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.
Фрагмент работы на тему "Статистический подход к оценке стоимости бизнеса в рамках развития инструментария интеграционной политики промышленных предприятий"
THE STATISTICAL APPROACH TO THE ASSESSMENT OF
BUSINESS VALUE THROUGH THE DEVELOPMENT OF
ECONOMIC INSTRUMENTS OF INDUSTRIAL ENTERPRISES
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
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
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%
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:
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 :
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
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
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
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
indicator, mln USD
The average sales
price of coal
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 . 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
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
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.
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
t t i
E [x ]
V b .
E [x ]
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
xt 1 x
? ? ?? ? ?
? ? ? ? ? ?
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:
t 1 t
t V ? b ? a x ? a ? ,
(1 r )
(1 r )(1 r )
? ? ? ? ? ?
(x x )
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;
? 366821.98 ? t
thousands RUB. Substituting the values obtained in (10) the
coal company’s cost value results in
? 348.80mln USD.
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
V S*N(d ) X*e *N(d )
B?S ? f ? ? ,
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 .
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
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. ?
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.
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
8. O. Maslenkova, Valuation of Enterprise (Business), Moscow:
9. F. Evans, D. Bishop, Assessment of companies in mergers and
acquisitions: the creation of value in private companies, Moscow: Alpina
10. S. Valyuh, B. Gadzhimet, E. Hours, Organization management
integrated company (structural solutions), Energy - XXI century, 3(65), 2007,
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
15. P. Fishburn, Utility theory for decision, Moscow: Science, 1978.
ИНФОРМАЦИЯ О СТАТЬЕ НА РУССКОМ ЯЗЫКЕ
ФГБОУ ВО «МГТУ им. Г.И. Носова», Магнитогорск
СТАТИСТИЧЕСКИЙ ПОДХОД К ОЦЕНКЕ СТОИМОСТИ
БИЗНЕСА В РАМКАХ РАЗВИТИЯ ИНСТРУМЕНТАРИЯ
ИНТЕГРАЦИОННОЙ ПОЛИТИКИ ПРОМЫШЛЕННЫХ
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
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.