ANALYSIS OF RISK AND UNCERTAINTY USING MONTE CARLO SIMULATION AND ITS INFLUENCE ON PROJECT REALIZATION *

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1 ANALYSIS OF RISK AND UNCERTAINTY USING MONTE CARLO SIMULATION AND ITS INFLUENCE ON PROJECT REALIZATION * GORAN KARANOVIC, MSc University of Rijeka, Faculty of Tourism and Hospitality Management, Croatia; gokarano@yahoo.com BISERA GJOSEVSKA, PhD Balkan Institute for Behavioral Research, Skopje, Macedonia; gjosevska@gmail.com Abstract: This paper examines the impact of risk and uncertainty on the the capital budgeting process in the modern business environment. The turbulent business surroundings, as well as the rapid technological, informational, and societal progress and scientific development add to the complexity of modern-day decision making, by exerting significant influence on the growing uncertainty during the capital budgeting process. A summary of the most common sources of risk and uncertainty in the capital budgeting process is given, as well as an overview of the most represented methods for the evaluation of financial efficiency in the capital budgeting procedure. The determination and quantification of risk and uncertainty regarding key variables is of paramount importance to the analysis in question, as is their influence on the distribution of the resulting values of the methods of evaluating capital budgeting. Exceptional attention in this paper has been given to the comparison and contrast of distribution of values procured from the use of the methods for the determination and quantification of risk and uncertainty. In the following case study the decision regarding the construction of a hotel the use of the Monte Carlo simulation method has been shown in the process of determining the probability distribution of net present value, as well as the forecasting of cash flows. The given example shows, through analysis and observation, the most important issues and advantages arising from the use of the Monte Carlo method as well as the shortcomings in the use of this model in business practice. Key words: risk, uncertaint, Monte Carlo simulation, capital budgeting, 1. Introduction This work includes an analysis of capital investments and examines them in the light of being a spiritus movens of business development both on a microand macro-economic level. Given that each development of the economic system, regardless of it being on a micro- or a macro- scale is founded on the notion of investment cycles, it is directly dependent on the dynamics, scope and * The International Conference on Economics and Administration, Faculty of Business and Administration, University of Bucharest, Romania ICEA FAA Bucharest, 8-9 th June 2012

2 146 GORAN KARANOVIC, BISERA GJOSEVSKA 2 intensity of the level of investment. In order for a company, or on a much larger scale the economy as a whole to develop and expand, constant investments are necessary. To this end, capital budgeting is extremely important because it is the main mechanism for planning large investments which define the future business and financial standing of the company. It may just as well be the incorrectly chosen capital, or incorrectly planned investment, that may lead to difficulties and even to a grinding halt of the company s operations. The main purpose of this work is to analyze the role and importance that determining risk and uncertainty in the capital budgeting process have on the financial efficiency of the project. Considering the significance of the choice of optimal capital investments on the operations of the company, which arises from the scope of expended cash, the company s management is bound to consider the impact of risk on the realization and overall financial performance of the project during the optimal decision making process. The process of capital budgeting involves the use of various computer programs which aid the management in the analysis and facilitate the making of precise and quality conclusions. It is on the basis of these conclusions that the management decides whether to accept or reject the capital investment under consideration. The grades and the ranking of the chosen investment opportunities, i.e. capital investments consists of undertaking numerous analyses and reaching conclusions regarding the acceptance or the rejection of the investment proposal. This paper examines the evaluation process and the impact of risk on it, including an overview of the most widely utilized methods, techniques and procedures on the basis of which the chosen capital investments are ranked and graded. The use of the Monte Carlo method in the process of risk and uncertainty determination as well as the impact of probability distribution on the analyzed results including the assessment of financial efficiency of the project contributes to a higher quality and more certain evaluation, ranking and selection of the optimal investment opportunity. The overview of the undertaken analysis, which explores the advantages and disadvantages of the use of the Monte Carlo simulation, is the authors attempt to contribute to a better understanding and further application in business practice, all with the intent of making better, more informed and higher-quality capital investment decisions. This work is correlated to recent research and to a certain extent it uses the already established, scientifically significant facts for the use of the Monte Carlo method in the capital budgeting process. The paper has drawn extensively on both scientific and professional literature in the field, which treats capital budgeting issues, as well as the impact of risk and uncertainty on investments.

