Abstract

Introduction. Relevance of the theme

    The most urgent problem now is to ensure effective management of the enterprise. Predicting the receipt of funds in the company budget allows you to plan activities and to take specific management decisions[1]. In this connection there is need for a focused analysis of the economic activities of enterprises, which is based on the use of methods of economic-mathematical modeling, adapted to the specifics of the studied companies.

    In this master's work will be reviewed by the communal business of the Donetsk City Council «Bureau of privatization and the exchange of the housing stock». Using methods of mathematical modeling and forecasting will be analyzed and predicted activities of the company economic performance.

Purpose and tasks of the research

    Currently developed economic and mathematical models for forecasting and management. In this work, it was necessary to explore the possibility of using such models for a particular company. This approach has several advantages associated with such properties of models, such as:

• reduced scale;
• reduce complexity;
• compliance with the key relationships between the different constituent elements as the original simulated object;
• ability to work as a simulated object;
• match the actual properties of the original (authenticity)[2,3].

Scientific novelty and practical value

    Scientific innovation is the creation of a new model of analysis and forecasting of economic indicators of the enterprise. It is also expected to review and compare existing models, identify their strengths and identify the main deficiencies.

    The practical value is that using a new model for the analysis of the company and guided its forecasts, you can quickly and effectively make specific management decisions and plan further activities[4].

Review of existing research and development

• http://www.science-kaluga.ru/books/ Improvement of financial forecasting and planning at the enterprises of housing-communal complex.
• http://www.nbuv.gov.ua/portal/ A mathematical model of the target company's solvency assessment.
• http://www.cfin.ru/press/management/ Analysis of methods of forecasting the crisis of commercial organizations using financial indicators.
• http://www.management.com.ua/finance/ Financial forecasting.

Main content

    n preparing the financial plan used methods of economic statistical forecasting[4,5]. Carry out forecasting of economic indicators for 2010 based on actual statistical data company from 2007 to 2009.

Table of basic statistical data:

№	Indicator	2007	2008	2009
1.	funds	85600	366300	768500
2.	total expenses, including	56600	184500	360300
3.	expenses for payment	31000	113800	231100
4.	allocations to social services	11700	43500	86700
5.	other operating expenses	13900	2600	42500
6.	depreciation charges	400	4500	11800
7.	pretax profit	28600	177300	305900
8.	profit tax	7200	44300	76500
9.	10% of profit to the city budget	2100	13300	22900

    To do this, we used the model pair linear regression, followed by the construction of confidence intervals for prediction and assessment of the quality of this forecast[6,7].

    Used economic-mathematical model was obtained by the following method:

• identification of the trend using the method of "moving average» (m = 3);
• construction of a linear pair regression equation;
• finding predictive values;
• construction of confidence intervals of prognosis;
• evaluation of the quality of forecasts and the probabilities of correct prediction.

    Forecasting financial and economic activities of enterprises and communal complex includes the following steps (pic. 1): analysis of baseline information in order to obtain a systematic description of the object of research, construction of a mathematical model based on a systematic description, updating of model based on verification and additional data[8].

Figure 1 — Algorithm for the development of mathematical model (animation, 7 shots, 5 cycles, 236x600, 102 Kb, made in the MP GIF Animator)

Methodology development of mathematical model
    1. To detect trends was used simple moving average with parameter m = 3:

    2. The equation of pair regression:

where a, b - parameters of the pair linear regression equation, — independent variable — i-th year,
— dependent variable — the amount of payments made in the budget for the i-th year.

Parameters of pair linear regression equation is given by:

where n — the volume of sales of services, — expectation of x and y, respectively.

    3. For calculation of predictive value confidence limits are:

where — Student statistics for (n-1) number of degrees of freedom, — dispersion:

где — predicted value (year forecast),

    4. Evaluation of the quality of forecasting
    Average relative prediction error:

    The relative standard error of prediction:

    The probability of correct prediction:

    Probability of error:

    Forecast:

Table forecast of economic indicators for 2010:

№   п/п	Indicator	2010
1.	funds	867700
2.	total expenses, including	447300
3.	expenses for payment	277300
4.	allocations to social services	104500
5.	other operating expenses	65500
6.	depreciation charges	23100
7.	pretax profit	565300
8.	profit tax	143100
9.	10% of profit to the city budget	42800

    In the analysis of economic-mathematical model were obtained qualitative results of statistical forecasting.

Evaluation of the quality of point forecasts:

№  п/п	Indicator	Forecast	Actual	Relative  prediction error	Quality of forecast accuracy
1.	funds	867700	950200	8,68%	good accuracy
2.	total expenses, including	447300	441200	1,38%	high accuracy
3.	expenses for payment	277300	274500	1,02%	high accuracy
4.	allocations to social services	104500	101400	3,06%	high accuracy
5.	other operating expenses	65500	65300	0,31%	high accuracy
6.	depreciation charges	23100	21400	7,94%	good accuracy
7.	pretax profit	565300	578100	2,21%	high accuracy
8.	profit tax	143100	144500	0,97%	high accuracy
9.	10% of profit to the city budget	42800	43300	1,15%	high accuracy

    Of the 9 indicators calculated for the 7 was obtained highly accurate prediction (relative error of prediction values range from 0.31% to 3.06%) and for 2 indicators obtained good accuracy of the forecast (with a relative error of prediction equal to 8.68% and 7,94%)

    The overall probability of correct statistical forecast for all indicators was 96.82% (probability of error - 3,18%), that indicating of adequacy of the principles of economic and mathematical models of the real economic situation and the correctness of the methods of statistical modeling.

Conclusions

    This work contributes to the development of practical planning and statistical prediction in state enterprises, the transition to the new progressive methods of economic analysis. Application of the research results will improve the accuracy of forecasting revenues and expenditures in the period ahead and will improve the quality of planning and, thus, increase the effectiveness of the enterprise.

References

1. Дуброва Т.А. Статистические методы прогнозирования в экономике: Учебное пособие. — М.: МЭСИ, 2004. – 60 с.

2. Литвинов А.Л. Компьютерное моделирование в экономике: Учебное пособие. — Белгород: Изд-во БелГУ, 2003. — 108 с.

3. Бережная Е.В., Бережной В.И. Математические методы моделирования экономических систем: Учебное пособие. — М.: Финансы и статистика, 2006. — 432 с.

4. Льюис К.Д. Методы прогнозирования экономических показателей — М.: Финансы и статистика, 1986. – 133 с.

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7. Замков О.О., Толстопятенко А.В., Череиных Ю.Н. Математические методы в экономике: Учебник. 2-е изд. — М.: Дело и Сервис, 1999. — 368 с.

8. Гагарин Ю.Е. Прогнозирование показателей финансово-хозяйственной деятельности предприятий коммунального комплекса // Прогрессивные технологии, конструкции и системы в приборо- и машиностроении: Материалы Всероссийской научно-технической конференции. — М.: Изд-во МГТУ им. Н.Э. Баумана, 2007. Ч. 2. С. 186–187.

9. Анфилатов В.С., Емельянова А.А., Кукушкин А.А. Системный анализ в управлении: Учебное пособие. — М.: Финансы и статистика 2002. — 368 с.

Important
    When writing this abstract master's work was not yet completed. Final completion: December 2010. Full text of the work and materials on the topic can be obtained from the author or his scientific adviser after that date.