Real Options Analysis in Carbon Storage
Student ID: S1878786
Name: Martijn Groenbroek
Study Program: M.Sc. Finance
Supervisor: Gijsbert Zwart
Word Count: 10,295
June 9, 2016
Abstract
Contents
1 Introduction 1
2 Literature Review 3
2.1 Carbon Capture and Storage . . . 3 2.2 Real Options in Carbon Capture and Storage . . . 4
3 The Energy Market 8
3.1 Pollution . . . 9 3.2 The Emissions Market . . . 10 3.3 Gas Storage . . . 13
4 Mathematical Foundation 15
4.1 Stochastic Processes . . . 15 4.2 Ito’s Lemma . . . 16 4.3 Contingent Claims Analysis . . . 17
5 Valuing Carbon Capture and Storage Investments 20 5.1 Valuing the Project . . . 20 5.2 Valuing the Option to Invest . . . 21
6 Numerical Examples 25
6.1 Parameters . . . 25 6.2 Results . . . 27 6.3 Robustness . . . 28
List of Figures
1 Energy Production in the Netherlands . . . 9
2 Carbon Emissions in the Netherlands . . . 10
3 Emission Allowance Price Trends in Europe . . . 11
List of Tables
1 Energy Production in the Netherlands, 2000 - 2014, in PJ . . . 8
2 Energy Production in the Netherlands, 2015 - 2030 forecast, in PJ . . . 8
3 Parameters of the Base Case . . . 26
4 Results of the Base Case (in mln EUR) . . . 27
5 Scenario 1: Change in β . . . 36
6 Scenario 2: Change in volatility . . . 36
7 Scenario 3: Change in risk-free rate . . . 37
8 Scenario 4: Change in µ . . . 37
9 Scenario 5: Change in CAPEX . . . 37
1.
Introduction
Technological change has created unprecedented growth in the last several centuries. We can now travel across the world in hours, rather than weeks. We can communicate with anyone on the planet in real time. We have all the world’s information at our fingertips through our smartphones. We have even sent people to the Moon, and landed spacecraft on the surface of Mars.
Such progress requires a lot of energy. Between 1800 and 2000, for instance, energy consumption per capita in England grew sevenfold (Beretta, 2007). It is reasonable to assume that the same trend holds for most of the developed world (IEA, 2015a). Because of this increase in energy consumption, we have seen a similar increase in energy production (Boden, Andres, and Marland, 2015).
Our dependency on energy, in the form of fossil fuels such as oil, gas, and coal, has given rise to a number of serious environmental and societal problems. While society as a whole is more prosperous than it has ever been, large parts of the world remain underdeveloped. Our need to continually increase our standards of living is threatening many ecological systems. Moreover, our focus on growth above everything else has introduced severe climate change. The emission of greenhouse gases is now generally believed to be one of the most important factors contributing to global warming. To help stop this problem, world leaders have joint forces multiple times, most notably in the Kyoto and Paris Protocols.
There are several ways to limit the side effects of our increasing need for energy. The most long-term solution, generally considered the only way in which the world can provide for its energy needs in the future due to limited concentrations of fossil fuels, is to develop cost efficient ways to produce renewable energy. Currently, the Netherlands is one of the lowest ranked developed countries in terms of percentage of energy from renewable sources, with only 5.6 percent of energy generated in a durable way (Giebels, 2016). Worldwide, only one-fifth of our current energy generation is in the form of renewables (REN21, 2014).
The aforementioned numbers show just how slow adoption rates have been for renewable energy production. While our demand for energy has risen, the fraction of energy production from renewable sources has not grown at the same rate. Boden et al. (2015) estimate that because of this, emissions due to burning of fossil fuels and industrial processes have increased by approximately 78 percent between 1970 and 2010.
commonplace, fossil fuels will still play an important part in meeting the energy demand of Dutch consumers (Rijksoverheid, 2015). We therefore have to look at alternative ways to limit carbon emissions.
One of the ways in which emissions can be reduced is by means of Carbon Capture and Storage (CCS). Under this scheme, carbon dioxide, as a byproduct of fossil fuels combustion, is captured and stored in depleted gas and oil fields. This technique, which is still relatively new and therefore expensive, can reduce the carbon footprint of the Dutch economy while new sources of energy production are developed.
In this thesis, we examine investment decisions in carbon storage facilities. We develop a mathematical model to value the investment in a carbon storage project. We use real options methodology because investments in energy projects have three characteristics that make it difficult to value using traditional methods: Uncertainty, irreversibility, and timing efficiency. The model we build is based on benchmark work by Dixit and Pindyck (1994).
We apply this model in a numerical example. We take the point of view of an organization that owns a depleted gas field in the North Sea. We want to determine the optimal exercise price of the option to invest in a carbon storage facility.
We find that investing in carbon storage in depleted gas fields in the Dutch part of the North Sea is not currently viable given today’s price of carbon emissions allowances. The current prices are well below trigger levels.
2.
Literature Review
2.1.
Carbon Capture and Storage
The Intergovernmental Panel on Climate Change (IPCC, 2005) defines Carbon Capture and Storage (CCS) as “a process consisting of the separation of CO2 from industrial and
energy-related sources, transport to a storage location and long-term isolation from the atmosphere.” It has the potential to reduce overall costs of emissions reduction, while at the same time providing flexibility to achieve reduction targets. However, as the IPCC acknowledges, success of such projects depends on a number of variables, including costs (such as installation costs and energy costs to run the facility) and regulatory aspects.
According to Middleton and Eccles (2013), current attempts at CCS have proven to be very expensive, in part due to technological difficulties. The considerable expense of such installations could explain why, as Walsh, O’Sullivan, Lee, and Devine (2014) note, “[a]t present there is still no commercially operating carbon capture and storage (CCS) unit anywhere in the world.” This raises the question why there is continued interest in developing carbon capture technologies.
