# Risk Assessment of Large-Scale Infrastructure Projects--Assumptions and Context
## 2 Materials and Methods
### Methods
#### 2.2.2 Sensitivity Analysis  
The outputs of the sensitivity analysis (elasticity coefficients and switching values of economic efficiency indicators) were investigated for individual projects in the following phase of the research in order to determine project resilience to changes in variables potentially affected by risks. The elasticity coefficients were determined both for investment costs and for all relevant socio-economic benefits, which as a total amount, form the income part of the economic CF (following the R1 risk). It can be seen from the data in Table 6 that variables such as accident rate, externalities, and/or total operating costs generally have low elasticity coefficients, and are not in most cases identified as critical variables. Investment costs and the time savings of infrastructure users already showed that they very often become critical variables (EC > 1). For this reason, occurrences of switching values (i.e., ENPV = 0), which show the influence of these critical variables, were investigated in the following phase of the research. Outputs were divided into the interval of changes up to 10%, up to 30%, and over 30%. It can be clearly seen from Table 7 that the projects showed a relatively high efficiency robustness; about 70% of projects met a limit of efficiency when changing one of these critical variables up to 30%. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Variable** & **0 \(\leq\) EC \textless{} 0.5** & **0.5 \(\leq\) EC \textless{} 1** & **1 \(\leq\) EC \textless{} 1.5** & **EC \(\geq\) 1.5** \\ \hline Total investment costs & 5 & 4 & 4 & 5 \\ Vehicle operating costs & 16 & 1 & 1 & 0 \\ User time costs & 1 & 7 & 5 & 5 \\ Accident rate & 13 & 3 & 0 & 2 \\ Other externalities & 13 & 2 & 0 & 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Frequency of elasticity coefficient (EC) values. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Risk No.** & **VH and H** & **M** & **Total** & **Dependent Variable** \\ \hline R1 & 3 & 5 & 8 & Revenues alias operating phase savings \\ R2 & 5 & 8 & 12 & Investment costs, beginning of the construction \\ R3 & 4 & 6 & 10 & Investment costs \\ R4 & 0 & 5 & 5 & Beginning of the construction \\ R5 & 0 & 9 & 9 & Beginning of the construction \\ R6 & 0 & 2 & 2 & Investment costs \\ R7 & 12 & 2 & 14 & Beginning of the construction \\ R8 & 8 & 5 & 13 & Investment costs \\ R9 & 0 & 1 & 1 & Investment costs, extension of construction, delay/shortening of the operational phase for evaluation \\ R10 & 0 & 1 & 1 & Investment costs, extension of construction, delay/shortening of the operational phase for evaluation \\ R11 & 0 & 2 & 2 & Investment costs, extension of construction, delay/shortening of the operational phase for evaluation \\ R12 & 0 & 0 & 0 & Operating costs, reduction of benefits under “Infrastructure \\ R13 & 0 & 0 & 0 & Changes in benefits under “Externalities” item \\ R14 & 0 & 0 & 0 & Influence on the beginning of construction \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Risk frequency according to their significance, including the dependent variable identification. The outputs of the sensitivity analysis and qualitative risk analysis showed that the total investment costs and time savings of transport infrastructure users represented fundamental risk variables that affected the efficiency of the investment projects. For this reason, these independent variables were tested by subsequent quantitative analysis, which was carried out by the Monte Carlo method, using Crystal Ball software [15]. In the case of the quantitative analysis, a relative index BCR was chosen, because it allows comparing the efficiency of projects of different sizes (investment demanding), and it shows the benefit of one invested currency unit. The utilization of the BCR index as one of the criterial indicators for the evaluation of the economic efficiency of public projects is methodically described in references [6,7].