shows the yearly average price. The average price of an emission allowances is much lower during the second period.

4.2 Correlations

Table 6. Yearly average price of emission allowance

Year Average price

2010 20.35 2011 18.41 2012 10.10 2013 5.36 2014 6.63 2015 7.92 2016 5.40 2017 5.56

Source: Bloomberg Finance L.P. (2018). Prices are in EUR/metric tonne.

Table 7. Correlation matrix

(1) (2) (3) (4)

Russian natural gas (1) 1

Dutch natural gas (2) 0.93** 1

Electricity (3) 0.82** 0.93** 1

Emission allowances (4) 0.33* 0.25 0.13 1

Note. this is the correlation between average monthly prices. **, and * denote a significance level of

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Table 7 shows the correlation between the variables used in this thesis. To calculate the

correlations, the average monthly price was calculated for Dutch natural, electricity and emission allowances. This way they could be compared to the Russian natural gas price, for which only monthly data is available. Unsurprisingly, the correlation between Russian natural gas and Dutch natural gas is high, with ρR,N = 0.93 and is significant at the 1% level. A high correlation of ρR,E = 0.82 and ρN,E = 0.93, both of which are significant at the 1% level, between the electricity price and both types of natural gas is also unsurprising, as gas powered plants are often used to generate electricity. The correlation between natural gas and emission allowances is not as high at ρR,C = 0.33 and ρN,C = 0.25, where only ρR,C is significant at the 10% level, which is most likely a result of gas powered energy generation being a relatively clean method. The correlation between electricity and emission allowances is low and insignificant at ρE,C = 0.13, which is slightly surprising as one would expect the generation of electricity to create a decent amount of emissions.

4.3 Parameters

Table 8 shows the parameters used in the model, their values and their descriptions. R0 is the starting price of Russian natural gas on 28 February 2018. Lx is the long-term

equilibrium level of Russian natural gas. Lr0 is the equilibrium level on 28 February 2018. kR is the speed of reversion of Russian natural gas towards its equilibrium level of Lr. It is calculated as kR = log 2/t1/2, where t1/2 is the expected half-life which is the time how long it takes for the gap between Rt and Lr. t1/2 is here assumed to be 5 years. σR is the volatility of the Russian natural gas price for the period January 2010 – February 2018. λR is the market price of risk for Russian natural gas. Normally this value is calculated by using Kalman filtering methods, however, as there was not enough forward contract data available this was not possible. Other papers on market price of risk for natural gas found either very small positive or very small negative values (Trolle & Schwartz, 2008; Wei & Zhu, 2006; Sadorsky, 2001; Haff, Lindqvist & Løland, 2008). Therefore, a value of 0.02 was chosen as the market price of risk. µR is the speed of reversion of Lr towards its long-term equilibrium level of Lx. This value is calculated as µR = log 2/t1/2 as well, however, t1/2 is here assumed to be 10 years. ξR is the volatility of the Russian gas equilibrium price. For simplicity, it is assumed to be the same as σR. λLr is the market price of risk for the Russian natural gas equilibrium price. The same goes here as for λR, therefore a value of 0.02 is used as well.

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2/t1/2, where t1/2 is the expected half-life which is the time how long it takes for the gap between Nt and Ln. t1/2 is here assumed to be 5 years. σn is the volatility of the Dutch natural gas price for the period January 2010 – February 2018. λn is the market price of risk for Dutch natural gas. As with the Russian equivalent, a value of 0.02 was chosen as the market price of risk. µN is the speed of reversion of Ln towards its long-term equilibrium level of Ly. This value is calculated as µN = log 2/t1/2 as well, however, t1/2 is here assumed to be 10 years. ξN is the volatility of the Dutch gas equilibrium price. For simplicity, it is assumed to be the same as σN. λLn is the market price of risk for the Dutch natural gas equilibrium price. The same goes here as for λn, therefore a value of 0.02 is used as well.