Recent research has yielded a number of studies that try to answer this question. Re-newable sources of energy production, Walsh et al. (2014) argue, are often intermittent: To maintain stability of the power system, fossil fuel sources are a required source of energy generation for at least the next few decades. Indeed, Fleten and N¨as¨akk¨al¨a (2010) estimate that over the next 15 years, fossil fuels will make up approximately 75 percent of all new electric power production capacity. In part, this can be explained by the relative abundance of coal, which makes it an interesting option for electricity generation (Walsh et al., 2014). However, coal, just like other fossil fuel sources, is one of the heaviest producers of CO2.
Therefore, while fossil fuel will not disappear over the next few decades, governments and utilities must push the boundaries of technological capability to ensure that as much carbon emissions as possible are captured and stored.
Carbon capture projects have the potential to help mitigate the effects of climate change. Eckhause and Herold (2014) report that the International Energy Agency (IEA) as well as the IPCC consider CCS to be an enabler in reducing CO2 emissions during the course
captured and stored efficiently.
Investment in carbon technology faces a number of hurdles. Cortazar, Schwartz, and Salinas (1998) find that companies in industries where high output price volatility is the norm are more hesitant to devote significant resources in environmental protection technologies. Similarly, firms that emit a large amount of greenhouse gases may have to purchase so-called emission allowances on the open market to offset their polluting behavior. The EU Emissions Trading Scheme (ETS), one such emissions markets, has volatile emission costs (Walsh et al., 2014). Organizations are thus not always able to accurately predict the financial costs of its carbon output. As Laurikka and Koljonen (2006) note, within the EU ETS, the value of these allowances have the potential to affect cash flows of a power plant during its entire technological lifetime: Firms face substantial price risk. Moreover, Abadie and Chamorro (2008) find that the pricing of these allowances is in some ways linked to policy. This creates even more price uncertainty.
Beyond undetermined pricing, which is arguably the most important source of risk, there are more sources of uncertainty facing firms. For instance, initiatives that comprise techno-logical capabilities are particularly precarious (Eckhause and Herold, 2014). The reasoning is that due to technological difficulties, investment in high-tech solutions is currently very expensive. However, intensive research and development work may push down the costs of such investments to an acceptable level in the future. Firms that face an investment decision thus have to consider whether it is in their best interest to postpone investment to some arbitrary future period, when costs may be lower, yielding higher returns on projects. Sim-ilarly, there is considerable uncertainty about the direction of emissions markets in general (Viteva, Veld-Merkoulova, and Campbell, 2014). Policy decisions could fundamentally alter the structure of carbon markets; this could change the price of emissions allowances or fossil fuels, leading to uncertain returns on carbon capture projects.
A third source of risk arises due to the very nature of carbon storage projects. Since a CCS unit is built to accommodate the a number of specific depleted gas fields, investments in these projects have irreversible features. The range of uses of a unit is very limited. If the well is full, or otherwise needs to be abandoned, the installation cannot easily be fitted to another field (Abadie and Chamorro, 2008).
2.2.
Real Options in Carbon Capture and Storage
flow (DCF) analysis when valuing investment decisions. As Sarkis and Tamarkin (2005) note, however, standard cost-benefit analysis ignores the value of the real option to delay an investment. Specifically, given that carbon investments have uncertain input and output prices, uncertain technological development, and sunk-cost characteristics, the value of post-poning an investment decision can be considerable. Sarkis and Tamarkin (2005) conclude that “[t]he advantage to organizations, therefore, of the real options approach is that [the option] value is not ignored, and becomes part of the decisions-making process.” The option value could significantly affect the optimal decision for firms. Siddiqui and Fleten (2010) similarly acknowledge this fact, stating that “real options trade off in continuous time the marginal benefits and costs of making decisions under uncertainty.”
The most extensive discussion of investment under uncertainty was written by Dixit and Pindyck (1994), who take the reader on a step-by-step exploration of the key attributes of real option theory. In their seminal work, the authors describe the characteristics of decision making under uncertainty, provide mathematical models for working with real options, and show intuitively how specific problems can be solved using their framework. As we will see, most of the papers on this topic follow the basic traits outlined in their work.
For an example of the option value, consider price uncertainty. As volatility increases, option theory (Hull, 2012) predicts that the value of an option to invest rises as well. It may therefore be optimal to postpone the investment decision to wait for markets where price volatility is increasing, since this has the potential to significantly increase prices, thus increasing the value of the option to invest (Laurikka and Koljonen, 2006). In general, the longer we wait, the higher the potential option value.
There have been a number of studies on investment decisions under uncertainty in the energy market at large. At the start of this century, Insley (2003) investigated the price development of emissions. Among other findings, she showed that emissions pricing tends to follow a geometric Brownian motion. This will be a useful finding later on, when we apply the real options methodology set out by Dixit and Pindyck (1994) to investment decisions in carbon capture and storage. Laurikka and Koljonen (2006) find that irrespective of the specific regulatory instrument, firms will need an incentive to invest in abatement technologies.
The International Energy Agency, by means of researchers Blyth, Yang, and Bradley (2007), for instance, apply option theory to derive the optimal price of carbon emissions. Throughout their work, they describe how investment decisions in the energy market can benefit from a real options approach. Taking the price of carbon as a stochastic variable and the price of energy as deterministic, they find that given market conditions prior to 2007, investment in CCS is not financially viable. This is in line with Abadie and Chamorro (2008), who report that immediate installation is not recommended from a financial perspective.
Whereas most studies take one model and apply it to carbon capture investments, Ram-merstorfer and Eisl (2011) analyze two models concurrently. The first model simply uses a constant convenience yield and dividend yield. Their second model is more complex, but more realistic, and utilizes a mean reverting process. In both models, Rammerstorfer and Eisl also find that investments in CCS are not currently profitable.
