Risk Analysis of investment projects, construction paper to write network _

Papers to write Net: [Abstract] Monte Carlo risk analysis model is an important means, often used in Engineering Investment projects, through Computer simulation, construction Investment projects can draw the risks and benefits distribution, then that meets the The rate of return and risk distribution of random numbers to simulate the kinds of situations, allowing risks to the project Investments are more close to the actual forecast.

[Keywords:] risk analysis, Monte Carlo simulation, Investment decisions

1 Overview
In practice, the analytical method used for risk analysis of projects sometimes encounter difficulties, for example, often times there is not enough profitability of the project according to the probability distribution of types of indicators to make clear judgments, or the distribution can not be A typical probability distribution to describe in this case, if we can know the impact on project profitability indicators of the probability distribution of the uncertainties, we can use simulation methods to conduct risk analysis of the project.

Project Economic evaluation of the project proposal and feasibility study report an important part, through the project's financial feasibility and Economic reasonableness of quantitative calculations, analysis and appraisal for the project provide the basis for scientific decision-making while also BOT, TOT, etc. New franchise investors, Investment and financing mode based on the project Investment decisions in the project Economic evaluation used in the basic data such as capital Investment, cost, product (service price, the construction period, and most come from the forecast of future conditions and estimates, the resulting evaluation and make decisions often have a certain degree of risk. In order to project Investment decisions based on reliable and comprehensive, in addition to the Economic evaluation of the basic program to calculate and analyze the Economic indicators, but also the need for uncertainty analysis and risk analysis, and proposed measures to avoid the risk.

Monte Carlo method is a random variable by the statistical test, stochastic simulation techniques to solve various problems of mathematical approximation, which is characterized by use of mathematical methods in Computer simulation of the actual probability of the process, and then to statistical processing, to solve a uncertainty of complex issues. to solve the economic problem of random probability, the Monte Carlo method is recognized as an economic and effective way, risk analysis in Investment project is very practical value in this paper, a construction company to test a projects, for instance, the use of Computer programming, try the Monte Carlo simulation Technology in the construction project risk analysis applications.

2 Project Overview
A construction company a mode of the BOT project is still in the design and bidding phase. In accordance with the results of the preliminary design estimates, the building construction business a 2.1375 million yuan Investment, liquidity 5.1537 million yuan, the annual operating costs of 30.665 million yuan.

According to the project implementation plan, the construction period of three years, annual investment in the use of 22%: 42%: 36%, production and operation period is set according to the economic life of 20 years, fixed assets, residual rate of 4% annual sales revenue is estimated at 65.7 million yuan, excluding value-added economic evaluation, taking into account only the urban maintenance and construction tax, additional education and flood control funds, according to the current benchmark rate of return internal rate of return standards for the construction Industry to take 4% to financial internal rate greater than the benchmark rate of return the project feasible. the basis of data in accordance with the above financial analysis, pre-tax internal rate of return 5.38%, payback period (including construction period 4.77 years, the financial net present value (i = 4% ) is 52.34 million yuan, can meet the minimum financial requirements, financial analysis from the perspective that the project is feasible.

3 simulation
Monte Carlo simulation of the implementation of the general steps are: to determine the risk variables, analysis of possible changes in the range of each variable and determine the probability distribution of these changes, the probability distribution of variable structure model of risk, through simulation, risk variables collected for each random number and the probability distribution of random numbers according to the sampling model into a variable value, the value of the sample evaluation form the basis of a set of economic data, the calculated evaluation values, and repeat the test, the number of simulated test results obtained after finishing the project evaluation the expected value, variance, standard deviation and probability distribution and its cumulative probability, cumulative probability plots to draw, you can find the project feasible or not feasible probability.

3.1 to determine the probability distribution of risk variables.

In the economic evaluation of projects, usually presumed method of historical data or expert survey method (commonly used in the Delphi method to determine the probability distribution of variables. This construction simulation using expert survey methods measure the distribution of risk variables to determine the model.

3.1.1 The probability distribution of construction investment. The probability distribution of construction investment using triangular distribution, invited experts, based on preliminary design estimates to predict the situation on the investment, the most optimistic estimate investment value, the maximum possible value, the most pessimistic value, strike expert opinion, on average, and calculate the standard deviation and dispersion coefficient, dispersion coefficient from the expert consistency requirements, estimated by calculation to determine the final triangle model, the result is: optimistic value 341,810,000 yuan, the value of the maximum possible value of the use of estimates 40213.75 million pessimistic value 442,350,000 yuan.