E0 is the starting price of electricity per MWh on 28 February 2018. Le is the long-term

equilibrium price level of electricity. ke is the speed of reversion of the electricity price towards its equilibrium level of Le. It is calculated as ke = log 2/t1/2, where t1/2 is the expected half-life which is the time how long it takes for the gap between Et and Le. t1/2 is here assumed to be 5 years. σe is the volatility of the electricity price for the period 2010-2017. λe is the market price of risk for electricity. As with the Russian and Dutch natural gas equivalents, a value of 0.02 was chosen as the market price of risk.

C0 is the starting price of an emission allowance on 28 February 2018. αC is the drift rate of the emission allowance rate. It is 0.02 as the number of allowances per year will decrease by 2.2% from 2020 onwards (Council Decision of 24 October 2014, 2014). As I expect that industries will try to decrease their emissions, the decrease in allowances should not translate completely in the price, leading to a drift rate of 2%, or 0.02. σC is the volatility of the emission allowance price of the period 2010-2017. λC is the market price of risk for electricity. As with the other variables, a value of 0.02 was chosen as the market price of risk. The number of emissions allowances that need to be purchased is D = 8485. The emissions are a result of the transport of natural gas, as according to GTS (2015) the plant itself does not actually produce emissions. According to Murrath (2009), 0.039 tonnes of methane are produced for every GWh of gas transported. This results in having to purchase 4843 emission allowances in the case where the Wobbe-index is 53 MJ/m3 and 8485 if the Wobbe-index is 51.8 MJ/m3. This difference is a result of the increase in the volume of natural gas that can be processed if the Wobbe-index is lower.

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20 Table 8. Parameters

Parameter Value Description

R0 21.62 Russian natural gas price in EUR/MWh 28 February 2018

Lx 21 Long-term equilibrium price of Russian natural gas

Lr0 19 Starting level of Russian equilibrium price level on 28 February 2018

kR 0.06 Speed of reversion of Russian natural gas price towards its "normal" level

σR 0.30 Volatility of Russian gas price

λR 0.02 Market price of risk for Russian natural gas

µR 0.03 Speed of reversion of Lr towards its longer-term equilibrium value Lx

ξR 0.30 Volatility of Russian gas equilibrium price

λLr 0.02 Market price of risk for the Russian natural gas equilibrium price

N0 17.63 Dutch natural gas price in EUR/MWh 28 February 2018

Ln0 19 Long-term equilibrium price of Dutch natural gas

Ly 18 Starting level of Dutch equilibrium price level on 28 February 2018

kN 0.06 Speed of reversion of Dutch natural gas price towards its "normal" level

σn 0.22 Volatility of Dutch gas price

λn 0.02 Market price of risk for Dutch natural gas

µN 0.03 Speed of reversion of Ln towards its longer-term equilibrium value Ly

ξN 0.22 Volatility of Dutch gas equilibrium price

λLn 0.02 Equilibrium price level risk of Dutch natural gas

E0 0.22 Dutch wholesale electricity price in EUR/MWh 28 February 2018

Le 0.3 Long-term equilibrium price of electricity

ke 0.30 Speed of reversion of Dutch electricity price

σe 0.21 Volatility of Electricity price in The Netherlands

λe 0.01 Market price of risk for electricity in The Netherlands

C0 14.70 Price of emission allowance EUR/metric tonne at 28 February 2018

αC 0.02 Drift rate of emission allowance price

σC 0.25 Volatility of emission allowance price

λC 0.02 Market price risk premium of emission allowance

I 480 Investment cost in millions of euros

A 442 Annual amount of electricity used in GWh

B 4

7

Amount of Russian natural gas used in bcm, values are for a Wobbe-index of 53 MJ/m3 and 51.8 MJ/m3 respectively

C 4.444

7.777

Amount of Dutch natural gas produced in bcm, values are for a Wobbe-index of 53 MJ/m3 and 51.8 MJ/m3 respectively

D 4848

8485

Number of emission allowances required, values are for a Wobbe-index of 53 MJ/m3 and 51.8 MJ/m3 respectively

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The market price of risk has a large influence on the value of the real option. The current value of 0.02 for every market price of risk was chosen on the basis of the findings of other papers. Table 9 shows the effects of changing the market price of risk for Dutch natural gas on the value of the real option. When the market price of risk for Dutch natural gas is 0, the value of the real option is €2509 million, while it is only €28 million when the market price of risk for Dutch natural gas is 0.05. The model is very sensitive to the value of the market price of risk that is chosen. However, this should not change the outcomes of the sensitivity analyses that are conducted in the rest of the paper, as it would only change the values of these outcomes, not the direction that the values move in.

