VIEWS: 24 PAGES: 26 POSTED ON: 4/16/2010
APPLYING VALUE-AT-RISK TO CAPITAL BUDGETTIGN DECISIONS OF BOT PROJECTS Chao-Hsien Sung Department of Finance, National Sun Yat-sen University No.70, Lien-Hai RD. Kaohsiung City, 80424, Taiwan ROC firstname.lastname@example.org Kuang-Erh Lai Department of Finance, National Sun Yat-sen University No.70, Lien-Hai RD. Kaohsiung City, 80424, Taiwan ROC email@example.com Wen-Tao Lee Department of Finance, National Sun Yat-sen University No.70, Lien-Hai RD. Kaohsiung City, 80424, Taiwan ROC firstname.lastname@example.org ABSTRACT The typically traditional methods in investment decisions include payback period, internal rate of return(IRR), and net present value(NPV). While each of these has specific advantages to different types of projects, all ignore the fact that the cash flows over the project life are varied rather than fixed. As a result, they are not able to provide the decision makers with information on risk exposure involved, which is also as important as returns. In this paper, we adopt the concept of value-at-risk(VaR) widely used in measuring market risks in recent years to evaluate risk level of a significant Build-Operate-Transfer(BOT) project in Taiwan - the InterContinental Container Terminal Project of Kaohsiung Harbour. BOT projects are characterized by high capital outlays, long lead times, and long operation periods, which make the forecasts of cash flows more difficult and expose participants to high level of financial risk. With the help of Monte Carlo Simulation as well as considering correlation among risk factors, we are able to see a clear picture of risk involved in an BOT project and provide a better decision. Keywords: capital budgeting, value-at-risk, BOT, Monte Carlo Simulation 1. INTRODUCTION Public infrastructure investments played an important role in driving economic development of a nation. Not only did they contributed in expanding formation of national economic capital and further promoting continuous growth in the future, but they also created many immediate employment opportunities to assuage social tension and instability. These benefits are most appreciated during the period of economic downturn. This is the reason why most nations facing global financial crisis spend huge amount of budget in infrastructure projects. The most important question lies in how to proceed large-sized projects effectively and efficiently. Naturally, the answer points to cooperate with privately-held enterprises. This not only help to fully take advantage of human resources, techniques and experience of privately owned to accelerate infrastructure development, but also help to attract abundant private capital without incurring large public expenditure and borrowing. In addition, there is also risk sharing among participants One of the most popular forms of cooperation is the build-operate-transfer(BOT) approach. In a BOT project, normally, a private entity receives concession from the public sector to finance, design, construct, and operate facilities stated in the concession contract and recovers its investment, operating and maintenance expenses from the project. At the end of the concession period, such projects are to be transferred back to the public sector. BOT model has been seen as a major trend during the recent two decades in the privatization of public sector infrastructure projects, and it is especially so in the rapidly developing regions. There are several aspects to differentiate between a BOT project and a normal capital budgeting investment. First, BOT projects generally involve more parties, including at least private investors, government agencies and financing institutions. This represents more contract obligations will be enforced to greatly increase business risk. Second, BOT projects are normally characterized by high capital amount, long lead time and operation periods. These characteristics all lead to complicated forecasts of cash flows, and thus expose the private investors to high levels financial, political, and market risks. As a result, these requires the decision to incorporate risk analysis into project appraisal methods from multiple participants’ views. While traditional capital budgeting investment decision methods such as payback period, net present value, and internal rate of return are still widely used by corporate practitioners, they are not sufficient to address the involved risks in a BOT infrastructure project. Therefore, we propose to apply newly popular risk management tool, value-at-risk(VAR), to supplement traditional evaluation approaches, using the case of InterContinental Container Terminal Project of Kaohsiung Harbour, Taiwan. Monte Carlo Simulation method is used to quantify primary risk factors during operation period. In addition, correlation of risk factors are also considered in this case to be closed to reality. As the largest commercial port in Taiwan, Kaohsiung Port plays a critical role in promoting import and export in the past. To cope with the trend toward large-sized vessels and to meet the demands of increasing container volume, the Kaohsiung Harbor has implemented Phase One of the Kaohsiung Intercontinental Terminal under a BOT scheme at a cost of NT$42.89 billions. Initial construction was launched on November 2nd, 2008, and the project is scheduled to be completed in 2011. The Terminal will boast four wharves, with a total length of 1,500 meters. Upon completion, the Intercontinental Terminal is expected to increase container capacity by three millions TEU, further enhancing competitiveness of Kaohsiung Harbout. Besides the first section, this paper is organized as follows. The second section will review empirical studies on BOT. Session 3 will start analysis from traditional approaches. Session 4 should proceed to Monte Carlo Simulation and VaR analysis of this Project. Session 5 concludes. 