The Economic Evaluation of Investments in the Energy Sector: A ...

The Economic Evaluation of Investments in the Energy Sector: A Model for the Optimization of the Scenario Analyses Gianluigi De Mare, Benedetto Manganelli, and Antonio Nesticò* Faculty of Engineering, University of Salerno, Italy {gdemare,anestico}@unisa.it, [email protected]

Abstract. The well-known evaluation indices do not allow to take into account the interaction between current investment alternatives and future decisions. The real options theory provides answers to the limits that the evaluators discovered in the traditional techniques of capital budgeting and allows to give a value to managerial flexibility, i.e. the ability of management to review its decisions on the basis of changes in the economic context. Implementing the traditional cash-flow analysis with the tool of real options, the study defines a logical-operational model capable of verifying the financial viability of investments in the energy sector. The model is applied to the economic study of a project to produce energy from renewable sources, specifically the construction of a new wind farm. The different operational phases of the model used for the optimization of the scenario analyses, return the value of the positive potential that can result from management flexibility and innovation. Keywords: Wind Farm Valuation, Real Options, Monte Carlo Simulation, Renewable Energy.

1

Introduction and Aim of Work

The economic evaluation of investment projects is crucial in the allocation of resources process, both public and private [1-2-3-4]. In order to express an opinion on the economic implementation of the project initiative, discounted cash flow (DCF) analysis can be used, with it comparing the monetary income and expenditure of an investment for a predetermined period of time [5-6]. The result of the analysis is expressed through the well-known evaluation indices, the Net Present Value (NPV), Internal Rate of Return (IRR) and payback period. These indices, however, do not allow to take into account the interaction between current investment alternatives and future decisions [7]. They are criteria that ignore the added value that could result from the flexibility and innovation management, capable of changing the course of the investments. According to Dixit A.K. and Pindyck R.S. [8]: «As a practical * This paper is to be attributed in equal parts to the three authors. B. Murgante et al. (Eds.): ICCSA 2013, Part II, LNCS 7972, pp. 359–374, 2013. © Springer-Verlag Berlin Heidelberg 2013

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G. De Mare, B. Manganelli, and A. Nesticò

matter, many managers seem to understand already that there is something wrong with the simple NPV rule as it is taught – that there is a value to waiting for more information and that this value is not reflected in the standard calculation. In fact, managers often require that an NPV be more than merely positive … It may be that managers understand a company’s options are valuable and that it is often desirable to keep those options open». The real options theory provides answers to the limits that the evaluators discovered in the traditional techniques of capital budgeting 1 and is applied in uncertain management environments characterized by high dynamism, due to it allowing to give a value to managerial flexibility, i.e. the ability of management to defer a project, extend it, or leave it, as well as to review its decisions on the basis of changes in the economic context [11-12-13-14-15-18-52-53]. This paper first examines the benefits resulting from the application of real options to the economic evaluation of projects. Implementing the traditional cash-flow analysis with the tool of real options, the study will then define a logical-operational model capable of verifying the financial viability of investments in the energy sector. The model is applied to the economic study of a project to produce energy from renewable sources, specifically the construction of a new wind farm. The description of the planned works is followed by the macroeconomic analysis of the area of interest, which shows that, in a difficult economic context such as the one currently being experienced by the world economy, the expansion of renewable energy sources is an opportunity not only for energy diversification and environmental protection, but also for research and employment. The DCF analysis shows the cost-effectiveness of the initiative. The evaluation is then implemented with the theory of real options. The real options of abandonment, postponement and expansion investment are considered. The Monte Carlo simulation is adopted for the calculations, using the Fairmat Academic software in two different scenarios: one in which the real options are considered and another in which all the decisions are made at the beginning. Comparing the results, it is clear that the average value of the extended NPV is greater than what is obtained in the base case. This means that the real options valorise the project. The highest value obtained is the monetary representation of the options. Fundamentally, the managerial flexibility that is taken into account with real options lengthens the probability distribution of the NPV toward positive values, since it offers the