Table 9. Value of real option for different values of the market price of risk of Dutch natural gas, λn.

λn Value of real option

0 2509 0.01 1515 0.02 744 0.03 297 0.04 101 0.05 28

Note. The value of the real option is given in millions of euros.

5. Results

5.1 Base and alternative case

In their report GTS (2015a) consider a Wobbe-index of 53 MJ/m3 for H-gas to be the base case.

They predict that H-gas will have this index in the future. However, the current Wobbe-index of H-gas is 51.8 MJ/m3. Therefore, both options will be used. The Wobbe-index of 53 MJ/m3 is the base case and a Wobbe-index of 51.8 MJ/m3 is the alternative option. As was mentioned in sector 3.3, the volume of gas that can be processed is limited by the maximum amount of nitrogen that can be produced. For the base case, the amount of H-gas that can be processed is 4 bcm. For the alternative case, the amount of H-gas that can be processed is 7 bcm. 5.2 Investing immediately

The first possibility to consider is immediately investing. This means investing at R0, LR0, N0, LN0, E0 and C0. By using eq. (35) we can calculate the present value of the annuity for Russian natural gas (PVR). For the base case, the annual amount of H-gas used is B = 4 bcm. By

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with C = 4.444 bcm, we get the value of the annuity for Dutch natural gas: PVN = €22,218 million. For electricity, the annual amount of electricity required is A = 442 GWh. By

multiplying eq. (39) with this number, we get a value of the annuity of PVE = €3,571.4 million. The annual amount of emission allowances that need to be purchased are D = 4843. By

multiplying this number with eq. (41), we get PVC = €2.15 million. The annual operating costs are E = €7 million, this value multiplied with eq. (42) gives PVO = €189 million. Therefore, the present value of the plant in the base case is, according to eq. (1):

𝑉(𝑅0, 𝐿𝑅0, 𝑁0, 𝐿𝑁0, 𝐸0, 𝐶0) = 𝑃𝑉𝑁 − 𝑃𝑉𝑅 − 𝑃𝑉𝐸 − 𝑃𝑉𝐶 − 𝑃𝑉𝑂 = −€1,505.7 𝑚𝑖𝑙𝑙𝑖𝑜𝑛. (1) The NPV is then, according to equation (2):

𝑁𝑃𝑉 = 𝑉(𝑅0, 𝐿𝑅0, 𝑁0, 𝐿𝑁 0, 𝐸0, 𝐶0) − 𝐼

= 𝑃𝑉𝑁 − 𝑃𝑉𝑅 − 𝑃𝑉𝐸 − 𝑃𝑉𝐶 − 𝑃𝑉𝑂 − 𝐼 = −€1,985.7 𝑚𝑖𝑙𝑙𝑖𝑜𝑛. (2) Table 10. Present values from investing at time t = 0

Present values Base case Alternative case

PVN 22218 38882 PVR 19961 34932 PVE 3571 3571 PVC 1 2 PVO 189 189 Plant value -1505 187 NPV -1985 -293

Note. All values are in millions of euros. PVN is the present value of the annuity for Dutch natural gas, PVR is the present value of the annuity for Russian natural gas, PVE is the present value of the annuity for electricity, PVC is the present value for the annuity for emission allowances and PVO is the present value of the annuity for operating costs. Plant value is the value of the plant at time t = 0. NPV is Plant value – I, where I = 480 million euros. τ1 is 2.5

and τ2 is 32.5.