2. LITERATURE REVIEW BOT model was first proposed by Turkish Premier Turgut Ozal in 1984 as a method to privatize public infrastructure. Tiong(1990) indicated that an BOT project contained a contract relationship between private sector and government agency, in which private entity established a concession company to engage in a series of activities of financing, designing, building and operating. As concession period expires, projects assets will be transferred back to government with or without redemption. Basic BOT project structure is illustrated in Figure 1. Figure 1 BOT project structure A number of literatures, typically Delmon(2005) and Vinter(1998), mentioned that the primary features of BOT projects included heavy capital outlay, technically complex and long lead time, long and comprehensive negotiations between participating parties, multiple risks involved and shared, project financing. In recent years, BOT has been seen as a popular model in infrastructure project around the world due to the following four reasons. 1. Economic growth boosts huge needs for infrastructure: Since public infrastructure is the backbone of continuous growth in the future, governments are expected to invest more to assure competitiveness. 2. Traditional capital sources provide limited financing size: Large capital outlay in an infrastructure project strains government financial position and create budget deficit, which demand access to abundant capital from private sector. 3. Inefficiency of public sector. The common problems in public-run projects are cost overrun and schedule delay, which results in great loss and bad management. Private sector is a reasonable alternative to cooperate. 4. Multiple implicit risks involved in infrastructure. BOT model can share risks by involving more parties and granting risk-adjusted profits. This is an acceptable model both to the public and private sector. Huang(1999) analyzed the behavior of cash flow and accumulated cash flow of BOT projects over different stages in a financial characteristic curve as in Figure 2. While constructing stage has negative cash flow, concession-operating stage is time to reap fruit with increasing higher cash inflow. He also address the decision indexes that deserves attention from standpoints of three main participants, including private investors, government agencies, and financing institutions. For private investors, payback years, internal rate of return, and NPV(net present value) should be the keys to look at in an investment decision. While government normally keep an eye on self-liquidation ratio(SLR), financing institutions care about debt coverage ratio(DCR) and Time interest earned(TIE). Figure 2 Financial characteristics in different stages Although Finnerty(1996) defined nine risk factors in BOT projects, including completing, technical, material supply, economic, financial, currency, political, environmental, and force majeure risk, in this paper, we focus on how to present financial risk. Value at Risk (VaR) is a widely used measure of the risk of loss on a specific portfolio of financial assets. Jorion(1997) defined VaR as a threshold value for a given portfolio, probability and time horizon, such that the probability that the mark-to-market loss on the portfolio over the given time horizon exceeds this value (assuming normal markets and no trading) is the given probability level. VaR could be derived from the probability distribution of portfolio’s future value f(w) under a given confidence level. It is the worst loss point w* that serves the following conditions, be it a continuous or discontinuous, fat-tail or thin-tail distributions. c * f ( w)dw w w* or 1 c f ( w)dw P( w W * ) p Not only did VaR get momentum in the international financial circle in recent years, but it had been regarded as a powerful tool in risk management. Dowd(1998) indicated the reason why VaR attracts much attention is that it can be applied in estimate market risk, credit risk and cash flow risk to improve accuracy of budget planning and decision. Volatility is critical in estimating VaR. While researchers normally estimate volatility of financial assets based on historical data, every BOT is unique in its scale, type of business, operational model, environmental factors, and concession contracts. Under this context, Luehrman(1998) suggested three methods to estimate volatility of investment project value. First by experience. This is to refer