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ISSN : 1598-7248 (Print)
ISSN : 2234-6473 (Online)
Industrial Engineering & Management Systems Vol.17 No.4 pp.769-782
DOI : https://doi.org/10.7232/iems.2018.17.4.769

# Investment Decision Making under Uncertainty Using Real Options Approach: A Case Study in Solar Power Plants of Iran

Department of Industrial Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran
Department of Industrial Engineering, Karaj Branch, Islamic Azad University, Karaj, Iran
September 30, 2017 April 19, 2018 November 22, 2018

## ABSTRACT

Nowadays, classic Discounted Cash Flow (DCF) approach is mostly used in order to evaluate various types of projects. Since projects in all around the world are confronting with different barriers, such as high risk, various kinds of uncertainty, the aforesaid classic approach cannot correctly determine the value of projects. Therefore, proposing practical and efficient approaches in evaluation of project in uncertain environment has drawn the attention of researchers in recent years. In this study, an efficient approach for valuing of solar photovoltaic power plants in Iran with real options is proposed and compared with the classic DCF approach. In order to evaluate the assumed real options, the binomial tree method is implemented. Eventually, Taguchi design experiment is used to analyze the performance of binomial tree and figure out how real options parameters effect on the value of project. The obtained results show that considering abovementioned real options increases the value of project comparing to the case with no real options (i.e. DCF approach). Moreover, the ranking of effective factors, participations percentage of each factors on response variable, and optimal combination of them are determined.

## 1. INTRODUCTION

Valuation is a tool for assessment; while assessment is a part of decision-making. Decision making in engineering projects is a challenging and important problem. Since, Projects relevant to the industry of energy, such as establishing power plants are faced with many uncertainties. Accordingly, they play a key role in the decision making of investors. Investors of such projects are always looking forward to figuring out whether that projects are justifiable or not; they also seek to determine how they can deal with uncertainties or even use their potential positive effect for projects. Governments encourage investing in establishing renewable power plants (such as photovoltaic and wind power plants) due to slightly pollution and environment issues. However, the investment in such power plants is faced with many uncertainties, which would create many difficulties for investors. According to this, this paper provides a better insight for investors where technological risks, price in the market, and rate of returns are considered to be uncertain. In other words, it determines the attractiveness or lack of attractiveness of projects to help them for investment.

Increasing population growth, climate change, and globalization are among the most important reasons that lie behind the increasing consumption of energy in all around the world. Renewable energies are among the best solution for dealing with the abovementioned problem, however, the high initial investment is the biggest barrier for development of this renewable energy sources (RES). To decide whether invest in these renewable energy sources (RES) or not, investors look for rational and reliable guarantees (Fernandes et al., 2011). Since the success rate of organizations directly depends on planned projects for future, such decisions seem to so much important (Remer and Nieto, 1995b). This decision is also important for the investors of the renewable energy industry. Governments encourage investing in establishing environmental friendly power plants (such photovoltaic and wind power plants). However, the investment in such an industry is faced with many uncertainties, which would create many difficulties for investors. According to this, an efficient decision making tool is required to help investors in such challenging problems. The valuation of projects is among the main decision making tools for such environments.

The projects valuation approaches are investment decision making tools which are mostly called project selection methods in the relevant literature (Verbeeten, 2006). Although researchers have proposed many different types of approaches for valuation of projects, but no one can claim that the obtained results by these approaches are 100% reliable; in fact, those approaches are preferable that provides more precise results (i.e. with less error). Approaches of valuation of projects can be categorized into two main categories; classic DCF, and real options approaches.

Classic DCF approach is recognized as the most popular approach in evaluation of projects. The obtained result by this approach consists of different financial indices, such as Net Present Value (NPV), Interest rate of Return (IRR), Payback Period (PP), and so on. While DCF approach is not able to suitably evaluate projects, researchers proposed another kind of approach which takes into account the real options (Fanipakdel et al., 2012). In DCF approach, it is assumed that all of required data are deterministic (i.e. the existing uncertainty on real world-problems are neglected). On the contrary, real options approach can successfully takes into account the existing uncertainty in the real world problem. Given that there are many factors in the project evaluation relevant to the renewable Energy source’s problems, DCF approach seems not to be an appropriate approach for valuation of projects in comparison to the real options one. Moreover, in contrast to DCF approach which merely provides two options for investors (i.e. continuing or stopping a project), real options approach considers options value and management flexibility to choose an appropriate option or combine multiple options with each other in order to provides a maximum project value result (Saeedi, 2013).

