Risk Assessment of Large-Scale Infrastructure Projects—Assumptions and Context

Jana Korytárová; Vít Hromádka

doi:10.3390/app11010109

Risk Assessment of Large-Scale Infrastructure Projects—Assumptions and Context

Korytárová, Jana;Hromádka, Vít 2020-12-24 00:00:00 applied sciences Article Risk Assessment of Large-Scale Infrastructure Projects—Assumptions and Context Jana Korytárová * and Vít Hromádka Faculty of Civil Engineering, Brno University of Technology, 60200 Brno, Czech Republic; hromadka.v@fce.vutbr.cz * Correspondence: korytarova.j@fce.vutbr.cz; Tel.: +420-733-164-369 Featured Application: The results of the presented research extend the methodology of economic analysis and risk assessment of large infrastructure projects. Abstract: This article deals with the partial outputs of large-scale infrastructure project risk assess- ment, speciﬁcally in the ﬁeld of road and motorway construction. The Department of Transport spends a large amount of funds on project preparation and implementation, which however, must be allocated effectively, and with knowledge of the risks that may accompany them. Therefore, documentation for decision-making on project ﬁnancing also includes their analysis. This article monitors the frequency of occurrence of individual risk factors within the qualitative risk analysis, with the support of the national risk register, and identiﬁes dependent variables that represent part of the economic cash ﬂows for determining project economic efﬁciency. At the same time, it compares these dependent variables identiﬁed by sensitivity analysis with critical variables, followed by testing the interaction of the critical variables’ effect on the project efﬁciency using the Monte Carlo method. A partial section of the research was focused on the analysis of the probability distribution of input variables, especially “the investment costs” and “time savings of infrastructure users” variables. The research ﬁndings conclude that it is necessary to pay attention to the setting of statistical characteris- tics of variables entering the economic efﬁciency indicator calculations, as the decision of whether or not to accept projects for funding is based on them. Citation: Korytárová, J.; Hromádka, Keywords: CBA; investment project; probability distribution; sensitivity analyses; risk assessment V. Risk Assessment of Large-Scale Infrastructure Projects—Assumptions and Context. Appl. Sci. 2021, 11, 109. https://dx.doi.org/10.3390/app1101 0109 1. Introduction Transport infrastructure projects are important carriers and supporters of economic Received: 1 December 2020 growth for national economies. Implementation of investment projects, in addition to the Accepted: 22 December 2020 direct beneﬁts for which they are implemented, brings growth potential for the national Published: 24 December 2020 economy; they reduce unemployment, increase the sales of design and implementation companies, and thus create revenue capacity on the demand side for purchases of goods Publisher’s Note: MDPI stays neu- and services. Implementation of investment projects will also be a key factor in alleviating tral with regard to jurisdictional claims the current COVID-19 pandemic effect in all national economies; e.g., the draft of the state in published maps and institutional budget of the Czech Republic brings record investments for the future, which have been afﬁliations. increased by CZK 178 billion for 2021 ( 6.7 billion). Even so, the supply of funds for project implementation is limited. Therefore, it is always necessary to choose for ﬁnancing only those projects that are efﬁcient. The efﬁciency of projects to be implemented is assessed in Copyright: © 2020 by the authors. Li- the ex-ante period, on the basis of feasibility study data, which is addressed in the form of censee MDPI, Basel, Switzerland. This a cost–beneﬁt analysis (CBA). article is an open access article distributed The authors of this article have been carrying out research into development in eco- under the terms and conditions of the nomic efﬁciency assessment of public transport infrastructure projects for a long time. In Creative Commons Attribution (CC BY) the present article they focused on the analysis of the economic outputs of road infras- license (https://creativecommons.org/ tructure projects, motorways, and class I roads via CBA. CBA has the largest explanatory licenses/by/4.0/). Appl. Sci. 2021, 11, 109. https://dx.doi.org/10.3390/app11010109 https://www.mdpi.com/journal/applsci Appl. Sci. 2021, 11, 109 2 of 12 power [1–4], which is based on the determination of cost-effectiveness against the total societal beneﬁts. Generally, four criteria are solved and monetized in large-scale transport infrastructure project appraisals: travel time savings, travel and operational costs, safety, and environmental cost, from different perspectives. In ref. [5] based on the modeling of economic cash ﬂows determined by these variables, the following economic efﬁciency indicators were established: economic net present value (ENPV), economic internal rate of return (ERR), and beneﬁt cost ratio (BCR) [6,7]. The values of the economic indicators were tested for critical variables and the switching values of indicators (threshold value of the indicator in terms of efﬁciency, e.g., ENPV = 0, ERR = discount rate) were deter- mined. In the following step, a quantitative risk analysis using the Monte Carlo method was performed for the identiﬁed critical variables. At the same time, a qualitative risk analysis, which considered potential risk factors using a risk register [7], was performed. It monitored the project risk impact, the occurrence probability, and deduced the risk relevance for the implementation and operation of the project. Individual projects that demonstrated a positive evaluation from all perspectives examined are ready for funding, and further phases of their life cycle can be launched for them. The research question addressed by the implemented research team was which variables are risky, how strong is their inﬂuence on economic efﬁciency, and whether and how the projects are resilient; robust to the potential risk interaction. This concerns questions of the connection of the qualitative and quantitative risk analysis, which dependant variables are resulting from the qualitative analysis, and if they are also considered in the quantitative analysis. In the case of the important critical variable it was the objective to test the changes of the efﬁciency of projects while using different probability distributions. Investors aim, not only to prevent project failure, but also to select the best alternatives among the available investment projects, so as to gain more beneﬁts and achieve better results [8]. In the investment decision-making process of large-scale projects, many risk factors can cause decision failure [9]. This is also why decision-support systems are of high importance for investors in the construction industry [10]. 2. Materials and Methods The aim of the research described in this paper was to ﬁnd the relations between the outputs of the qualitative risk analysis, sensitivity analysis, and quantitative risk analysis, which were performed in the evaluation of the economic efﬁciency of transport infrastructure projects, as part of the modeling of economic Cash Flow (CF) of their life cycle. For the case study, a set of projects being prepared for realization in the Czech Republic was chosen. The authors of the paper have many years of experiences in the evaluation of projects in Czech transport infrastructure, and during these years they were able to collect a large amount of input data. However, the authors would like to emphasize that for the presented procedures, and partly also for the results, it is possible, respecting individual speciﬁcs of economic evaluation in other countries, to relate them to projects carried out abroad. The research sample consisted of 20 large-scale transport infrastructure projects from the Czech Republic, which were the pre-investment phase in the 2018–2020 period, and with proven economic efﬁciency. Only those projects that could be compared with each other due to the fact that they were processed according to the same methodological procedure, e.g., according to the Departmental Methodology valid since 2017 [7], were included in the research sample. Net cash ﬂow (NCF) for the calculation of economic ratios consisted of the savings in the costs of the suggested (investment) variant related to the zero variant (without investment). The calculation formula consists of four types of particular beneﬁts; socio- economic savings. They are savings in travel and operating costs, savings in travel time costs, reduction in accident costs, and savings in exogenous costs. The time value of money determining the amount of the discount rate for the calculation of the ENPV indicator was set at 5% for the Czech Republic in the EU programming period 2014–2020. Appl. Sci. 2021, 11, 109 3 of 12 The research presented in this article examined project risk frequency, and the impact on their economic efﬁciency and robustness of economic efﬁciency indicators, using sen- sitivity analysis, and ﬁnally involved conﬁrmation or refusing the robustness of projects according to the previous step by determining the cumulative probability of achieving project economic efﬁciency using the Monte Carlo method. To assess the real risk of failure associated with the investment, changes in the values of economic performance indicators deriving from the simultaneous change of several project variables had to be identiﬁed [11]. As stated by [12], one of the risk assessment tools is the Monte Carlo method, which combines and develops both sensitivity analysis, and scenario analysis, methods. In the resource material, Ref. [13] focused on the Monte Carlo method used in the case of the earned value management methodology. Bowers also provided a broader view of the issue of project risk assessment [14]. 2.1. Data Table 1 presents the research sample projects with their basic characteristics. It states the undiscounted economic investment costs (i.e., investment costs excluding VAT reduced by a conversion coefﬁcient 0.807), economic internal rate of return (ERR), economic net present value (ENPV), and cost beneﬁt ratio (BCR), which was calculated according to the following relation: B ENPV = 1 + (1) C IC where: BCR: Cost Beneﬁt Ratio ENPV: Economic Net Present Value IC: Discounted Investment Costs Table 1. Basic economic data on research sample projects. IC ERR ENPV No. Name of the Project BCR % P1 Vestec connection 73,655,517 13.15% 134,141,506 2.90 P2 I/22 Draženov-Horažd’ovice 253,477,033 5.67% 25,929,610 1.11 P3 I/27 Kaznejov, bypass 91,192,128 9.50% 74,002,422 1.83 I/13 Ostrov-Smilov, P4 141,082,434 5.88% 19,811,383 1.15 right bank I/13 Ostrov-Smilov, P5 116,820,770 7.52% 50,193,343 2.01 left bank P6 I/26 Horšovský Týn 50,375,269 5.60% 4,578,849 1.09 P7 D0 Brezin ˇ eves-Satali ˇ ce var. 1 371,886,072 39.45% 2,576,573,157 8.28 P8 D0 Brezin ˇ eves-Satali ˇ ce var. 2 434,933,917 30.46% 2,395,820,591 6.92 P9 D0 Brezin ˇ eves-Satali ˇ ce var. 3 757,919,450 17.89% 1,934,644,942 3.81 P10 I11– Hradec Králové, tangent 111,776,135 17.24% 336,621,090 4.15 P11 I/18 Pr ˇíbram-bypass var. 1 28,417,453 14.20% 54,410,634 2.96 P12 I/18 Pr ˇíbram-bypass var. 2 49,497,029 13.21% 74,973,161 2.61 P13 I/50 Bucovice ˇ 78,579,450 7.56% 32,937,152 1.44 P14 I/36 Trnová-Fablovka-Dubina 53,652,370 19.20% 190,286,624 4.73 P15 I/11 Nové Sedlice-Opava Komárov 91,436,523 5.52% 7,834,232 1.09 P16 I/26 Holysov, bypass 56,624,471 9.19% 42,452,457 1.80 P17 D10 Praha-Kosmonosy 361,367,050 5.72% 35,994,616 1.11 P18 I/67 Bohumín-Karviná 83,937,876 5.33% 4,067,671 1.05 P19 D43 Boritov-Star ˇ é Mesto ˇ 56,624,471 9.19% 42,452,457 1.80 P20 D27 Preštice-Klatovy ˇ 128,638,259 5.12% 22,333,326 1.02 Source: Feasibility Studies of Investment projects, The State Fund for Transport Infrastructure SFDI, authors’ own processing. Appl. Sci. 2021, 11, 109 4 of 12 Qualitative risk analysis is generally based on expert opinions on the risks that threaten a particular investment project. Lists of risks are usually created, based on the knowledge of the issues addressed, which contain risks that are relevant and common for the given type of projects. A risk register was created in the Czech Republic for the purposes of risk assessment of the road infrastructure projects speciﬁed above [7]. The list of risks according to the risk register is given in Table 2. Table 2. Risk register according to the Departmental Methodology of the Czech Republic. No. Risk Description Demand-related risks R1 Different development of demand than expected Risks related to the project design R2 Inadequate surveys and inquiries in the given locality R3 Inadequate estimates of project work costs Administrative and public procurement risks R4 Delays in awarding R5 Building permit Risks related to the land purchase R6 Land price R7 Delays in land purchase Risks related to construction R8 Exceeding investment costs R9 Floods, landslides, etc. R10 Archaeological ﬁndings R11 Risks related to the contractor (bankruptcy, lack of resources) Operational risks R12 Higher maintenance costs than expected Regulatory risks R13 Environmental requirement change Other risks R14 Public opposition Source: Departmental methodology of the Ministry of Transport [7]. 2.2. Methods The methodological procedure was based on collection, analysis, and examination of relevant data concerning the economic efﬁciency assessment of individual investment projects. The outputs were aimed at answering research questions concerning the intercon- nectedness of individual analyses of future project uncertainties. 2.2.1. Qualitative Analysis The signiﬁcance of project risks (R) was divided into four categories: very high (VH), high (H), medium (M), and low (L). This was determined on the basis of the product of the project risk impact intensity (I) and its occurrence probability (p), with a ﬁve-interval scale of both variables, according to the following relation: R = I p (2) Appl. Sci. 2021, 11, 109 5 of 12 The probability (value) and the impact intensity had the determined ranges presented in following Tables 3 and 4. Table 3. Scale of risk occurrence probability (p). Classiﬁcation Verbal Description Percentage Expression A Very improbable 0–9% B Improbable 10–32% C Neutral 33–65% D Probable 66–89% E Very probable 90–100% Source: Departmental methodology of the Ministry of Transport [7]. Table 4. Scale for risk impact intensity (I). Category Name Verbal Description I Imperceptible no signiﬁcant effect on expected social beneﬁts of the project long-term project beneﬁts are not affected but corrective II Mild measures are needed loss of expected social beneﬁts of the project, mostly ﬁnancial III Medium loss and in medium- and long-term time horizon, corrective measures may solve the problem large loss of expected social beneﬁts of the project, occurrence of adverse effects causes a loss of the IV Critical project’s primary function; corrective measures, even if taken on a large scale, are not sufﬁcient to prevent major losses signiﬁcant to complete loss of function of the project, project V Catastrophic objectives cannot be achieved even in the long term Source: Departmental methodology of the Ministry of Transport [7]. Table 5 shows the occurrence frequency of very high, high, and medium risks in the researched sample of projects, according to the risk register (see Table 1). In addition to the risk frequency, the table also shows the dependent variable, which enters the economic CF of the projects as a basis for the calculation of economic efﬁciency indicators. It is clear from the overview given in Table 5 that the most signiﬁcant risks for transport infrastructure projects identiﬁed in the pre-investment phase lie in the estimation of future demand for new infrastructure use (R1), design and preparatory work (R2), (R3), delays in obtaining construction permits (R5), land purchase (R7), and excess of project costs (R8). The R1 risk is related to the demand, which affects the income part of the projects in the operational phase of their life cycle by a possible reduction in their expected socio-economic beneﬁts. The inﬂuence of other risks has a direct impact on investment costs, which thus become a signiﬁcant variable in the economic assessment. Appl. Sci. 2021, 11, 109 6 of 12 Table 5. Risk frequency according to their signiﬁcance, including the dependent variable identiﬁcation. VH and H M Risk No. Total Dependent Variable Risks Risk 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 Investment costs, extension of construction, delay/shortening of the R9 0 1 1 operational phase for evaluation Investment costs, extension of construction, delay/shortening of the R10 0 1 1 operational phase for evaluation Investment costs, extension of construction, delay/shortening of the R11 0 2 2 operational phase for evaluation Operating costs, reduction of beneﬁts under “Infrastructure R12 0 0 0 operating costs” item R13 0 0 0 Changes in beneﬁts under “Externalities” item R14 0 0 0 Inﬂuence on the beginning of construction Source: Feasibility Studies of Investment projects, SFDI, authors’ own processing. 