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23 5.3 The value of the real option with different maturities

The second scenario that is evaluated is the impact that different maturities of the option have on the value of the real option. Table 11 shows the value of the real option for both the base and alternative case for different maturities ranging from a maturity of t = 0 to t = 5, i.e. from 0 to 5 years. It should be noted that the values are given in millions of euros and rounded to the closest million. Even though it shows that the value of the option is zero, it might not mean that the value is zero. For example, in the base case the value of the real option is shown as zero for t = 2.5, but this value is actually €386.360. This can be better seen in Figure 1, which shows the value of the real option as a function of the time to maturity for the base case. In this figure, it can be seen that the value of the real option slowly increases as the time to maturity increases.

Table 11. Effects of time to maturity on real option value

Base case Alternative

Time to maturity Real option value Real option value

0 0 0 0.25 0 53 0.5 0 109 0.75 0 158 1 0 204 1.25 0 243 1.5 0 282 1.75 0 323 2 0 358 2.25 0 394 2.5 0 427 2.75 1 462 3 1 499 3.25 2 529 3.5 4 564 3.75 5 599 4 7 627 4.25 10 659 4.5 13 689 4.75 17 717 5 20 750

Note. The time to maturity is given in years. The value of the real

option is measured in millions of euros, rounded to the closest million. The time to maturity is the only variable that changes; all other parameters are held constant. In the base case, a Wobbe-index of 53 MJ/m3 is used. In the alternative case a Wobbe-index

of 51.8 MJ/m3 is used.

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time t = 0 to €750 million at time t = 5. For every increase in maturity there is an increase in the value of the real option. This can be seen in Figure 2 as well, which shows the value of the real option as a function of the time to maturity for both the base and alternative case.

Figure 1. Value of real option as a function of time to maturity for the base case

Copeland and Antikarov (2001) mention that the value of the real option should increase as the time to maturity increases. As we can see in Table 11, the value of the real option does indeed increase as the time to maturity increases, for both the base and alternative case. By being able to postpone the investment the firm is able to gather more information. The increase in maturity also means that the chance that the option becomes in-the-money increases, which increases the value of the option.

The value at a maturity of five years is considered the basis case, which is €20 million for the base case and €750 million for the alternative case. The scenarios that follow after this all have the basis case included in them. The basis cases are marked bold in the tables that contain the results. The differences in the value of the real option at the basis case are a result of Monte Carlo noise.

Figure 2. Value of real option as a function of time to maturity 5 10 15 20 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 V al ue o f rea l o pt io n in m ill ions of €

Time to maturity in years

Value of real option as a function of time to maturity

Base case -200 200 400 600 800 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 V al ue o f rea l o pt io n in m ill io ns o f €

Time to maturity in years

Value of real option as a function of time to maturity

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25 5.4 Different levels of uncertainty

The third scenario looks at the effects on the value of the real option for a change in the volatility of Dutch natural gas σn and the volatility of the Dutch equilibrium price level, ξN. Table 12 shows the effects of a change in σn and an equal change in ξN on the value of the real option. From the literature review, the value of the real option is expected to increase as uncertainty increases, as an increase in uncertainty improves the upside potential while downside losses are limited. For the base case, this seems to be the case: the value of the real option does show an increase when σn and ξN increase, from €20 million at σn = ξN = 0.22 to €865 million at σn = ξN = 1 although with some small decreases at certain points. These decreases are a result of the simulation method. For the alternative case, the real option value increases from €506 million at σn = ξN = 0.3 to €1881 million at σn = ξN = 1. There are also some small decreases here as a result of the simulation method.

Table 12. Effects of different levels of uncertainty of Dutch gas prices

Base case Alternative

σn and ξN Real option value Real option value

0.05 258 2574 0.1 72 1937 0.15 23 1378 0.2 18 906 0.22 20 742 0.25 27 605 0.3 48 506 0.35 91 513 0.4 152 577 0.45 233 737 0.5 321 893 0.55 291 949 0.6 474 1154 0.65 552 1257 0.7 661 1467 0.75 561 1294 0.8 586 1548 0.85 746 1462 0.9 788 1288 0.95 848 1130 1 865 1881

Note. σn is the volatility of the Dutch natural gas price. ξN is the volatility of the

