The dissertation research is aimed at studying the issues of assessing and managing the value of a company. The work develops new methods and offers ready-made cost management solutions.

Relevance of the research topic As it develops market relations In Russia, the most important factor in the competitiveness of domestic enterprises in the long term is the existence of a fundamental goal of business development - an increase in its value through the production of products (works, services) that contribute to the innovative development of the economy, which is in demand by end consumers and society. An experience developed countries shows that the positive dynamics of the value of an enterprise (business) predetermines its long-term and sustainable functioning, contributes to the growth of the welfare of society and social economic development countries. The need to measure the effectiveness of management and investment projects, support of various business transactions, such as auctions and tenders for the sale of blocks of shares of enterprises, conducting bankruptcy proceedings, alienation of property for the needs of the state, have created a need for a reliable assessment of the value of assets and businesses.

Until now, the methodology of modern approaches to assessing the value of an enterprise and business, in part, has “problem areas”, and in a number of situations it has no solutions at all. At the same time, the unresolved nature of these issues, primarily in theoretical terms, hinders the development of economic entities that base their behavior on the rational choice of available alternatives.

In view of the above, and also taking into account the activation of innovative development Russian economy and its modernization, the relevance of the stated research topic seems reasonable.

Purpose and objectives of the study. The main purpose of the study is to increase the validity of the enterprise (business) valuation through the development and development of the mathematical apparatus in terms of theoretical approaches and methodological tools. At the same time, a comparative study of cost and income approaches to valuation is used, and the main factors influencing the value of an enterprise are studied. In addition, within the framework of the dissertation research, mathematical and instrumental models of methods for analyzing the cost of enterprises, ways quantification entrepreneurial risks and rationale investment decisions. The work reflects the development of the theoretical foundations of the methodology and design tools, incl. methods of formalized representation of the subject industry.

The goal set determined the following main objectives of the study:

To systematize the theoretical and methodological foundations for determining the value of a business and companies, to clarify and supplement the existing methodological apparatus for estimating the value of a business.

Substantiate the methodological principles of a new approach to assessing the value of a company that combines elements of cost and income approaches.

Develop methods for predicting depreciation, taking into account the planned volumes capital investments, their depreciation rates in the absence of information on the initial cost of the property.

Develop a methodology for assessing the cost of control over an enterprise, controlling and blocking stakes, the corresponding premiums for control and discounts in the absence of control elements, as well as methods for assessing the company's structural divisions.

Clarify and supplement existing approaches to assessing discount and capitalization rates, taking into account the objects of discounting, discounting methods, the base and currency of calculation, taxation and changes in the debt burden.

Develop an algorithm for calculating the parameters of an additional issue of shares, such as the shares of investors (including in investment businesses through the introduction of technologies and know-how into the management company), the value of shares of "old" and "new" shareholders after the additional issue, and also propose methods for assessing shares with significant changes in the capital structure in the forecast period.

Develop algorithms for evaluating the structural divisions of the company, as well as evaluating equity capital in the presence of a cross ownership structure.

Reveal the relationship between the values ​​of liquid and illiquid assets of the enterprise.

The object of research is the value of the enterprise (business). The subject of the study is the methodology, methodological approaches and tools for estimating the value of an enterprise (business), Studying the object of study as a tool for managing an enterprise and capital.

Theoretical and methodological basis- methodology of investment analysis and financial mathematics, provisions of corporate finance, methodology and standards for valuation activities, statistical analysis.

Biggest Influence The ideas and results of this work were formed by the works of the following authors: R. Braley and S. Myers, A. Damodaran, G. M. Desmond, R. E. Kelly, T. Copeland, T. Koller and J. Murrin, V. F. Sharp, H. J. Alexander and J. W. Bailey, D. Morris, F. M. Scherer, D. Ross, J. Fishman, S. Pratt, C. Griffith, C. Wilson, S. Meltzer and R. Hampton, D. Hay, L.I. Abalkina, P.L. Vilensky, A.G. Gryaz-nova, I.A. Egereva, V.S. Efremov, N.G. Danilochkina, V.V. Kossova, V.N. Livshits, S.A. Smolyak, V.K. Senchagova, N.N. Treneva, A.G. Shakhnazarova and DR