Considering the importance of renewable power plants in all around the world with respect to environmental issues, development of such power plants (e.g. solar power plants) is so much important for governments. Consequently, valuation of such projects is important too. Given that real options approach outperforms the classic DCF approach in valuation of projects in uncertain environments, we want to implement real options approach for valuation of solar power plants of Iran. To best of our knowledge, most of researchers used this approach for wind or hydropower plants, and they did not apply this approach for other types of power plants, such as solar, biomass power plants, and so on. In this paper, we are looking forward to figure out the benefits of real options approach over the DCF one in the case of project valuation of solar power plants.Since Iran has great resources in supplying solar energy, we want to implement this efficient approach for valuation of solar photovoltaic power plants in Iran. Furthermore, Taguchi design experiment will be implemented to evaluate the performance of binomial tree method.

The remainder of this paper is as follows; after a comprehensive literature review in Section 2, basic principal and concepts of real options approach are reviewed in Section 3. In Section 4, both DCF and real options approaches are compared with each other; eventually, conclusion is proposed in Section 5.

## 2. LITERATURE REVIEW

From 1970s, energy sector has changed due to significant technology development and modifications in the condition of market. Therefore, the classic approaches of project valuation were not able to predict the value of projects precisely. In fact, sector has modified from its stable and exclusive condition into changing and competitive condition. Thus, the real options approach recognized as one of the practical tools in valuations of projects in this sector (Awerbuch et al., 1996).

For the first time, Venetsanos et al. (2002) used real options approach in project valuation of wind power plants. Since they considered the existing uncertainty in supplying wind energy in their investigations, they could not use classic DCF approach instead of real options one. Comparing the obtained results showed that both approaches provides completely different results. While the real options approach indicated that the value of intended project is positive, classic DCF approach indicated that the NPV is negative. Davis and Owens (2003) studied the application of real options approach in Research and Development (R&D) investments. They valuated the R&D projects of renewable Electricity (non-hydro) of united states federal. They also proposed a model to determine the optimal level of annual costs of R&D projects of renewable united states federal. Yu et al. (2006) applied real options approach in valuation of policymaking for renewable energy industry in Spain. They used this approach to evaluate switching tariff for different wind generation assets, and determine the policy for energy market of Spain.

Kjaerland (2007) implemented real options approach to identify and evaluate the hydro-power investment opportunities in Norway. They also studied the relationship between the price of electricity and decision time on optimal investment in hydro-power sector. Siddiqui et al. (2007) evaluated the R&D projects of renewable energy of US federal. They used binomial tree method and showed the efficiency of this method. Bøckman et al. (2008) used real options approach for valuation of small hydro-power projects in Norway which are subject to various types of uncertainties. They reached to this conclusion that there is a unique price limit for starting such projects. Munoz et al. (2009) proposed a model to evaluate investment on wind power plants. for this purpose, they used the defer and abandon options, also applied their model to several case studies. Martínez-Ceseña et al. (2011) showed that planned projects with real options approach have higher expected value in comparison to the planned projects with other approach. They also implemented the advanced options methodology for the projects of generation of renewable electricity.

Given that wind energy is considered to be highly uncertain, Lee (2011) studied the application of real options approach in wind power plants of Taiwan. The obtained results of their study showed that real options approach provides efficient results for such uncertain environments. Regarding to risk, flexibility, and carbon emission rate of projects of clean development mechanisms, Kokkaew and Sampim (2014) implemented real options approach and risk theory to evaluate these projects in terms of economic. Santos et al. (2014) studied and compared the classic DCF and real options approaches with each other in hydropower plants. They considered the option to defer the investment, and showed that this option increases the value of intended projects. Kim et al. (2014) applied real options approach to evaluate the R&D investment on wind power plants of South Korea. They showed that implementing the real options approach increases the value of such projects in comparison to the classic DCF approach. Zhang et al. (2014) studied the application of real options approach in valuation of policy making for solar energy in China. They reviewed policy making from point if views of government and investors. Jeon et al. (2015) proposed a methodology for optimization of economic subsidies and R&D investments on technology of renewable energies, simultaneously. To forecast the required subsidy for photovoltaic systems, they implemented real options approach in a real case study of South Korea.