to how other projects with similar characteristics proceed to estimate volatility as well as take opportunity cost into consideration. Second, to estimate based on indirect but related historical industry data, or to use option pricing method to derive implicit volatility. Third, we could take advantage of computer technology to do Monte Carlo Simulation. This is to simulate cash flows of an investment project with appropriate settings, and further to describe probability distribution of returns by iterating large number of simulations. While there are a couple of approaches to estimate VaR, as shown in Table 1, and there are advantages and disadvantages in each, one of the powerful and widely-used method is Monte Carlo Simulation(MCS). In MCS, we use a random process to simulate behaviors of risk factors, with an aim to approximating distributions in real world and determining VaR. For example, we normally assume the behavior of stock price follows geometric Brownian Motion, dSt / St dt dWt , where Wt is a Wiener process or Brownian motion and μ ('the percentage drift') and σ ('the percentage volatility) are constants. The more the simulation number of times, the closer we can approximate real situations. MCS, however, is not without drawbacks. By choosing the wrong random process for risk factors, it will lead to model risk. In addition, large repeated samplings and complicated computer techniques consume huge cost. Therefore, the appropriate approach to choose should be based on the knowledge of characteristics and limitations of each approach as well as specialities of financial asset, then pick one that matches mostly. Table 1 VaR estimation approaches and characteristics Dalta-normal Delta-gamma Historical Monte Carlo Stress approach approach simulation Simulation Test Value Normal normal No No No distribution Valuation Linear linear full full Full Cash flow Yes Yes No No No Mapping Time variation Yes Yes No Yes Subjective Risk database Historical Parameters in Data and data for Scenario Risk database values of key a random requirement two order Assumption variables process computation 3. TRADITIONAL ANALYSIS AND RESULTS To begin with, we have to establish a financial model to generate cash flow for the InterContinental Container Terminal Project of Kaohsiung Harbour based on a couple of assumptions as in Table 2 and various estimated operating benefits and costs. While the most significant operating benefits for concession company are loading and unloading fee and machinery usage fee, which account for 31.75% and 40.71% respectively, the largest costs spend in royalty, land rent, facilities maintenance and repurchase, and administrative expenses. Given the above information, we are able to contracture yearly balance sheet, income statement, and cash flow statement of concession company by EXCEL. Table 2 Basic information and assumptions of Project Project parameters Assumptions Concession period 50years, from 2006~2055 Capital structure Equity : Debt = 3:7 Inflation rate 1.23% Annual throughput 1.8 million TEU(80% of capacity) Loan rate 7% Required return from shareholders 15% Tax rate 25% WACC(weighted average cost of capital) 8.18% As practitioners normally choose cash flow rather than accounting profit in the evaluation, we could plot cash flow and accumulated cash flow over years in terms of whole project view and shareholders’ view as in Figure 3, to see how they change over project period. “cf” and “ccf” stands for annual and accumulated cash flow in whole project view respectively, and “ccf” and “eccf” are annual and accumulated cash flow in shareholders’ view. While annual cash flow is negative during constructing period, most of operating period show positive and flat due to the fixed assumptions, which result in little variation in revenues. The two negative years in 2027 and 2042 indicate heavy repurchase costs. The difference in accumulate cash flow between two views results from financing activities that demands interest payment. Figure 3 Financial characteristics curve of Project Based on the annual financial statements, we can easily determine those indexes listed in Table 3. We define self-liquidation ratio(SLR) as the present value of total cash flow during operating period to the present value of total constructing and repurchase cost during constructing and operating period. Government agency looks at this index to see whether private participation is feasible. As we see this ratio is 1.26, greater than 1, this project is completely self-liquidated, and private investment can be recovered from operating profit. Additionally, besides initial cash outflows, more cash outflow(mostly repurchase costs) happens in subsequent years, we should calculate MIRR(Modified Internal Rate Of Return) rather than traditional IRR to avoid multiple solutions. Since both NPVs from different views are greater that zero, the MIRR(=8.598%) in whole project’s view greater than WACC(=8.18%) and MIRR(=15.0642%) in shareholders’ view greater than requested return from shareholders(=15%), this Project is feasible. Table 3 Investment decision indexes Whole Project’s view Shareholders’ view Accumulated NPV $2,654,164 Accumulated NPV $100,231 Return of Investment Return of Investment 8.598% 15.0642% (MIRR) (MIRR) Self- liquidation rate(SLR) 1.2640 Profitability index 1.0289 7 years after Profitability index 1.2202 Nominal payback period operating 8 years after 34 years after Nominal payback period Discounted payback period operating operating 21 years after Discounted payback period operating From financial institutions’ view, debt coverage ratio(DCR) is one of the most important index to assure debt payment, another similar index is time interest earned(TIE). The higher both of indexes, the stronger ability concession company possesses to repay debt. Normally, financial institutions request DCR to be 1.4~1.7 and TIE greater than 2. As we can see the financing indexes in Table 4, since both DCR and TIE meet the requirements, the financing plan is feasible. Table 4 Financing Indexes DCR TIE Minimum 1.60 2.74 Maximum 4.52 69.06 Average 2.77 12.07 Sensitivity Analysis Sensitivity analysis is used to see what will happen to those decision indexes when a critical variable changes. This belongs to a type of risk analysis. For example, in this project, the critical variables include operating revenue(fee per TEU), operating costs, throughput, loan rate, inflation rate. We recalculate each decision index for every variable change within an appropriate scope. The results show in Table 5. Table 5 Results of sensitivity analysis As we can see from Table 5, the following situations will drive NPV lower than 0, thus turn Project infeasible. First, in whole project’s view, when operating revenues(fee per TEU) falls lower than 10% and throughput falls lower than 15%. Second, in shareholders’ view, when operating revenues fall lower than 5%, operating costs increase over 5%, throughput falls lower than 5%, loan rate increases over 8%, and inflation rate falls lower than 0.73%. As for financing indexed, while DCR only falls to lower than 1 on condition that operating revenues fall lower that 10%, it remain above 1.2 in all the other situations. TIE falls to under 2 in case of operating revenues fall lower than 15% and loan rate increases over 9%. We can further graph five critical risk factors against four main decision indexes(SLR, NPV, DCR, TIE) to see the extent and direction of effects. For example, we could see clearly in Figure 4, while operating revenues and throughput have positive effects on SLR, the effects of operating costs are negative. Figure 4 Effects of risk factors changing on SLR 4. MONTE CARLO SIMULATION AND VAR ANALYSIS Monte Carlo Simulation is a flexible approach of approximating real world by combining sensitivity analysis, scenario analysis, and probability distribution of risk factors. Practically, we use computer to do simulations and generate a large number of values according to a pre-set rules. In this Project, simulation steps are as follows. Step 1: To determine risk factors: We pick three factors in this case, which include throughput, operating costs, and inflation rate. While we exclude operating revenues(fee per TEU) due to the fact that it was set by policy and thus volatility is small, loan rate is removed because it is not appropriate to do Monte Carlo Simulation. Step 2: To decide probability distribution and parameters for each risk factor. We assume normal distribution in percentage change of each risk factor, and collect historical data of past 10 years (1993~2003, as in Figure 5) to determine related parameters as in Table 6. The maximum and minimum are the extreme values that a simulation value allows. Figure 5 Historical trends of risk factors Table 6 Historical statistics of risk factors Percentage change Percentage change Percentage change of throughput of operating costs of inflation rate Maximum 17.0513% 13.4272% 9.7333% Minimum 0.1952% -2.5262% -0.5099% Average 7.1565% 3.5973% 2.0190% Standard deviation 5.4466% 5.3973% 2.7963% Step 3: Considering correlation of risk factors by Cholesky decomposition While many researches neglect correlation of variables in a multiple-factor analysis, we take a further step to consider correlation of risk factors in this case and compare with results without considering correlation. This is done by Cholesky decomposition. First, we calculate the correlation coefficients of risk factors from the historical values, the results shown in Table 7. By Pearson test, only correlation between percentage change of throughput and operating costs is significant and shows positive relationship(0.5328). Table 7 Correlation coefficient matrix of risk factors Percentage change Percentage change Percentage change of throughput of operating costs of inflation rate Percentage change of throughput 1 0.5328 -0.0982 Percentage change of operating costs 0.5328 1 0.1098 Percentage change of -0.0982 0.1098 1 inflation rate Put this matrix into MATLAB to determine the following Triangular matrix(A) needed to transform random variables into correlated variables. 