1

The limitations of the traditional techniques of capital budgeting in defining and evaluating some characteristic aspects of investments in real assets, can be described by three characteristics: uncertainty (technical and market), irreversibility of the investment, flexibility to dynamically adapt to changing choices environmental conditions [9]. In particular, the standard techniques are effective in short-term evaluations, but are not able to model the uncertainty of wider horizons. Barnett M.L. [10] emphasizes that these techniques do not consider the ability of management to control the risk and deal with situations of loss, so as to lead to discard those investments that are riskier but bearers of great strategic potential. See also Kogut B. and Kulatilaka N. [18]. For more details on the limits of the Net Present Value and the differences between the assumptions of the NPV and economic reality, see Mun J. [19] as well as Luehrman TA [20].

The Economic Evaluation of Investments in the Energy Sector

361

opportunity to reap the benefits of positive scenario developments and, simultaneously, allows to intervene in order to contain the negative impact of unfavorable changes in the variables that affect the investment.

2

The Investment as a Source of Real Options

In traditional DCF analysis, uncertainty is considered by adopting a probability distribution on the different possible scenarios or by adjusting the discount rate [16-17]. Consequently, a higher level of uncertainty reduces the value of the project. On the contrary, in the real options approach2, greater uncertainty may result in a higher value of the investment, if managers use the options to respond flexibly to events. This is expressed by the criterion of NPVextended, given from the sum of NPVbase, which expresses the NPV in the absence of strategic opportunities, and the value of real options OP, which represents the value of the project for management adaptability. Thus, management must look at the markets in terms of the evolution of uncertainty, determining the degree of exposure of investments and then placing them in a manner to derive maximum benefit from the uncertainty itself. The literature on option pricing was first written in the 1970s with the works of Black F. and Scholes M. [21], di Merton R.C. [22] e di Cox J.C., Ross S.A. and Rubinstein M. [23]. The first references to real options appeared the first half of the 1980s. However, the term real options was founded in 1977 through the intuition of Myers S.C.[24]: «The value of the firm as a going concern depends on its future investment strategy. Thus it is useful for expositional purposes to think of the firm as composed of two distinct asset types: 1) real assets, which have market values independent of the firm’s investment strategy, and 2) real options, which are opportunities to purchase real assets on possibly favorable terms». Real options apply the theory of financial options to the analysis of real assets. The elements that distinguish an option are: The stock price (S), i.e. the value of the underlying asset; The time to maturity, time period of validity of the right; The strike price (X), i.e.the price to pay to exercise the right; The volatility (σ2), given by the standard deviation of returns of the underlying asset; The risk free rate (r), provided by the performance of non-risky investments, typically government bonds. In the application of real options to the economic evaluation of investments, the underlying asset S can be the NPV of the project. Obtained with traditional DCF analysis, the NPV is then the starting point to implement the real options. The time to maturity is the period within which the option is deemed exercised. Volatility is the standard deviation of implied returns or percentage changes in values that characterize the underlying project or stochastic variable. Adopting a process perspective, the evaluation of investments aimed at enhancing strategic opportunities is divided into three main phases [7]: 2

Copeland, T. and Antikarov, V. [25] define the real option «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». Similarly, Kogut, B. and Kulatilaka, N. [26].

