**2. Materials and Methods**

In this study we concentrated on the wind speed distribution in the Golan heights area, using the information available from the meteorological service of the Israel Ministry of Transport [31], gathered by the Merom Golan meteorological station, one of the 84 Israeli meteorological facilities, which is situated at the relevant area [32], for the year 2014. The file used includes 52,066 data points gathered during the specified period. This includes sample values of the wind speed, one observation for every 10 min or 144 values per day (except for some non-significant missing values) [33]. We describe the data analytically using the Weibull probability density function (PDF). This is commonly accepted as the most appropriate function describing the wind speed statistical frequencies at a given location in most world locations. These data are essential for the planning of the wind turbine optimal choice [7].

The Weibull PDF is determined, in addition to a random variable X, representing here the wind speed, by two parameters, which are location dependent. They are a shape parameter k (dimensionless) and a scale parameter λ (m/s for the wind speed), which, together, determine the following PDF form:

$$f(\mathbf{x}; \lambda, k) = \begin{cases} \frac{k}{\lambda} \left(\frac{\mathbf{x}}{\lambda}\right)^{k-1} e^{-\left(\frac{\mathbf{x}}{\lambda}\right)^{k}}, & \mathbf{x} \ge \mathbf{0} \\ \mathbf{0}, & \mathbf{x} = \mathbf{0} \end{cases}$$

Both PDF parameters are important for choosing the best location for the appropriate wind turbine, which imply the wind farm's economic value [34].

The wind velocity determines the electric power output. We will evaluate the power output based on wind statistics and turbine characteristics in the results section. As the electric power is sold to the users, the remaining question in evaluating the value of the installation is how much money the user will pay for their power consumption, in other words, "what is the market value of the power?", which reflects on the economic value of the installation. In the following, we describe the methods used for such evaluation.

While the generic discounted cash flow (DCF) approach using the net present value (NPV) criterion is generally adopted to evaluate investments, the DCF method is inappropriate for a rapidly changing investment situation (Dixit and Pindyck [20]; Herath and Park [21]; Lee and Shih [11]) and does not consider managerial flexibility in investment decisions (Hayes and Abernathy [23]; Hayes and Garvin [24]; Trigeorgis and Mason [25]; Trigeorgis [26]). In the current study, we consider a two-stage approach—one turbine at the 1st stage and a field of 50 at the 2nd stage; along with the possibility to withdraw at the 2nd stage. Hence, the scenario is a one in which managerial flexibility can be practiced.

Currently, the real option analysis method is widely applied in many studies for the valuation of renewable energy investment projects, for example Lee and Shih [11] and Kumbaro ˘glu, Madlener, and Demirel [27]. See also Boomsma, Meade, and Fleten [28] and Menegaki [29]. We thus apply in this paper the real options analysis method for the evaluation of the economic value of wind energy turbines in a specific location. In particular, we analyze the value of the investment opportunities that add value to the investment due to managerial flexibility (in the case of energy market price drop, one may abandon the investment). It is worth mentioning that the option valuation method has become more sophisticated by using approaches such as the binomial lattice, the mean reverting jump-diffusion method, and stochastic volatility model. It is also used for other types of hazards such as technological risks (Deng [30], Menegaki [29], Siddiqui, Marnay, and Wiser [31]), which may include a change in the wind regime, in our case, or power output reduction of the turbine. See also Davis and Owens [32] and Baringo and Conejo [33].

However, we decided to adopt the basic Black–Scholes equation of a financial market [35] because we were focused on the underestimated value of the option to abort the investment in an environment where it is not possible to foresee the standard deviation using numerical tools.

In this study, we analyzed the possibility of installing additional turbines in the Asanyia mountain in the Golan Heights in order to extract profit from wind-generated power. We have partly based our study on the known results of wind turbine construction and use in Israel [36], while part of the numbers presented here are rather rough estimates. The decision to construct a field, which is a collection of many turbines, can be divided into two stages: in the 1st stage we build one unit. After building and operating this single unit for few years and gaining confidence in the technical and financial output, the 2nd stage, regarding the decision of building the entire turbine field, is made, based on electricity price at this stage as well as the future predicted energy evaluation.

We evaluate the uncertainty over future electricity market price as an economic value of an underlying asset of a real option using the Black–Scholes equation [35]:

$$\mathcal{C} = \mathcal{S}\_0 \ N(d\_1) - \mathcal{K}e^{-rT}N(d\_2)$$

where

$$\begin{aligned} d\_1 &= \frac{\ln(\mathcal{S}\_0/K) + \left(r + \sigma^2/2\right)T}{\sigma\sqrt{T}}, \\ d\_2 &= \frac{\ln(\mathcal{S}\_0/K) + \left(r - \sigma^2/2\right)T}{\sigma\sqrt{T}} = d\_1 - \sigma\sqrt{T}. \end{aligned}$$

We use the following notations: *C* is the call option value, *S*<sup>0</sup> is the market price of the underlying asset, *K* is the exercise price, *r* is the annual risk-free return, *T* is the duration of the period (the number of years) till exercising the real option (constructing the entire turbine field), and *σ* is the annualized standard deviation (StD) of the return of the underlying asset. *N* is the symbol of the Gaussian cumulative probability density function (CDF).