Just last year, Wang and Du (2016) took a slightly different approach. These authors use a quadrinomial, instead of a binomial, model based on the theory of real options. They argue this makes their predictions more realistic. Moreover, instead of examining only one or two sources of uncertainty, as has been done before, Wang and Du examine four sources of uncertainty in the Chinese market: carbon price, fossil fuel price, investment cost, and government subsidy. Comparing the value of the option with the NPV investment rule, they find that currently, investments are not profitable. Most notably, even a full subsidy by the government could not induce investors to execute the project based on financial motives alone. Abadie and Chamorro (2008) reach a similar conclusion in their study.
Walsh et al. (2014) note in their work that previous literature has shown that investment costs should be considerably lower if CCS technology is to be deployed at a large scale. As Eckhause and Herold (2014) explain, this is in part caused by low prices of CO2, which
change policy events.
3.
The Energy Market
Energy generation is comprised of a number of different sources of production. Broadly, we identify two categories: fossil fuels and renewables. The former category includes sources such as gas, oil, and coal, while the latter includes wind, solar, and hydroelectricity. Table 1 shows that actual energy production in the Netherlands depends for the largest part on natural gas (178 PJ in 2014) and coal (106 PJ in 2014). While the share of production of renewable sources is increasing, the trend has been stable over the last five years.
Table 1: Energy Production in the Nether-lands, 2000 - 2014, in PJ 2000 2005 2010 2013 2014 Total 324.6 362.8 425.3 363.1 369.2 Natural gas 189.0 209.5 264.9 194.5 178.1 Coal 84.3 83.0 78.8 88.4 106.1 Other fossil 17.5 18.8 15.6 14.8 16.4 Nuclear 14.1 14.4 14.3 10.4 14.7 Renewables 10.8 26.9 40.4 43.9 42.1 Other 9.0 10.1 11.3 11.1 11.8 Source: adapted from ECN (2015). Natural gas includes energy production by conventional power plants as well decentralized sources.
Let us now take a look at the forecasts (Table 2 on page 8). We note that the share of natural gas is expected to decline over the next 15 years, but that the share of coal is expected to first increase and then stabilize around current levels. The primary new source of energy will be renewables. The results in the table show the determination of the government to mitigate climate issues over the long term. Until then, and indeed for years after 2030, fossil fuels will continue to play an important role in Dutch energy generation. To reach the global carbon targets, it is thus important that the fossil fuel power plants emit fewer greenhouse gases.
Table 2: Energy Production in the Netherlands, 2015 - 2030 forecast, in PJ 2015 2016 2017 2020 2023 2025 2030 Total 351.7 325.4 334.9 376.4 463.1 486.0 498.1 Natural gas 99.0 103.0 110.5 109.3 130.2 143.2 117.2 Coal 162.9 127.8 119.5 106.5 110.2 109.4 110.6 Other fossil 20.9 17.7 18.0 18.5 20.0 20.4 21.7 Nuclear 15.1 15.1 15.1 15.1 15.1 15.1 15.1 Renewables 49.6 57.4 67.2 122.3 183.0 193.2 228.9 Other 4.2 4.5 4.7 4.7 4.6 4.6 4.6
Graphically, we depict the energy production trends in the Netherlands in Figure 1. The graph clearly shows that the share of fossil fuels will gradually decrease, while the share of renewable sources increases.
Fig. 1. Energy Production in the Netherlands Source: adapted from ECN (2015)
3.1.
Pollution
One of the major reasons carbon markets exist, as Sarkis and Tamarkin (2005) note, is that the energy industry is the major upstream producer of carbon dioxide emissions. While increasingly more effort is put into creating cleaner sources of energy (see, e.g., IEA (2015b)), emissions are a constant issue that needs to be addressed adequately.
Zooming in on the Netherlands, the ECN (2015) finds that current emissions are approx-imately 196 Mt CO2. Over the next 15 years, given current policy, emissions are expected
to reduce only slightly, to 175 Mt CO2 in 2030. Figure 2 depicts this trend. There is a
steady yet minor decrease in expected emissions between now and 2030. At this pace, the Netherlands will still contribute a large share to pollution. According to Le Qu´er´e et al. (2013), power plants running on gas and coal make up 60 percent of CO2 emissions; it is
Fig. 2. Carbon Emissions in the Netherlands Source: Adapted from ECN (2015)
It is useful here to take a step back and briefly discuss why carbon emissions exist and why it is important to mitigate these problems. Balclar, Demirer, Hammoudeh, and Nguyen (2016) note that fast economic growth could lead to emissions, which degrade the environment. Deterioration of our living environment, in turn, negatively affects human health, thereby reducing the quality of life. Global warming, as caused by greenhouse gases emissions, has been widely studied over the past decades. Ever since the United Nations Kyoto Protocol put the issue of global warming on the world agenda (Sarkis and Tamarkin, 2005), governments, businesses, and the public have been increasingly aware of the effects of carbon emissions. The consensus is that decisive action has to be taken now to prevent a major global warming by the end of the current century.
3.2.
The Emissions Market
To mitigate the problems of carbon emissions, governments have proposed legislation that helps contain the negative effects of our growing need for energy. Under the Kyoto Protocol, which served as the blueprint for the European Union Burden Sharing Agreement, emission rights are allocated to nations, not to individual legal entities (Abadie and Chamorro, 2008). For instance, the Netherlands as a whole may be allowed to emit 100 units, but no cap is put on individual organizations. To ensure that utilities and other industries have ways to conduct business and still meet the emissions requirements, the European Commission has developed the European Emissions Trading Scheme, with the primary goal of reducing the carbon footprint of the Union (European Commission, 2003).
carbon trading has increased threefold over the last 10 years. With the creation of emission markets, organizations have to determine the trade-offs in costs between investing in projects that will help reduce emissions (thereby lowering emission costs) and paying for permits to discharge emissions. Sarkis and Tamarkin (2005) find that organization are now involved in trading greenhouse gas emission permits to address this issue. Kossoy et al. (2015) report that there is substantial evidence that the importance of carbon pricing is increasing: There are now almost double the number of carbon pricing instruments since 2011.