Dutch equilibrium price level. The value of real option is measured in millions of euros. σn and ξN are the only parameter that change in the model; all other

parameters are held constant. In the base case, a Wobbe-index of 53 MJ/m3 is

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26

However, the decrease in real option value as σn increases from σn = ξN = 0.05 to σn = ξN = 0.2 for the base case and from σn = ξN = 0.05 to σn = ξN = 0.3 for the alternative case are not in line with the literature. Here, we would expect the value of the real option to increase as well. A possible explanation for this is that this is actually an option on a spread between Russian natural gas and Dutch natural gas. These have a strong correlation of ρ = 0.93, therefore they

compensate each other when the volatilities are comparable, leaving no or less optionality. However, if one of the volatilities is substantially higher, it dominates the total volatility of the spread, increasing the value of the option.

Another interesting observation is that the value of the real option does not seem to change when ξN is held constant compared to the case where ξN = σn. This can be seen in Figure 3, which shows the value of the real option for different values of σn, as well as the real option value for different values of σn where ξN is held constant. More uncertainty in the equilibrium price level does not increase the value of the real option, while the literature suggests that this increase in uncertainty should manifest as an increase in the value of the option. Table 13 shows the values of the real option if ξN is held constant. For the base case, the real option value first decreases from €128 million at σn = 0.05 to €20 million at σn = 0.2, after which it increases to €607 million at σn = 1. For the alternative case decreases from €1985 million at σn = 0.05 to €595 million at σn = 0.3, after which it starts increasing again to €1453 million at σn = 1, with some small decreases in between as a result of the simulation method.

Figure 3. Comparison of the value of the real option for the base and alternative case where σn = ξN compared to where σn increases but ξN is held constant

500 1000 1500 2000 2500 3000 0 0.2 0.4 0.6 0.8 1 V al ue o f real o pti o n in m ill io ns o f € σn

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27 Table 13. Effects of a change in σn when ξN is held constant

Base case Alternative

σn Real option value Real option value

0.05 128 1938 0.1 55 1521 0.15 28 1154 0.2 20 849 0.22 21 748 0.25 24 666 0.3 42 595 0.35 86 627 0.4 147 729 0.45 232 855 0.5 323 994 0.55 386 1160 0.6 454 1282 0.65 579 1416 0.7 649 1641 0.75 744 1671 0.8 467 1768 0.85 408 1793 0.9 626 1624 0.95 568 1348 1 607 1453

Note. σn is the volatility of the Dutch natural gas price. ξN is the volatility of the

equilibrium price level of Dutch natural gas. The value of real option is measured in millions of euros. σn is the only parameter that changes in the model; all other

parameters are held constant. In the base case, a Wobbe-index of 53 MJ/m3 is

used. In the alternative case a Wobbe-index of 51.8 MJ/m3 is used.

5.5 Change in equilibrium level

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28

From Table 14 it becomes clear that a decrease in equilibrium price level for Dutch natural gas from its original value of LY = 20 decreases the value of the real option. An increase in the equilibrium price level of Dutch natural gas increases the value of the real option. This is a logical consequence of keeping all other parameters equal: equal parameters for all cost

functions means that the costs will stay the same, while the value of the revenues can change. A decrease in the equilibrium price level of Dutch natural gas means that in the long-term the revenues will decrease as well, and vice-versa for an increase. This is in line with what was expected from the literature: An increase in the value of the underlying asset should increase the value of the real option (Copeland and Antikarov, 2001). An increase in revenues would increase the value of the plant, which is the underlying asset, therefore increasing the value of the real option.

Table 14. Effects of a different equilibrium price level for Dutch natural gas

Base case Alternative

Ly Real option value Real option value

16 0 22 17 1 58 18 3 147 19 8 356 20 20 743 21 52 1354 22 133 2089 23 294 2900 24 573 3728

Note. Ly is the equilibrium price level of Dutch natural gas. The value of real

option is measured in millions of euros. All parameters but Ly are held constant.

In the base case, a Wobbe-index of 53 MJ/m3 is used. In the alternative case a

Wobbe-index of 51.8 MJ/m3 is used.