The degree of development of the problem. Many publications and regulations are devoted to the problems associated with the valuation of enterprises and their property. In the works of Alklychev A.L., Arkhipov A.I., Arslanov Z., Livshits V.N., Bogachev V.N., Kleiner G.B., Milner B.Z., Dynkin A.A., Shchiborshch K.V. the most general aspects of the methodology of investment analysis and economic development are considered. In the works of Berens V., Havranek P.M., Birman G., Vilensky P.L., Livshits V.N., Orlova E.R., Smolyak S.A., Volkov I.M., Grachev M.V. ., Melnikova A.V., Nechaeva M.L., Volkonsky V.A., Gurvich E.T., Kuzovkina A.I., Saburova E.F. studied investment and project analysis. As part of the coverage of the problems of financial management and investment evaluation, this topic is covered in foreign sources by such authors as: R. Brailey and S. Myers, Krushwitz L., O "Brien J. and Srivastava S., Sharp U.F., Alexander G. J. Bailey J. V., Cheng F. Li, J. I. Finnerty, Sherer F. M., Ross D. In many domestic publications, attention is paid to a detailed study of the project, investment and financial analysis as well as competitiveness analysis. This can be found in the works of the following authors: L.V. Kantorovich, A.L. Weinstein, M.G. Zaelsky, Kachalov R.M., Masse P., Milner B.Z., S.A. Smolyak, V.N. Livshits, P.L. Vilensky, E.R. Orlova, Fatkhutdinova P.A. The issues of financial analysis, planning and management are considered in the works of Berens V., Khavranek P.M., Birman G., Schmidt S., Vilensky P.L., Livshits V.N., Smolyak S.A., Volkov I.M. ., Gracheva M.V., Desmonda G.M., Kelly R.E., Egereva I.A., Kollas B., Danilochkina N.G., Orlova E.R., Fedotova M.A., Gryaznova A. G., Pervozvansky A.A., Pervozvanskoy T.N., Prudnikova V.I., Nikonova I.A., Fatkhutdinova R.A., Fishburn P.S., Khan D., Hay D., Morris D., Chetyrkin E.M. ., Sheremeta A.D., Shchiborshch K.V., Bea F.K., Dihtla E., Schweitzer M., Altmena E.I. The problem of the cost of capital was studied in the works of R. Brayley, S. Myers, P.L. Vilensky, V.N. Livshits, S.A. Smolyak, S.V. Gribovsky, G.M. Desmond, R.E. Kelly, Egereva H.A., Copeland T., Koller T., Murrina J., Krushvitsa L., Kuznetsova O.A., Kukoleva E., Zakharova M., Mikhailets V.B., Modigliani F., Miller M., Fedotova M.A. . Gryaznova A.G., Pervozvansky A.A., Pervozvanskoy T.N., Pratt

S.P., Ferris C., Petit B.P., Fishman J., Griffith C., Wilson C., Abrams J.B., Arditi F.D., Barnea A., Fisher B., Gibbons M.R. ., Litzenberg R.H., Damodaran A., Evans F.S., Strimbu K.L., Fama Yu.F., Kenneth R.F., Fuller R., Gordon M.J., Halpern P J., Hailey C.B., Hamada R.C., Henderson G.W., King M.A., Lee S.F., Zumwalt J.K., Lintner J., Markowitz G.M., Marsha T.A., Merton R.C., Masoulis R.V., Nelson S.R., Gordon P., Ross S.A., Schafer S.M., Sharpe V.F., Solomon E., Laey J., Sorensen E.H., Williamson D .BUT. Most successful Russian enterprises in recent years have demonstrated a positive trend in the introduction of advanced systems for analyzing production, investment, financial and marketing activities, and at present their effectiveness has been confirmed by practical experience in their use.

Theoretical aspects of the subject of dissertation research have been developed in the works of such foreign scientists and specialists as G. Alexander, I. Ansoff, N. Antill, R. Braley, J. Bailey, F.P. Boer, A. Gregory, A. Damodaran, G. Desmond, C. Griffith, R. Hampton D. Hay, L.A. Cunningham, R. Kelly, T. Koller, T. Copeland, A.R. Lajoux, K. Lee, C.F. Lee, S. Myers, S. Meltser, M. Miller, F. Modigliani, D. Morris, J. Murrin, A. Rappoport, S.F. Reed, S. Pratt, D. Ross, W. Sharp, F. Scherer, J. Fishman, J.I. Finnerty, C. Wilson, C. Walsh. Unfortunately, we have to admit that the experience accumulated abroad cannot always be applied in modern Russian conditions. So, for example, the capital assets pricing model (CAPM) used abroad to determine the value of the discount rate for shareholders' cash flows is not often used in Russia due to the lack of recognized statistics on the average market return on shares, market premiums and beta coefficients. In this regard, it is necessary to find ways to solve specific problems. Russian market. In this regard, it should be noted the work of Russian scientists and experts on this subject - L.I. Abalkina, P.L. Vilensky, A.G. Gryaznova, C.B. Gribovsky, N. G. Danilochkina, V. S. Efremov, A.N. Kozyreva, V. N. Livshits, B.JI. Makarova, I.A. Nikonova, T.P. Prudnikova, E.V. Sachko, S.A. Smolyaka, T.V. Tazikhina, O.V. Tikhonova, N.N. Treneva, V.N. Trishina, M.A. Fedotova, and others. At the same time, it should be noted that the authors listed above and the approaches they propose do not cover all the problems that arise in this part - simply because "one cannot grasp the immensity." This dissertation is intended, to some extent, to expand the existing developments in this part.