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%. Table 6. Frequency of elasticity coefﬁcient (EC) values. Variable 0 EC < 0.5 0.5 EC < 1 1 EC < 1.5 EC 1.5 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 Appl. Sci. 2021, 11, 109 7 of 12 Table 7. Switching values of project efﬁciency. Variable/Switching Value 0 PH < 10% 10% PH < 30% PH 30% Total investment costs 3 3 13 Time savings of users 2 3 14 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]. The authors focused on comparing two assumptions of the probability distribution of the investment costs critical variable. The simulations were therefore performed in two variants, in the ﬁrst variant the beta- PERT probability distribution was chosen for the investment costs, in the second variant a triangular asymmetric probability distribution was used. In order to be able to correctly compare the impact of the use of partial probability distributions of investment costs on the overall project results, an equally normal distribution was used for the second critical variable “time savings of infrastructure users” for both simulation variants. The parameters of the probability distribution of investment costs in the case of the beta-PERT probability distribution assumption were therefore chosen as follows: Minimum project value reduced by 10%, Most likely project value, Maximum project value increased by 50%. The parameters of the probability distribution of investment costs in the case of the asymmetric triangular probability distribution assumption were, in accordance with the recommendations arising from the background source [9], set with parameters comparable with the beta-PERT probability distribution, i.e., as follows: Minimum project value reduced by 10%, Most likely project value, Maximum project value increased by 50%. Probability distribution for the time savings of infrastructure users was chosen as a normal probability distribution, where the mean value corresponded to the project value of time savings and standard deviation 10%. 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). Appl. Sci. 2021, 11, x FOR PEER REVIEW 8 of 12 Appl. Sci. 2021, 11, 109 8 of 12 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). Table 8. Results of the simulation of a random cost-effectiveness variable. Investment costs beta-PERT probability distribution. Table 8. Results of the simulation of a random cost‐effectiveness variable. Investment costs beta‐ PERT probability distribution. Statistics Forecast Values Statistics Forecast Values Trials 10,000 Base Case 1.112 Trials 10,000 Mean 1.045 Base Case 1.112 Median 1.047 Mean 1.045 Standard Deviation 0.047 Median 1.047 Variance 0.002 Standard Deviation 0.047 Coeff. of Variation 0.0449 Variance 0.002 Minimum 0.876 Coeff. of Variation 0.0449 Maximum 1.194 Minimum 0.876 Range Width 0.318 Maximum 1.194 Range Width 0.318 The resulting probability distribution for the random BCR variable is shown in the The resulting probability distribution for the random BCR variable is shown in the following chart. following chart. Figure 1. Probability distribution for a random cost benefit ratio (BCR) variable. Investment costs Figure 1. Probability distribution for a random cost beneﬁt ratio (BCR) variable. Investment costs beta‐PERT probability distribution. beta-PERT probability distribution. Simulation results, when an asymmetric triangular probability distribution for total Simulation results, when an asymmetric triangular probability distribution for total investment costs and a normal probability distribution for time savings of the infrastruc‐ investment costs and a normal probability distribution for time savings of the infrastructure ture users were chosen, are shown in Table 9 and Figure 2. The simulated quantity de‐ users were chosen, are shown in Table 9 and Figure 2. The simulated quantity dependent pendent variable was cost‐effectiveness (BCR). variable was cost-effectiveness (BCR). Table 9. Results of the simulation of a random cost‐effectiveness variable. Investment costs: asym‐ Table 9. Results of the simulation of a random cost-effectiveness variable. Investment costs: asym- metric triangular probability distribution. metric triangular probability distribution. Statistics Forecast Values Trials 10,000 Statistics Forecast Values Base Case 1.112 Trials 10,000 Mean 0.978 Base Case 1.112 Median 0.980 Mean 0.978 Standard Deviation 0.060 Median 0.980 Variance 0.004 Standard Deviation 0.060 Coeff. of Variation 0.004 Variance 0.004 Coeff. of Variation 0.004 Minimum 0.747 Maximum 1.146 Range Width 0.400 Appl. Sci. 2021, 11, x FOR PEER REVIEW 9 of 12 Appl. Sci. 2021, 11, 109 9 of 12 Minimum 0.747 Maximum 1.146 Range Width 0.400 The resulting probability distribution for the random BCR variable of the project D10 The resulting probability distribution for the random BCR variable of the project D10 Prague-Kosmonosy is shown in the following chart. Prague‐Kosmonosy is shown in the following chart. Figure 2. Probability distribution for a random BCR variable. Investment costs: asymmetric trian‐ Figure 2. Probability distribution for a random BCR variable. Investment costs: asymmetric triangu- gular probability distribution. lar probability distribution. It is evident from the probability distribution shown in Figures 1 and 2 that with a It is evident from the probability distribution shown in Figures 1 and 2 that with a certain certainpr prob obability abilitythe therandom randomBCR BCRvariable variablewill willtake takevalues valuesb below elow the thecritical criticalvalue, value,and and the project will therefore be economically inefficient. the project will therefore be economically inefﬁcient. Table 10 shows the outputs of the quantitative analysis of all the researched projects Table 10 shows the outputs of the quantitative analysis of all the researched projects for for both both variants variants of of the the consider consider ed edpr proba obability bilitydistribution distributionof ofthe theinvestment investmentcosts costscritical critical variable. variable. The The ta table ble for for eaeach ch project project pres prente esented d thet fol helo following wing statistic statistical al charact characteristics eristics indi‐ indicators: BCR: mean, median, standard deviation (s), and certainty level (CL). cators: BCR: mean, median, standard deviation (σ), and certainty level (CL). Table 10. Statistic characteristics of project BCR values. Table 10. Statistic characteristics of project BCR values. Variant 1 Variant 2 Variant 1 Variant 2 No. BCR No. BCR Mean Median σ CL Mean Median σ CL Mean Median s CL Mean Median s CL P1 2.90 2.73 2.73 0.15 100 2.57 2.57 0.17 100 P1 2.90 2.73 2.73 0.15 100 2.57 2.57 0.17 100 P2 1.11 1.00 0.97 0.06 47 0.94 0.94 0.06 18 P2 1.11 1.00 0.97 0.06 47 0.94 0.94 0.06 18 P3 1.83 1.50 4.51 0.07 100 1.43 1.44 0.10 100 P3 1.83 1.50 4.51 0.07 100 1.43 1.44 0.10 100 P4 1.15 1.09 1.09 0.05 96 1.02 1.02 0.06 64 P4 1.15 1.09 1.09 0.05 96 1.02 1.02 0.06 64 P5 1.43 1.35 1.35 0.06 100 1.28 1.28 0.06 100 P5 1.43 1.35 1.35 0.06 100 1.28 1.28 0.06 100 P6 P6 1.09 1.09 1.03 1.03 1.03 1.03 0.07 0.07 66 66 0. 0.97 97 0.0.97 97 0. 0.08 08 37 37 P7 8.28 8.19 8.19 0.13 100 8.12 8.12 0.14 100 P7 8.28 8.19 8.19 0.13 100 8.12 8.12 0.14 100 P8 6.92 6.85 6.85 0.11 100 6.78 6.78 0.12 100 P8 6.92 6.85 6.85 0.11 100 6.78 6.78 0.12 100 P9 3.81 3.74 3.74 0.07 100 3.68 3.68 0.08 100 P9 3.81 3.74 3.74 0.07 100 3.68 3.68 0.08 100 P10 4.15 3.97 3.97 0.08 95 3.91 3.91 0.09 100 P10 4.15 3.97 3.97 0.08 95 3.91 3.91 0.09 100 P11 2.96 2.05 2.05 0.08 100 1.98 1.99 0.10 100 P11 2.96 2.05 2.05 0.08 100 1.98 1.99 0.10 100 P12 2.61 2.46 0.46 0.12 100 2.31 2.31 0.14 100 P12 2.61 2.46 0.46 0.12 100 2.31 2.31 0.14 100 P13 1.44 1.22 1.23 0.06 100 1.15 1.16 0.08 97 P13 1.44 1.22 1.23 0.06 100 1.15 1.16 0.08 97 P14 4.73 4.44 4.44 0.07 100 4.37 4.38 0.09 100 P14 P15 4.73 1.09 4.44 1.02 4.44 1.02 0.07 0.06 10 65 0 4. 0.96 37 4.0.9 38 6 0. 0.07 09 10 310 P16 1.80 1.69 1.70 0.08 100 1.60 1.60 0.09 100 P15 1.09 1.02 1.02 0.06 65 0.96 0.96 0.07 31 P17 1.11 1.05 1.05 0.05 83 0.98 0.98 0.06 37 P16 1.80 1.69 1.70 0.08 100 1.60 1.60 0.09 100 P18 1.05 0.99 0.99 0.05 41 0.92 0.92 0.07 11 P17 1.11 1.05 1.05 0.05 83 0.98 0.98 0.06 37 P19 1.80 1.69 1.70 0.08 100 1.59 1.59 0.09 100 P20 1.02 0.96 0.96 0.04 16 0.90 0.90 0.05 2 Appl. Sci. 2021, 11, 109 10 of 12 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. 