Sisodia et al. (2016) applied real options approach in policy making of wind energy in Spain. They also applied Monte Carlo Simulation and PDE methods, and considered the project value to be uncertain. Kim et al. (2017) studied the application of real options approach in decision making about investment in new energies. Using this approach in hydropower power plants in Indonesia, they showed that real options approach would help developed countries to use renewable energies. Kozlova (2017) reviewed the application of this approach used in previous investigation. They mentioned that many developed countries have used the real options approach. Based on Kozlova (2017), most previous investigations have studied this approach merely for wind energy and bioenergy. Thus, studying the application of this approach for other types of renewable energies seems to be interesting.

### 2.1. Valuation of Projects in Energy Sector of Iran

Fanipakdel et al. (2012) used real option approach for valuation of mineral projects. They compared Monte Carlo Simulation and Least Square Method (LSM)in their investigation. The obtained results showed that the LSM outperformed the Monte Carlo Simulation. Khalili Araghi et al. (2014) applied real options approach in valuation of development of South Pars Gas field in Iran. They showed that real options approach increased the value of such projects (i.e. projects with high risk) comparing to the classic DCF approach.

In light of above-provided literature review, it is clear that real options approach is efficient in valuation of projects of renewable energies. Furthermore, this approach is efficient to deal with uncertainty and high risk of investment on renewable energies. It is clear that most of researchers used this approach for wind energy and bioenergy, and they did not apply this approach for other types of renewable energies, especially photovoltaic energies.

On the other hand, this approach is rarely used for investment on renewable energies in under-developed countries (such as Iran). Therefore, we think analyzing the performance of this approach for renewable energies in such countries is worthwhile.

## 3. BASIC CONCEPTS AND PRINCIPALS OF REAL OPTIONS APPROACH

Option is the right of buying (Call) or selling (Put) an asset under certain circumstances; it does not bring any commitment for the investors (Black and Sholes, 1973). Predetermined price of option is called exercise price, and predetermined time of option is called time to maturity. When investors have the right to apply the option any time before the maturity date, it is called American options; but when investors have the right to apply the option merely at the maturity date, it is called European options (Johnsen, 2014).

Real options approach, which considers various options for investors in valuation of projects, is originated form pricing theory (Fernandes et al., 2011). This approach covers the disadvantageous of classic DCF approach such that it can consider the existing uncertainty in real world problems. Real options approach can be divided into six following categories according to the condition of markets:

• - The option to defer: This option lets investors to postpone the investment to a time later. It means that investors with such option can invest at the present time or wait to gather more information about their investment.

• - The option to abandon: In the case with downward slopping in the market, investors with this option can stop all of the current operations, and sell some of their capital equipment in order to acquire liquidity.

• - The option to switch (input, output, and process): If price depends on the demand in the market, management can make a trade-off by integration of outputs (flexibility in production); consequently, identical values of output can be acquired by different values of input (flexibility in process). In fact, management can exchange two different operations with each other.

• - Expansion option: When condition of market is better than what investors expect, this option lets them to develop their investment.

• - Contraction option: When condition of market is worse than what investors expect, this option brings an opportunity for them to miniaturize their investment.

• - Growth option: This option lets investors the permission of early investment.

Since the options to abandon, switch, and contraction option have been founded based on selling the current investment, they are called as the sell options; on the other hand, the rest of options are called the call options (Lee, 2011;Knudsen and Scandizzo, 2011).

### 3.1. Financial and Real Options Theory

Given that real options approach is originated form the financial options approach, basis of this approach is developed according to pricing of financial options approach which was developed by Black and Scholes (1973). Table 1 shows the similarity between both approaches.

It is worth mentioning that financial options are derived contractions of stock market which enter to stock market in order to decrease the risk of investment (Fanipakdel et al., 2012). Value of each option depends on the stock price of underlying assets (S), exercise price of option (K), risk-free rate (rf), volatility (σ), and maturity date of option (T).

### 3.2. Models of Valuation with Real Options Approach

Kulatilaka and Amram (1999) divided the valuation models with real options approach into 3 sub-categories: 1- Dynamic programming including decision tree and binomial tree methods, 2-Partial differential equations (including Black & Sholes model), and 3- Simulation.

