Экономические науки/Математические методы в экономике

 Master student Aristombaeva M.T.,

students Abilkhanova Zh.K., Auezova A.S., Kozhakova D.N., Sambetova M.E.

Research supervisor Candidate of Technical Sciences Kurmanov B.K.

Kazakh-British Technical University, Kazakhstan

 

Assessment of attractiveness of the investment project by the method imitating modelling

 

The investment project is developed, based on certain assumptions on capital and current expenses, sales volumes of manufactured products, prices of goods, project time frame. Regardless of the quality and validity of these assumptions, future development related to the implementation of the project is not ambiguously. In this case, using of investment design consider uncertainty and risk aspects.

In analyzing of investment projects modern economists faced with need to consider risk so cash flows of any project can be represented in the probability-theoretic sense of some-of random variables. In this case, all parameters of economical mathematical cash flow models are divided into Quasideterministic (parameters that are unchanged and exactly knownin the development of this investment project) and random (impacted by several factors: economic, political, social, etc.). Since all parameters of economical mathematical models of cash flows interact with each other so statistical characteristics of random cash flows can be found with using of simulation cash flows [1].

If we assume that the annual output (Q), the expected cost (p), variable cost per unit of output (v) and annual fixed costs (F) is the value of Quasideterministic, the cash flow for a given tax rate (t) can be determined by the formula:

С =

 

otherwise

 

In general, these variables in the formula are random variables with given distribution laws and procedure of finding random cash flows to conduct a series of algebraic operations on random variables and in the result to get distribution law of the random cash flows. Such task is quite time-consuming and not always feasible, because addition or multiplication operations of random variables described by distribution law are quite complex.

Simulation modeling is one of the most powerful methods for the analysis of economic systems. In general, imitating is the process of conducting experiments on the computer with mathematical models of complex real-world systems. The objectives of these experiments can be different from identifying properties and laws of the system to solving specific problems. With the development of computer software and hardware the using of simulation modeling has grown considerably in economic sphere. Currently, it is used to solve problems in internal control of companies and modeling management on macroeconomic level.

Imitating modeling is based on the use of random number generators. Random number generator is a computer program that generates sequence of random numbers in accordance with a certain distribution. In general, conducting of imitating experiments in the implementing of following steps:

·                     establish the relation between input and output indicators in the form of the mathematical equation or in equality;

·                     set the laws of probability distribution of  key parameters of the model;

·                     carry out a computer simulations of the key parameters of the model;

·                     calculate the main characteristics of the distributions of input and output indicators;

·                     analyze the results and make a decision.

Actuality of the question is the using of imitating modeling technology to allow to do analysis of all factors and circumstances that may lead to a decrease in expected future income, compared with the predicted [2].

For the simulation of random cash flows we used modern object-oriented system GPSS World (General purpose simulation system), which is a universal language of imitating modeling [3,4].

We assume that the price of the product, production volume and variable costs per unit are random numbers, which distributed by the normal distribution law with given mean value and deviation from the average. Modeling algorithm of cash flows with the using of blocks GPSS World is shown in Figure1. In the figure were used the following notations: Srok–period of the project (n); Zena - average price for unit of the product(p); Obem - average annual production volume (Q); Perem - average variable cost  for unit of the product (v); Post - fixed cost for the year (F); Invest - initial investment (I0), Stavka - tax rate (t); Diskont- discount rate (d); Opit - number of ongoing imitating experiments.

In the modeling also were used the number of variables, description and formulas for calculation that are given in table 1.

Table 1 – Calculated variables used in imitation modeling

Description  

Notation

Formula

Income for year without paying tax

DoNalog

X$RObem*(X$RZena-X$RPerem)-Post

Income for year with paying tax

PsNalog

V$DoNalog-V$Nalog

Average value of given price in project period

VZena

X$NZena/Srok

Present value

PrivStoim

X$DenPotok/(1+Diskont)^X$God

The sum of paid tax for year

Nalog

V$ObNalog*Stavka

 

         This algorithm is explained as following:

Block GENERATE forms a single transact (dynamic object), which  in this case will constitute a calculator (occurrence of a dynamic object to GPSS block initiates the activation of the block).

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When the transact entered to the block SAVEVALUE (save value) put a value of 1 in the stored value TOpit, indicating thereby  that the first imitating experiment is begin. Testing block TEST (test) checks the correctness of  execution number of experiments (LE means ≤). If the execution is correct, the imitation will continue. In other case the transact goes to TERMINATE block and imitating modeling will be finished.

Next two SAVEVALUE blocks are the counter of experiments and sets the initial value of counter of number of the project`s past years to 1, which initiatethe beginning of the first year of project.

Following TEST LE block controls the end of the project period. If the period is not done, costs, variable expenses and the amount of products will be played by normal distribution law (next three blocks of SAVEVALUE). When the project period is finished, the group of blocks TABULATE (record in the table) will put statistic data into corresponding table and block TRANSFER (transfer) moves it to next experiment.

Block TEST G (>) checks whether to pay tax on profit or not (the profit is available). If yes, that is defined a cash flow after payment tax and further the group of SAVEVALUE blocks accumulating data on receipts, the paid tax and on the specified cost from year to year for project life term follows. Then carried transition to the next year's project (via the TRANSFER block).

To illustrate of the given imitatingmodelling we consider specific example.

Let project period is n=5. Cost of the production, annual output and annual variable expenses are distributed in normal distribution law with mean value p=320, Q=15000, v=230, the average deviations make 10% of percent of average random values. Also it is considered that annual constant expenses F=700000, volume of investment I0=600000, a tax rate of t = 30% and norm of discount d=15%. The number of imitating experiments equal 1000, it is enough toreceive certain results.

In the process of modelling we will take that average value of the price for the project period is 320,03 monetary units, production volume – 74951 units of products, variable expenses – 1149,5 monetary units, the cash flow after payment of a tax makes 2277601.03 monetary units, the volume of the paid tax – 976114.728 monetary units. The specified cost makes 1479953 that for our example almost exceeds investment volume twice.

We will note that results of the modeling can differ from calculation results in assuming of deterministic values to several percent depending on degree of dispersion of random variables from the average. In our example (the dispersion from the average is10%) the calculated value of a cash flow after payment of the tax is 2275000 that differs from results of modeling approximately for 0,1%.

In conclusion, using of imitating modeling devicesallows to consider uncertainty factors, on the basisof  using of random variables in modellingthat gives opportunity to present an economic situation as it is possible closer to reality that increases objectivity of an assessment. Such approach considerably increases probability of making correct decisions in the choice of investment projects.

References:

1.     Yurshevich E.A. Imitating modeling of risks in business processes. Transport and communication. Volume 3, No. 4, M., 2002

2.     Leifer L.A, Vozhik S.V., Dubovkin A.V. Using of imitating modeling for forecasting of cash flows of the enterprise and risk analysis in the business assessment. The property relations in the Russian Federation, No. 4, M., 2003

3.     GPSS World Tutorial Manual. Copyright Minuteman Software. Holly Springs, NC, U.S.A. 2001.

4.     Kurmanov B. K., Kurmanov G. B. Development of imitating models on GPSS World. Manual. – Almaty: Publishing center JSC KBTU, 2011.