4. Discussion It can be concluded from the above-stated calculations that one of the important settings of the input variables is their assumed probability distribution. From the avail- able literature research and the authors’ own expert opinion, it can be assumed that the investment costs variable tends to have a rather asymmetric probability distribution. This was also conﬁrmed by the CBA guide [6], which considers an asymmetric triangular proba- bility distribution in the range 5% to 20%. Makovšek [16], who dealt with a long-term analysis of cost over-runs of road constructions in Slovenia, addressed this issue in detail. Two fundamental conclusions emerged from his analysis: the fact that cost over-runs are systematic (not randomly distributed around zero) and that cost over-runs appear constantly over a time period of several decades and do not decrease (and thus do not show signs of improved forecasting tools and methods). A conclusion can also be drawn from these deductions, that the probability distribution of investment costs tends to be rather asymmetric. An interesting comparison was published by Emhjellen [17], who dealt with the dif- ference of values when setting different limits of normal distribution and their effect on the resulting values. Kumar [18] noted that the concessionaire aims to bear minimal cost, so maximum probability occurs at lower cost values, and hence it followed a lognormal probability distribution. Jakiukevicius [19,20] worked with normal and triangular distribu- tions, for which he set theoretical parameters which he, based on simulations, converted to log logistics parameters. Kumar [18] adhered to a lognormal distribution of project costs. Gorecki [21] used a triangular distribution. The Czech author Hnilica [22] worked with the beta-PERT distribution, which he considered to be smoother, with possible values more concentrated around the most probable value, and the probability decreases towards the limit values faster than linearly. The authors of this article believe that the beta-PERT distribution best ﬁts an expert estimate of the investment costs behaviour in comparing their values in the ex-ante and ex-post phases. The authors of this article carried out project simulations as mentioned above, assuming both a probability distribution of beta-PERT, and an asymmetric triangular one, and state that the results of the outputs in the expected value of “BCR-mean” ranged up to 7% for all of the projects. The outputs of all projects in both variants of solutions proved the normal distribution of the BCR indicator. The authors of the background research [4] reached the same results, where they stated that an experiment which identiﬁes a pseudo-random number sequence as normally distributed Appl. Sci. 2021, 11, 109 11 of 12 was carried out. The reading of the frequency distribution of the evaluation indicator provides information of extreme importance, as regards the riskiness of the investment project [23]. 5. Conclusions It is clear from the above-stated ﬁndings that attention must be paid to the setting of statistical characteristics of variables which enter into the calculations of economic efﬁciency indicators, and on the basis of which it is decided whether or not to accept projects for ﬁnancing. At present, data on post-audits of major transport infrastructure projects are beginning to be collected and analysed in the Czech Republic, and it is expected that the analyses will make possible, among other things, reaching more precise assumptions. Although the projects proved efﬁcient, a combination of negative changes to both variables can already bring projects with a certain value of probability into negative results. Based on the analysis of the research sample, it is clear that it cannot be clearly established for projects that a certain value of the BCR ratio predicts 100% stability of the project under the action of several critical variables. It is obvious from the mean value simulations determining the expected BCR value that projects with BCR < 1.1 show, at a certain percentage of probability, and at the critical variable limits speciﬁed above, that they shall not be 100% effective. However, the variance of the results obtained was large. Project P10 also showed an interesting result; a relatively high mean BCR ratio showed with a 5% probability that it will not be effective. The results of the research point to the fact that it is always necessary to perform a quantitative analysis, since the results of the combination of the interaction of critical variables cannot be derived from the partial results of the sensitivity and qualitative analyses. The result will always depend on the absolute values of the critical variables of each unique project. Author Contributions: Conceptualization. J.K. and V.H.; methodology. J.K. and V.H.; validation. J.K. and V.H.; formal analysis. J.K. and V.H.; investigation. J.K. and V.H.; resources. J.K. and V.H.; data curation. J.K. and V.H.; writing—original draft preparation. J.K. and V.H.; writing—review and editing. J.K. and V.H.; visualization. J.K.; supervision. J.K.; project administration. J.K.; funding acquisition. J.K. Both authors have read and agreed to the published version of the manuscript. Funding: This research was funded by project Brno University of Technology No. FAST-S-20-6383 Selected Economic and Managerial Aspects in Construction Engineering. Acknowledgments: This paper has been worked out under the project of Brno University of Tech- nology no. FAST-S-20-6383 Selected Economic and Managerial Aspects in Construction Engineering. Conﬂicts of Interest: The authors declare no conﬂict of interest. References 1. Demart, S.; Roy, B. The uses of cost-beneﬁt analysis in public transportation decision-making in France. Transp. Policy 2009, 16, 200–212. [CrossRef] 2. Hyard, A. Cost-beneﬁt analysis according to Sen: An application in the evaluation of transport infrastructures in France. Transp. Res. Part A Policy Pract. 2012, 46, 707–719. [CrossRef] 3. Jones, H.; Moura, F.; Domingos, T. Transport Infrastructure Project Evaluation Using Cost-Beneﬁt Analysis. Procedia Soc. Behav. Sci. 2014, 111, 400–409. [CrossRef] 4. Mackie, P.; Worsley, T.; Eliasson, J. Transport Appraisal Revisited. Res. Transp. Econ. 2014, 47, 3–18. [CrossRef] 5. Korytárová, J.; Papežíková, P. Assessment of Large-Scale Projects Based on CBA. Procedia Comput. Sci. 2015, 64, 736–743. [CrossRef] 6. Sartori, D. Guide to Cost-beneﬁt Analysis of Investment Projects. Economic appraisal tool for Cohesion Policy 2014–2020. In Directorate-General for Regional and Urban Policy; European Commission: Brussels, Belgium, 2014; ISBN 978-92-79-34796-2. 7. Ministry of Transport of the Czech Republic (MoT CZ). Departmental Guideline for the Evaluation of Economic Effectiveness of Transport Construction Projects. 2017. Available online: https://www.sfdi.cz/soubory/obrazky-clanky/metodiky/2017_03_ departmental-methodology-full.pdf (accessed on 25 August 2020). 8. Mokhtari, H.; Kiani, K.; Tahmasebpoor, S. Economic evaluation of investment projects under uncertainty: A probability theory perspective. Sci. Iran. 2020, 27, 448–468. [CrossRef] Appl. Sci. 2021, 11, 109 12 of 12 9. 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Abstract