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1. analysis of the risk profile; 2. strategic analysis of the profile; 3. quantitative analysis. The three phases are not strictly sequential. There are some connections between different times, but the logic is either circular or iterative. Risk profile analysis is the basis for the quantitative analysis and mainly consists of two essential moments. The first is the estimate of the NPV basis, i.e. the present value of cash flows resulting from the deterministic component of the investment. The second is to identify the critical variables and the consequent modelling of the stochastic component of the project, which is the process that describes the evolution of the value of the initiative over time. The variation in time t of the value of an uncertain variable, which may coincide with the value of the underlying S, is describable by means of a stochastic diffusion process (geometric Brownian motion) and represented by the equation: S S

µ · dt

σ · dz

(1)

The two terms that describe the uncertain variable is the instantaneous expected return μ and instantaneous volatility σ of the value of the underlying S. The analysis of the instantaneous yield is based on the determination of a deterministic parameter μ that represents the trend value around which it is believed that the total value of the uncertain variable can evolve. From a geometric point of view, this value may coincide with the slope of the straight line interpolating the historical values of the variable. The volatility should then be estimated, which can be interpreted as the standard deviation of returns of the underlying asset. The second step is to analyse the strategic profile of the project. It should recognise the possible areas of flexibility of the project in order to verify the predetermined scenarios. This leads to the identification of real options and their parameters (strike price, the value of the underlying asset, volatility, expiration date). The third step is to analyse the quantitative profile. The aim is to arrive at the value of strategic opportunities, i.e. the estimate of the extended value of the project. To this end, the real options, once identified and defined, must be evaluated. Amram, M. and Kulatikala, N. [27] recognize three general evaluation methods: 1) the pde method solves a partial differential equation (pde) that equals the change of value in the option to the change of value in the equivalent portfolio, 2) the dynamic programming method outlines possible future outcomes, from which it then infers the future value of the optimal strategy, and 3) the simulation method establishes, for thousands of possible outcomes, the average value of the optimal strategy based on the decision made [28]. In the frequently used Monte Carlo simulation method [29-30], the optimal investment strategy at the end of each path is determined and the payoff calculated. The current value of the option is found by calculating the average of the payoffs and then discounting the average value thus obtained. This method can manage many aspects of the applications to the real world.


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The real options theory is applied to evaluate investments in various sectors. According to Triantis A. and Borison A. [31], the main sectors are: intensive capital industries with uncertain cash flows (e.g., investments in natural resources and engineering), those that have suffered substantial structural changes and thus make the most traditional techniques evaluation unreliable (e.g., the production of electricity), as well as those in which the strategic prospects are the main determinants of value creation (e.g., high-technology sectors, innovation, research and development). In recent years, not only in Italy, the energy sector has undergone regulatory changes as well as changes in its market logic, passing from being a regulated and monopolistic sector to a liberalized, uncertain and highly competitive one. These changes have pioneered the application of real options theory [9], making it possible to consider the intrinsic value of investment flexibility. For energy production from renewable sources projects, this ability has become particularly important [32], as demonstrated by the various applications in current literature [33-34-35]. Applications specific to the wind energy sector are, among others, those of MunõzHernández J.I., Contreras J., Caamaño J. and Correia P.F. [36], as well as Venetsanos K., Angelopouloua P. and Tsoutsos T. [37]. For the latter, the authors identify uncertainties and attributes of the resources that are used for the production of energy. Subsequently, the following real options have been identified: option to defer development, time to build option (staged investment), option to alter the operating scale, option to abandon, growth options.

3

DCF Analysis for the Economic Evaluation of a Wind Farm

Characteristics of the project. Through the installation of nine wind turbines, 7 with a power of 2.5 MW and 2 with a power of 1.5 MW, the project involves the construction and operation of a wind farm with a total capacity of 20.5 MW. The wind turbines are arranged along underground power lines that carry power to a transformer station (20/150 kV) and then to a new power station (380/150 kV), owned by Terna SpA, to enter the National Transmission Grid (NTG). The area covered by the plant falls within the Municipality of Vallata (AV), in the eastern part of the Campania Region (Italy). The total area of the wind farm is about 4 km2. The area covers an altitude of between 600 and 750 metres above sea level. The land has been obtained by signing preliminary agreements with the owners for the acquisition of surface rights and the right of way and conduits. The sector. Renewable energy sources are going through a period of great development in the world. The sector has not been affected by the current financial crisis and is projected to achieve the objectives set by the EU for 2020 with the climate and energy package of January 24, 2012: 20% reduction of greenhouse gas emissions, increase up to 20% savings energy, increase to 20% of energy consumption from renewable sources. In the European Union, over the next 40 years further investment will be required [38]. The REN21 [39] report shows the significant growth of investments in renewable energy, indicating China with 48.9 billion dollars primarily used