All of abovementioned approaches have different input values, and are suitable for different situations. Dynamic programming approach brings the opportunity of seeing values and intermediate decisions for investors. This approach provides worthwhile information relevant to the option and engaging with complex structures (Fernandes et al., 2011). As a part of dynamic programming approach in valuations of projects with real options, binomial tree is a backward induction method which is suitable for both American and European options, and has high flexibility (Khalili Araghi et al., 2014). It should be noted that this approach was first proposed by Cox et al. (1979).

As another part of dynamic programming approach in valuations of projects with real options, decision tree method is mostly used for graphical representation of events. This method provides a possibilistic path for the events that can happen. partial differential equations including Black & Sholes formula is used to calculate a value of an option when the stock price is constant changing with continuum possible future values. The formula depends on the price of underlying stock, its volatility, the exercise price, time maturity of the option and risk-free rate (Johnsen, 2014). In simulation approach, many random and possible paths from the current time up to the last time allowed for final decision making of an option will be generated; afterward, values of payment will be calculated for each generated path in order to determine the optimal path.General simulation method which is used for real options approach, called Monte Carlo simulation.

### 3.3. Real Options Approach and Uncertainty

In real options approach, higher uncertainty in investment leads to higher value of real option (Huchzermeier and Loch, 2001).

To be more precise, resulting value of flexibility has direct relationship with the uncertainty of variables of the project value function. Although in classic DCF approach, the mentioned relationship is not considered. In DCF approach, high uncertainty is interpreted as high risk in project which decreases the NPV of them. While in the real options approach, high uncertainty is interpreted as increment in domain of optimistic section of risk’s probability distribution (Fanipakdel et al., 2012).

### 3.4. Applications of Real Options Approach

Lander and Pinches (1998) identified and introduced the application of real options approach in real world problems as 16 following areas: 1. Natural resources, 2. Competitive business, 3. Production, 4. R&D, 5. Inventory, 6- Interest rate, 7. Public goods, 8. Mergers and acquisitions, 9. Labor, 10. Environment development, 11. Corporate behavior, 12. Venture capital, 13. Advertisement, 14. Hysteretic effect, 15. Environmental protection, and 16. Legal.

## 4. CASE STUDY : VALUATION OF THE SOLARPHOTOVOLTAIC POWER PLANT

Given that Iran has been located on the solar belt, it has great resources in supplying solar energy. In this country, average radiation in a year is equal to 4.5 up to 5.5 Kwh/m2 (300 hours of radiation in a year) which covers about two third of all country. According to initial feasibility studies, Iran is capable of installation of 120 thousand megawatts solar energy. Until 2013, about 254 megawatts renewable power plants were founded in this country that merely 38 megawatts of mentioned number were related to solar power plants (Data information center of Iran’s power industry organization, 2015).

As one of the biggest cities of this country, Khorasan is a potential region for foundation of solar power plants due to its geographical conditions. With 313 sunny days in a year, this city has about 1742 hours of radiation (in average) in a year (Adeli et al., 2014). In this paper, we study one of the biggest photovoltaic power plants which is located in this city. The intended power plant is a 250 kilowatts capacity. Since power department of this city is looking forward to develop these kinds of project in near future, we will compare the valuation of this by both mentioned approaches (i.e. classic DCF and real options approaches) in the rest of this paper.

To implement both mentioned approaches, some input parameters relevant to this power plant are required. Table 2 provides the specifications of intended power plant and all other assumptions for this problem.

This power plant has two types of costs (i.e. initial investment costs, and production costs) which are defined as follows:

• - Initial investment costs: This type of costs includes the largest part of whole costs for running a power plant; initial investment costs include purchasing, installation and initiation of photovoltaic systems. Since this power plant is connected to the central distribution network of Khorasan, costs of connection have been added to the initial investment costs.

The initial investment costs for this power plant has been summarized in Table 3.

• - Production costs: As another major costs of each power plant, production costs consist of costs of maintenance and switching equipment over the useful life of power plant. We have set maintenance costs equal to 1.2% of initial investment for each year. By considering that the useful life of photovoltaic panels are more than 20 years, and the useful life of inventors are 12 years, we have set the production costs equal to the purchasing costs of inventors for one time.