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29 Figure 4. Value of real option for different values of the long-term equilibrium price level of Dutch natural gas, Ly

5.6 Effects of the risk-free rate

The fifth scenario looks at the effect of a change in the risk-free rate, rf, on the value of the real option. Table 15 shows the real option value for different values of the risk-free rate. For the base case, the value of the real option remains constant at around €20-21 million, while for the alternative case the value decreases from €798 million at rf = 0.25% to €579 million at rf = 2%.

Table 15. Effects of a change in the risk-free rate

Base case Alternative

r Real option value Real option value

0.25% 20 798 0.5% 20 766 0.61% 20 746 0.75% 20 731 1% 20 695 1.25% 20 668 1.5% 21 637 1.75% 20 608 2% 21 579

Note. r is the risk-free rate. The value of real option is measured in millions of

euros. All parameters but r are held constant. In the base case, a Wobbe-index of 53 MJ/m3 is used. In the alternative case a Wobbe-index of 51.8 MJ/m3 is used.

500 1000 1500 2000 2500 3000 3500 4000 16 17 18 19 20 21 22 23 24 V al ue o f real o pti o n in m ill io ns o f € Ly

Value of real option as a function of L

y

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30

The literature on real options suggests that the value of the real option should increase when interest rates increase (Copeland and Antikarov, 2001). However, the value of the option actually decreases when the risk-free rate increases, at least for the alternative case. Fernández (2001) explains this as follows: “the negative effect of increased interest rates on the present value of the expected cash flows (as on the value of shares) is always greater than the positive effect of the reduction of the present value of the exercise price.”

In the model used in this thesis, the interest rate is only used to discount the future cash flows. That is, the value of the future cash flows does not depend on the interest rate, the interest rate is only used to discount the future cash flows. Because of the option, the values of the future cash flows are always positive. An increase in interest rate would therefore increase the discounting of the future cash flows and reduce their value. This reduction in the value of the cash flows would in turn reduce the value of the real option.

Figure 5 shows the value of the real option as a function of the risk-free rate for both the base and alternative case. For the alternative case, the decrease in real option value can be seen clearly. For the base case this is harder to see as the real option value is very small and remains around the same level. The small increases are a result of the simulation method.

Figure 5. Value of real option for different values of the risk-free rate

100 200 300 400 500 600 700 800 900 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 V al ue o f real o pti o n in m ill ions of € rf

Value of real option as a function of r

f

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31 5.7 Effects of a change in cost of investment

The final scenario looks at the effect of a change in the investment cost, I, on the value of the real option. Table 16 shows the value of the real option for different values of the investment cost I, from I = €400 million to I = €625 million. The value of the real option decreases from €23 million at I = €400 million to €16 million at I = €625 for the base case. For the alternative case, the value decreases from €792 million at I = €400 million to €683 million at I = €625 million. Figure 6 shows this relation graphically: It shows the value of the real option for different values of I for both the base and alternative case. Here it can be seen clearly, for the alternative case, that the value of the real option decreases as the value of the investment increases. For the base case it is harder to see as the value of the real option is very small.

Table 16. Effects of a change in investment cost I

Base case Alternative

I Real option value Real option value

400 23 792 425 22 775 450 23 761 475 21 750 480 20 744 500 20 743 525 20 736 550 17 723 575 17 713 600 17 692 625 16 683

Note. I is the investment cost of building the new plant. The value of I and the

real option are measured in millions of euros. All parameters but I are held constant. In the base case, a Wobbe-index of 53 MJ/m3 is used. In the alternative

case a Wobbe-index of 51.8 MJ/m3 is used.

From the literature review, an increase of the exercise price should decrease the value of the real option (Copeland and Antikarov, 2001). Here, the cost of investment is the exercise price. When the exercise price decreases, the underlying asset, which is the plant here, becomes more in-the-money which increases the value of the option. When the exercise price increases, the underlying asset becomes more out-of-the-money, which decreases the value of the option. The decrease in real option value when the investment cost increases is therefore in accordance with what is expected from the literature.

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