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in the wind industry as well as research of new wind farm technologies. Wind energy can significantly contribute to solving the world's energy problems, as highlighted by the various reports published by the International Energy Association [40], the European Commission [41] and the European Wind Energy Association (EWEA). In Italy, wind energy production is growing. Especially in the South, due to the topography and wind of its territory, as demonstrated by 84% of the number of national facilities and 98% of installed capacity. The untapped potential is also remarkable, as reported by SVIMEZ and SRM [42]. The study of the demand for electricity is carried out by processing data provided by Terna Rete Italy [43-44]. If the production of electricity is compared with its application in the Campania region, there is a deficit for 2011 of 9,136 GWh, or 47.7%. This deficit is now offset by imports. Starting form an annual consumption of 3,014 kWh per capita, the demand for electricity in the town of Vallata and surrounding municipalities in the first and second crown is estimated. From the results, there is domestic demand equal to 133.8 GWh/year. Estimates of income and residual value of the works. The energy produced by the wind farm will be sold to the grid operator, which represents the direct user of the system. With the liberalization of the electricity production introduced in Italy by Legislative Decree no. N. 79/1999, selling electricity produced from renewable energy sources has become easier, with the guarantee of sale to the network. Producers can sell energy in two different ways: 1) through dedicated withdrawal, 2) on the free market. It is also possible to consume the energy produced. Withdrawal involves supplying electricity to the Energy Services Operator (ESO)3, which pays for it. This service from the ESO therefore avoids that producers have to manage the selling of energy, namely placement on the Power Exchange or drawing up of bilateral contracts. Once on the grid, the energy is sold. In particular, the Power Exchange, administered by the Electricity Market Operator (GME) has been operating in Italy since April 2004. Currently, the energy produced by wind turbines connected to the grid, can be stimulated with two alternative support mechanisms: Green Certificates (GC) or the allinclusive rates (TO), the latter only in the case of power plants with less than 200 kW. GCs are negotiable securities, issued on the basis of the amount of electricity produced by the plants. The commercial value of a CV is derived from the Bersani Decree (Legislative Decree no. 79/1999) and subsequent amendments. This framework has imposed on those operators who enter the network or import more than 50 GWh/year, an obligation for a percentage to come from renewable sources. This requirement may be satisfied through the purchase of GCs relative to energy from renewable sources produced by other operators. The unit price of the GC is updated monthly. As an alternative to GCs, the TO, reserved for wind turbines with less than 200 kW of power, are fixed rates of remuneration of electricity fed into the grid. The TO 3

The ESO is a holding company that supports the development of renewable energy sources through the management and delivery of the relevant incentives.