3 3 ANALYSIS OF RISK AND UNCERTAINTY USING MONTE CARLO SIMULATION AND ITS INFLUENCE ON PROJECT REALIZATION Literature review The academic community has only recently, during the 1980 s, started focusing its scientific research on the benefits of the Monte Carlo method, in which it evaluates all of its advantages and shortcomings (Hertz 1979; Lawrence, Sundem and Geijsbeek 1978; David and Roy 1980; Chandan 1984; Peiser 1984), although it is important to note that the simulation process in capital budgeting has been researched and analyzed even earlier (Rodolfo and Subrata 1968; Kryzanowskia, Lusztiga and Schwab 1972). During the 1980 s, and even before, many scientific studies and inferences considered Monte Carlo simulations as exceptionally complex, expensive and requiring profound knowledge in order to understand the sophisticated computer software, in addition to having sufficient grasp of economic and financial issues. Under the influence of the information and technology boom of the 1990 s, which saw the personal computer become an indispensable tool for every middle-income household universally spread throughout the world, along with the development of software solutions which executed the simulation process consisting of thousands of iterations compress within the span of a few seconds all the while presenting elaborate graphs and statistical tables, as well as recommendations for risk and uncertainty assessment in the capital budgeting process, the Monte Carlo analysis had gathered an ever-growing momentum. This method has become the subject of very intensive recent research, especially its input in the capital budgeting process regarding the assessment of risk and uncertainty levels (Simon and Richard 1992; Hughes 1995, Hurley 1998; Kelliher 2000; Hoesli, Elion and Bender 2005; Kwak and Ingall 2007; Maged, et al. 2010; Tadeu, et al. 2012), as well as its application in business practice. 3. Determining risk, uncertainty and their influence on the analysis of the project realization Various definitions on the concepts of risk and uncertainty can be found in the scientific and professional auditorium, each of them slightly different. Numerous authors define risk in a different way, as shown in Table 1, originating from Paul Hopkins (2010, 12). Even though the word risk carries mainly negative connotations, the use of the term in the field of finance is being acknowledged as the probability of an event occurring, which may result in a negative, or a positive outcome. Therefore, risk may be linked to the uncertainty of a positive outcome occurring. Profitability risk may not necessarily mean a negative deviation of planned quantities; it may also be a positive deviation, i.e. a general deviation of forecast and planned from actual quantities. Considering the long-term character of capital investments, the realization of forecast

4 148 GORAN KARANOVIC, BISERA GJOSEVSKA 4 fundamental components on the basis of which a decision regarding the execution of capital investment projects is being made carries a relatively high level of risk. Table 1. Definitions of risk Institution ISO Gide 73 ISO Institute of Risk Management (IRM) Orange Book from HM Treasury Institute of Internal Auditors Alternative Definition by the author Risk Definition Effect of uncertainty on objectives. Note that an effect may be positive, negative, or a deviation from the expected. Also, risk is often described by an event, a change in circumstances or a consequence. Risk is the combination of the probability of an event and its consequence. Consequences can range from positive to negative. Uncertainty of outcome, within a range of exposure, arising from a combination of the impact and the probability of potential events. The uncertainty of an event occurring that could have an impact on the achievement of the objectives. Risk is measured in terms of consequences and likelihood. Event with the ability to impact (inhibit, enhance or cause doubt about) the mission, strategy, projects, routine operations, objectives, core processes, key dependencies and / or the delivery of stakeholder expectations. It is a well-known fact that there exists no such capital investment which carries no risk until the project is completed. Each business opportunity, that is each possibility of returning a profit is being determined by a certain level of risk. A successful realization of capital investments ascertains, in the long run, the successful operation of each business entity individually. If the realization of capital investments falls short so negative results appear, a negative spillover may emerge, affecting the operations of the entire business entity. In accordance with the above, the management of the business entity should, while planning and budgeting, identify all the possible risks. Moreover, it should employ such methods and techniques that would help quantify the risks, so as to define the scope of their influence on the capital budgeting process as well as to incorporate them in the forecasts and the profitability calculations. During the capital budgeting process, numerous factors affecting the profitability of investment are being forecast, such as the quantity sold, cost and revenue issues, capital structure, number of employees and many others. By determining the risk and the probability of realization of planned events and the influence on planned factors of capital investment, as well as by estimating the total sum of the probabilities of planned events and their consequences occurring, the