1 0.5329 0.0982 A 0 0.8462 0.1916 0 0 0.9766 Step 4: Proceed Monte Carlo Simulation We then do simulations 10,000 times for each risk factor based on parameters, maximum and minimum values, and correlation transformation matrix A. For comparison, we choose three scenarios of parameter settings. Scenario A: 1. considering correlation of risk factors 2. risk factors ~ N ( historical value , historical value ) 3. given maximum and minimum. The simulation results and correlation coefficient matrix are in Table 8 and 9. Table 8 Simulation statistics under Scenario A Percentage change Percentage change Percentage change of of throughput of operating costs inflation rate Maximum 17.0490% 13.4250% 9.7332% Minimum 0.1961% -2.5214% -0.5099% Average 7.8495% 4.6949% 2.9332% Standard deviation 4.0414% 3.8524% 2.1116% Table 9 Correlation matrix of risk factors under Scenario A Percentage change Percentage change Percentage change of throughput of operating costs of inflation rate Percentage change of throughput 1 0.3426 -0.0712 Percentage change of operating costs 0.3426 1 0.1034 Percentage change of inflation rate -0.0712 0.1034 1 Scenario B: 1. Considering correlation of risk factors 2. risk factors ~ N ( historical value , historical value ) given maximum of percentage change of throughput is 25%, 3. which is the maximum capacity of this Project. The simulation results and correlation coefficient matrix are in Table 10 and 11. Table 10 Simulation statistics under Scenario B Percentage change Percentage change Percentage change of throughput of operating costs of inflation rate Maximum 24.7750% 24.5080% 11.3790% Minimum -13.5340% -17.0680% -8.6615% Average 7.1452% 3.6238% 2.0270% Standard deviation 5.4247% 5.4348% 2.8112% Table 11 Correlation matrix of risk factors under Scenario B Percentage change Percentage change Percentage change of throughput of operating costs of inflation rate Percentage change of throughput 1 0.5377 -0.0896 Percentage change of operating costs 0.5377 1 0.1199 Percentage change of inflation rate -0.0896 0.1199 1 The only difference between parameter settings in Scenario A and B is to relax the maximum historical assumption on percentage change of throughput to 25%, which brings higher variation into the simulation results as seen from Table 10. Scenario C: 1. Ignore correlation of risk factors 2. risk factors ~ N ( historical value , historical value ) 3. given maximum of percentage change of throughput is 25%. The simulation results and correlation coefficient matrix are in Table 12 and 13. Table 12 Simulation statistics under Scenario C Percentage change Percentage change Percentage change of throughput of operating costs of inflation rate Maximum 24.2920% 22.9540% 12.3580% Minimum -14.0850% -15.6780% -9.1364% Average 7.0680% 3.5829% 2.0001% Standard deviation 5.4457% 5.4513% 2.8085% Table 13 Correlation matrix of risk factors under Scenario C Percentage change Percentage change Percentage change of throughput of operating costs of inflation rate Percentage change of throughput 1 0.0214 -0.0063 Percentage change of operating costs 0.0214 1 0.0018 Percentage change of inflation rate -0.0063 0.0018 1 Since we also relax the assumption on correlation of risk factors, correlation coefficients are close to zero, which means risk factors do not affect each other and this is unrealistic. We only mean to do comparison with Scenario B. As a result, Scenario B seems the most reasonable parameter setting for following VaR analysis. Step 5: Estimating VaR for investment decision indexes of participating parties In this step, we should proceed to analyze the VaR of primary indexes from three participating parties’ views based on the parameter setting in Scenario B. Government agency’s view: We calculate NPV, MIRR and SLR and the result are shown in Table 14. Government normally looks to SLR in determining project feasibility as well as royalty and subsidy. If SLR is greater than 1, it means the operating revenues can completely cover investment costs. In this Project, the average and minimum SLR is 1.6353 and 0.7295, the probability of financial infeasibility is 3.58%. Table 14 Simulation results under Scenario B(government agency’s view) standard probability of Index average maximum minimum deviation under criteria NPV 7,272,043 6,735,265 62,587,593 -1,985,279 3.58% MIRR 8.94% 0.44% 10.39% 7.55% 3.66% SLR 1.6353 0.5064 5.1276 0.7295 3.58% The probability distribution of SLR under Scenario B is skewed right as in Figure 6. We then calculate VaR of SLR under the confidence level of 99%, 95% and 90%, and the results is 0.8989, 1.0288, and 1.1150 respectively. This means that the probability of SLR falling under 0.8989 is 1%, and we have 95% confidence that SLR will not fall under 1.0288. Although some infrastructure projects may have low SLR of indicating financial infeasibility, they may possess high economic and strategic profits. In such case, government may consider proceed on its own. Figure 6 Probability distribution of SLR Private Investors’ view: The three key decision indexes are NPV, MIRR and PI, and simulation results based on Scenario B are shown in Table 15. While average NPV and PI are 1,494,498 and 1.34 respectively and both represent financial feasibility, probability of less than criteria for both indexes are in 14.42% level, which is much higher than in whole project’s view. This is because