365

remunerate only the electricity fed into the grid, while the GC remunerate all the net energy produced, thus also rewarding any portion that is self-consumed. The GC and TO are recognized for a period of 15 years, with both mechanisms being managed by the ESO. In the case of GC, in addition to the incentive, manufacturers can count on an additional income: the value of electricity produced. Placing the energy produced into the network (for sale on the electricity market, “dedicated withdrawal” or “net metering”) or auto-consumption. On the other hand, the TO are only a source of revenue. In light of the above, for the wind farm assessed, the revenues are derived from: the sale on the energy market; the sale of Green Certificates. To estimate the revenue from the sale of energy, the average price of electricity and GC in the year preceding the assessment were referred to. In 2012, these prices are respectively 75.48 €/MWh and 74.12 €/MWh [45]. The overall manufacturability of annual plants must also be known. To this end, maps of the producibility of electricity supplied taken from the Atlante Eolico Italiano were consulted. The project area has specific values of productivity between 3,000 and 3,500 MWh/MW. For the evaluation of the system being studied, the average value of 3,250 MWh/MW was used. From the calculations, this results in a net annual production for the entire system of 58,630 MWh. Applying the productivity data, the unit value of the two items of revenue provided, it follows that the system can generate the following annual revenue: Annual revenue (from 1 to 15 years) = (75.48 + 74.12) €/MWh × 58,630 MWh = €8,771,048.00 ; Annual turnover (from 16 to 20 years) = 75.48 €/MWh × 58,630 MWh = €4,425,392.40 . It is also worth considering the residual value of the works at the end of 20 years referred to in the evaluation. This residual value is equal to 0-5% of the initial investment [46]. In this case study, it is assumed 2.5% of the initial investment, i.e. €891,750. Cost estimate. This is obtained as the sum of the investment and operating costs. The interest on the debt should also be considered. Investment costs. The total cost of a wind turbine per kW installed varies significantly depending on the country of reference, ranging from 1,000 €/kW to 1,350 €/kW [41]. In Italy, the investment costs are higher than the average of other countries, since most of the plants are installed in hilly or mountainous areas, with sometimes being difficult to access them. For a typical configuration of wind turbine installed on the ground with a total average output of 20 MW at a site of medium complexity, the investment cost ranges from 1,550 €/kW for large systems installed in areas with low complexity, up to a maximum of 2,000 €/kW for small systems installed at sites with a complex orography [40]. Considering an average cost of 1,740 €/kW, the construction of the wind turbine under study requires an investment of € 35,670,000.

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The useful life of a wind turbine system is usually over 20 years [37-47-36-38]. At the end of its useful life, there are two possibilities: 1) dismantling of the site, 2) replacement of the machines installed with new wind turbines. For the second solution, known as “repowering”, the removal of the old machines should be considered. The removal costs of a single wind turbine are between € 20,000 and € 40,000. In case of withdrawal of the investment, the removal costs of the machines must be added the remediation costs of the site. Operating costs. These include personnel costs, maintenance costs and royalties, as detailed in the financial plan. In particular, the maintenance costs are derived from Amicarelli V. and Tresca F.A. [48]. Royalties are paid to the local part of the private company that operates the plant, to the extent of 3.6% of the total revenue per annum. Repayment schedule of the loan. The intention is to take out a loan for the amount of € 21,402,000, equal to 60% of the total investment costs. The remaining 40% is given by private capital. A ten-year amortization schedule at a constant rate is drawn up, with an annual interest rate of 7% currently applied in Italy for funding in the wind sector. The annual interest is included in the financial plan. The financial plan. It is prepared over a 20 year period. The investment costs are assumed to be all concentrated in the 1st year. The evaluation is carried out at constant prices. The cash flows are discounted at the discount rate of 5%, already adjusted for inflation [49] The pre and post-tax results are estimated, taking into account: - the IRES (corporate income tax), calculated ats the rate of 27.5% on profit before taxes - IRAP (Regional Tax on Productive Activities), which in the Campania region is equal to 4.97% of pre-tax gross staff costs and financial charges. The results of the financial plan are in Table 1. The processing of cash flows allows for the evaluation indices, both pretax and post-tax (Table 2). Table 1. Financial Plan. All the amounts are in €uro year

1

2

3

4

5

6

7

INCOME Sale of energy Green Certificates

4,425,392

4,425,392

4,425,392

4,425,392

4,425,392

4,425,392

4,345,656

4,345,656

4,345,656

4,345,656

4,345,656

4,345,656

COSTS Investment Staff Maintenance Royalty

-35,670,000 -255,041

Interest on debt GROSS PROFIT -35,925,041 IRES IRAP

-40,000

-40,000

-40,000

-40,000

-40,000

-40,000

-255,041

-510,081

-510,081

-510,081

-510,081

-510,081

-315,758

-315,758

-315,758

-315,758

-315,758

-315,758

-1,498,140

-1,389,708

-1,273,687

-1,149,543

-1,016,710

-874,578

6,662,110

6,515,501

6,631,523

6,755,666

6,888,500

7,030,631

1,832,080

1,791,763

1,823,669

1,857,808

1,894,337

1,933,424

325,808

318,595

324,303

330,411

336,946

343,939


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Table 1. (continued) NET PROFIT