5 5 ANALYSIS OF RISK AND UNCERTAINTY USING MONTE CARLO SIMULATION AND ITS INFLUENCE ON PROJECT REALIZATION 149 management of the company decides the risk of realization and the total profitability of starting a capital investment cycle. The sources of risk can be expressed at the level of capital investment, i.e. at the level of the project, investment memorandum or at the level of a company, while negative effects could be transferred from the project or the investment memorandum on the operations of the entire business entity. In addition, risks may be expressed on the level of the entire market, or economy, thus it is customary that the effects of those risks are being transferred to the capital investment project, as well as on all the business entities operating in the market at the time. Table 2, as seen in Merna and Smith (1996, quoted in Merna and Al-Thani 2005, 15) exhibits an overview of the verious souces of risk which may appear and influence not only the realization of the capital investment, and also given the overview of all sources of risk that may arise and that may have effect on the realization of capital investments as well as those that can affect an already started project or an entire company. Table 2. Typical Sources of Risk to Business from Projects Heading Political Environmental Planning Market Economic Financial Natural Project Change and uncertainty in or due to: Government policy, public opinion, change in ideology, dogma, legislation, disorder (war, terrorism, riots) Contaminated land or pollution liability, nuisance (e.g., noise), permissions, public opinion, internal/corporate policy, environmental law or regulations or practice or impact requirements Permission requirements, policy and practice, land use, socio-economic impacts, public opinion Demand (forecasts), competition, obsolescence, customer satisfaction, fashion Treasury policy, taxation, cost inflation, interest rates, exchange rates Bankruptcy, margins, insurance, risk share Unforeseen ground conditions, weather, earthquake, fire or explosion, archaeological discovery Definition, procurement strategy, performance requirements, standards, leadership, organisation (maturity, commitment, competence and experience), planning and quality control, programme, labour and resources, communications and culture

6 150 GORAN KARANOVIC, BISERA GJOSEVSKA 6 Technical Regulatory Human Criminal Safety Legal Design adequacy, operational efficiency, reliability Changes by regulator Error, incompetence, ignorance, tiredness, communication ability, culture, work in the dark or at night Lack of security, vandalism, theft, fraud, corruption Regulations (e.g., CDM, Health and Safety at Work), hazardous substances (COSSH), collisions, collapse, flooding, fire and explosion Those associated with changes in legislation, both in the UK and from EU directivesthe above list is extensive but not complete The above list is extensive but not complete After the company management determines all sources of risk that can affect the capital investments it is necessary to quantify their impact on efficiency. Quantification of the risk involves the determination of the probability of a risky event occurring, and in case of the event occurring, predicting and quantifying its impact on the overall profitability of capital investment. The main problem that emerges in the process of risk determination is in which way to determine the probability of occurrence of a negative or positive event. Capital budgeting process and its values in large part is shown like a subjective opinion, judgment about process and values of capital investment, one or more managers, i.e. judgment of project managers, and it could raise the question of reliability and validity of risk assessment. Aven considers the question of reliability of risk predicting and its perception, stating that it is a judgment (belief, appraisal) held by an individual, group or society about risk... As we have seen, there are many ways of looking at risk, and consequently there are different interpretations of risk perception. (2010, 84). In the process of determining the probability of the outcome of some event and risk of some process or event persons are basing their predictions on their attitudes, the beliefs, the assessment of current situation, and on their knowledge of used research and scientific methods. Renn and Rohrmann (2000) define certain important elements that can have influence on the perception of the risk: - intuitive heuristics and judgment processes with respect to probabilities and damages; - contextual factors relating to the perceived characteristics of the risk (e.g. familiarity or naturalness) and to the risk situation (e.g. voluntariness, personal controllability);

