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The Financial Risk Analysis of a BOT infrastructure project the



                                 Chao-Hsien Sung
               Department of Finance, National Sun Yat-sen University
              No.70, Lien-Hai RD. Kaohsiung City, 80424, Taiwan ROC

                                     Kuang-Erh Lai
               Department of Finance, National Sun Yat-sen University
              No.70, Lien-Hai RD. Kaohsiung City, 80424, Taiwan ROC

                                      Wen-Tao Lee
               Department of Finance, National Sun Yat-sen University
              No.70, Lien-Hai RD. Kaohsiung City, 80424, Taiwan ROC

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
     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
     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

                   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
                   Normal           normal           No               No            No
  Valuation         Linear          linear           full            full           Full
  Cash flow
                     Yes             Yes             No               No            No
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

     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
                   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
                                     8 years after                                34 years after
     Nominal payback period                           Discounted payback period
                                     operating                                    operating
                                     21 years after
     Discounted payback period
     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


     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
                                     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   0.9766 

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%,
                  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
     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
       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
    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.

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