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Список литературы по оценке бизнеса > Статистический подход к оценке стоимости бизнеса в рамках развития инструментария интеграционной политики промышленных предприятий

Статистический подход к оценке стоимости бизнеса в рамках развития инструментария интеграционной политики промышленных предприятий

Карелина М.Г. Статистический подход к оценке стоимости бизнеса в рамках развития инструментария интеграционной политики промышленных предприятий // Приложение математики в экономических и технических исследованиях. 2016. № 1 (6). С. 58-66.

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Фрагмент работы на тему "Статистический подход к оценке стоимости бизнеса в рамках развития инструментария интеграционной политики промышленных предприятий"

УДК 332.14 M.G.Karelina NMSTU, Magnitogorsk THE STATISTICAL APPROACH TO THE ASSESSMENT OF BUSINESS VALUE THROUGH THE DEVELOPMENT OF ECONOMIC INSTRUMENTS OF INDUSTRIAL ENTERPRISES INTEGRATION POLICY1 Abstract. At present, a positive trend in the development of corporate integration processes in industrial economics of the Russian Federation is frequently accompanied by a negative dynamics in their efficiency indicators. This causes the necessity for development of an integrated approach to integration transaction valuation using mathematical and statistical methods of research in order to increase the competitiveness of the Russian industry under conditions of the economic sanctions. The paper presents the methodical approach developed to value business appraisal of industrial enterprises based on the integration of profitable, costbased, sales comparative approaches and the method of real options using weights Fishburne. In this paper, we propose a methodical approach that provides an integrated value appraisal of the target company and preliminary substantiates the expediency of mergers and acquisitions. In addition, this methodical approach is the foundation for high quality and reliable evaluation of the synergistic effect. Keywords: integration, valuation method, mergers and acquisitions, statistic approach, company value. Currently, the dynamics of prices for raw materials in Russia, as well as throughout the world, is a special challenge to the established system of pricing for the production of metallurgical companies. Under these circumstances, the Russian steel company announced its decision to purchase one of the coal companies, which in 2008 was included in a government list of strategic companies in Russia. This should allow the creation of a highly vertically integrated structure and result in an increase in the value of the steel company. The determination of the value of the coal company by the discounted cash flow method is based on the expectation that the metallurgical company will not be able to pay for this business the sum greater than the present value of future incomes from this business. 1 The work is performed under the grant of the President of the Russian Federation for state support of young Russian scientists – PhDs (МК-5339.2016.6) At the appraisal of coal company’s value the risk-free rate rf was determined at the level of profitability of the Russian Federation federal loan bonds (the issuer is the Ministry of Finance of the Russian Federation, the general services agent is the Central Bank of the Russian Federation). Then, based on the average profitability of FLB the rate of earnings on risk-free investments is equal to rf=10.11%. The average market rate of return rm is determined on the base of the revenue position on the security market in the sector to which the valued company belongs. Since among all coal companies of the Russian Federation the shares of Southern Kuzbass Coal Company are longest-listed on the stock exchange (RTS since 2003) ordinary income shares of Southern Kuzbass Coal Company were taken as the average market rate of return rm. Thus, rm is 16.72%. The beta coefficient ? is a measure of systematic (market) risk for the coal companies in developing markets (including Russia) and is equal 0.37. Then, the following was obtained: ?10.11? 0.37(16.72 ?10.11) ?12.56% CAPM r . A cash flow to equity model was chosen as a cash flow model in order to evaluate the coal company by the DCF method. At the same time with efficient management of the company, the term of its life tends to infinity. The terminal value of the project is determined to take into account incomes which business can bring beyond the forecasting period [6-9]. In the present study, the Gordon model was chosen to calculate the company’s value in post-forecasting period, according to which the determination of business value is carried out by income capitalization of the first post-forecasting year on the capitalization rate, which takes into account the long-term growth rate of cash flows. Net cash flow on capital in the post-forecasting period is equal to 194.67 million USD. In accordance with the market conditions of coking coals, experts from Economic Directorate of the Ural Metallurgical Company estimated long-term rates of cash flow growth in the residual period at the level ?