7 7 ANALYSIS OF RISK AND UNCERTAINTY USING MONTE CARLO SIMULATION AND ITS INFLUENCE ON PROJECT REALIZATION semantic associations relating to the risk source, the people associated with; - risk and circumstances of the risk-taking situation trust and credibility of the actors involved in the risk debate (quoted in Aven 2010, 84). Thus, it is important to note that risk and the perception of the risk is based on the subjectivity of person or group of persons who are planning and evaluating capital investment. Doubt in the accuracy of predicted risk arises as consequence of the perception of risk and also that people rely on limited number of heuristic principles which reduce the complex tasks of assessing probabilities and predicting values to simpler judgment operations. In general, these heuristic are quite useful, but sometimes they lead to serve and systematic errors (Tversky and Kahneman 1974). People don t perceive situations in same way and do not behave the same, and that emerges from particularity, uniqueness and individuality of the each human being. Therefore, it is these propensities of each human that have an impact on different perceptions of the same observed fact and from it arises the problem of unified determination of probability of risks and it outcomes to particular business activity in the capital budgeting process. Subjectivity is a key factor in assessing risk. Whether a problem is perceived in terms of potential gains or losses will not be assessed as a simple mathematical calculation of the problem, but as a subjective fear, often linked to the consequences of outcomes. (Merna and Al-Thani 2005, 25 26). Most decisions concerning key variables of the capital budgeting are under the influence of uncertainty and risk, and that risk of capital budgeting can be viewed at the level of investment and the level of risk for the operation of a company. To estimate the individual risk of the capital investment the project, various analyses and simulations are used, most common of them being: a) sensitivity analysis; b) scenario analysis; c) decision tree; d) Monte Carlo simulation. Sensitivity analysis is the most commonly used method for measuring the impact of risk and uncertainty on the key variables of the capital budgeting. In the process of planning, the question of risk arises: what unexpected events can happen and what changes can occur on the observed variables, and also what variables and their impact have most effect on the profitability of the capital investment. The purpose of the sensitivity analysis is to directly assess the stability and strength of the decision to be made and its capability to stand in front of the future trials of various factors, taken into consideration at the

8 152 GORAN KARANOVIC, BISERA GJOSEVSKA 8 moment of making the decision (Bujoreanu 2011, 46). Usually in most of the industries profitability of capital investments depends on these key variables: initial investment costs, capital cost i.e. discount rate, sales price, volume of sale, fixed costs, variable costs, tax (primarily income tax, but and other taxation), inflation and change of course. Scenario analysis is one of the basic methods that are used for analyzing and measuring the impact of risk and uncertainty on capital investment. First steps in research, development, and usage the scenario analysis found in American corporations in the 50 s of the past century. The pioneer of development on that area is Stanford University and its belonging think-tank Stanford Research Institute (SRI) founded in (Fučkan 2007, 73). For conducting scenario analysis first the managers must determine those key variable that have the most significant impact on profitability and efficiency of the capital investment. Then the managers of the company are predicting the three most likely distributions of previously set key variables. First setting up the most likely scenario and his values distribution of key variables, secondly the best and third worst scenario. Up on set scenarios management is calculating financial ratios, and indicators methods that are used to calculate efficiency of the capital budgeting (NPV, IRR, PP, MIRR, IP etc.). The main advantage of the scenario analysis over the sensitivity analysis is expressed through the possibility of determining risk by distribution probability of occurrence of some event, however it has some imperfections. Main imperfection of this analysis is presented through limited numbers of scenarios that are analyzed, therefore, a limited number of probability distributions of the key variables, and thus the limited number of different heights of profitability indicator. Hence, in process of determining the key variables and their values in the scenario analysis the management is limited to three scenarios, while in the real life there are is unlimited number of possible scenarios of events that can occur and to have some effect on the probability distribution. The Monte Carlo simulation has been developed as an improved scenario analysis. Decision tree, unlike to sensitive and scenario analysis measures the risk of the all major decisions in the process of capital budgeting that are made from the phase of investing to the phase of effectuation. Orsag states that the usage of the decision tree is carried out for projects that require multiple investments over a long period of time. Such projects are common when it comes to investment in the brand new production-business capacity (2002, 226). Decision tree provides to management not only the possibility of measuring the risk of capital budgeting but also the possibility of visualizing the future decisions and actions that will have to be make. They are also easy to construct