On the other hand, revenue from the sales can be called the only source of income for such a power plant. According to official tariff ministry of power (Iranian guaranteed purchase rate of electricity generated in renewable power plant, 2015), price of each Kwh electricity for solar power plants with capacity of 10 megawatts or less is equal to 6750 Rials(IRR). In the case that the power plant is connected to the central distribution network, 148 Rials(IRR) will be added to the aforesaid price.

### 4.1. The Classic DCF Approach

Based on abovementioned information, valuation of this power plant has been done by means of different classic DCF approaches in the first step, such as NPV, Interest Rate of return (IRR), and Payback Period (PP) (Oskounejad, 2008); then, the obtained results of all indices of economic analysis have been provided in Table 4. It should be noted that all indices of economic analysis in this paper has been calculated by COMFAR III software.

As shown in Table 4, all three mentioned approaches (i.e. NPV, IRR, and PP) have accepted this power plant as a profitable project; but comparing the values of initial investment costs (i.e. 25,56 Billion Rials) with NPV (i.e. 11,81 Billion Rials) shows the low attractiveness of this project for investors.

As previous investigations indicated, real options approach shows the real value of a project in comparison to the classic DCF approach. Therefore, we want to compare these two approaches for the valuation of discussed power plants in the rest of paper.

### 4.2. The Real Options Approach

Generally, real options approach can be called as the expanded form of the classic DCF approach. In fact, expanded NPV consists of two parts: NPV of total cash flow (i.e. value of the static NPV), and value of options; therefore, we can formulate the real options approach as follows:(1)

(1)

The difference between expand and static NPV determines the value of real options. As stated in previous section, there are two forms of options (i.e. American and European options) which require numerical methods to be calculated. The binomial tree is one the widely used methods in valuation of options. Due to its simplicity, and backward induction, binomial tree methods lets investors to decide when to use or not use the available options. In contrast to the proposed model by Black and Scholes (1973), binomial tree method can divide the accessible time to maturity date into discrete sub-periods. These subperiods are shown by Δt and value of options will be determined for each of these sub-periods. In binomial tree methods, each node shows the value of underlying asset in that sub-period. If the value of underlying asset starts form S at the first moment, it can increase to uS or decrease to dS at the last moment. Values of u and d are calculated according to Eqs. (2) and (3), respectively (Hull, 2006):

$u = e σ Δ t$
(2)

$u = e σ Δ t$
(3)

where, σ refers to the volatility of the value of underlying asset. Figure 1 shows a binomial tree for the underlying asset.

When the value of underlying asset (S), exercise price (K), and u and d are known, valuation of projects in forward induction form will be possible. But for the backward induction, determination of the value of the last node is required which is explained in the following.

In the first step, the values of call and put options are calculated as Eqs. (4) and (5), respectively (Hull, 2006).

(4)

(5)

In the return path (from right to left), the value of each node increases with a risk-free rate probability of p ; or it decreases with probability of q (where q=1−p). Eqs. (6) and (7) determines the value of p and q. It is worth mentioning that the value of risk-free rate is considered to be less than u3 and more than d (i.e. d < rf < u3).

$p = ( e r f . Δ t − d ) / ( u − d )$
(6)

$q = 1 − ( e r f . Δ t − d ) / ( u − d )$
(7)

Eventually, value of each node in return path is calculated as Eq. (8) Noted that the value of first node shows the project value with the option(Hull, 2006).

$f = e − r f . Δ t ( p f u + ( 1 − p ) ) f d$
(8)

Given that we are studying a solar photovoltaic power plant with a large initial investment in this study, considering some options, such as stopping or contraction of this power plant for less activation is not reasonable. Based on our correspondence with the experts of renewable Energy Organization of Iran, we reached to this point that the option to defer for such a project is much more reasonable. It means that investors can defer investment when the NPVstatic value is less than the option value, or they can invest when the NPVstatic value is more than the value of option; consequently, we have considered two types of this option named technology learning curve, and structure of internal market in this study for the valuation of intended solar power plant. It is worth mentioning that we have assumed that both abovementioned options are American one.

#### 4.2.1. The Option To defer – Technology Learning Curve

The first option that we want to study in this paper is the technology learning curve option. Since learning is the product of the experience, increment of experience leads to decrement in costs of technology exponentially. Unit cost of technology is determined based on the division of the currency by the installed capacity of power plant (Kwh). Technology learning curve is calculated based on Progress Ratio (PR) which refers reduced cost per unit installed for each doubling of global cumulative capacity, given as percentage of the initial investment cost. Learning Rate (LR) also refers to the percentage of cost reduction in the same doubling period, and is calculated based on PR (Winkler et al., 2009). Unit cost of technology, PR, and LR are calculated according to Eqs. (9), (10), and (11), respectively (Nemet, 2006).