=0,5%. Therefore, terminal value is equal to: 1614.19mln USD. 0.1256 0.005 194.67 ? ? TV ? Net debt of the coal company at the time of the integration transaction was D = 526 million USD. At that time the coal company value according to the method of discounted cash flows was: ? 822.86 ? (1614.19*0.2025) ?526 ? 623.65mln USD. DCF V The cost approach is based on the principle of substitution: the company’s cost is no more than charges for replacing of all its integrated parts. The basic formula of the cost approach is as follows [10]: The company's value = Assets - Liabilities. The method of net assets under the cost approach is based on a balance adjustment in connection with the fact that the book value of assets and liabilities of the company does not always correspond to their real value. Under business valuation when using the method of net assets (Order of the Ministry of Finance of the Russian Federation and Federal Securities Market Commission of January 29, 2003 On approval of the Procedure of Appraisal of Net Assets of Joint Stock Companies No 10n, 03-6 / pz) the traditional balance of the enterprise is replaced by the adjusted balance, in which all the assets and liabilities are shown on the market or any other suitable current value. Then, the value of the coal company in accordance with the method of net assets is ? 227.45mln USD. NA V A comparative approach is a combination of methods for value company appraisal, based on the comparison of the valued object with its analogues in respect of which there is information on prices. In Russia, two methods of the comparative approach: capital market and transaction market are commonly used for company valuation. The transaction method is based on a direct comparison of the valued enterprise with analogous ones in respect of which the price of a controlling interest or the company as a whole is known. The use of valuation multipliers within the transaction method is based on the assumption that analogue companies have a sufficiently close relationship between the price and the most important financial indicators. Thus, the price of the enterprise can be determined by multiplying finance indicator by the corresponding multiplier. With a relatively small sample of analogue companies, there is a problem - the error of statistical calculations. At the same time when determining any multiplier according to its sampling values (for individual analogue companies), one can assume that these values are normally distributed [11]. Then, when determining the required number of analogue companies n, in order to a multiplier M with a given probability ? lies within a certain range ( (M ) (M ), (M ) (M )) ? i ??? i ? i ? ?? i , the problem was solved on finding the centre of the normal distribution with a known dispersion [12-13]. Thus, for relationship between dispersion and mathematical expectation equal to 0.15, and the probability of ? equal to 95% entering the range ?(Mi) ?13% , the sample size of analogue companies must be equal to 5. A key point in searching analogue companies is to find information on transactions with blocks of shares. Since the information on mergers and acquisitions without the participation of the state is enclosed, the data on the sale of large blocks of shares is generally relative to the auctions for privatization held by the state. Despite the fact that many researchers consider multipliers calculated on profits the best accurate valuation, the author of the study had primarily denied them. This is because under present conditions Russian companies try to overvalue the cost of their production in every possible way in order to minimize income tax. The use of the multiplier on the book value of equity in cost calculation of the coal company also seems inappropriate since the book value of Russian companies too often deviates significantly from its market value. Thus, the relationship "company’s price - income" is a widely used multiplier. Income indicators are subject to the least misstatement among all the financial indicators of the Russian companies, however, this multiplier should also be used with great caution since at different proportions of the debt to equity capital ratio its use may result in significant misstatements. Since at selection of analogue companies the debt to equity capital ratio was taken as a criterion for the comparability of companies, we selected this multiplier for the study. Considering that the coal company is a company in the raw material sector, we also used the multipliers based on the characteristics of resource stocks