-35,925,041

Year

8

4,504,222

4,405,144

9

4,483,551

10

4,567,447

11

4,657,216

12

4,753,269

13

14


4,425,392

4,425,392

4,425,392

4,425,392

4,425,392

4,425,392

4,425,392

4,345,656

4,345,656

4,345,656

4,345,656

4,345,656

4,345,656

4,345,656

-40,000

-40,000

COSTS Staff Maintenance Royalty

-40,000

-40,000

-40,000

-40,000

-40,000

-510,081

-510,081

-510,081

-1,020,162

-1,020,162

-315,758

-315,758

-315,758

-315,758

-315,758

-315,758

-315,758

Interest on debt

-722,497

-559,770

-385,653

-199,347

GROSS PROFIT

7,182,712

7,345,439

7,519,556

7,195,781

7,395,128

7,395,128

7,395,128

IRES IRAP

1,975,246

2,019,996

2,067,878

1,978,840

2,033,660

2,033,660

2,033,660

351,421

359,428

367,994

352,064

361,872

361,872

361,872

NET PROFIT

4,856,045

4,966,016

5,083,684

4,864,877

4,999,596

4,999,596

4,999,596

Year

15

16

17

18

-1,020,162 -1,020,162

19

20


4,425,392

4,425,392

4,345,656

4,345,656

4,425,392

4,425,392

4,425,392

4,425,392 891,750

COSTS Staff Maintenance Royalty

-40,000

-40,000

-40,000

-40,000

-40,000

-40,000

-1,020,162

-1,020,162

-1,020,162

-1,020,162

-1,020,162

-1,020,162

-315,758

-315,758

-159,314

-159,314

-159,314

-159,314

GROSS PROFIT

7,395,128

7,395,128

3,205,916

3,205,916

3,205,916

3,205,916

IRES IRAP

2,033,660

2,033,660

881,627

881,627

881,627

881,627

361,872

361,872

155,763

155,763

155,763

155,763

NET PROFIT

4,999,596

4,999,596

2,168,526

2,168,526

2,168,526

2,168,526

Interest on debt

Table 2. Evaluation Indices

NPV IRR Payback period

pre-tax

post-tax

40,690,170 € 17.97% 7 years

16,428,785 € 10.73% 10 years

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4


Real Options and Monte Carlo Simulation for the Case Study

The following real options have been identified: 1. Abandonment Option. Before the execution of the works, this option may be exercised for incorrect predictions about the characteristics of windiness or financial difficulties for the investor. If electricity prices become no longer acceptable, the project is deferred. 2. Deferment Option. If the investor fears a drop in prices of electricity and/or Green Certificates, may defer the investment over time until he gets more information or reassurance. The option can only be implemented prior to the execution of works and often depends on the perspective of regulatory changes. 3. Expansion Option. It expands the investment if the macroeconomic conditions for the wind energy sector improve, or if the legislation introduces more incentives. The option is exercisable after the completion of the works and until the end of the evaluation period (American option). It involves the installation of additional 5 wind turbines of 2.5 MW, with an increase in capacity of 61% and an additional investment cost amounting to € 21,750,000. Having identified the possible real options, the project NPV is assumed as an underlying assets [25-20]. The value of the asset without options has already been estimated with the traditional DCF analysis (Market Asset Disclaimer).