$C t = C 0 ( q t q 0 ) − b$
(9)

$P R = 2 − b$
(10)

$L R = 1 − P R$
(11)

where Ct, qt, and b refer to unit cost of technology (currency/ kilowatt), cumulative amount of installed capacity, and exponent defining the slope of the power function.

Rubin et al. (2015) claimed that LR for photovoltaic power plants in all around the world is at least equal to 10% and at most equal to 47%. Furthermore, Sharifi et al. (2009) showed that LR for photovoltaic power plants in Iran is equal to 20% (consequently, PR = 80%).

In project valuation with real options, it is really complicate to estimate the volatility parameter of project value. One reason that lies behind this difficulty is relevant to lack of historical data for underlying asset. Given that there was no photovoltaic power plant in Iran previously, valuation of such projects is to complex. Therefore, we have implemented the proposed method by Kimiagari and Nasiri (2012) to determine the volatility parameters.

Probability Index (PI) of a project is calculated based on the division of the present value of future cash flows by required investment cost. When PI value is larger than 1, it means that the intended project is acceptable in terms of PI. Standard deviation of LN(PI) function shows the volatility of parameters of project.

In the next step, Profitability Index (PI) is calculated based on Eq. (12).

(12)

where LRC refers to the least required investment cost which is equal to intial investment cost for the intended project.

Altogether, we have considered a triangular distribution function on initial investment (as the input of simulation including three values for the LR where the first, second and third values show the probability of pessimistic, probable, and optimistic conditions, respectively (Forbes et al., 2011).Therefore, the required triangular distribution function is equal to (10%, 20%, 47%) and the outputs of simulation are NPV and LN(PI), as mentioned before standard deviation of LN(PI) shows the volatility of the project.

And finally, volatility for the technology learning curve option is determined by Monte Carlo Simulation. In order to increase accuracy, we have set the number of iterations equal to 50000 times in this study. It is noteworthy that we have performed all simulation in the Crystal ball software.

#### 4.2.2. The Option to Defer – Structure of Internal Market

The second option that we want to study in this paper is the structure of internal market option. In the other words, we want to figure out how usage of domestic equipment effect on the value of photovoltaic power plant. Although, the internal market does not play an important role in supplying the required equipment for such power plants in Iran, but is hoped that the role of internal market becomes more highlighted in near future.

According to our correspondence with experts of New Energy Organization of Iran, we reached to this conclusion that evaluation and prediction of the future condition of internal market in Iran is too much complex. As like as technology learning curve option, we have considered a triangulardistribution function consisting of three values for the price of photovoltaic system installation per each Kwh; where the first, second and third values show the probability of pessimistic, probable, and optimistic conditions, respectively (Forbes et al., 2009).Based on the prediction of experts of New Energy Organization in Iran, the required triangular distribution function for the price of PV system installation for each kwh in the upcoming 5 years is set equal to (22000000 Rials, 48000000 Rials, 52000000 Rials).

And finally, volatility for the structure of internal market option is determined by Monte Carlo Simulation. In order to increase accuracy, we have set the number of iterations equal to 50000 times for this option too.

### 4.3. Computational Results

In this sub-section, value of discussed project is calculated for both defined options, and has been compared with the obtained value by classic DCF approach in Section 4.1.

Monte Carlo Simulation has shown that volatility of intended power plant in the learning curve technology option, is equal to 31%. The required parameters for binomial tree in “The option to defer – technology learning curve” has been set according to the provided values in Table 5 and used in the rest of paper.

The obtained binomial tree for the technology learning curve option has been illustrated in Figure 2.

As shown in Figure 2, the total NPVexpanded value of this project is equal to 24,6479 Rials. As noted, subtraction of NPVexpanded and NPVStatic shows the value of options. Therefore, value of considered real option (i.e. technology learning curve) is equal to 12,83 (Value of real options = 26,6479 −11,81) . Since value of considered real option is greater than the NPVStatic, it is preferable to defer the project to 4 years later. It is clear that the value of this project is higher in the real option approach comparing to the classic DCF approach.