for its valuation: ? company’s value - coal production; ? company’s value - prospected coal reserves. We calculated the price of the coal company on the base of the multiplier values (see Table 1). Table 1 - Calculation of the coal company’s value using multipliers Coal company performance indicator, mln USD Multiplier value The average sales price of coal company, mln USD gross incomes 501.03 company’s value – income 0.85 425.88 coal mining 610.70 company’s value – mining 0.74 451.92 prospected coal reserves 106.80 company’s value – prospected coal reserves 4.79 511.57 The use of different multipliers gives various options for the company's value. So the average price of the coal company with the use of the multiplier "the company’s value - income" amounted to 422.88 million USD; with the use of the multiplier "the company’s value - coal production" - 451.92 million USD; with the use of the multiplier "the company’s value - prospected coal reserves" - to 511.57 million USD. The choice of the result is based on giving a percentage weight to each cost option. Assuming that all three multipliers are equal in importance the value of the coal company results in ? 463.12million USD T V . At present, increased significance of the latest methods of business valuation allows them to be used in practice both for valuation by foreign investors and for making incompany decisions that are more considered and focus on cost management in the long term. Among such methods is a method of real options. The most important feature of an optional method of business valuation is its ability to take into account the rapidly changing economic environment in which the company acts. At the same time, a ROV-method has not yet been recognized in full; limits and possibilities of its application are still the point for discussion. Nevertheless, experts in the field of evaluation pay attention to this method in different countries that results in conclusion that its research is an urgent task and for Russia. The Ohlson model and Black-Scholes model are the best-known models for determining the company’s value based on the method of real options. The peculiarity of the Ohlson model is the use of abnormal incomes. The concept of abnormal incomes is based on the following assumptions. Let bt be the book value of the company at time t and dt - dividends paid during the year in the period from t-1 to t [14]. Then the total income of the shareholder (denoted as xt) for the period t is the dividend plus the addition of book value of the company: xt? bt ? bt?1 ? d . The model described is the Edwards-Bell-Olson model (EBO). In the light of this, the company's cost in the Edwards-Bell-Olson model will be equal to: r g x V b t t EBO ? ? ? . where EBO V is the company's cost in the Edwards-Bell-Olson model; g is the expected average annual growth rate. In the Olson model, the dynamics of abnormal incomes was proposed in contrast to their invariance condition, as in the Edwards-Bell-Olson model. (1) (2) In accordance with this, the economic meaning of the term "abnormal incomes" has been changed. According to the Olson model, the company’s value at time t is equal to the initial "accounting" value of the company plus the sum of discounted abnormal incomes: ?? ? ? ? ? n i 1 i t t i 0 OL t (1 r) E [x ] V b . where E [x ] t t?i is a predicted value of abnormal incomes. Thus, in order to find the final cost value it is necessary to set an explicit expression for the predicted abnormal income values. Olson proposed the following time dynamics of the abnormal income behaviour: t 1 t 2,t 1 t 1,t 1 a t a xt 1 x ? ? ? ? ? ? ?? ? ? ? ? ? ? ? ? . where ? is the given empirical value indicating which part of the abnormal income in the previous year remains in the current year; ? is the value characterizing the difference between the expected and actual value of abnormal incomes; ? is the given empirical value indicating which part ? of the last year is preserved in the current year ( ? ? 0 ); ? is the normally distributed error with zero mean (considered noise, not related to the speed of the abnormal-income decrease). Expression shows that abnormal incomes with time tend to zero magnitude. This means that, in comparison with other companies the valued company eventually loses its original "advantages" relating to the situation on the market and its income tends to the determined average market rate of return, that is, to a discount rate r. We obtain the desired result: 2 t a t 1 t OL t V ? b ? a x ? a ? , where (1 r ) a 1 ? ?? ? ? ; (1 r )(1 r ) 1 r a 2 ? ? ? ? ? ? ? ? ; (x x ) a t 1 a t t ?? ? ? ? ? . The Committee for appraisal activities of the Chamber of Commerce and Industry of the Russian Federation recommends taking for ? and ? the values equal to 0.62 and 0.32. Then a1 is equal 1.226; a2 is equal 2.764; (3) (4) (5) ? 