Fig. 3. Emission Allowance Price Trends in Europe Source: European Energy Exchange AG (2016)
However, carbon markets are highly volatile (Balclar et al., 2016). As Figure 3 shows, there are severe spikes, both upward and downward. The increasing importance of carbon pricing suggests the need for policies aimed at stabilizing the carbon price. This raises three questions. First, how are current markets designed and what kind of problems does this create? Second, what will have to change to solve these problems? And third, what is the trigger price of carbon? The first two questions will be addressed now. We will try to solve the last question after we have developed the required mathematical tools.
The European Union Emissions Trading Scheme (EU ETS) is the main driver of the global carbon market (Viteva et al., 2014). It is the first of its kind, and it is still the largest carbon pricing instrument in the world (Kossoy et al., 2015). In this section, we will explore the characteristics of the EU ETS.
emissions from sectors covered under this system by 21 percent in 2020 compared to 2005. Then, in 2030, the objective is to reduce emissions by another 20 percentage points, or by 43 percent versus 2005 levels. Under the constraints of the cap, firms receive or purchase emission allowances. These allowances can be traded (European Commission, 2016).
Kruger, Oates, and Pizer (2007) report that the trading aspect of the carbon market is unique: It results in a peculiar system, where the demand for permits is set at the EU level, but the supply is determined by the decisions of all the member states. Supply is thus decentralized, while demand is centralized. This has a very important implication, argue Kruger et al. (2007), because it is difficult for any one State to predict the market price of allowances. This makes it hard to set National Allocation Plans for emissions.
Contrary to the goal of EU ETS described above, where prices should be high enough to create an incentive for organizations to reduce emissions, Eckhause and Herold (2014) note that the prices of allowances remain low. This makes it unlikely for early adopters of abatement technologies to recover investment costs. It is therefore expected that firms will not want to invest in technologies until the price is either sufficiently high, or investment costs sufficiently low. This creates a paradox: Investment costs will only decrease if research is carried out that will make these projects cheaper. Such research often requires the devel-opment of facilities that showcase the potential of these technologies. The problem, however, is that these projects require significant funds, and companies are not willing to invest due to low economic gains.
Some researchers argue that the EU ETS in its current form suffers from a structural design issue that makes prices hard to predict. Whereas standard commodity markets trade frequently, the market for emission permits is much less liquid (Abadie and Chamorro, 2008). As noted above, firms only need to have enough allowances to cover their emissions at the end of the year. Therefore, trading only occurs at certain intervals. This could cause volatility to spike during these intervals. While the European Climate Exchange (now ICE) does trade frequently, researchers agree1 that the current ETS does not operate optimally.
It is clear from the discussion above that the European Union Emissions Trading Scheme needs revision. Convery (2008) contends that regulatory institutions have a key role in shap-ing carbon markets. Because these markets operate across national borders, a joint effort is required to further develop systems that push up the costs of carbon emissions. As Mon-tero (2004) states, to overcome problems of incomplete enforcement and uncertainty of the benefits of pollution control, policy makers are now paying more attention to environmental markets.
The European Commission is one of the institutions that is actively trying to reshape its
current system to make it more resilient in the future. The EU ETS is now in its third phase, which has started in 2013 and is projected to run through 2020. Changes approved in 2009 include a new cap on emissions, which will be reduced at a faster pace than before. More important, perhaps, is the development of a “New Entrants Reserve,” which sets 300 million allowances aside to fund development of innovative renewable energy technologies and carbon capture and storage (European Commission, 2016). Kossoy et al. (2015) highlight some of these changes, and argue that it makes the EU ETS more resilient against macroeconomic conditions.
3.3.
Gas Storage
Carbon emissions can be captured at major emission sources such as refineries and power plants. It can then be transported by pipeline to a few different kinds of storage facilities. Specifically, we identify salt caverns, aquifers, and depleted gas fields. Salt caverns are man-made storage facilities. While this means we can easily determine storage capacity, development costs of salt caverns are estimated to be very high (U.S. Energy Information Administration, 2011). Aquifers are underground layers of water-bearing permeable rock. Development costs of aquifers are also estimated to be high (Khan, Mushtaq, Hanjra, and Schaeffer, 2008). Finally, there are depleted gas fields.
In the Netherlands, there are a large number of depleted gas fields. Most of these fields are located in the North Sea. We can use these depleted gas fields as storage facilities for CO2.
Gas fields have a number of advantages of salt caverns and aquifers. Most importantly, since these fields are depleted, a lot of infrastructure is already in place. To transport the carbon dioxide to the gas fields, we can to make use of exiting gas lines. Sometimes, additional installations have to be built for this purpose. The investment model in this thesis accounts for the development of new infrastructure for this purpose.
4.
Mathematical Foundation
Before we embark on the analysis of carbon capture and storage, we have to introduce the required mathematics. In this chapter, we explain the stochastic process, Ito’s Lemma, and contingent claims analysis. These concepts will be used multiple times in the next chapter. In this chapter, we follow the methodology of Dixit and Pindyck (1994).
4.1.
Stochastic Processes
A stochastic process is a variable that evolves at least partially random over time. The price of a stock is an example of a stochastic process. It fluctuates randomly, but is expected to have a long-run positive rate of growth. These fluctuations describe continuous-time stochastic processes: the time index t is a continuous variable. We will use these processes throughout this paper.
A Wiener process, more commonly known as Brownian motion, is a continuous-time stochastic process. It has three essential characteristics. First, it is a Markov process. This implies that the probability distribution for future values is only dependent on the present state of the variable, and not on its past distribution. Second, the Wiener process has independent increments. This means that the probability distribution for the change in a variable over any time interval is independent of any other interval. Third, changes in the process over a finite interval of time are normally distributed. The variance of this distribution increases linearly with time.
