# Risk Assessment of Large-Scale Infrastructure Projects--Assumptions and Context
## 3 Results  
The performance of the quantitative analysis can be demonstrated on one of the projects of the tested set. The D10 Prague-Kosmonosy project, with a total investment cost of CZK 9,272,678,497 ($361,367,050), was used as an example. Simulation results when the beta-PERT probability distribution of total investment costs and the normal probability distribution for time savings of the infrastructure users were chosen, are shown in Table 8 and Figure 1. The simulated quantity dependent variable was cost-effectiveness (BCR).  
\begin{table}
\begin{tabular}{c c c c} \hline
**Variable/Switching Value** & **0 \(\leq\) PH \textless{} 10\%** & **10\% \(\leq\) PH \textless{} 30\%** & **PH \(\geq\) 30\%** \\ \hline Total investment costs & 3 & 3 & 13 \\ Time savings of users & 2 & 3 & 14 \\ \hline \end{tabular}
\end{table}
Table 7: Switching values of project efficiency.  
The resulting probability distribution for the random BCR variable of the project D10 Prague-Kosmonos is shown in the following chart.  
It is evident from the probability distribution shown in Figures 1 and 2 that with a certain probability the random BCR variable will take values below the critical value, and the project will therefore be economically inefficient.  
Table 10 shows the outputs of the quantitative analysis of all the researched projects for both variants of the considered probability distribution of the investment costs critical variable. The table for each project presented the following statistical characteristics indicators: BCR: mean, median, standard deviation (\(\sigma\)), and certainty level (CL).  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \multirow{2}{*}{**No.**} & \multirow{2}{*}{**BCR**} & \multicolumn{6}{c}{**Variant 1**} & \multicolumn{6}{c}{**Variant 2**} \\ \cline{2-10}  & & **Mean** & **Median** & \(\sigma\) & **CL** & **Mean** & **Median** & \(\sigma\) & **CL** \\  
The outputs of all projects showed a normal distribution of the BCR indicator. The research in [11] came to the same results, where an experiment which was identified as a pseudo-random number sequence as normally distributed was carried out.  
In the interpretation of results it is necessary to respect certain limits connected with the elaborated analysis. As mentioned above, in this paper is presented the case study elaborated using projects being prepared for realization in the Czech Republic. Even if the original methodical steps used in this paper are generally accepted and used, it is necessary to respect certain national specificities in the evaluation of public investment projects. The next limit, which it is necessary to consider, is the definition of probability distributions for the simulation. In the presented analysis it was for the random variable \"investment costs\", and the triangle and beta-PERT probability distributions were alternatively used, which is in harmony with the present state in the references, and opinions of other experts. However, it is not possible to exclude that the real probability distribution of investment costs of partial projects will be different. However, for the correct evaluation, and the identification of the influence of the selected probability distribution on the results of the evaluated projects it was necessary to uniformly use the chosen probability distributions. In a similar limitation, it is necessary to also note the probability distributions of the random variable \"time savings of infrastructure users\". In this case it was uniformly selected for both variants of the simulation normal probability distribution, even if the real probability distribution of this variable can be, for partial projects, slightly different.