9 9 ANALYSIS OF RISK AND UNCERTAINTY USING MONTE CARLO SIMULATION AND ITS INFLUENCE ON PROJECT REALIZATION 153 and follow, and they may be compressed into a decision table for developing a decision tree. So it is necessary to: - Identify all the conditions that might exist. - Identify all the possible actions to take in response to a given set of conditions. - Logically draw lines reflecting the sequence of conditions and the appropriate actions to take for each condition. Note: Each condition should have at least two actions from which to choose (Kliem and Ludin 1999, 40). Monte Carlo simulation eliminates the shortage of the scenario analysis, expressed in a limited number of scenarios and probability distributions, therefore Seitz and Ellison, emphasizing the importance this method states that is a technique that has been used for nearly four decades in capital investments analysis (2005, 385). For calculating Monte Carlo simulation complex software packages commonly are used by which management is setting up scenario models and calculating distributions of key variables. Simulation analysis allows the financial manager to develop a probability distribution of possible outcomes, given a probability distribution for each variable that may change (Peterson and Fabozzi 2002, 142). Therefore, Monte Carlo simulation represents an upgraded scenario analysis, but instead of a limited small number (3) of scenarios, software packages generate from several hundred up to several thousand scenarios, where they can simulate not only profitability indicators, such as net present value, profitability index, internal rate of return, but they can also be programmed to simulate entire simulation models for predicting net cash flows. Monte Carlo simulation is realized through: 1) establishing the key variables that have effect on prediction and on the required function (eg. NPV, net cash flow, IRR etc.); 2) determining the values of the selected key variables, and their distribution in the anticipated form (normal, triangular, uniform distribution etc.); 3) determining and calculate the mutual correlation of the key variables if it exists; 4) determining the predicted and required function; 5) combining determinate key values, and calculating expected and required functions; 6) iterating the previous procedure several hundred to several thousand times; 7) analyzing of the result obtained by Monte Carlo analysis.

10 154 GORAN KARANOVIC, BISERA GJOSEVSKA Monte Carlo simulation case study of the building hotel An application of the Monte Carlo simulation in capital budgeting is presented in a case study of building a new hotel. The management of the hotel company is planning capital budgeting building a new hotel with 100 rooms for which building it necessary to invest monetary units (m.u.). With business and financial prediction, and with financial plans it is predicted that the period of investment is two years, where investment costs planned for the first year are m.u., and for the second year m.u. In the third year of the project it is planned that the hotel will start with business and it is marked like beginning of the effecting period. Company has secured some of the necessary fund (retained earnings), and part of the fund is planned to get through bank loan, and for the other part is going to issue a preferred shares. In accordance with capital structure the management of the company can predict and calculate the cost of capital through weighted cost of capital (WACC) that is calculated using the most common form: w a = weight of retained earnings, k s = cost of retained earnings w d = weight of debt, k d = cost of debt after taxation w p = weight of preferred shares, k p = cost of preferred shares Table 3. Calculation of the weighted cost of capital Source of the Singular cost of Weighted cost Weight capital capital of source Retained earnings % 1.92 % Debt % 4.90 % Preferred shares 10 15% 1.5 % WACC 8.32% By using business prediction and financial plans the management has determined the key variables (Table 4) that have effect on profitability and overall judgment of acceptance of the investment project. The planned key variables represent the highest likelihood of realization and at the same time the lowest, the highest and the mean, i.e. most likely values for triangular distribution with which a Monte Carlo simulation can be carried out.

11 11 ANALYSIS OF RISK AND UNCERTAINTY USING MONTE CARLO SIMULATION AND ITS INFLUENCE ON PROJECT REALIZATION 155 Table 4. Predicted key variables for triangular distribution Sales price , Volume sale 28, ,00 18, Variable cost 6,683, ,00 4,455, Fixed cost 3,774, ,00 4,172, Initial investment cost 31,489, ,00 31,489, Cost of capital 6.66% 8,32% 10.00% Net cash flow 7,762, ,00 9,593, With the conducted calculation and analyzed results of the Monte Carlo simulation, the management is able to determine net cash flows and net present value, and also is able to establish the probability distribution of these two variables. In the first model and set of calculation a model is presented for determining net cash flow. Monte Carlo simulation of net cash flow is conducted on trials, where its probability distribution is determined in ranges of minimum value of 7.441, m.u. to the maximum value of 10,040, m.u. The mean of the net cash flow is 9,309, m.u, what is visible from Picture 1, marked with vertical line on the chart. On the right side of the picture we can see statistic where median is 9,434,760 m.u. and represents the mean value of the cash flow. Standard deviation, i.e. value of the average deviation from the mean is 488, m.u., a and skewness of this Monte Carlo simulation is -0,1 and indicates slight negative asymmetric distribution of the key variables in relation to the distribution mean. Picture 1. Predicted net cash flows with Monte Carlo simulation