366821.98 ? t thousands RUB. Substituting the values obtained in (10) the coal company’s cost value results in ? 348.80mln USD. OL V According to the Black-Scholes model, the company's cost value is represented as the call option value, consisting of the company’s assets and liabilities. At the same time, the Black-Scholes model is considered as the "ultimate" case of the binomial model. The initial premise of the model is the normal probability distribution. Based on this premise the basic formula of the model is made (in relation to a European call option on the right to purchase the asset): V S*N(d ) X*e *N(d ) 2 r t 1 B?S ? f ? ? , where B S V? is the value of the appraised company; S is the value of a company’s asset; X is the value of liabilities; rfis the risk-free rate; t is duration of company’s debt; The results in the value of the coal company equal to ? 379.48mln USD B?S V in accordance to the Black-Scholes model. At the same time, for the integrated business valuation it is necessary to determine the weighting coefficient for every appraisal value of the valued company. For this, we suggest to place all values in decreasing order of their importance and to determine the significance of the i-th value according to the Fishburne rule [15]. Let us consider the order of weights Fishburne construction. On the base of considerations of generally accepted appraisal practices and practical experience of business appraisers of International Academy of Appraisal and Consulting and Committee for appraisal activities of the Chamber of Commerce and Industry of the Russian Federation: DCF T OL B S NA V ? V ? V V ? V? ? . Then the weights Fishburne for the integrated value business appraisal of the coal company takes the following form . The integrated value appraisal of the coal company was calculated 463,99mln USD. Vинт. ? Reference 1. M. Polikarpova, Functioning mechanism modelling of the Russian market of mergers and acquisitions in 2004-2010, Vestnik of Nosov Magnitogorsk State Technical University, 3, 2011, pp. 95-102. 2. M. Polikarpova, Risk analysis and the effectiveness of mergers and acquisitions of Russian companies, Moscow: NPO MAX Group, 2012. 3. Business valuation textbook. second edition (ed. A.G. Gryaznova. M.A. Fedotova), Moscow: Finansy i statistika, 2009. (6) 4. D. Fishmen, Sh. Pratt, K. Griffit, K. Uilson, Guide to Business Valuations, Moscow: Kwinto-Consulting, 2008. 5. V.Popkov, E. Yevstafyeva. Business Valuation. Diagrams and tables: Textbook. Saint Petersburg: Piter, 2007. 6. A. Damodaran, Valuation of assets, Moscow: Potpourri, 2011. 7. N. Chebotarev, Valuation of Enterprise, Moscow: Dashkov and Co., 2014. 8. O. Maslenkova, Valuation of Enterprise (Business), Moscow: KnoRus, 2011. 9. F. Evans, D. Bishop, Assessment of companies in mergers and acquisitions: the creation of value in private companies, Moscow: Alpina Pablishar, 2004. 10. S. Valyuh, B. Gadzhimet, E. Hours, Organization management integrated company (structural solutions), Energy - XXI century, 3(65), 2007, pp.70-79. 11. S. Aivazian, I. Enyukov, L. Meshalkin, Applied Statistics. Dependency Research, Moscow: Finance and Statistics, 1985. 12. N. Kremer , Probability theory and mathematical statistics, Moscow: Unity, 2003. 13. V. Mkhitarian, Data analysis, Moscow: Yurayt Publishing, 2016. 14. Guidelines on the business valuation using the Ohlson model and the Black-Scholes model, Moscow: International Academy of Valuation and Consulting, 2010. 15. P. Fishburn, Utility theory for decision, Moscow: Science, 1978. ИНФОРМАЦИЯ О СТАТЬЕ НА РУССКОМ ЯЗЫКЕ М.Г. Карелина ФГБОУ ВО «МГТУ им. Г.И. Носова», Магнитогорск СТАТИСТИЧЕСКИЙ ПОДХОД К ОЦЕНКЕ СТОИМОСТИ БИЗНЕСА В РАМКАХ РАЗВИТИЯ ИНСТРУМЕНТАРИЯ ИНТЕГРАЦИОННОЙ ПОЛИТИКИ ПРОМЫШЛЕННЫХ ПРЕДПРИЯТИЙ Аннотация. В настоящее время в экономике промышленности РФ положительная динамика развития процессов корпоративной интеграции в нередких случаях сопровождается отрицательной динамикой показателей их эффективности. Это обуславливает необходимость разработки комплексного подхода к формированию оценки интеграционных сделок с использованием математико- статистических методов исследования для повышения конкурентоспособности промышленности РФ в условиях введения экономических санкций. В статье представлен разработанный методический подход к оценке стоимости бизнеса промышленных предприятий на основе интеграции доходного, затратного, сравнительного подхода, метода реальных опционов с использованием системы весов Фишберна. Предложенный методический подход позволяет получить комплексную оценку стоимости компании-цели и формирует предварительное обоснование целесообразности слияний и поглощений, служит базой для качественной и надежной оценки синергетического эффекта. Ключевые слова: интеграция, метод оценки, слияний и поглощений, статистический подход, стоимость компании.

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