financial leverage involved in this view and maximum percentage change of risk factors increase. Table 15 Simulation results under Scenario B(shareholders’ view) Standard probability of Index average deviation maximum minimum under criteria NPV 1,494,498 1,591,206 12,747,048 -1,791,213 14.42% MIRR 15.59% 0.57% 17.26% 12.84% 14.42% PI 1.3394 0.3225 2.6937 0.3804 14.42% Probability distribution of NPV under Scenario B is graphed in Figure 7. The critical values in the left-tail of 1%, 5%, and 10% to determine VaR under the confidence level of 99%, 95%, and 90% respectively show in Table 16. Under Scenario B, we have 90% confidence in that NPV not losing over 183,195 thousands, 95% confidence that NPV not losing over 465,330 thousands. Only 1% probability that NPV will losing over 897,637 thousands. We can also see the necessity of considering correlation of risk factors from this table. Take 95% confidence level as example, VaR in Scenario C(-655,989), which is without correlation of risk factors, is 1.41 times more than that in Scenario B(-465,330), which considers correlation. The difference is significant Figure 7 Probability Distribution of NPV Table 16 VaR for NPV under three confidence level for three scenarios 1% 5% 10% Scenario A -130,492 196,584 436,297 Scenario B -897,637 -465,330 -183,195 Scenario C -1,166,083 -655,989 -339,792 Financial institutions’ view: The important decision indexes in this view are DCR and TIE. Financial institutions would always like to make sure that cash flows generated during project life are able to repay principal and interest, and this is translated into criteria of DCR be over 1.4 and TIE over 2 from a conservative way in this research. The simulated results for these two indexes under three scenarios are listed in Table 17. Under Scenario B, average DCR is 1.77 and TIE is 3.09. While probability of DCR falling under criteria is only 2.64%, the probability for TIE is zero. The risk exposure of financial institutions is surely less than that of private investors and government agency in this regard. Table 17 Simulation results under three Scenarios Standard probability of Index average maximum minimum deviation under criteria DCR 1.8403 0.1695 2.3107 0.3045 0.49% Scenario A TIE 3.1867 0.2392 4.1422 2.5414 0.00% DCR 1.7730 0.2535 2.5313 0.2223 2.64% Scenario B TIE 3.0946 0.2959 4.3630 2.0135 0.00% DCR 1.7638 0.3035 2.5363 0.1664 4.36% Scenario C TIE 3.0923 0.3538 4.4568 1.7662 0.06% Probability distribution of DCR and TIE is shown in Figure 8 and 9, and critical values in the left-tail of 1%, 5%, and 10% are listed in Table 18. Under Scenario B, we have 90% confidence that DCR will be fall under 1.57 and 95% confidence that it will not fall under 1.5. As we see several extreme values in Figure 8, that brings 1% critical value down to 0.32. As for TIE, under all confidence level, VaRs are greater than the criteria 2, which means interest payments can almost be secured during project life. Table 18 VaR for DCR and TIE under three confidence level DCR 1% 5% 10% Scenario A 1.5554 1.6373 1.6773 Scenario B 0.3191 1.4998 1.5733 Scenario C 0.2944 1.4249 1.5274 TIE Scenario A 2.6995 2.8154 2.8833 Scenario B 2.4261 2.6226 2.7211 Scenario C 2.2877 2.5296 2.6502 Figure 8 Probability Distribution of DCR Figure 9 Probability Distribution of TIE Step 6: Sensitivity analysis of VaR In the previous step, we generate VaR of decision indexes by Monte Carlo Simulation, which based on fixed parameters of three risk factors that derived from historical values. However, if we choose the wrong parameters, the consequences will be quite different. To overcome this model risk, we can complement by doing sensitivity analysis, focusing on volatility of key risk factors. By doing so, a more complete picture of project risk exposure should present. From previous analysis, throughput is the most important risk factor based on its effects on BOT project either from government agency’s view, private investors’ view or financial institutions’ view. We then do stimulations based on parameters setting in Scenario B, except that volatility of throughput is set to be -2%, -1%, +1%, +2%, +3%, +4%, +5% deviate from original value 5.45%. Government agency’s view: We do Monte Carlo Simulation to see the effects of percentage change in volatility on SLR. The results are shown in Table 19. As we can see, there is not much difference on average SLR through all volatility level, even increases to 10.45%(5.45%+5%), but the probability of SLR being under 1 has increased over two times from original 3.58% to 8.85%. Table 19 SLR under different volatility settings Percentage change Standard Probability average maximum minimum of volatility deviation of under 1 -2% 1.6376 0.4968 4.8895 0.7474 3.19% -1% 1.6293 0.4969 4.4643 0.7002 3.28% 0% 1.6353 0.5064 5.1276 0.7295 3.58% 1% 1.6248 0.5121 4.6678 0.6984 3.99% 2% 1.6080 0.5046 4.8246 0.0845 4.87% 3% 1.5913 0.5100 5.5421 -3.5469 5.78% 4% 1.5677 0.5058 5.1117 0.5272 7.09% 5% 1.5465 0.5147 5.1103 -3.4050 8.85% The VaR of SLR under confidence level of 90%, 95%, and 99% for each volatility level is listed in Table 20. As volatility changes, project decision may change