applied sciences Article Risk Assessment of Large-Scale Infrastructure Projects—Assumptions and Context Jana Korytárová * and Vít Hromádka Faculty of Civil Engineering, Brno University of Technology, 60200 Brno, Czech Republic; hromadka.v@fce.vutbr.cz * Correspondence: korytarova.j@fce.vutbr.cz; Tel.: +420-733-164-369 Featured Application: The results of the presented research extend the methodology of economic analysis and risk assessment of large infrastructure projects. Abstract: This article deals with the partial outputs of large-scale infrastructure project risk assess- ment, speciﬁcally in the ﬁeld of road and motorway construction. The Department of Transport spends a large amount of funds on project preparation and implementation, which however, must be allocated effectively, and with knowledge of the risks that may accompany them. Therefore, documentation for decision-making on project ﬁnancing also includes their analysis. This article monitors the frequency of occurrence of individual risk factors within the qualitative risk analysis, with the support of the national risk register, and identiﬁes dependent variables that represent part of the economic cash ﬂows for determining project economic efﬁciency. At the same time, it compares these dependent variables identiﬁed by sensitivity analysis with critical variables, followed by testing the interaction of the critical variables’ effect on the project efﬁciency using the Monte Carlo method. A partial section of the research was focused on the analysis of the probability distribution of input variables, especially “the investment costs” and “time savings of infrastructure users” variables. The research ﬁndings conclude that it is necessary to pay attention to the setting of statistical characteris- tics of variables entering the economic efﬁciency indicator calculations, as the decision of whether or not to accept projects for funding is based on them. Citation: Korytárová, J.; Hromádka, Keywords: CBA; investment project; probability distribution; sensitivity analyses; risk assessment V. Risk Assessment of Large-Scale Infrastructure Projects—Assumptions and Context. Appl. Sci. 2021, 11, 109. https://dx.doi.org/10.3390/app1101 0109 1. Introduction Transport infrastructure projects are important carriers and supporters of economic Received: 1 December 2020 growth for national economies. Implementation of investment projects, in addition to the Accepted: 22 December 2020 direct beneﬁts for which they are implemented, brings growth potential for the national Published: 24 December 2020 economy; they reduce unemployment, increase the sales of design and implementation companies, and thus create revenue capacity on the demand side for purchases of goods Publisher’s Note: MDPI stays neu- and services. Implementation of investment projects will also be a key factor in alleviating tral with regard to jurisdictional claims the current COVID-19 pandemic effect in all national economies; e.g., the draft of the state in published maps and institutional budget of the Czech Republic brings record investments for the future, which have been afﬁliations. increased by CZK 178 billion for 2021 ( 6.7 billion). Even so, the supply of funds for project implementation is limited. Therefore, it is always necessary to choose for ﬁnancing only those projects that are efﬁcient. The efﬁciency of projects to be implemented is assessed in Copyright: © 2020 by the authors. Li- the ex-ante period, on the basis of feasibility study data, which is addressed in the form of censee MDPI, Basel, Switzerland. This a cost–beneﬁt analysis (CBA). article is an open access article distributed The authors of this article have been carrying out research into development in eco- under the terms and conditions of the nomic efﬁciency assessment of public transport infrastructure projects for a long time. In Creative Commons Attribution (CC BY) the present article they focused on the analysis of the economic outputs of road infras- license (https://creativecommons.org/ tructure projects, motorways, and class I roads via CBA. CBA has the largest explanatory licenses/by/4.0/). Appl. Sci. 2021, 11, 109. https://dx.doi.org/10.3390/app11010109 https://www.mdpi.com/journal/applsci Appl. Sci. 2021, 11, 109 2 of 12 power [1–4], which is based on the determination of cost-effectiveness against the total societal beneﬁts. Generally, four criteria are solved and monetized in large-scale transport infrastructure project appraisals: travel time savings, travel and operational costs, safety, and environmental cost, from different perspectives. In ref. [5] based on the modeling of economic cash ﬂows determined by these variables, the following economic efﬁciency indicators were established: economic net present value (ENPV), economic internal rate of return (ERR), and beneﬁt cost ratio (BCR) [6,7]. The values of the economic indicators were tested for critical variables and the switching values of indicators (threshold value of the indicator in terms of efﬁciency, e.g., ENPV = 0, ERR = discount rate) were deter- mined. In the following step, a quantitative risk analysis using the Monte Carlo method was performed for the identiﬁed critical variables. At the same time, a qualitative risk analysis, which considered potential risk factors using a risk register [7], was performed. It monitored the project risk impact, the occurrence probability, and deduced the risk relevance for the implementation and operation of the project. Individual projects that demonstrated a positive evaluation from all perspectives examined are ready for funding, and further phases of their life cycle can be launched for them. The research question addressed by the implemented research team was which variables are risky, how strong is their inﬂuence on economic efﬁciency, and whether and how the projects are resilient; robust to the potential risk interaction. This concerns questions of the connection of the qualitative and quantitative risk analysis, which dependant variables are resulting from the qualitative analysis, and if they are also considered in the quantitative analysis. In the case of the important critical variable it was the objective to test the changes of the efﬁciency of projects while using different probability distributions. Investors aim, not only to prevent project failure, but also to select the best alternatives among the available investment projects, so as to gain more beneﬁts and achieve better results [8]. In the investment decision-making process of large-scale projects, many risk factors can cause decision failure [9]. This is also why decision-support systems are of high importance for investors in the construction industry [10]. 2. Materials and Methods The aim of the research described in this paper was to ﬁnd the relations between the outputs of the qualitative risk analysis, sensitivity analysis, and quantitative risk analysis, which were performed in the evaluation of the economic efﬁciency of transport infrastructure projects, as part of the modeling of economic Cash Flow (CF) of their life cycle. For the case study, a set of projects being prepared for realization in the Czech Republic was chosen. The authors of the paper have many years of experiences in the evaluation of projects in Czech transport infrastructure, and during these years they were able to collect a large amount of input data. However, the authors would like to emphasize that for the presented procedures, and partly also for the results, it is possible, respecting individual speciﬁcs of economic evaluation in other countries, to relate them to projects carried out abroad. The research sample consisted of 20 large-scale transport infrastructure projects from the Czech Republic, which were the pre-investment phase in the 2018–2020 period, and with proven economic efﬁciency. Only those projects that could be compared with each other due to the fact that they were processed according to the same methodological procedure, e.g., according to the Departmental Methodology valid since 2017 [7], were included in the research sample. Net cash ﬂow (NCF) for the calculation of economic ratios consisted of the savings in the costs of the suggested (investment) variant related to the zero variant (without investment). The calculation formula consists of four types of particular beneﬁts; socio- economic savings. They are savings in travel and operating costs, savings in travel time costs, reduction in accident costs, and savings in exogenous costs. The time value of money determining the amount of the discount rate for the calculation of the ENPV indicator was set at 5% for the Czech Republic in the EU programming period 2014–2020. Appl. Sci. 2021, 11, 109 3 of 12 The research presented in this article examined project risk frequency, and the impact on their economic efﬁciency and robustness of economic efﬁciency indicators, using sen- sitivity analysis, and ﬁnally involved conﬁrmation or refusing the robustness of projects according to the previous step by determining the cumulative probability of achieving project economic efﬁciency using the Monte Carlo method. To assess the real risk of failure associated with the investment, changes in the values of economic performance indicators deriving from the simultaneous change of several project variables had to be identiﬁed [11]. As stated by [12], one of the risk assessment tools is the Monte Carlo method, which combines and develops both sensitivity analysis, and scenario analysis, methods. In the resource material, Ref. [13] focused on the Monte Carlo method used in the case of the earned value management methodology. Bowers also provided a broader view of the issue of project risk assessment [14]. 