We express a Wiener process as follows:
dz = t
√
dt, (1)
where dz is an increment of a Wiener process, and t is a normally distributed random
variable with zero mean and a standard deviation of one.
We can use the fundamental building blocks of the Wiener process to develop more interesting stochastic processes. All of these more generalized stochastic processes are special cases of the Ito process:
dx = a(x, t)dt + b(x, t)dz, (2)
where dz is the increment of a Wiener process, and a(x, t) and b(x, t) are known, non-random, functions. The stochastic process for x(t) is continuous-time.
dx = αxdt + σxdz, (3)
where dz is the increment of a Wiener process, α the drift parameter, σ the variance, and dx the change in x over an infinitesimally small period of time.
4.2.
Ito’s Lemma
The stochastic processes introduced above are continuous in time. They are also not differentiable. However, as we indicated above, we will often need to work with geometric Brownian motions and its derivatives. We therefore need to introduce another fundamental building block of real options investment, and stochastic processes in general: Ito’s Lemma. We will explain Ito’s Lemma using a Taylor series expansion. Suppose that x(t) follow the Ito process in equation (2). Consider a function F (x, t) that is at least twice differentiable in x and once in t. We have to find the total differential equation of this function, dF . If we apply the rules of calculus, we find this differential equation in terms of first-order changes in x and t:
dF = ∂F ∂xdx +
∂F
∂tdt. (4)
Since F (x, t) is at least twice differentiable in x, suppose we also wish to include higher-order terms for changes in x. This would change our differential equation:
dF = ∂F ∂xdx + ∂F ∂tdt + 1 2 ∂2F ∂x2(dx) 2 + 1 6 ∂3F ∂x3(dx) 3 + .... (5)
In ordinary calculus, we know these higher-order terms go to zero in the limit as dx tends to 0. To determine whether this effect holds here as well, expand the third term in equation (5):
(dx)2 = a2(x, t)(dt)2+ 2a(x, t)b(x, t)(dt)32 + b2(x, t)dt. (6)
Terms in (dt)32 and (dt)2 go to zero faster than dt as it becomes infinitesimally small, so
we ignore these terms. This yields
(dx)2 = b2(x, t)dt. (7)
dF = ∂F ∂tdt + ∂F ∂xdx + 1 2 ∂2F ∂x2(dx) 2. (8)
We will use this result in the next chapter, where we value the option to invest in carbon capture and storage projects.
4.3.
Contingent Claims Analysis
We use the contingent claims method for valuing the opportunity to invest in a carbon capture and storage facility. Contingent claims analysis is firmly rooted in financial economics theory. To value the investment opportunity, imagine it is a new asset. The economy as a whole has a large number of assets that are already traded. Our goal is to form a replicating portfolio that exactly mimics the return and risk characteristics of existing assets. The price of the investment asset must equal the market value of the portfolio. If it does not, we have the possibility of arbitrage. We assume that the underlying uncertainty of the investment can be modeled using an Ito process.
Suppose the profit of a project depends on a variable x. Think of x as the output price of a firm. We assume x follows a geometric Brownian motion
dx = αxdt + σxdz, (9)
where α is the growth rate parameter, σ signifies the proportional variance, and dz is the increment of a standard Wiener process.
We assume that the stochastic fluctuations in the output price x can be spanned by assets in financial markets. In fact, it is sufficient that the risk inherent in x, namely via the dz term, can be replicated by a portfolio of traded assets2.
Contingent claims analysis builds a portfolio using long and short positions. The long position is an investment in the project. The short position is n units of output x. We have to determine n to make the portfolio riskless. When the portfolio is riskless, it must earn the risk-free rate of return. We can use these properties to derive the differential equation that solves our investment problem.
Proceeding with the properties discussed above, let V (x) be value of a project when the output price is x. Then V (x) is a function of x and as such follows a geometric Brownian motion: dV = (αxVx+ 1 2σ 2x2V xx)dt + σVxxdz. (10)
We now want to build a replicating portfolio with the price P . Since this portfolio is perfectly correlated with the value of the project, its price follows a similar stochastic process. Investors will only hold the asset (the project to value) if it provides a sufficiently high return. Part of this return will be in the form of the expected price appreciation, α. Another part of the return may be in the form of dividends, δ. Let µ = α + δ be the total expected rate of return of the asset.
The total expected return must be sufficient to compensate investors for risk. Now, financial theory states that risk itself is not what matters; nondiversifiable risk does. Since the market as a whole provides the maximum available diversification benefits, the covariance of the rate of rate of the asset with that of the market portfolio together determine the risk premium.
We will assume that the risk-free rate r is exogenous. An example of an exogenous risk-free rate is the return on government bonds. The capital asset pricing model states that
µ = r + β(rm− r), (11)
where β is the sensitivity of the asset to the market, and rm is the return of the market.
We will assume that α is less than the risk-adjusted return µ. If this is not true, the firm would never invest, because the value of the project would be unbounded; that is, it is forever better to hold on to the option to invest. We will let δ denote the difference between µ and α, that is, δ = µ − α. Since α is assumed to be less than µ, we are assuming δ > 0. If this assumption holds, the expected rate of capital gain on the project is less than µ. It is thus an opportunity cost of delaying investment in the project. This is analog to saying that we delay executing the option to invest. If δ were zero, there would be no incentive to hold the option, and we would never invest. We therefore assume δ > 0.
It is useful to discuss what the parameter δ implies. It is by assumption that the output of the investment is a commodity that can be stored. This implies that δ is the convenience yield for storage, which means that it represents the flow of benefits that investors receive for holding the commodity. As an example, suppose we have a gas field that is used as storage. When the price of imported gas is too high, we can utilize this gas storage facility and reap the benefits.