accordingly. Take 95% confidence level as example, when volatility change from original point(=5.45%) to +3% point(=8.45%), SLR turns from 1.0288 to 0.9831, which means the project changes from able to self-liquidate to unable to self-liquidate. This will prompt government agency to consider more attractive terms on the BOT concession contracts. As we can see in Figure 10, as volatility deviate more from original point, the higher the confidence level, the greater the VaR percentage change will happen. Table 20 VaR of SLR under different confidence level SLR 99% 95% 90% critical percentage critical percentage critical percentage value change value change value change -2% 0.9203 2.38% 1.0420 1.28% 1.1265 1.03% -1% 0.9184 2.18% 1.0420 1.28% 1.1189 0.35% 0% 0.8989 0.00% 1.0288 0.00% 1.1150 0.00% 1% 0.8994 0.06% 1.0220 -0.66% 1.0988 -1.45% 2% 0.8686 -3.37% 1.0029 -2.52% 1.0863 -2.57% 3% 0.8497 -5.47% 0.9831 -4.45% 1.0688 -4.14% 4% 0.8257 -8.14% 0.9612 -6.57% 1.0439 -6.37% 5% 0.7691 -14.43% 0.9224 -10.34% 1.0173 -8.76% Figure 10 SLR: percentage change of critical value in different confidence level Private investors’ view: The effects of volatility change on NPV is shown in Table 21. Although average NPV keeps positive under all volatility levels, probability of NPV turning negative rising to 29.20%, two times higher than original point(14.42%). Table 21 NPV under different volatility settings Percentage change Standard Probability average maximum minimum of volatility deviation of under 0 -2% 1,513,392 1,499,805 11,882,629 -1,197,418 12.18% -1% 1,476,787 1,529,645 10,570,225 -1,426,858 13.57% 0% 1,494,498 1,591,206 12,747,048 -1,791,213 14.42% 1% 1,414,044 1,617,168 11,187,478 -2,622,873 17.02% 2% 1,324,748 1,638,926 11,690,866 -2,949,234 19.90% 3% 1,234,061 1,684,115 14,661,261 -3,983,903 22.98% 4% 1,111,523 1,717,205 12,588,054 -3,806,626 26.15% 5% 1,008,245 1,778,333 12,826,779 -4,438,421 29.20% The VaR of NPV under confidence level of 90%, 95%, and 99% for each volatility level is listed in Table 22. As volatility increases, critical value in left-tail of NPV move leftward and change scope increases, and when volatility decreases, critical value in left-tail move rightward. This is the same as in SLR, but change scope is much larger. As we can see in Figure 11, the percentage change of critical value in low confidence level is higher than that in high confidence level, this is exactly contrary to what happens in SLR. Table 22 VaR of NPV under different confidence level NPV 99% 95% 90% percentage percentage critical percentage critical value critical value change change value change -2% -737,354 -17.86% -345,494 -25.75% -82,636 -54.89% -1% -770,552 -14.16% -390,235 -16.14% -138,998 -24.13% 0% -897,637 0.00% -465,330 0.00% -183,195 0.00% 1% -1,058,742 17.95% -597,692 28.44% -305,828 66.94% 2% -1,352,824 50.71% -758,568 63.02% -420,883 129.75% 3% -1,673,818 86.47% -919,384 97.58% -552,589 201.64% 4% -1,935,041 115.57% -1,170,259 151.49% -752,335 310.67% 5% -2,278,525 153.84% -1,426,727 206.61% -971,622 430.38% Figure 11 NPV: percentage change of critical value in different confidence levels Financial institutions’ view: We simulate the effects of volatility change on DCR and TIE. The results are shown in Table 23 and Table 24. The average DCR decreases along with volatility increases. While average DCR is still larger than the criteria of 1.4 as volatility increases to 10.54%, probability of falling under 1.4 has already increased from original 2.64% to 15.71%. TIE behavior is much the same with that in DCR, with change scope is much less. The probability of falling under criteria 2 is also small. Table 23 DCR under different volatility settings Percentage change Standard Probability average maximum minimum of volatility deviation of under 1.4 -2% 1.7853 0.1786 2.2194 0.2676 1.18% -1% 1.7764 0.2086 2.2831 0.2589 1.62% 0% 1.7730 0.2535 2.5313 0.2223 2.64% 1% 1.7387 0.3045 2.3309 0.1955 4.45% 2% 1.7077 0.3595 2.3819 0.1822 6.76% 3% 1.6700 0.4140 2.3322 0.0538 9.38% 4% 1.6256 0.4675 2.3917 0.0953 12.60% 5% 1.5823 0.5138 2.3441 0.0522 15.71% Table 24 TIE under different volatility settings Percentage change Standard Probability average maximum minimum of volatility deviation of under 2 -2% 3.0954 0.2351 4.0121 2.2000 0.00% -1% 3.0876 0.2584 4.0950 2.0079 0.00% 0% 3.0946 0.2959 4.3630 2.0135 0.00% 1% 3.0638 0.3095 4.2105 1.8153 0.06% 2% 3.0399 0.3368 4.1328 1.7327 0.11% 3% 3.0127 0.3627 4.1390 0.8217 0.45% 4% 2.9792 0.3872 4.1495 1.3013 0.77% 5% 2.9466 0.4176 4.1459 0.7498 1.62% The VaR of DCR and TIE under confidence level of 90%, 95%, and 99% for each volatility level is listed in Table 25 and Table 26, and percentage change of critical value for both indexes against different confidence level are graphed in Figure 12 and Figure 13 respectively. Since there are several extreme values in probability distribution of DCR, thus higher volatility might invite large effects on the decision. For example, under 95% confidence level, as volatility increase 3%, critical value change from acceptable 1.4988 level to unacceptable 0.3036 level. This will causes much difference in financial institutions’ loan decisions. We should be