0  Introduction

The ability to gain is the key that links different participators of BOT project. But the profit forecasted has close affiliation with the risk that project faces. According to BOT highway project the amount of investment is large, the period of construction is long and its liquidity is not so good. The complexity of its environment, contract, financing brings huge uncertainty of profit in the future, too. Investment faces risk. So a reasonable financial analysis about risk of a project is key factor that may influence whether decision is right or not. At the same time it is an effective means to measure, avoid or control risk.

In China the active method which is usually used to appraise BOT project can be described as follow: evaluating the ability to gain by figuring out and comparing some indexes given such as IRR(internal rate of return), NPV(net present value), investment recovery period and using sensitivity analysis method to evaluate the extent of influence about these indexes by uncertain factors. But it isn’t feasible to order several projects when the index of IRR is used. How to work out the solution and analyze the solution aren’t so easy. So it is regarded that NPV is better.^{[5] [6]} By choosing appropriate basic yield(cost of capital) certain cash flow forecasted is used to calculate NPV. But it is not an effective method that can measure and evaluate risk and earnings synthetically and consider the relationship between each other. And when it is used to evaluate BOT project of highway, there are several shortcomings showed as follow:

There isn’t enough reason to confirm the value of base discount rate. Discount rate (Ri) reflects the lever of risk of project’s cash flow. ^[1] And NPV is determined by its value. But how to get reasonable Ri that can reflect risk of the given project correctly and is recognized widely is still a question when we want to evaluate a BOT project of highway. As could be seen in some documents from the government and in practice.

The result of forecast according as certain cash flow model is so single that it couldn’t show complicated impact of lots of uncertainty events upon BOT project during the period of investment cycle. Sensitivity analysis couldn’t settle the question about how to deal with the probability of different uncertainty events and it couldn’t describe the relationship between risk and earnings either.

Although it is important to analyze influence of each risk factor before evaluating a project, as we all know, there isn’t any touch between evaluation activity and risk analysis, risk management activities. Only qualitative analysis is executed when risk management task is performed. 

Therefore in order to guarantee success to investors of BOT projects, to build a reasonable and feasible financial evaluation model about risk is quite important. The rest of this article will present some improved suggestions.

1   Calculate appropriate adjusted discount rate

Discount rate reflects the lever of risk consisting in a project. As we all know, the effect of risk premium need to be considered as well as annual inflation rate, interest rate without risk. But different participators have different points of view about risk premium. The agreement is hard to be made. So a reasonable and accepted model that is used to settle this dispute is required. CAPM model that is widely adopted in money market is such a wonderful one. It can reflect the extent of risk of given asset effectively. Suppose money market maintains in equilibrium, prospective earnings of certain asset must equal to opportunity cost of the investment. And it must be minimal prospective return of the investment which bears certain extent of risk. ^[2] CAPM can describe the characteristic of earnings and risk about certain capital perfectly by two parameters: expectation and variance of the income.

Two types of risk make up of the total risk of a given asset in CAPM model. One is system risk and another is non-system risk. System risk is related to the status of the whole market. Non-system risk results from those events that only influence price of individual asset. CAPM model thinks diversification can avoid all the non-system risk. So only system risk is considered when an investment is being evaluated. Since CAPM model gets rid of disturbing factors only related to separate asset, It can always focus on such more useful information as industry type of investment, financial leverage. So its result of analysis will incarnate essential of cost of capital perfectly. ^{[1] [3] [4]} The expression of expected revenue of asset in CAPM model is showed as follow:

E(R_i)  --- expected revenue of asset I;

          R_f    --- interest rate without risk;

          E(R_m) --- expected revenue of market;

          βi   --- ratio of asset I to market on risk

In practice, we could let R_f equal to the interesting rate of national debt, whose time limit approximates to the construction period of the project. By Making regression analysis of yield from market E(R_m) and history yield from the highway asset or similar, we can figure out β_i. Then E(R_i) can be worked out by formula (1). Suppose β_i is changeless and the risk is close to that of history in future, E(Ri) can be regarded as the adjusted risk discount rate to be used when the highway project is evaluated.

E(R_i) is yield from capital stock. If total cash flow is considered, we need to calculate the weighted average cost of capital（WACC） and it will be regarded as adjusted risk discount rate. Its expression is showed as follow:

WACC ＝ weighted average cost of capital;

K_e＝ cost of capital stock;

K_d＝ cost of debt after tax, K_d＝ cost of debt×（1－ tax rate）；

E /（E＋D）＝ ratio of market value of capital stock to that of total assets;

D /（E＋D）＝ ratio of market value of debt to that of total assets.