For the structure on internal market option, the obtained binomial tree has been shown in Figure 3.Monte Carlo Simulation has shown that volatility of intended power plant in structure of internal market option is equal to 18%.

As shown in Figure 3, the total NPVExpanded value of this project is equal to 26,4453 Rials. As noted, subtraction of NPVexpanded and NPVStatic shows the value of option. Therefore, value of considered real option (i.e. structure of internal market) is equal to 14,63 (Value of real options = 26,4453−11,81) . Since value of considered real option is greater than the NPVstatic , it is preferable to defer the project to 5 years later. It is clear that the value of this project is higher in the real option approach comparing to the classic DCF approach.

### 4.4. Performance Analysis of Binomial Tree with Taguchi Experiments Design

To enhance the performance of binomial tree method, we are looking forward to apply the Taguchi design of experiments, which optimizes and finds the best possible values of input factors of problems. For this purpose, we take the following steps; it should be noted that we have used Minitab 16 to implement the mentioned Taguchi design of experiments.

Step 1: In order to optimize the performance of binomial tree method’s performance, we have to determine the response variables and effective factors at first. In this specific problem, we have only one response variable which is the value of project by applying option; remained time to maturity date, volatility of project, and risk-free rate are also considered as controllable factors, within a framework of the binomial tree.

Step 2: Considering the type of problem, we have defined three levels for all three recognized controllable factors which tries to exploit all possible conditions for these factors. Values of these factors are provided in Table 6.

Since the market of our problem is an oligopoly, and there is no chance for competitive activities, the defined levels are confined and compatible to economy and photovoltaic of Iran. Regarding the first factor, first and second options’ time to maturity are four and five years, respectively; therefore, we investigate the trend of the binomial tree by considering levels of time be equal to 3, 4, and five years. These periods are selected on Iran’s renewable energy organization scheme basis. The volatility derived from first and second options were respectively 31% and 18%. We assume these two rates as two levels and select 25% as the middle level in order to determine the impact of increasing volatility on the binomial tree as well as the most effective option. Turning to free risk rate, first 17% was considered for both options. Since the government has planned to decrease the interest rate to 15%, we seek to show that decreasing this rate throughout time impacts the difference between applied discount rate in traditional method and risk-free rate in binomial tree; therefore, we introduce three levels (i.e., 15%, 16%, and 17%) for this method.

Step 3: Since greater values of response values is preferable (i.e. values of project has to be maximized), we have selected “larger the better” experiments. We performed all 9 designed experiments by Minitab 16, and entered their corresponding response value in Minitab 16 (as shown in Figure 4). It is worth mentioning that we have assumed that there is no interaction between mentioned factors.

#### 4.4.1. Analysis of Results

To prove that abovementioned factors are important, and how much they effect on the response variable, we have performed an Analysis of Variance (ANOVA). The obtained results of ANOVA have been provided in Table 7.

Hypotheses testing is defined as follows:

• H0: Selected factors are ineffective on the response variables

• H1: Selected factors are effective on the response variables

Since the reliability is considered to be 95% (confidence interval equal to 0.05%), and by considering that ANOVA statistic of each selected factor is higher than basic test statistic (, v1, v2 = F0.05, 1, = 8.51 ), it can be declared that the suitable factors are selected and examined. In addition, the P-value for each factor is lower than 0.05, which implies the authenticity of what is mentioned.

Adjusted R2 is equal to 99.94%. In other words, of 100 percent response variable, 99.94% is explained by the factors. This approves the desirability of the condition.

Table 7 shows that all aforesaid factors are important; moreover, value of R2 also shows that the response variable is described almost entirely by considered factors.

Given the conducted Taguchi design experiment is based on “larger the better”, larger mean value of factors shows the greater impact of them on response variable. Since Figure 5 shows the mean effects of factors on response variable, the factors with steeper slop have higher impact on response variable.