We will assume that the return from our portfolio is from capital gains only; the portfolio does not pay dividends. We thus require that the portfolio return equals
dP = µP dt + σP dz (12)
5.
Valuing Carbon Capture and Storage Investments
In chapter 2, we defined the characteristics of carbon capture and storage projects. We identified three sources of uncertainty: price uncertainty, technological uncertainty, and ir-reversibility. The first source of uncertainty refers to the fluctuations in carbon emissions allowances. These make the pricing of such instruments highly variable and thus uncertain. Secondly, as discussed previously, carbon investments are still on the brink of technological capabilities. Due to this, technologies that are currently used for carbon capture purposes may become outdated soon, making the technology we use today obsolete and expensive. Fi-nally, investments in carbon abatement solutions are often irreversible, because once pipelines and an injection facility are built, these cannot be dismantled and relocated.
In chapter 2 we proposed the use of real options investment to counter some of these issues. Imagine that the right to invest in a carbon capture installation is analog to a financial call option: It is a real option. Just as with financial options, we have the possibility to delay executing the option, or to let the option expire if we think it is not beneficial to exercise. In this chapter, we will use real options methodology to analytically solve the problem of the optimal investment threshold.
In the following, we take the example of a depleted gas field (such as the ones that we could find in the North Sea). We want to develop a use-case where we inject CO2 into these
gas fields. In this example, we assume that the gas field is completely depleted and can thus be fully filled with carbon emissions. Of course, to prepare the field for carbon storage requires a significant capital expenditure. After the initial investment period, we assume the gas field will be filled instantaneously. This requires ongoing operating expenditures.
The analysis in this chapter uses the contingent claims analysis (refer to chapter 5 for an overview of the methodology). We will first value the project. Once we have the basic model set up, we will continue to value the option to invest. The solutions to this problem derive largely from the work of Dixit and Pindyck (1994), with exceptions noted.
5.1.
Valuing the Project
The value of the project is the difference between the total cost of investment I, which consists of the initial capital expenditures and the continued operational costs), and the foregone CO2 allowance expense once the plant is operational. The profit of the allowance
expense depends on p: the price of carbon. Following Abadie and Chamorro (2008), the price of carbon follows a geometric Brownian motion
where α is the growth rate, σ the proportional variance, and dz the increment of a Wiener process.
The installation of a carbon capture unit will, once completed, produce a fixed output. Let P be the total profit, that is, the carbon price p multiplied by output q. We can thus allow P to follow the similar geometric Brownian motion:
dP = αP dt + σP dz. (14)
The value of the project is simply the value of the output: V (P ) = P .
5.2.
Valuing the Option to Invest
We follow the method of contingent claims analysis in this section to determine the value of the option to invest. The value of an option to invest F (P ) holds uncertainty since it depends on the price of carbon and is a function of P . Since we use contingent claims analysis, we assume that the uncertainty over the value of the option can be replicated using asset in the economy, that is, that the value of F (P ) can be spanned by existing assets.
Following Dixit and Pindyck (1994), we build a risk-free portfolio to achieve this purpose. The portfolio consists of one long position in an option to invest and a short position of n units of P , that is, n = F0(P ). We want to choose n such that the portfolio is riskless. The short position costs n = F0(P )P . Hence, the value of the portfolio is Φ = F − F0(P )P . An investor in the short position has to pay dividends equal to δndt over the time interval dt. This ensures that someone is willing to hold the equivalent long position. The total return from holding the portfolio is thus
dF − F0(P )dP − δP F0(P )dt. (15)
Apply Ito’s Lemma to obtain an expression for dF :
dF = F0(P )dP + 1 2F
00
(P )(dP )2. (16)
The total return on the portfolio is
1 2F
00
(P )(dP )2− δP F0(P )dt. (17) From equation (14), we know that (dP )2 = σ2P2dt. We thus know that the return on the portfolio is given by
1 2σ
2P2F00
Since this return is risk-free, we have that rΦdt = rF − F0(P )Pdt:
1 2σ
2P2F00
(P )dt − δP F0(P )dt = rF − F0(P )Pdt. (19) If we now divide through by dt and rearrange terms, and noting that the return is risk-free, we have the equation that F (P ) must satisfy:
1 2σ
2P2F00
(P ) + (r − δ)P F0(P ) − rF = 0. (20)
Equation (20) is a second-order linear differential equation dependent on the first and second-order derivatives of F (P ). Since this equation is linear in the dependent variable and its derivatives, we can express its general solution as APβ. If we try this solution by substitution into equation (20), and collect terms, we have:
1 2σ
2β2+ β(r − δ − 1
2σ
2) − r = 0 (21)
The value of the option to invest F (P ) must satisfy three boundary conditions:
F (0) = 0, (22)
F (P∗) = P∗− I, (23) F0(P ) = 1. (24)
Condition (22) follows from the observation that if the stochastic process for P goes to zero, it will stay at zero. The option to invest will thus be of no value when P = 0. The other two conditions follow from consideration of the optimal investment region. P∗ is the price at which it is optimal to invest now. Then (23) says that a firm receives a net payoff P∗− I if it decides to invest. This is called the value-matching condition. Finally, condition (24) is the smooth-pasting condition. It states that the slopes of the option value and the net payoff should be equal in the boundary P∗. It is important to note that the third condition does not necessarily yield the only solution to our investment problem. There could be other points that math conditions (22) and (23). These results, however, are locally optimal. It is only when condition (3) is met, that we find the optimal exercise price. We can therefore also label condition (24) the optimality condition.
β1 = 1 2− r − δ σ2 + s (r − δ) σ2 − 1 2 2 + 2r σ2 > 1, (25) and β2 = 1 2− r − δ σ2 − s (r − δ) σ2 − 1 2 2 +2r σ2 < 0. (26)
The conditions β1 > 1 and β2 < 0 follow from the properties of the characteristic
quadratic equation that was derived above3.