Research methods - theory and principles of corporate finance, methods of statistical, quantitative and qualitative analysis, financial mathematics, numerical methods, logical approaches.

Information support - legislative and regulatory acts, works of domestic and foreign authors, data from Rosstat, RIA "RosBusinessConsulting", non-profit partnerships"Stock RTS exchange”, ROO, MICEX, as well as the financial statements of organizations that applied for services to the author of this dissertation.

The scientific novelty of the dissertation work lies in the development of theoretical aspects, methodological principles and new approaches to determining the value of the property of an enterprise, as well as in clarifying and supplementing some existing methods property valuation. In particular, the following innovations can be noted in this study:

1. Methodological principles are substantiated, and a new hybrid method for evaluating business and shareholders' (founders') capital is proposed, called by the author "modified cost approach", which consists in combining the concepts of cost and income approaches. This approach makes it possible to assess the business and the capital of shareholders, taking into account the necessary time and costs for replacing the business, the costs of promotion, as well as the risks of the initial stage of formation (the so-called costs of overcoming start-up difficulties).

2. Formulas are proposed for estimating the value of an entrepreneur's profit, the calculation of which has always caused difficulties in assessing the value of real estate objects.

4. Methods for forecasting depreciation deductions have been developed, taking into account the planned volumes of capital investments, their norms of depreciation deductions. The use of these methods is also possible in the absence of information on the initial cost of depreciable property.

5. The concept of the minimum volume of the investment program (IPrms) is introduced - the volume of investments below which irreversible depreciation of fixed production assets occurs (and, as a result, operating cash flows decrease), - and a method for forecasting it is proposed.

6. Methods have been developed to estimate the cost of control over an enterprise, controlling and blocking stakes, as well as the corresponding premiums for control and discounts for the absence of control elements.

7. Methods for evaluating the structural divisions of the company are proposed:,

8. Algebras developed interest rates, allowing to correctly take into account the constituent elements of discount rates - real, nominal, risk-adjusted and risk-free. Within these algebras, formulas for calculating risk premiums have also been developed, one of which is in good agreement with the concept of a reliable cash equivalent and the well-known Gordon formula.

9. Methods are proposed for transforming capitalization rates applied to one type of income into capitalization rates applied to other types of income, as well as a method for transforming the value of a discount rate expressed in one currency into a discount rate expressed in another currency.

10. A method is proposed for reflecting the tax factor in capitalization rates when assessing the market value of a business.

11. A modified model for discounting dividends has been derived.

12. An algorithm for calculating the parameters of an additional issue is proposed: the shares of investors, the value of shares of "old" and "new" shareholders after the additional issue. This algorithm, in particular, makes it possible to evaluate the share of investors in the company's capital who contribute to authorized capital assets such as new technologies.

13. Invariant with respect to traditional models of capitalization and discounting are proposed in assessing the market value of a business, within which capitalization / discounting is carried out separately for cash inflows and outflows. It is shown how to link the parameters of the proposed models with the parameters of traditional capitalization and discounting models.

As part of the cost approach to business valuation, a method is proposed for valuing blocks of shares in companies with a cross ownership structure.

New ways of valuing shares with significant changes in the capital structure in the forecast period are proposed; the previously existing numerical methods for estimating the discount rate for changes in the capital structure are developed.

The relationship between the values ​​of liquid and illiquid assets of an enterprise is revealed, which is due to the influence of a number of external factors, such as the difference in prices of demand and supply of illiquid assets, profitability of assets, market interest rates, expected time of ownership of property, the risk of selling illiquid property, etc.

Several methods are proposed for numerical estimation of the discount rate by market extraction methods: iterative sales comparison method, implied net present value comparison methods, known interest rate adjustment methods taking into account differences in yield volatility.