K_d reflects financial risk of project and influence of tax policy. The less individual risk BOT project bears, the less cost of debt project bears. So it can be recognized that To choice a contractor which holds advantage of capital, credit, management, technique will lessen risk of implementation of project effectively. Certainly, if all of participators including government, loaners are of one mind, the individual risk of project will decrease fundamentally.

2  Introduce risk manage of project into financial analysis to measure source of risk

In financial analysis the risk of BOT highway project may be considered the difference between expectant income of project and that in practice. The income of Workable highway is made up of pike and toll. The payout is made up of investment of prepare, construction cost and maintenance cost. There are direct factors and indirect factors that influence cash flow of project. Direct factors include: status of local supply and demand of traffic in future, local law and code, contract terms, time span of delay, construction cost and operating cost and so on. Indirect factors include: change of political environment, market, status of performing contract and project management, accident etc. All of these uncertainty factors make up of the individual risk of a project. Investors must identify, analyze and respond all of the risk factors roundly and calculate the probability and possible loss one by one to guarantee success of a project. As we all know, that is just the task of traditional risk management. Some risk factors can be eliminated, decreased by investors’ management and investigation. Some can be transferred by contract and insure or settled by counterclaim. But the others are out of control. If investors have no choice to face these risks, they need to consider each of them, measure the loss in quantitative analysis.

Two tasks need to do if we want to introduce risk management of project into financial analysis. The one is to take above expense for cost, which is used to transfer and decrease certain risk factors. Another is to perform sensitivity analysis and relativity analysis to build a set that includes irrelevant uncertain events. Analytical method and simulation method are usually used when we want to know final influence of each risk factor upon the whole BOT project. But how to build a practicable model that is close to the physical model is still a question when analytical method is used. And how to express each variable and the relationship between each other blocks the use of Monte-Carlo Simulation. A simple and applied method is required in practice. ^[7]

3   Advanced evaluation method

Workable highway is this kind of asset that can produce cash flow in future. So discounting cash flow model could be used to find whether the investment is advisable. But how to relate each risk factor to the total earnings of a project is still a question after analyzing all of the risk factors. We think that the especial decision tree model which combines discounting cash flow model, scenario analysis and probability analysis can evaluate financial status of project under uncertain condition. The process is showed as follow: The decision tree includes a series of in-order risk factors which come from the collection of risk factors built in previous phase. The decision tree has an only origin and several branches. Each branch is made up of a series of in-order nodes denoting certain states of all the risk factors. Because each risk factor has several certain states and each branch includes a given state collection which reflects a certain condition of business, we can get several instances, namely, scenario that maybe occur. Each scenario corresponding a certain financial position can be forecasted and analyzed individually. The integration of all the scenarios reflects truly the risk of the project. ^[2] Scenario analysis needn’t consider how to build the relationship between each risk variable and target variable and the relationship between risk variable each other. The decision tree model has no constraint that the risk factor is independent. These points provide practicability for use of this method. ^[6]

Assume that the collection of uncertain events is Z（Z1，Z2，…，Zk，…，Zm）. In the collection, m is the number of the events that require considering. Assume that there are lkd kinds of states corresponding to every risk event. The state collection of each event and its corresponding probability distribution that are denoted by Xk（Xk1，Xk2，…，Xklkd）and Pk（Pk1，Pk2，…，Pklkd）respectively. They can be obtained by risk management technology. Because every risk event has an effect on each period’s cash flow of the BOT project and because a given scenario determines a special status of every risk event, a certain cash flow sequence corresponds to a certain scenario. Consequently investment project has w = l1d ×l2d×…×lkd ×…×lmd kinds of possible financial states (or possible scenario). The probability that each scenario occurs is: ^[6]

In this formula, j=1，…，w；j1=1，…，l1d；j2=1，…，l2d；…；jm=1，…，lmd。

Assume that under each scenario, the BOT project’s discounted net cash flow of each period is denoted respectively by: NPV1,NPV2,…,NPVj, …,NPVw, so the net present value of the cash flow sequence Yj is:

i = WACC or E(R_i) --- base discount rate calculated above.

Under this uncertain condition, net present value of project could be expressed by chance variable NPV with certain probability distribution. Its expectation E(NPV) is expressed as follow:

P21

P22

P21

P23

P22

P23

P21

P11

起点

X11

X12

X13

X21

X22

X23

…

…

Xk1

Xm1

Xmk

Xmlmd

…

Xk3

Xm1

Xmk

Xmlmd

…

Risk factors： Z1             Z2        …   Zk …           Zm m

P12

P13

P22

P23

scenario1

scenario2

scenariow

Figure 1 decision tree--scenario analysis

scenariojjj1

start point