The general solution to equation (21) is thus
F (P ) = A1Pβ1 + A2Pβ2, (27)
where A1 and A2 are constants to be determined. Boundary condition (22) implies4 that
A2 = 0, leaving the solution
F (P ) = APβ1. (28)
We can rewrite the value-matching and smooth-pasting conditions as
A1(P∗)β1 = P∗ δ − I, (29) β1A1(P∗)β1−1 = 1 δ. (30)
Solving the above system yields
P∗ = β1 β1− 1 δI, (31) A1 = (β1− 1)β1−1I−(β1−1) (δβ1)β1 . (32)
In equation (31), P represents the total costs of carbon dioxide emissions. We obtain the optimal price p of one unit by dividing by the amount of total emissions allowances q:
p∗ = β1 (β1− 1)q
δI. (33)
3The equation Q(β) has the shape of an upward-pointing parabola. As Q(0) = −r and Q(1) = −δ, we
have that one root is larger than 1, while the other is negative.
Since the value of the project is V (P ) = P , the value threshold is
V∗ = β1 (β1− 1)q
δI. (34)
6.
Numerical Examples
The methodology presented in the previous chapter is abstract. Since it can be used to value tangible investment projects, we provide a numerical example in this chapter. The goal here is to familiarize the reader with applications of the real options methodology. We use data gathered from a number of sources to value an investment in underground carbon storage in the North Sea. The Netherlands has for a long time owned these fields, and now that they are depleted, it might be of interest to examine if these fields can be converted to carbon storage. We first introduce the parameters of our calculations in the next section. In the second section, we estimate the trigger price of carbon allowances and compare this with market realities. Finally, in the third section, we perform a number of robustness test.
6.1.
Parameters
The methodology we have presented in chapter 5 relies on a number of parameters. For instance, we need to know the discount rate at which to value the project, but also the investment costs, carbon price characteristics, and time span, among others. Table 3 on page 26 provides the parameters we use to determine the base case. In this section, we explain each of these parameters.
The main uncertainty in the model presented in the previous chapter is the development of the carbon allowance price. The first step is thus to model a few of the characteristics of this price path. We start by determining the growth rate of the allowance price. Using price data from the European Energy Exchange AG, we find a compound annual growth rate of the allowance price of -0.085 over the period from 2009 to 20165. Note this implies
that the carbon price has declined in the past 7 years. The second parameter we calculate from the carbon price data is the volatility. We find a volatility of 30 percent over the past 123 trading days ending May 5, 2016. The annualized volatility is therefore 49.1 percent6.
Next, it is important to know the size of the investment. To determine the investment costs, we have to know how large our gas storage is. We assume a well with a capacity of 120 MTon CO2. Cronenberg et al. (2009) find that the capital expenditures (CAPEX) of similar
projects are approximately e1.3B. The size of the investment depends on the location of the reservoir. If the reservoir is farther from shore, or at greater depth, the capital expenditures may increase. In our calculations, we use e1.3B as our assumed investment. Cronenberg et al. (2009) also find that operating expenses (OPEX) are approximately e143M per year.
5We calculate the growth rate as the compound annual growth rate: CAGR(t
o, tn) =
(V (tn)/V (t0))
1 tn−t0 − 1.
We assume our investment has similar characteristics. To determine our total investment costs, we estimate the project will be operational for 20 years. We therefore discount the capital expenditures at the rate µ, which is detailed in Table 3. Summing CAPEX and OPEX yields a total investment ofe3.244B.
Since the project will be operational for 20 years, we expect the cash inflows to be of similar length. We therefore need to discount the cash flows by the appropriate rate. We use the capital asset pricing model (CAPM) to find the discount rate. We take the risk-free rate as the yield of the ten-year Netherlands Government bond7. We find that the risk-free rate is 0.45 percent. We also estimate the beta of the carbon price with the AEX between November 10, 2015 and May 5, 2016. We find a beta of 0.720. Finally, following Koller, Goedhart, and Wessels (2010) we take the equity risk premium to be 5 percent. Using the parameters we discussed above, we find that the appropriate discount rate is 4.05 percent. We assume this number is fixed for the duration of the project.
Since we now know all the parameters, we can calculate the remaining inputs for our valuation model. We find that δ = µ − α is 12.6 percent. We determine that A is 0.003, and β1 is 2.026. We use these numbers in the next section, where we discuss the results of our
analysis.
Table 3: Parameters of the Base Case Parameter Inputs α -8.52% σ 49.05% I 3,244a t 20b CAPM Parameters r 0.45% β 0.720 M RP 5.00% Parameter Results A 0.004 β1 2.026 δ 0.126 µ 4.05% a In mln EUR bIn years
6.2.
Results
In this section, we present the results of our initial calculations. Using the parameters discussed in the previous section, we calculate the trigger price for the project. We make the simplifying assumption that there are no alternative uses for this depleted gas field. While we could use it as seasonal gas storage, doing so would take us away from the focus of this thesis. Table 4 presents the figures. The threshold for the carbon price at which we would execute the option to invest is e67.11 per metric tonne of CO2.
The trigger price we have determined is low compared to earlier results by for instance Blyth et al. (2007), Abadie and Chamorro (2008), and Rammerstorfer and Eisl (2011), who find that carbon capture and storage investments are not profitable until the price reaches at least e100 per metric tonne of carbon emissions. It should be noted that each of these articles determines the optimal investment price from the point of view of a utility company. In this paper, however, we take a different view: We own a depleted gas field and are willing to convert it to a carbon storage facility. The required investment costs as well as the operating costs are lower. Comparing our results to similar exploratory research by Cronenberg et al. (2009), we find that our results are in line with this study.
We conclude that investment is not currently financially attractive. The last-recorded emissions allowance price is e6.50. Since our trigger price is above this level, we do not exercise our option to invest at this point in time.