2.1. Data Table 1 presents the research sample projects with their basic characteristics. It states the undiscounted economic investment costs (i.e., investment costs excluding VAT reduced by a conversion coefﬁcient 0.807), economic internal rate of return (ERR), economic net present value (ENPV), and cost beneﬁt ratio (BCR), which was calculated according to the following relation: B ENPV = 1 + (1) C IC where: BCR: Cost Beneﬁt Ratio ENPV: Economic Net Present Value IC: Discounted Investment Costs Table 1. Basic economic data on research sample projects. IC ERR ENPV No. Name of the Project BCR % P1 Vestec connection 73,655,517 13.15% 134,141,506 2.90 P2 I/22 Draženov-Horažd’ovice 253,477,033 5.67% 25,929,610 1.11 P3 I/27 Kaznejov, bypass 91,192,128 9.50% 74,002,422 1.83 I/13 Ostrov-Smilov, P4 141,082,434 5.88% 19,811,383 1.15 right bank I/13 Ostrov-Smilov, P5 116,820,770 7.52% 50,193,343 2.01 left bank P6 I/26 Horšovský Týn 50,375,269 5.60% 4,578,849 1.09 P7 D0 Brezin ˇ eves-Satali ˇ ce var. 1 371,886,072 39.45% 2,576,573,157 8.28 P8 D0 Brezin ˇ eves-Satali ˇ ce var. 2 434,933,917 30.46% 2,395,820,591 6.92 P9 D0 Brezin ˇ eves-Satali ˇ ce var. 3 757,919,450 17.89% 1,934,644,942 3.81 P10 I11– Hradec Králové, tangent 111,776,135 17.24% 336,621,090 4.15 P11 I/18 Pr ˇíbram-bypass var. 1 28,417,453 14.20% 54,410,634 2.96 P12 I/18 Pr ˇíbram-bypass var. 2 49,497,029 13.21% 74,973,161 2.61 P13 I/50 Bucovice ˇ 78,579,450 7.56% 32,937,152 1.44 P14 I/36 Trnová-Fablovka-Dubina 53,652,370 19.20% 190,286,624 4.73 P15 I/11 Nové Sedlice-Opava Komárov 91,436,523 5.52% 7,834,232 1.09 P16 I/26 Holysov, bypass 56,624,471 9.19% 42,452,457 1.80 P17 D10 Praha-Kosmonosy 361,367,050 5.72% 35,994,616 1.11 P18 I/67 Bohumín-Karviná 83,937,876 5.33% 4,067,671 1.05 P19 D43 Boritov-Star ˇ é Mesto ˇ 56,624,471 9.19% 42,452,457 1.80 P20 D27 Preštice-Klatovy ˇ 128,638,259 5.12% 22,333,326 1.02 Source: Feasibility Studies of Investment projects, The State Fund for Transport Infrastructure SFDI, authors’ own processing. Appl. Sci. 2021, 11, 109 4 of 12 Qualitative risk analysis is generally based on expert opinions on the risks that threaten a particular investment project. Lists of risks are usually created, based on the knowledge of the issues addressed, which contain risks that are relevant and common for the given type of projects. A risk register was created in the Czech Republic for the purposes of risk assessment of the road infrastructure projects speciﬁed above [7]. The list of risks according to the risk register is given in Table 2. Table 2. Risk register according to the Departmental Methodology of the Czech Republic. No. Risk Description Demand-related risks R1 Different development of demand than expected Risks related to the project design R2 Inadequate surveys and inquiries in the given locality R3 Inadequate estimates of project work costs Administrative and public procurement risks R4 Delays in awarding R5 Building permit Risks related to the land purchase R6 Land price R7 Delays in land purchase Risks related to construction R8 Exceeding investment costs R9 Floods, landslides, etc. R10 Archaeological ﬁndings R11 Risks related to the contractor (bankruptcy, lack of resources) Operational risks R12 Higher maintenance costs than expected Regulatory risks R13 Environmental requirement change Other risks R14 Public opposition Source: Departmental methodology of the Ministry of Transport [7]. 2.2. Methods The methodological procedure was based on collection, analysis, and examination of relevant data concerning the economic efﬁciency assessment of individual investment projects. The outputs were aimed at answering research questions concerning the intercon- nectedness of individual analyses of future project uncertainties. 2.2.1. Qualitative Analysis The signiﬁcance of project risks (R) was divided into four categories: very high (VH), high (H), medium (M), and low (L). This was determined on the basis of the product of the project risk impact intensity (I) and its occurrence probability (p), with a ﬁve-interval scale of both variables, according to the following relation: R = I p (2) Appl. Sci. 2021, 11, 109 5 of 12 The probability (value) and the impact intensity had the determined ranges presented in following Tables 3 and 4. Table 3. Scale of risk occurrence probability (p). Classiﬁcation Verbal Description Percentage Expression A Very improbable 0–9% B Improbable 10–32% C Neutral 33–65% D Probable 66–89% E Very probable 90–100% Source: Departmental methodology of the Ministry of Transport [7]. Table 4. Scale for risk impact intensity (I). Category Name Verbal Description I Imperceptible no signiﬁcant effect on expected social beneﬁts of the project long-term project beneﬁts are not affected but corrective II Mild measures are needed loss of expected social beneﬁts of the project, mostly ﬁnancial III Medium loss and in medium- and long-term time horizon, corrective measures may solve the problem large loss of expected social beneﬁts of the project, occurrence of adverse effects causes a loss of the IV Critical project’s primary function; corrective measures, even if taken on a large scale, are not sufﬁcient to prevent major losses signiﬁcant to complete loss of function of the project, project V Catastrophic objectives cannot be achieved even in the long term Source: Departmental methodology of the Ministry of Transport [7]. Table 5 shows the occurrence frequency of very high, high, and medium risks in the researched sample of projects, according to the risk register (see Table 1). In addition to the risk frequency, the table also shows the dependent variable, which enters the economic CF of the projects as a basis for the calculation of economic efﬁciency indicators. It is clear from the overview given in Table 5 that the most signiﬁcant risks for transport infrastructure projects identiﬁed in the pre-investment phase lie in the estimation of future demand for new infrastructure use (R1), design and preparatory work (R2), (R3), delays in obtaining construction permits (R5), land purchase (R7), and excess of project costs (R8). The R1 risk is related to the demand, which affects the income part of the projects in the operational phase of their life cycle by a possible reduction in their expected socio-economic beneﬁts. The inﬂuence of other risks has a direct impact on investment costs, which thus become a signiﬁcant variable in the economic assessment. Appl. Sci. 2021, 11, 109 6 of 12 Table 5. Risk frequency according to their signiﬁcance, including the dependent variable identiﬁcation. VH and H M Risk No. Total Dependent Variable Risks Risk 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 Investment costs, extension of construction, delay/shortening of the R9 0 1 1 operational phase for evaluation Investment costs, extension of construction, delay/shortening of the R10 0 1 1 operational phase for evaluation Investment costs, extension of construction, delay/shortening of the R11 0 2 2 operational phase for evaluation Operating costs, reduction of beneﬁts under “Infrastructure R12 0 0 0 operating costs” item R13 0 0 0 Changes in beneﬁts under “Externalities” item R14 0 0 0 Inﬂuence on the beginning of construction Source: Feasibility Studies of Investment projects, SFDI, authors’ own processing. 