12 156 GORAN KARANOVIC, BISERA GJOSEVSKA 12 By analyzing the results of the Monte Carlo simulation and distribution of cash flow of capital investment in the construction of the hotel we can conclude with 50% certainty that net cash flow will be in range of minimum 9,037, to maximum of 9,692, m.u., which range indicates a satisfactory overall profitability of capital investment. With regards to the conclusion from the above, the cash flows satisfy the criterion of positive net present value. In addition, it is possible to determine the sensitivity of the net cash flow to the key variables, what is presented in Picture 2. Analyzing sensitivity of the key variables to net cash we can conclude that biggest impact has variable costs, sales price and volume of sale (32.9%), while fixed costs have the smallest impact (1.4%). However it should be emphasized that these data should be taken with caution. Picture 2. Sensitivity cash flow to key variables With the second model of Monte Carlo simulation we were calculating the probability distribution of net present value for the same project building a hotel; the data of triangular distribution for key variables were taken from table 1. Using computer software results are presented in the following picture, where the central value of the net present value is 4,467,244 m.u. Also, with simulation the minimum value of the net present value is calculated at 7,710,832 and the maximum value of 19,941,337 m.u. Form the right side and statistical information we can read that the median is 4,133,811, standard deviation of 5,617,008 m.u. what indicates on average deviation of the mean,

13 13 ANALYSIS OF RISK AND UNCERTAINTY USING MONTE CARLO SIMULATION AND ITS INFLUENCE ON PROJECT REALIZATION 157 and skewness is 0,2475 and indicates on slight positive asymmetric distribution of the key variables in relation to the mean value. From the conducted simulation we can determine with 75% certainty that the minimal net present value is -2,225,187, maximal 11,468,217, and most likely 4,467,224 m.u., what is evident form the picture below. With Monte Carlo simulation the management has more quantitative and precise determination of probability distribution of net present value compared to other methods (sensitive, scenario analysis, tree decision etc.) which are commonly used to measure risk and uncertainty in the capital budgeting process. Picture 3. Predicted NPV with Monte Carlo simulation But besides the shown calculations which are due to better visibility as well as a higher-quality readibility and easier analysis presented in a graphic form, the use of software solutions enables a cumulative display of the oscillations and an inverse cumulative display of the oscillations of net present values, as shown in the following pictures.

14 158 GORAN KARANOVIC, BISERA GJOSEVSKA 14 Picture 4. Cumulative frequency of the NPV Picutre. 5. Reverse cumulative frequency of the NPV Except for being used as a tool to determine and analyze the realization of a representative probability distribution of the possible future net present values, the application of the Monte Carlo simulation method by using computer

15 15 ANALYSIS OF RISK AND UNCERTAINTY USING MONTE CARLO SIMULATION AND ITS INFLUENCE ON PROJECT REALIZATION 159 programs allows for a presentation of correlations and mutual influences of key variables. These relationships correlation and the mutual impact of key variables contribute to a greater understanding of the problem and the detection of potential risks during the period of framing the project s financial viability. By analyzing the correlation among the key variables from the Picture one can determine the probable risks which may emerge from unforeseen changes. The lower picture shows a perfect negative correlation between the increase in price and quantity of goods sold, as well as the increase in price and variable cost, and a perfectly positive correlation between the quantity of goods sold and variable cost. Such almost perfect results are the outcome of those previously forecast and determined correlations and changes among observed key variables. Picture 6. Correlation between key variables Picture 7 shows the minimum and maximum values of the forecast net present value, centered around the mean, for different significance levels for the predicted outcome. A more in-depth analysis of Picture 8 renders a possibility of 10% that the net present value of the project involving the construction of a hotel lies in the interval from 3,200,000 up to a little less than 5,000,000 monetary units. On the other hand, the minimum net present value is spread from cca -4,000,000 up to 14,000,000 monetary units.