4.1

Uncertainty Estimate

The uncertainty of the market is represented by the volatility of the underlying asset. In this regard, Méndez M., Goyanes A. and Lamothe P. [47] wrote that for the design of a wind farm: «Various alternative solutions are often used to assess volatility: 1) Taking the market return volatility of a similar company; an approximation would thereby be made that might lead to error, since finding a company whose characteristics exactly match those of the project would be no easy task. 2) Using the volatility of those elements that generate the project’s cash flows, such as, for instance, the volatility of electric power prices; however, these elements only partially reflect the project’s uncertainty. 3) We thus turn the market into a complete market, for we assume the project’s market value to be its present value and assess volatility by simulating its expected returns from year 0 to year 1. This allows us to combine all market uncertainties into a single one: the volatility of the project». For the case study, the volatility is estimated based on the NPV. Estimate the volatility of the NPV with risk analysis. Risk analysis is designed to identify adverse events that may affect the feasibility of the project, in order to assess the extent to which uncertainties can affect the NPV of the project. The analysis starts from the identification and characterization of the uncertainties of the project. For the wind farm under investigation, the following uncertainties have been identified.


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1. Uncertainty about the overall annual manufacturability of the plant. In the previous section, a specific average producibility of 3,250 MWh/MW was assumed, which corresponds to the value of 58,630 MWh used in the evaluation. For the Municipality of Vallata, the Atlante Eolico Italiano gives a range of 3,000-3,500 MWh/MW, upon which a triangular probability distribution for the overall manufacturability of the system is based, with minimum and maximum values respectively of 54,120 MWh and 63,140 MWh. 2. Uncertainty in the selling prices of energy. To construct the distribution of the probability of the selling price of electricity, the average monthly real prices in the period 2005-2012 were analysed. There is a minimum price of 54.94 €/MWh and a maximum price of 112.63 €/MWh. It assigns a normal type probability distribution, characterized by: ─ an average of

∑

80.53 €/MWh ;

─ a standard deviation

∑

12.59 €/MWh , defined in the

range from 54.94 €/MWh to 112.63 €/MWh. 3. Uncertainty on the price of Green Certificates. The real average annual prices of GCs in the period 2005-2012 were analysed. The trend line of prices has the equation 6.5378 13,228 . Temporally extending this trend, estimates of 67.77 €/MWh for 2013 and 61.23 €/MWh for 2014 are obtained. Considering the trend in the figure, a triangular type probability distribution is assumed, where: ─ the mean value is of 74.12 €/MWh used in estimating deterministic revenues; ─ the minimum value is 61.23 €/MWh (forecast for 2014); ─ the maximum value is of 81.80 €/MWh at 2011 (the possibility that in the future, there will be higher prices of 74.12 €/MWh, is confirmed by the data of January 2013 which sees a price of 79.52 €/MWh). It is worth noting the probability distributions of the uncertain variables, the risk analysis is implemented with the Monte Carlo simulation method. This method involves extracting a large number of possible scenarios from a multivariate distribution determined by the probable hypotheses on the parameters of the analysis, that then allows for the calculation of statistics on the sample extractions. The Oracle Crystal Ball software is used. For the post-tax NPV, the results are shown in Figure 1. The standard deviation is 5.694.136 €. The volatility σ of the NPV is 31.24%. 4.2

The Value of Real Options

The flexibility of the wind farm project is a function of the real options of deferral, abandonment and expansion. To estimate the value of the options and their interactions, the Fairmat Academic software was used, which implements the Monte Carlo technique for the European option [29] and the least-squares approach for the American approach [50].