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%. Table 6. Frequency of elasticity coefﬁcient (EC) values. Variable 0 EC < 0.5 0.5 EC < 1 1 EC < 1.5 EC 1.5 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 Appl. Sci. 2021, 11, 109 7 of 12 Table 7. Switching values of project efﬁciency. Variable/Switching Value 0 PH < 10% 10% PH < 30% PH 30% Total investment costs 3 3 13 Time savings of users 2 3 14 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]. The authors focused on comparing two assumptions of the probability distribution of the investment costs critical variable. The simulations were therefore performed in two variants, in the ﬁrst variant the beta- PERT probability distribution was chosen for the investment costs, in the second variant a triangular asymmetric probability distribution was used. In order to be able to correctly compare the impact of the use of partial probability distributions of investment costs on the overall project results, an equally normal distribution was used for the second critical variable “time savings of infrastructure users” for both simulation variants. The parameters of the probability distribution of investment costs in the case of the beta-PERT probability distribution assumption were therefore chosen as follows: Minimum project value reduced by 10%, Most likely project value, Maximum project value increased by 50%. The parameters of the probability distribution of investment costs in the case of the asymmetric triangular probability distribution assumption were, in accordance with the recommendations arising from the background source [9], set with parameters comparable with the beta-PERT probability distribution, i.e., as follows: Minimum project value reduced by 10%, Most likely project value, Maximum project value increased by 50%. Probability distribution for the time savings of infrastructure users was chosen as a normal probability distribution, where the mean value corresponded to the project value of time savings and standard deviation 10%. 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). Appl. Sci. 2021, 11, x FOR PEER REVIEW 8 of 12 Appl. Sci. 2021, 11, 109 8 of 12 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). Table 8. Results of the simulation of a random cost-effectiveness variable. Investment costs beta-PERT probability distribution. Table 8. Results of the simulation of a random cost‐effectiveness variable. Investment costs beta‐ PERT probability distribution. Statistics Forecast Values Statistics Forecast Values Trials 10,000 Base Case 1.112 Trials 10,000 Mean 1.045 Base Case 1.112 Median 1.047 Mean 1.045 Standard Deviation 0.047 Median 1.047 Variance 0.002 Standard Deviation 0.047 Coeff. of Variation 0.0449 Variance 0.002 Minimum 0.876 Coeff. of Variation 0.0449 Maximum 1.194 Minimum 0.876 Range Width 0.318 Maximum 1.194 Range Width 0.318 The resulting probability distribution for the random BCR variable is shown in the The resulting probability distribution for the random BCR variable is shown in the following chart. following chart. Figure 1. Probability distribution for a random cost benefit ratio (BCR) variable. Investment costs Figure 1. Probability distribution for a random cost beneﬁt ratio (BCR) variable. Investment costs beta‐PERT probability distribution. beta-PERT probability distribution. Simulation results, when an asymmetric triangular probability distribution for total Simulation results, when an asymmetric triangular probability distribution for total investment costs and a normal probability distribution for time savings of the infrastruc‐ investment costs and a normal probability distribution for time savings of the infrastructure ture users were chosen, are shown in Table 9 and Figure 2. The simulated quantity de‐ users were chosen, are shown in Table 9 and Figure 2. The simulated quantity dependent pendent variable was cost‐effectiveness (BCR). variable was cost-effectiveness (BCR). Table 9. Results of the simulation of a random cost‐effectiveness variable. Investment costs: asym‐ Table 9. Results of the simulation of a random cost-effectiveness variable. Investment costs: asym- metric triangular probability distribution. metric triangular probability distribution. Statistics Forecast Values Trials 10,000 Statistics Forecast Values Base Case 1.112 Trials 10,000 Mean 0.978 Base Case 1.112 Median 0.980 Mean 0.978 Standard Deviation 0.060 Median 0.980 Variance 0.004 Standard Deviation 0.060 Coeff. of Variation 0.004 Variance 0.004 Coeff. of Variation 0.004 Minimum 0.747 Maximum 1.146 Range Width 0.400 Appl. Sci. 2021, 11, x FOR PEER REVIEW 9 of 12 Appl. Sci. 2021, 11, 109 9 of 12 Minimum 0.747 Maximum 1.146 Range Width 0.400 The resulting probability distribution for the random BCR variable of the project D10 The resulting probability distribution for the random BCR variable of the project D10 Prague-Kosmonosy is shown in the following chart. Prague‐Kosmonosy is shown in the following chart. Figure 2. Probability distribution for a random BCR variable. Investment costs: asymmetric trian‐ Figure 2. Probability distribution for a random BCR variable. Investment costs: asymmetric triangu- gular probability distribution. lar probability distribution. It is evident from the probability distribution shown in Figures 1 and 2 that with a It is evident from the probability distribution shown in Figures 1 and 2 that with a certain certainpr prob obability abilitythe therandom randomBCR BCRvariable variablewill willtake takevalues valuesb below elow the thecritical criticalvalue, value,and and the project will therefore be economically inefficient. the project will therefore be economically inefﬁcient. Table 10 shows the outputs of the quantitative analysis of all the researched projects Table 10 shows the outputs of the quantitative analysis of all the researched projects for for both both variants variants of of the the consider consider ed edpr proba obability bilitydistribution distributionof ofthe theinvestment investmentcosts costscritical critical variable. variable. The The ta table ble for for eaeach ch project project pres prente esented d thet fol helo following wing statistic statistical al charact characteristics eristics indi‐ indicators: BCR: mean, median, standard deviation (s), and certainty level (CL). cators: BCR: mean, median, standard deviation (σ), and certainty level (CL). Table 10. Statistic characteristics of project BCR values. Table 10. Statistic characteristics of project BCR values. Variant 1 Variant 2 Variant 1 Variant 2 No. BCR No. BCR Mean Median σ CL Mean Median σ CL Mean Median s CL Mean Median s CL P1 2.90 2.73 2.73 0.15 100 2.57 2.57 0.17 100 P1 2.90 2.73 2.73 0.15 100 2.57 2.57 0.17 100 P2 1.11 1.00 0.97 0.06 47 0.94 0.94 0.06 18 P2 1.11 1.00 0.97 0.06 47 0.94 0.94 0.06 18 P3 1.83 1.50 4.51 0.07 100 1.43 1.44 0.10 100 P3 1.83 1.50 4.51 0.07 100 1.43 1.44 0.10 100 P4 1.15 1.09 1.09 0.05 96 1.02 1.02 0.06 64 P4 1.15 1.09 1.09 0.05 96 1.02 1.02 0.06 64 P5 1.43 1.35 1.35 0.06 100 1.28 1.28 0.06 100 P5 1.43 1.35 1.35 0.06 100 1.28 1.28 0.06 100 P6 P6 1.09 1.09 1.03 1.03 1.03 1.03 0.07 0.07 66 66 0. 0.97 97 0.0.97 97 0. 0.08 08 37 37 P7 8.28 8.19 8.19 0.13 100 8.12 8.12 0.14 100 P7 8.28 8.19 8.19 0.13 100 8.12 8.12 0.14 100 P8 6.92 6.85 6.85 0.11 100 6.78 6.78 0.12 100 P8 6.92 6.85 6.85 0.11 100 6.78 6.78 0.12 100 P9 3.81 3.74 3.74 0.07 100 3.68 3.68 0.08 100 P9 3.81 3.74 3.74 0.07 100 3.68 3.68 0.08 100 P10 4.15 3.97 3.97 0.08 95 3.91 3.91 0.09 100 P10 4.15 3.97 3.97 0.08 95 3.91 3.91 0.09 100 P11 2.96 2.05 2.05 0.08 100 1.98 1.99 0.10 100 P11 2.96 2.05 2.05 0.08 100 1.98 1.99 0.10 100 P12 2.61 2.46 0.46 0.12 100 2.31 2.31 0.14 100 P12 2.61 2.46 0.46 0.12 100 2.31 2.31 0.14 100 P13 1.44 1.22 1.23 0.06 100 1.15 1.16 0.08 97 P13 1.44 1.22 1.23 0.06 100 1.15 1.16 0.08 97 P14 4.73 4.44 4.44 0.07 100 4.37 4.38 0.09 100 P14 P15 4.73 1.09 4.44 1.02 4.44 1.02 0.07 0.06 10 65 0 4. 0.96 37 4.0.9 38 6 0. 0.07 09 10 310 P16 1.80 1.69 1.70 0.08 100 1.60 1.60 0.09 100 P15 1.09 1.02 1.02 0.06 65 0.96 0.96 0.07 31 P17 1.11 1.05 1.05 0.05 83 0.98 0.98 0.06 37 P16 1.80 1.69 1.70 0.08 100 1.60 1.60 0.09 100 P18 1.05 0.99 0.99 0.05 41 0.92 0.92 0.07 11 P17 1.11 1.05 1.05 0.05 83 0.98 0.98 0.06 37 P19 1.80 1.69 1.70 0.08 100 1.59 1.59 0.09 100 P20 1.02 0.96 0.96 0.04 16 0.90 0.90 0.05 2 Appl. Sci. 2021, 11, 109 10 of 12 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. 