As shows in Figure 5, response variable will be optimal where the first, second, and third factors are at third, third, and first levels. In fact, the value of project will be optimal when these factors are adjusted in the way previously mentioned. Given that we have performed an incomplete Taguchi design of experiments, a confirmation experiments for validation of optimal results is required. Therefore, we have calculated the Confidence Interval (CI) for this problem based on Eq. (13) (Arash et al., 2009):

$C I = F α . v 1 . v 2 × V e N / ( 1 + p )$
(13)

where p, N, and Ve refer to the freedom degree, number of all experiments, and variance of error, respectively. Thus, CI will be equal to 0.135 ($18.51 × 0.0022 2.25$). Considering the estimated mean value of response variable at the optimal level factors is equal to 26.5995, the optimal range of response variable is equal to (26,4645, 26,7345). To prove that the obtained results by Taguchi design experiments are reliable, we have to calculate the value of mentioned project by binomial three method when the factors are set at their optimal level. Forasmuch as the binomial three method has indicated that the value of mentioned project is equal to 26,56484 (which is between the estimation interval), we can conclude that the obtained results by Taguchi design experiments are reliable.

Table 8 also shows how we have determined the most and least effective factors. According to Table 8, remained time to maturity date is the most effective factors (with 93% share), and risk-free rate and volatility are placed in the second and third positions, respectively. where S is “sum of square”, and P is “participation” (Mirvar, 2012).

## 5. CONCLUSION

The classic DCF approach was not efficient in the valuation of projects with high uncertainty and high economic risk. The classic approaches do not consider the cash flow changes based on the market changes or the sensitivity of investors. Since such changes are common and important, thus, the classic approaches are in short supply of beneficial information about the projects condition. To resolve such problems, the real options approach has been proposed that could provide more precise information for the decision-makers, and let them make a practical decision. Nowadays, investors usually use this approach in uncertain environments such as energy environment. Meanwhile, using the real options approach in renewable energy industry would be efficient due to high economic risk and uncertainty.

Using solar energy (especially establishing photovoltaic power plants) is growing in Iran. As stated, the real options approach would be better for these kind of power plants rather than the classic approach. To show this, we have evaluated a 250 kilowatts photovoltaic power plant using the classic DCF and real options approaches in this study. First, the project has been evaluated using the classic DCF approach. The results showed that the project is economic (11.81 billion Rials). However, the net present value of this project was small compared to the initial investment (25.56 billion Rials) and made the project less interesting for investors. Second, the same project has been evaluated using the real options approach. Noted that we applied two options to defer (i.e., technology learning curve and structure of internal market); then, the Monte Carlo simulation showed that the volatility of power plants is equal to 0.31 and 0.18 regarding each of options, respectively. Finally, the value of this project was assessed using binomial tree method. The results showed that the project value is equal to 24.64 and 26.44 billion Rials with respect to the first and second options, respectively. It is evident that implementing each of two mentioned options in the real options approach has significantly increased the project value compared to the classic approach. To be more precise, using the first and second options increased the project value 12.86 and 14.63 billion Rials, respectively. Therefore, the real options approach outperforms the classic DCF approach.

Then, the Taguchi Design Method was applied to analyze the results provided by binomial tree method and figure out the effective factors on the value of options. Based on the obtained results of Taguchi design experiments, it became clear that the value of project will be optimal when t, σ , and rf were adjusted at third, third, and first levels, respectively. By means of CI, we proved that the optimal result by Taguchi design experiments are reliable. Furthermore, while was RSq(adj) equal to 99.94%, we showed that the recognized factors describe almost entirely the response variable. Eventually, we showed that the remained time to maturity date with 93% share is the most effective factor.

Future studies should take in to consideration additional uncertain variables, such as supply, demand levels, in order to show the superiority of real options approach comparing to the classic DCF. Given that our analysis has limitation that Iran’s electricity pricing is regulated, thus it would be worthwhile to extend this research by consideration of free market pricing mechanism.

## Figure

A general illustration for the paths of binomial tree method (Mun, 2002).

Evolution of the underlying asset and the project value of defer in the case of technology learning curve option.

Evolution of the underlying asset and the project value of defer in the case structure of internal market option.

Orthogonal design of Taguchi experiments (L9).

Mean effects of factors on response variable.

## Table

Similarity between real and financial options approaches (Santos et al., 2014;Dixit and Pindyck, 1994)

The specifications of intended power plant and all other assumptions

The initial investment costs for the intended photovoltaic solar power plant

The obtained results of all indices of economic analysis for classic DCF approach

The required parameters for Binomial tree method in the case of technology learning curve

Values of controllable factors in different levels

The obtained results of ANOVA

Values of effectiveness of each factor

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