The practical significance of the dissertation work lies in the possibility of using the results obtained to improve the procedures for calculating the cost of objects of assessment, the validity of managerial decisions on financial, economic and investment activity, improving the system of training specialized specialists in educational institutions. The developed recommendations, methods and elements of the methods can be used by owners of property complexes of enterprises, as well as by various persons, organizations and structures involved in business consulting, arbitration, financial planning and taxation. Separate results of the work were used and implemented in the work of the Expert Council of the all-Russian self-regulatory organization of appraisers "Russian Society of Appraisers".

The materials of the dissertation research are used in the educational process of the Moscow Institute of Physics and Technology in teaching the courses "Corporate Finance" and "Theory of Real Options". The results of the dissertation research can be included in the training courses "Corporate Finance", " Financial management”, as well as special courses on the problems of valuation and company management.

Approbation of work. The main provisions of the work were directly used by the author in the process of carrying out work on the assessment of the value of objects of assessment, which were property complexes, blocks of shares and debentures enterprises such as Ikea, OJSC GAZ, Lebedinsky Mining and Processing Plant, Euroset, Irkutskenergo, Akron, Novokuznetsk Aluminum Plant, AHC Tupolev, SE VVO Selkhozproeksport, SE " Novoexport, State Enterprise Promsyreimport, CJSC MTU-Intel, MAYER J. Expo, Colloid Graphite Preparations LLC, Cryogenservice, etc. Certain provisions of this work (for example, a modified cost approach) have become part of the business valuation practice and objects commercial real estate in Avers LLC (St. Petersburg). Based on the results of a number of works carried out, seminars were held to improve the skills of business appraisers, with which the author spoke at the Intersectoral Institute for Advanced Studies (MIPK at the Plekhanov Russian Academy of Economics), as well as many author's seminars were held in various cities of the Russian Federation. A number of results of the dissertation work were reported at the First International Conference on Business Valuation (Bangkok, 2008), the conference of lessors (2007, Moscow), the scientific and practical conference " Monetary reform and inflation in Russia” (2003). The results of the research were used in the practical activities of the National Council for Valuation Activities (there is gratitude from the Chairman of the National Council for Valuation Activities G.O. Gref), the Russian Society of Appraisers (where official editions were prepared and approved guidelines Regional Public Organization for Evaluation and Expertise of Reports), the Ministry of Economic Development (there is a gratitude from the Minister E.S. Nabiullina), the RFBR, the Federal Property Management Agency, at the author’s place of work, as well as in a number of commercial structures, which the author was consulting.

Publications. The applicant has 39 published works, including 34 works on the topic of the dissertation. The main theoretical and applied results of the dissertation were published by the author personally in 4 monographs (volume - 89.5 pp), 34 articles, incl. 11 in journals recommended by the HAC. The total volume of publications published on the topic of the dissertation personally by the author is over 109.7 printed sheets.

Structure and scope of work. The dissertation consists of an introduction, five chapters, a conclusion, a list of references and five appendices. The total volume of the dissertation is 371 pages (including the main part of 310 pages), contains 23 figures, 53 tables, a bibliography of 266 titles.

Chapter 5 Conclusions

When deriving a final judgment on the value of a business valued by various approaches, you can use the method described in this chapter "from the perspective of the seller and from the perspective of the buyer." At the same time, it is necessary to operate with homogeneous objects of assessment: before the averaging procedure, all of them must be brought to a single assessment base: at the control level or at the minority level, at the liquid or illiquid level. If the result of the valuation is to obtain the value of a portion of the share capital, consideration should be given to applying a discount or premium for the absence or presence of control. For this purpose, an algorithm for estimating these premiums/discounts, presented in this chapter, has been developed.

To assess the value of the structural divisions of the company, the model presented in this chapter was proposed.

CONCLUSION

In this dissertation work, an analysis of the existing concepts of objects of assessment and methods for their assessment was carried out, new valuation methods and techniques were proposed to assess the value of existing enterprises and businesses, as well as individual parameters of valuation models and methods, new objects of assessment and methods for their assessment were identified.

The process of assessing the value of a company is inextricably linked with the adequacy and correctness of the applied assessment methodology. The currently existing methodological base is constantly evolving, which, in the author's opinion, can be evidenced by individual fragments of this dissertation work, within which it was possible to solve the following problems and draw the following conclusions.

