# A Comprehensive Methodology for Investment Project Assessment Based on Monte Carlo Simulation
## 3 Application of the Methodology on a Virtual Investment Project
### Simulation of NPV by Monte Carlo Method  
Distribution functions express the stochastic nature of the input variables. They can be defined based on data obtained from their registration for a certain period. In this case, there must be a sufficient number of data for the FIT function to be used. In the case of our investment project, the distribution function was chosen by estimation according to the stochastic behavior of the variables. The distribution functions, as they are defined, are presented in Table 5. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Input Variables**} & \multirow{2}{*}{**Unit**} & \multicolumn{4}{c}{**Value**} \\ \cline{3-5}  & & **A** & **B** & **C** \\ \hline \multirow{2}{*}{Planned production} & t/year & 850 & 130 & 140 \\  & h/t & 6.0 & 7.6 & 7.5 \\ \multirow{2}{*}{Average production time} & EUR/t & 1300 & 1600 & 1800 \\  & Variable costs & EUR/t & 370 & 550 & 650 \\ \multirow{2}{*}{Nominal time of the line} & h/year & & 8760 & \\  & & h/year & & 460 & \\ \multirow{2}{*}{Loss times (repairs, cleaning, and others)} & h/year & & & \\  & & h/year & & 7300 & \\ \multirow{2}{*}{Operating time of the line} & h/year & & & \\ \multirow{2}{*}{Number of shifts} & day & & & \\ \multirow{2}{*}{The length of a shift} & h/shift & & & \\ \multirow{2}{*}{Fixed costs personal (\%= annual} & EUR/year & & 120,000 \\  & & & & \\ \multirow{2}{*}{Fixed costs other (\%= from investment costs)} & EUR/year & & 43,896 \\ \multirow{2}{*}{Income tax} & \% & & 21 \\  & Discount rate & \% & 3.5 \\ \multirow{2}{*}{Investment costs} & EUR & & 1,463,190 \\ \multirow{2}{*}{**NPV**} & **EUR** & & **3,778,179** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Input variables and NPV calculation. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{4}{c}{**Forecast Accuracy**} \\ \cline{2-4}  & **A** & **B** & **C** \\ \hline MAPE & \(1.59\%\) & 4.15\% & 19.06\% \\ RMSE & \(1.97\) & 0.54 & 3.4 \\ MAD & \(1.24\) & 0.44 & 2.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Accuracy of demand forecasts. By assigning distribution functions to the stochastic variables and running the simulation, 10,000 attempts were made to calculate the NPV. The result is a forecast of the NPV financial indicator, including its statistical profile. The results of the simulation are presented in the form of a histogram (Figure 5) or in tabular form. These are mainly the statistical characteristics of the simulated variable. The simulation found that for the preliminary production plan, the mean NPV is EUR 3,761,324, and the standard deviation (\(\sigma\)) is EUR 123,008. One indicator of the level of risk is precisely the standard deviation, which indicates the reliability of the forecast. In practice, the predicted NPV is within 68% confidence in the interval of the mean NPV \(\pm\)\(\sigma\). One of the risk analysis methods is a sensitivity analysis. The diagram in Figure 6 shows the seven most serious input stochastic transformations, which contribute the most to the overall uncertainty of the NPV forecast. If the column is to the right of the y-axis, it is a revenue item, if it is to the left, it is a cost item. Figure 5: Histogram NPV—forecast by Monte Carlo simulation.