Table 4: Results of the Base Case (in mln EUR) Parameter Value Va 6,405.09 F(P)b 3,161.20 P* 805.30 p*c 67.11d
The results of the base analysis using the frame-work developed in the previous chapter. Note that the value p* is determined by dividing the value
of P* by the capacity of the storage facility (120
MTon CO2).
a The value of the project.
bThe value of the option to invest.
6.3.
Robustness
The final section of this chapter examines what happens when the critical parameters change. If we postpone investment, it is well possible that some of these values do not stay constant over time. While we assume the parameters are constant from the moment we exercise the option, until we do these may change at any time. We therefore include a number of robustness checks.
6.3.1. Scenario 1: Change in beta
Table 5 in Appendix A on page 36 shows how the trigger price of one emissions allowance is affected by a change in the beta of the capital asset pricing model. There are several reasons beta might change. For instance, it could occur as the result of a structural change in the market, or because of a change in the risk profile of the firm. We find that a change in beta, from 0.1 up to 1, does not significantly change the trigger price of carbon.
6.3.2. Scenario 2: Change in volatility
Table 6 in Appendix A on page 36 shows how the trigger price of one emissions allowance is affected by a change in the volatility of the price. Not surprisingly, we find this parameter shift has the most significant effect on the trigger price. The price is e67.11 in our base model, where volatility is approximately 50 percent. If we decrease volatility to 10 percent, we find the trigger price drops to e35.39, which is almost half its original value. Moreover, when we increase the volatility to 90 percent, we find the price has to be at least e144.40 for the investment to be financially interesting. Clearly, volatility has a large effect on the decisions we might make. We clearly see this reflected in Figure 4: The slope of the line increases after we reach current volatility levels. For values over 50 percent, we see that the trigger price has to increase by an increasingly higher amount. It is thus important to monitor the volatility of the carbon price closely and to examine its effects on our calculations regularly.
6.3.3. Scenario 3: Change in risk-free rate
Fig. 4. Trigger Carbon Price Levels for Varying Volatility Levels
6.3.4. Scenario 4: Change in return
Table 8 in Appendix A on page 37 shows how the trigger price of one emissions allowance is affected by a change in the return of the capital asset pricing model. This could occur as a result of changes in the risk-free rate, beta, or the market risk premium. Since we have discussed the first and second reasons in the previous two subsections, we focus on a change in the risk premium. Since the estimate for the risk premium we have used is based on data that spans a century (Koller et al., 2010), we do not expect the risk premium to change drastically in the future. While a change in return does seem to have a significant effect on the trigger price of carbon, we do not expect this effect to occur.
6.3.5. Scenario 5: Change in CAPEX
6.3.6. Scenario 6: Change in OPEX
7.
Concluding Remarks
We develop a mathematical decision-making tool for carbon capture and storage in-vestments. Using real options theory, we construct a framework for valuing an investment project. We then gather data on a number of key parameters to provide a numerical imple-mentation of the model.
We find that investing in carbon storage in depleted gas fields in the Dutch part of the North Sea is not currently viable considering the price of carbon emissions allowances. The current prices are approximately 25 percent below trigger levels. However, given develop-ments over the past six months, we do expect investment to be possible in the future.
We consider a number of deviations from our base parameters. We find that a shift in the price process, resulting in a shift of volatility of the emissions price, has a significant effect on the trigger price of the investment project. Moreover, we find that changes in the capital and operating expenditures due to technological uncertainty also have a noticeable effect on the trigger price. Finally, we find that changes in the risk-free rate, beta, and return of the project do not seem to have a large effect on the required price level.
We recognize, however, that this analysis is only valid given a number of assumptions. For instance, we assume that once the carbon price is at trigger levels, we exercise the option to invest and immediately get the benefits of our investment. We thus have to assume that we inject all CO2as soon as we decide to execute our option. We also assume that our critical
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Appendix A - Scenario Analysis Results
Table 5: Scenario 1: Change in β
β p* (in EUR) 0.4 68.73 0.5 68.17 0.6 67.66 0.7 67.19 0.8 66.78 0.9 66.41 1.0 66.08
Scenario 1 shows the effects of different values for the CAPM β on the trigger price of carbon al-lowances. The original value for β is 0.720; the corresponding trigger price p* is 67.11 EUR.
Table 6: Scenario 2: Change in volatility
σ (in %) p* (in EUR)
10.00 35.39 20.00 39.56 30.00 46.48 40.00 56.09 50.00 68.39 60.00 83.37 70.00 101.02 80.00 121.37 90.00 144.40 100.00 170.12
Scenario 2 shows the effects of different values for the volatility of the carbon price on the trigger price of carbon allowances. The original value for σ is 49.05%; the corresponding trigger price p* is
Table 7: Scenario 3: Change in risk-free rate r (in %) p* (in EUR)
0.00 66.89 0.20 66.98 0.40 67.08 0.60 67.18 0.80 67.28 1.00 67.37
Scenario 3 shows the effects of different values for the risk-free rate on the trigger price of carbon allowances. The original value for˚is 0.45%; the corresponding trigger price p* is 67.11 EUR.
Table 8: Scenario 4: Change in µ β (in %) p* (in EUR)
2 69.28 3 68.11 4 67.15 5 66.37 6 65.76 7 65.31
Scenario 4 shows the effects of different values for the CAPM µ on the trigger price of carbon al-lowances. The original value for µ is 4.05%; the corresponding trigger price p* is 67.11 EUR.
Table 9: Scenario 5: Change in CAPEX CAPEX (in mln EUR) p* (in EUR)
600 52.44
1,000 60.71
1,400 68.99
1,800 77.26
2,200 85.54
Table 10: Scenario 6: Change in OPEX OPEX (in mln. EUR) p* (in EUR)
1,400 56.04 1,600 60.18 1,800 64.32 2,000 68.45 2,200 72.59 2,400 76.73 2,600 80.87