very much cautious in choosing volatility and confidence level. As for TIE, most critical values under three confidence level are greater than criteria 2, thus the effect of this index on decision is little. Table 25 VaR of DCR under different confidence level DCR 99% 95% 90% critical percentage critical percentage critical percentage value change value change value change -2% 1.3162 312.52% 1.5730 4.88% 1.6251 3.29% -1% 0.3589 12.48% 1.5371 2.49% 1.6029 1.88% 0% 0.3191 0.00% 1.4988 0.00% 1.5733 0.00% 1% 0.2838 -11.06% 1.4250 -4.99% 1.5316 -2.65% 2% 0.2594 -18.70% 1.2928 -13.80% 1.4780 -6.06% 3% 0.2399 -24.81% 0.3036 -79.76% 1.4169 -9.95% 4% 0.2244 -29.67% 0.2750 -81.66% 1.3046 -17.08% 5% 0.2093 -34.41% 0.2553 -82.98 0.3044 -80.65% Table 26 VaR of TIE under different confidence level TIE 99% 95% 90% critical percentage critical percentage critical percentage value change value change value change -2% 2.5547 5.30% 2.7147 3.51% 2.7948 2.71% -1% 2.5023 3.14% 2.6707 1.83% 2.7601 1.43% 0% 2.4261 0.00% 2.6226 0.00% 2.7211 0.00% 1% 2.3480 -3.22% 2.5545 -2.60% 2.6634 -2.12% 2% 2.2340 -7.92% 2.4729 -5.71% 2.5989 -4.49 3% 2,1241 -12.45% 2.4005 -8.47% 2.5425 -6.56% 4% 2.0392 -15.95% 2.3111 -11.88% 2.4619 -9.52% 5% 1.9053 -21.47% 2.2300 -14.97% 2.3939 -12.06% Figure 12 DCR: percentage change of critical value in different confidence levels Figure 13 TIE: percentage change of critical value in different confidence levels 5. CONCLUSIONS While researches on BOT in the past generally focus on single participant’s view to analyze feasibility, in this paper we cut into from three primary participants’ views to analyze the decision indexes of their concerns, including SLR for government agency, NPV for private investors, and DCR and TIE for financial institutions. A BOT project cannot be successful without all three participants’ involvements. We apply Monte Carlo Simulation to approximate behaviors of risk factors in this project rather than follow traditional and subjective method to generate cash flows, which is then used to determine decision indexes. Additionally, in the simulation process, we take correlation of risk factors into account by adopting Cholesky decomposition, which is a fact normally ignored by other researches. Finally, the newly popular risk evaluation tool – VaR – is used in this study to show more risk exposure information about decision indexes. We come to the following conclusions: 1. Private investors face largest uncertainty and probability of the decision index NPV falling under criteria(>0) is greatest due to the financial leverage they use. Under this situation, they have to forecast more accurately about risk factors. In this regard, Monte Carlo Simulation and sensitivity analysis are good approaches to adop. Financial institutions face the smallest risk with lowest probability of DCR and TIE falling under criteria. 2. “throughput” is the most important risk factor in this BOT project, no matter from views of government agency, private investors, or financial institutions. It is necessary to do a comprehensive study to reach a more accurate forecast on this factor and install an effective risk management strategy to counter adverse trends. 3. The correlation of risk factors plays critical role in generating critical values of decision indexes. Without considering this point is not realistic and will lead to wrong investment decisions. 4. The parameter(volatility) changes of risk factors have effects on VaR of decision indexes. As volatility increases, critical value of left-tail moves leftward, and as it decreases, critical value of left-tail move rightward. Therefore, if the probability distribution of a decision index is left-skewed, then critical value will be affected by volatility and confidence level, and further may change final decision. We have to be very cautious in this case. REFERENCES Delmon, Jeffrey, 2005, Project finance, BOT projects and risk., Baker & Taylor Books Dowd Kevin. 1998. Beyond Value at Risk：The New Science of Risk Mamagement. John Wiley ＆ Sons Ltd. Finneryty, John, 1996, Project Financing, John-wily & Sons Inc. Huang, Ming-Shen, 1999, The financing and financial adjustment in traffic BOT infrastructure project, Journal of Social-Economic law, No. 23. Chinese version. Huang, Ming-Shen, 1999, The financing and financial adjustment in traffic BOT infrastructure project, Journal of Social-Economic law, No. 23. Chinese version. Luehrman, A. Timothy, 1998, Investment Opportunities as Real Options: Getting Started on the Numbers, Harvard Business Review, Robert Tiong, L.K., 1990, BOT Projects: Risks and Securities, Journal of Construction Management and Economics, University of Reading, UK, September, Vol. 8, p. 315-328. Robert Tiong, L.K., Alum, J., 1997. Evaluation of proposals for BOT projects, International Journal of Project Management, UK, Vol. 15, No. 2, p. 67-72. Sudong Ye, Robert L. K. Tiong, 2000, Npv-at-risk method in infrastructure project investment evaluation, Journal of construction engineering and management, May/June, pp. 227-233. Vinter, G.D., 1998, Project Finance, 2nd ed. London: Sweet & Maxwell. 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