3.1.2 operating costs and the probability distribution of sales revenue. Operating costs and sales revenue of normal probability distribution are used to invite experts on the operating costs and revenue expectations, the probability distribution and estimate the range. Select three experts estimates of operating costs are calculated examples are as follows: first the expected operating costs, experts say $ 30 million, ten thousand yuan in 2760-3240 within the scope of the probability of 90%, or 32.4 million yuan in 2760 - the probability outside 10%, less than 27.6 million yuan (32.4 million yuan or more than 5% probability that the expected value of 30 million yuan more than 2.4 million to reduce the probability of 5%, check the standard normal distribution probability table or by a Computer program to calculate was deviation of -1.645, which is equivalent to deviate from the expected value-1.645ð, so standard deviation ð = 240/1.645 = 146 million. Similarly, other experts calculate the expected operating costs and the estimated standard deviation value, the results in Table 1. Experts estimate that the average standard deviation of the results is 164 million, 247 variance, coefficient of dispersion, the consistency required to meet experts, to determine the probability distribution of operating costs subject to N (3037,1642) positive state distribution.

Using the same method, estimated by experts to determine the probability distribution of operating income subject to N (6570,3802) of the normal distribution, the process is omitted.

3.2 extracted random number to generate the value of the variable sampling
This simulation process is completely done by a Computer program, using programming languages ​​to provide a random number of random number function to get. Links to free download http://www.hi138.com of capital investment, operating costs and sales revenue for random number, as the probability of a random number as a variable value, and in accordance with the appropriate probability distribution model into the sample values ​​of random variables, transformation process is as follows:
3.2.1 Construction Investment obey the triangular distribution, the direct use of the mathematical meaning of the probability that the triangle area to strike a random variable.

3.2.2 operating costs and sales revenue is normally distributed, a normal map on the shaded area of ​​the probability of a random number generator value, the probability value by the standard normal distribution probability table or check the computer program calculated by sampling from the expected value the deviation, the sample can determine the value of random variables: sample value (x) = expected value + - standard deviation × difference.

3.3 Sample evaluation index value calculated
Identified a group of construction investment, sales and other operating costs and sample values ​​of random variables to this set of sample data is the basis for economic evaluation, liquidity management costs in accordance with the expected value of the sample to adjust the ratio to calculate project economics evaluation index value. common evaluation indicators of financial net present value, internal rate of return, payback period, etc., the general financial internal rate of return in calculating the period according to the following formula using computer spreadsheet interpolation method for solving FIRR:
NPV =
Capital inflows which include sales and CI calculated residual value of the end of recovery, recycling liquidity outflow of capital construction investment, including CO, sales taxes and operating cost.

3.4 Simulation results and number of tests on the results of impact analysis
Repeat the above randomized trials, intended to simulate the number of results after each test to the frequency of occurrence as a probability, according to the internal rate of return from small to big to sort, collate all the results of the expectations, variance, standard deviation, and calculate the cumulative probability , to strike a financial internal rate of return is less than the benchmark rate of return of the cumulative probability to determine the probability of the project is feasible or not feasible. The number of tests works as a simulation 2000 times, finishing the simulation results, the average internal rate of return was 5.64%, variance 1.93, the dispersion coefficient of 24.63%. According to the internal rate of return calculation to sort ascending, to determine the internal rate of return below the benchmark rate of return of 4% cumulative probability of 12.75%, internal rate of return that is greater than or equal to 4% probability of 87.25%, showing that the project's financial risk.

4 Computer simulation
Monte Carlo simulation for risk analysis, repetitive calculation process, workload, general use computer programs to complete. In order to Monte Carlo simulation Technology into the sewage treatment project economic evaluation of risk analysis, the author uses visual programming language Visual Foxpro developed a computer program.

Using the program, according to experts, the survey results to determine the distribution of risk variables model, to achieve a normal distribution with the probability of conversion from the difference (calculated in the standard normal distribution table of data, and generate random numbers drawn sample and calculating the economic evaluation indicators, a set number of tests under repeated simulation and modeling, see the simulation results, the probability of forming simulation charts, etc., to achieve short time to complete the calculation of thousands of simulation, analysis and output the statistics in Table 2 in P2.8G computer program using the number of tests at a different time-consuming simulation, which is 2000 times when the number of tests in a mock takes only 2.97 seconds, repeated 20 times total simulation time of about 1 minutes, if the number of tests of 10000 times, 20 times the cumulative time-consuming repeated simulations will reach 5 minutes.

In the construction project feasibility study report in the economic evaluation, risk analysis has a high requirement, the probability of project risk analysis is important, and Monte Carlo simulation techniques is an important means of simulation analysis. Based on a Construction As an example, the preparation of a computer program for Monte Carlo simulation analysis, the probability of the project feasible or not feasible, provided for the construction of decision-making basis and feasibility study for the project risk analysis case, both the BOT, TOT and other new franchise model for project investment and financing decisions of investment risk analysis to provide a reference.


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