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Fig. 1. Probability distribution of the post-tax NPV

The model requires the measurement of the risk-free discount rate, due to it being the rate of return on government bonds in the medium to long term. From the auction of ten-year BTP 30/01/2013, the rate is 4.17%. Table 3 shows the input data for the calculations, which were carried out in relation to two cases: 1. all the real options are exercisable; 2. all the decisions are already taken at time 0 (base case). Table 3. Input data of the analysis model Parameter

Value

Description

NPV

16,428,785 €

σ

31.24 %

NPV without considering the value of the real options Volatility of the NPV

rf

4.17 %

I1

1,783,500 €

S

0

Risk-free discount rate (BTP 10 year) Capital expenditure: for the study of the wind speed profile of the site, the design of systems for the administrative process (building permits, environmental impact assessment, etc.). Between 2 and 5% of the investment costs [38] Recovery value in the abandonment option

e

61%

Rate of expansion capacity

Ie

21,750,000 €

Additional investment costs

The stochastic process that evolves the NPV of the project is characterized by a geometric Brownian motion [34-36-51]. In Fairmat, the interactions between the decisions are described in a window called Option Map. For the mapping of the options, the software allows to select different types of options, which are represented with different coloured diamonds: Pink diamond, decision already made; Green diamond, European option; Blue diamond, American option. For the case study, every kind of option is associated with the corresponding payoffs and the expiration time.


371

The study and design phases are identified with a pink diamond. It is therefore considered a committed option. The expiration time is one year and the payoff is equal to the cost of I1. An operator Or can choose the best among the following options (investment or abandonment option). The investment can be started immediately or deferred for up to two years: it is therefore considered an American style option (blue diamond), that is exercisable at any time until the expiration date. At the same time, it is considered an abandonment option (American put option, blue diamond), exercisable as an alternative investment. In this second case, the payoff coincides with the recovery value, i.e. is null. Finally, it is possible to exercise an expansion option, after the investment. This is an American call option, with a payoff equal to max(eV1–Ie,0). At this point, the Monte Carlo simulation is implemented and the extended NPV calculated as an average over a sample of 5000 paths. It is a NPVextended of € 20,554,931, with a standard error of 342,558 and a standard deviation of 24,222,536. The project is also evaluated in the base case, i.e. without considering the flexibility of the real options. In this case, the operator Or is disabled, without the possibility of abandoning the project, the options become already taken American decisions (committed option). There is an obligation to defer the investment at year 3 and expand the production capacity at year 20. In this case, the NPV is € 15,344,549, lower than the value obtained with the deterministic analysis (€ 16,428,785) since the investment is deferred at year 3. The standard error is 380,166 and the standard deviation of 26,881,803. Comparing the results of the two scenarios, it is clear that the average value of the NPV in the case of the real options is larger than what is obtained in the base case. The difference between the two values is of € 5,210,382. This difference shows that the real options approach allows to exploit the strategic opportunities and operational flexibility of the investment. The higher value is the monetary representation of the options identified through the examination of the dynamic aspects of the proposed wind farm. In addition, comparing the probability distributions of the NPV, it is worth noting that in the case of the real options, the values are always positive, while in the base case without options, it is possible to have negative values among the simulated paths. In fact, management flexibility moves the probability distribution of the NPV towards positive values.

5

Conclusions

Traditional DCF analysis shows the limits in all the cases in which the possibility of management to vary the course of an investment as a result of changes occurred in the economic context is marked. This happens in a sector characterized by strong dynamism, and thus uncertain financial viewpoints, such as that of renewable energy. In such situations, it is appropriate to carry out the economic evaluation of projects by defining a logical-operational process in order to understand the different effects of

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possible scenario evolutions. Improvement of the results is due to the implementation of analysis tools such as those described in this work. The reference is to the theory of real options, applicable today in a rather expeditious way with the software available, and the Monte Carlo simulation method, which makes it possible to trace a large number of development paths of the project. The different operational phases of the model used for the optimization of the scenario analyses require a careful selection of the data sources. Only the rigorous processing of numerical information allows for the correct characterization and quantification of the parameters that determine the extent of the extended NPV of the project. This returns the value of the positive potential that can result from management flexibility and innovation. In implementing a wind farm project, the economic evaluation shows great validity, allowing to express a value investment with real options that 34% higher than the value of the same project in the base case , i.e. in the case in which all decisions are taken at time zero.

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