16 160 GORAN KARANOVIC, BISERA GJOSEVSKA 16 Picture 7. Minimal and maximal values of NPV center around the mean 4. Conclusions and implications It can be summarized that risk and uncertainty are present in every capital budgeting process. The main question that arises in management decision making, however, is the one relating to the impact risk and uncertainty will have on the investment. Comparing the most commonly used methods, it can be concluded that the Monte Carlo simulation has become not only a recommended, but also a necessary, or even yet, an obligatory tool, given that it is one of the most complete and comprehensive methods for the assessment of the impact risk and uncertainty have on capital investments. The Monte Carlo simulation is superior to all the other currently available methods in the category of the number of iterations, that is, trial calculations including different key variable. The case study of a decision-making process regarding the construction of a hotel demonstrates in a profound, yet elegant way the merit and usefulness of simulation in predicting the most commonly used method NPV for evaluating capital investments. The net present value analyzed in the case study, as calculated by Monte Carlo simulation, demonstrates that the company s management have the possibility to precisely determine the impact of risk and uncertainty on the efficiency of the capital investment. The main implication of this analysis is to bring closer to the scientific and professional auditorium the advantages of Monte Carlo simulation in

17 17 ANALYSIS OF RISK AND UNCERTAINTY USING MONTE CARLO SIMULATION AND ITS INFLUENCE ON PROJECT REALIZATION 161 business practice and make it a standard tool of university curricula. Studies on this subject could be expanded and include company surveys and the use of discounted methods. Reference: Aven, Terje. (2010): Misconceptions of Risk. Chichester: John Wiley & Sons. Bujoreanu, Iulian N. (2011): «WHAT IF (Sensitivity Analysis)» Uredio Cezar Vasilescu. Journal of Defense Resources Management 2011 vol 2 no (Regional Department of Defense Resources Management Studies) 2, br. 1, Chandan, Gurnani. (1984): "Capital Budgeting: Theory and Practice." The Engineering Economist: A Journal Devoted to the Problems of Capital Investment 30, no. 14, David, J. Oblak, and J. Helm, Jr Roy. (1980): "Survey and Analysis of Capital Budgeting Methods Used by Multinationals." Financial Management 9, no. 4, Fučkan, Đurđica. «Scenario metode oblikovanja i upravljanja poslovnom budućnošću.» Uredio Ferdo Spajić. Računovodstvo i financije (Hrvatska zajednica računovođa i financijskih djelatnika) 8, (Kolovoz 2007): Hertz, David B. "Risk Analysis in Capital Investment." Edited by Adi Ignatius. Harvard Business Review (Harvard Business School Publishing Corporation) 57, no. 5 (September-October 1979): Hoesli, Martin, Jani Elion, and Andre Bender. (2005): "Monte Carlo Simulations for Real Estate Valuation." June or (accessed March 2012). Hopkin, Paul. (2010): Fundamentals of risk management: understanding, evaluating, and implementing effective risk management. London: Kogan Page Limited Hughes, William T. (1995): "Risk analysis and asset valution: A Monte Carlo Simulation using stochastic rents." The Journal of Real Estate Finance and Economics 11, no. 2, Hurley, J. W. (1998): "On the Use of Martingales in Monte Carlo approaches to multiperiod Parameter Uncertainty in Capital Investment Risk Analysis." The Engineering Economist: A Journal Devoted to the Problems of Capital Investment 43, no. 2, Kelliher, C.F. (2000): "Using Monte Carlo Simulation to Improve Long-term Investment Decisions." Appraisal Journal 68, no. 1, Kliem, Ralph L., and Irwin S. Ludin. (1999): Tools and Tips for Today's Project Manager. Newtown: Project Management Institute Kryzanowskia, Lawrence, Peter Lusztiga, and Bernhard Schwab. (1972): "Monte Carlo Simulation and Capital Expenditure Decisions A Case Study." The Engineering Economist: A Journal Devoted to the Problems of Capital Investment 18, no. 1, Kwak, Young Hoon, and Lisa Ingall. (2007): Exploring Monte Carlo simulation applications for project management. Risk Management 9, no. 1,

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