# Evaluating the Effect of Financing Costs on PV Grid Parity by Applying a Probabilistic Methodology
## 2 Materials and Methods
### Economic Parameters Used in the Study
#### 2.3.2 Capital Recovery Factor  
In Equation (4), the simple Capital Recovery Factor calculation [33] is defined, which is a dimensionless parameter:  
\[\alpha=\frac{r}{1-\left(1+r\right)^{-L}} \tag{4}\]  
where \(r\) is the interest rate (percentage) and \(L\) is the lifetime of the system (years).  
Obtaining a loan can be quite complicated in some countries like Spain (with relatively high interest rates of \(\sim\)10%) [32]. Due to the financial issues encountered in Spain and the retroactive changes in the PV law over the past few years, the average interest rate rose to 10%. In this paper, the likely interest rates are considered at 6%. However, this figure is considered a variable parameter.  
Figure 1: Probability density function (PDF) of the annual yield used in the Monte Carlo probabilistic method.  
The interest rate is driven by a triangular PDF [18], with 4% being the lowest value and 12% the highest value. The mean would be 6% [4], where most of the loan cases provided by the banks are likely going to be. All this data has been extracted from online loan comparison research. The floor established is stated at 4% in the research, and it is very difficult to see values below this number. The maximum values have been established at 12% as values above that number are considered nonattractive (negative IRRs). Establishing the mean at 6%, the shape of the triangular PDF looks scalene, giving more cases above 4% than below [32]. For IRR calculation purposes, we consider the 12-year loan as standard.  
In Figure 2, we can see the triangular PDF of the interest rate.  
Table 1 shows the capital recovery factor values calculated, manually, using Equation (4) for various interest rates. The lifetime of the system is 25 years.  
The value of the Capital Recovery Factor varies depending on the interest rate (\(r\)). The latter applies to the three cases studied, as the PDF of the financial cases are the same regardless of the system power and the energy production.  
Applying the Monte Carlo method and using the triangular PDF of the interest rate (Figure 2), we obtained the histogram corresponding to the recovery factor shown in Figure 3. We calculated 10,000 iterations.  
\begin{table}
\begin{tabular}{c c c c c c} \hline Interest rate (\%) & 12 & 10 & 8 & 6 & 4 \\ \hline Recovery factor (\(\alpha\)) & 0.1275 & 0.1102 & 0.0937 & 0.0782 & 0.0640 \\ \hline \end{tabular}
\end{table}
Table 1: Capital Recovery Factor calculation.  
Figure 3: Histogram of the annual recovery factor used in the Monte Carlo method.  
Figure 2: Probability density function (PDF) of the interest rate used in the Monte Carlo method.  
A summary of the PDFs of all the variables described previously is shown in Table 2.  
Because the model used in this work is based on the FiT, the lifetime of the project was assumed to be 25 years, as this also coincides with the modules' 25-year warranties.  
Table 3 presents the initial investments required in construction of a 6 kWp PV system (5 kW nominal power), considering all system losses.