4. Discussion It can be concluded from the above-stated calculations that one of the important settings of the input variables is their assumed probability distribution. From the avail- able literature research and the authors’ own expert opinion, it can be assumed that the investment costs variable tends to have a rather asymmetric probability distribution. This was also conﬁrmed by the CBA guide [6], which considers an asymmetric triangular proba- bility distribution in the range 5% to 20%. Makovšek [16], who dealt with a long-term analysis of cost over-runs of road constructions in Slovenia, addressed this issue in detail. Two fundamental conclusions emerged from his analysis: the fact that cost over-runs are systematic (not randomly distributed around zero) and that cost over-runs appear constantly over a time period of several decades and do not decrease (and thus do not show signs of improved forecasting tools and methods). A conclusion can also be drawn from these deductions, that the probability distribution of investment costs tends to be rather asymmetric. An interesting comparison was published by Emhjellen [17], who dealt with the dif- ference of values when setting different limits of normal distribution and their effect on the resulting values. Kumar [18] noted that the concessionaire aims to bear minimal cost, so maximum probability occurs at lower cost values, and hence it followed a lognormal probability distribution. Jakiukevicius [19,20] worked with normal and triangular distribu- tions, for which he set theoretical parameters which he, based on simulations, converted to log logistics parameters. Kumar [18] adhered to a lognormal distribution of project costs. Gorecki [21] used a triangular distribution. The Czech author Hnilica [22] worked with the beta-PERT distribution, which he considered to be smoother, with possible values more concentrated around the most probable value, and the probability decreases towards the limit values faster than linearly. The authors of this article believe that the beta-PERT distribution best ﬁts an expert estimate of the investment costs behaviour in comparing their values in the ex-ante and ex-post phases. The authors of this article carried out project simulations as mentioned above, assuming both a probability distribution of beta-PERT, and an asymmetric triangular one, and state that the results of the outputs in the expected value of “BCR-mean” ranged up to 7% for all of the projects. The outputs of all projects in both variants of solutions proved the normal distribution of the BCR indicator. The authors of the background research [4] reached the same results, where they stated that an experiment which identiﬁes a pseudo-random number sequence as normally distributed Appl. Sci. 2021, 11, 109 11 of 12 was carried out. The reading of the frequency distribution of the evaluation indicator provides information of extreme importance, as regards the riskiness of the investment project [23]. 5. Conclusions It is clear from the above-stated ﬁndings that attention must be paid to the setting of statistical characteristics of variables which enter into the calculations of economic efﬁciency indicators, and on the basis of which it is decided whether or not to accept projects for ﬁnancing. At present, data on post-audits of major transport infrastructure projects are beginning to be collected and analysed in the Czech Republic, and it is expected that the analyses will make possible, among other things, reaching more precise assumptions. Although the projects proved efﬁcient, a combination of negative changes to both variables can already bring projects with a certain value of probability into negative results. Based on the analysis of the research sample, it is clear that it cannot be clearly established for projects that a certain value of the BCR ratio predicts 100% stability of the project under the action of several critical variables. It is obvious from the mean value simulations determining the expected BCR value that projects with BCR < 1.1 show, at a certain percentage of probability, and at the critical variable limits speciﬁed above, that they shall not be 100% effective. However, the variance of the results obtained was large. Project P10 also showed an interesting result; a relatively high mean BCR ratio showed with a 5% probability that it will not be effective. The results of the research point to the fact that it is always necessary to perform a quantitative analysis, since the results of the combination of the interaction of critical variables cannot be derived from the partial results of the sensitivity and qualitative analyses. The result will always depend on the absolute values of the critical variables of each unique project. Author Contributions: Conceptualization. J.K. and V.H.; methodology. J.K. and V.H.; validation. J.K. and V.H.; formal analysis. J.K. and V.H.; investigation. J.K. and V.H.; resources. J.K. and V.H.; data curation. J.K. and V.H.; writing—original draft preparation. J.K. and V.H.; writing—review and editing. J.K. and V.H.; visualization. J.K.; supervision. J.K.; project administration. J.K.; funding acquisition. J.K. Both authors have read and agreed to the published version of the manuscript. Funding: This research was funded by project Brno University of Technology No. FAST-S-20-6383 Selected Economic and Managerial Aspects in Construction Engineering. Acknowledgments: This paper has been worked out under the project of Brno University of Tech- nology no. FAST-S-20-6383 Selected Economic and Managerial Aspects in Construction Engineering. Conﬂicts of Interest: The authors declare no conﬂict of interest. References 1. Demart, S.; Roy, B. The uses of cost-beneﬁt analysis in public transportation decision-making in France. Transp. Policy 2009, 16, 200–212. [CrossRef] 2. Hyard, A. Cost-beneﬁt analysis according to Sen: An application in the evaluation of transport infrastructures in France. Transp. Res. Part A Policy Pract. 2012, 46, 707–719. [CrossRef] 3. Jones, H.; Moura, F.; Domingos, T. Transport Infrastructure Project Evaluation Using Cost-Beneﬁt Analysis. Procedia Soc. Behav. Sci. 2014, 111, 400–409. [CrossRef] 4. Mackie, P.; Worsley, T.; Eliasson, J. Transport Appraisal Revisited. Res. Transp. Econ. 2014, 47, 3–18. [CrossRef] 5. Korytárová, J.; Papežíková, P. Assessment of Large-Scale Projects Based on CBA. Procedia Comput. Sci. 2015, 64, 736–743. [CrossRef] 6. Sartori, D. Guide to Cost-beneﬁt Analysis of Investment Projects. Economic appraisal tool for Cohesion Policy 2014–2020. In Directorate-General for Regional and Urban Policy; European Commission: Brussels, Belgium, 2014; ISBN 978-92-79-34796-2. 7. Ministry of Transport of the Czech Republic (MoT CZ). Departmental Guideline for the Evaluation of Economic Effectiveness of Transport Construction Projects. 2017. Available online: https://www.sfdi.cz/soubory/obrazky-clanky/metodiky/2017_03_ departmental-methodology-full.pdf (accessed on 25 August 2020). 8. Mokhtari, H.; Kiani, K.; Tahmasebpoor, S. Economic evaluation of investment projects under uncertainty: A probability theory perspective. Sci. Iran. 2020, 27, 448–468. [CrossRef] Appl. Sci. 2021, 11, 109 12 of 12 9. Liu, Y.; Ting-Hua, Y.; Cui-Qin, W. Investment decision support for engineering projects based on risk correlation analysis. Math. Probl. Eng. 2012, 2012. [CrossRef] 10. Marovic, ´ I.; Androjic, ´ I.; Jajac, N.; Hanák, T. Urban road infrastructure maintenance planning with application of neural networks. Complexity 2018. [CrossRef] 11. Nesticò, A.; He, S.; De Mare, G.; Benintendi, R.; Maselli, G. The ALARP Principle in the Cost-Beneﬁt Analysis for the Acceptability of Investment Risk. Sustainability 2018, 10, 4668. [CrossRef] 12. Bilenko, D.; Lavrov, R.; Onyshchuk, N.; Poliakov, B.; Kabenok, Y. The Normal Distribution Formalization for Investment Economic Project Evaluation Using the Monte Carlo Method. Montenegrin J. Econ. 2019, 15, 161–171. [CrossRef] 13. Acebes, F.; Pajares, J.; Galán, J.M.; López-Paredes, A. A new approach for project control under uncertainty. Going back to the basics. Int. J. Proj. Manag. 2014, 32, 423–434. [CrossRef] 14. Bowers, J.; Khorakian, A. Integrating risk management in the innovation project. Eur. J. Innov. Manag. 2014, 17, 25–40. [CrossRef] 15. Software Oracle Crystal Ball, Perpetual Licencs, 2020–2021. Available online: https://www.oracle.com/cz/applications/ crystalball/ (accessed on 25 August 2020). 16. Makovšek, D. Systematic construction risk cost estimation mechanism and unit price movements. Transp. Policy 2014, 35, 135–145. [CrossRef] 17. Emhjellen, K.; Emhjellen, M.; Osmundsen, P. Investment cost estimates and investment decisions. Energy Policy 2002, 30, 91–96. [CrossRef] 18. Kumar, L.; Apurva, J.; Velaga, N.R. Financial risk assessment and modelling of PPP based Indian highway infrastructure projects. Transp. Policy 2018, 62, 2–11. [CrossRef] 19. Jasiukevicius, L.; Vasiliauskaite, A. Risk Assessment in Public Investment Projects: Impact of Empirically-grounded Methodology on Measured Values of Intangible Obligations in Lithuania. Procedia Soc. Behav. Sci. 2015, 213, 370–375. [CrossRef] 20. 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Risk Assessment of Large-Scale Infrastructure Projects—Assumptions and Context

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Risk Assessment of Large-Scale Infrastructure Projects—Assumptions and Context

Risk Assessment of Large-Scale Infrastructure Projects—Assumptions and Context

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