In the first chapter of the thesis, it was concluded that when assessing the value of an enterprise (business), the objects of assessment are the benefits of specific entities from a certain type of activity within a certain organizational structure, and when assessing the value of an enterprise (company) - the benefits of specific entities from the use of the property complex of this enterprise.

In the second chapter of the dissertation work, the following results were obtained: a modified cost approach was proposed (pp. 80-89), within which the main disadvantages of the cost approach were eliminated (ignoring the time required to replace the "ensemble" of assets, ignoring the costs of promotion and overcoming starting difficulties) and no need to build long flow forecasts net income(benefits) inherent in most of the income approach methods used (with the exception of the SPYG model). three models for assessing the liquidation value of appraised objects have been developed (pp. 63-70). proposed approaches to the valuation of knowledge and competencies of employees (pp. 53-57). revealed a non-linear dynamics of the value of liabilities and equity capital of companies, the amount of liabilities of which is commensurate with the value of (their) assets (pp. 75-80).

In the third chapter of the dissertation work, the following results were obtained:

A system for calculating the cash flows of shareholders is proposed (p. 92128), which combines the traditional method of calculation (which the author of the dissertation called inside) and an alternative method of calculation based on cash flows external to the company that are directly related to shareholders (called outside by the author). It is shown under what condition the flows of shareholders calculated according to the inside and outside accounting systems lead to a single result, and when - to different ones. Also within the framework of this system, the difference in the calculations of shareholder flows based on data from external and management reporting is shown.

Interest rate algebras "on the demand side" (pp. 320-326) and "on the supply side" have been developed. For "demand-side" rates, four "cumulative" staking algebras and a risk-adjusted staking algebra have been developed.

On the basis of the developed interest rate algebra, the proof of the convergence of the reliable cash equivalent model with the discounting model using risky discount rates for the limiting case - an infinite period (pp. 152-154) is given.

A theoretical study of the effect of inflation on the risk premium was carried out, as a result of which it was concluded that when nominal discount rates are calculated, inflation affects the observed risk premium (pp. 159-163).

An improved model of dividend discounting is proposed, which additionally takes into account the limited period of ownership of shares and the expected exchange rate return (pp. 207-210).

New cash flow capitalization models are proposed, within which different discount rates are applied for cash inflows and outflows. The convergence of these models with the traditional cash flow capitalization model using a single cash flow balance capitalization rate is shown (pp. 200-205).

Formulas for calculating discount rates on pre-tax and post-tax bases have been developed. For cash flow capitalization models for equity capital and for invested capital, the convergence of valuation results obtained by applying the correct valuation parameters calculated on a pre-tax and post-tax basis is shown (pp. 180-200).

Alternative methods for numerical assessments of discount rates by market extraction methods based on the iteration method, information on discounts of producers and sellers, as well as insurance rates are proposed (pp. 153-158).

Methods have been developed for predicting depreciation in the absence of information on the initial cost of fixed assets, taking into account the planned volume of capital investments in fixed assets (p. 120125).

In the fourth chapter of the dissertation work, the following results were obtained:

A general discounting algorithm has been developed for changing the capital structure in the forecast period in an arbitrary order (p. 212223);

Particular valuation methods have been developed for cases where one or two significant changes in the ratio of own and borrowed funds are expected in the forecast period, due to a change in the debt burden or an additional issue of shares (pp. 224-232).

The method of equity capital valuation has been adjusted using the discounted model of flows of all invested capital for cases where a significant change in the debt burden is expected in the forecast period (pp. 228-232).

The influence of the additional issue on the value of the business, the issuer's share capital and the value of one share has been studied (p. 232237).

A method is proposed for calculating the share of investors in the capital of high-tech companies in cases where investors make contributions both in cash and in non-monetary (technology) forms (p. 249253). This method is especially relevant in situations where potential investors offer large companies new technologies, the introduction of which can significantly change the return on invested capital and the risks of operating activities.

A method for calculating the cost of equity capital and blocks of shares in companies with a cross ownership structure is proposed (pp. 254-259).

In the fifth chapter of the dissertation work, the following results are obtained:

A model for evaluating the structural divisions of a company is proposed (pp. 273-287).

A methodology for estimating the cost of control over companies is proposed and, on its basis, an assessment of the value of premiums and discounts for the presence / absence of control (pp. 287-299).

A paradox has been revealed (pp. 304-309), which consists in the fact that, under certain conditions, for individual companies, the valuation of their 100% block of shares may be of less value (value) for investors than the valuation of a smaller block of the same shares. The conditions for the emergence of this paradox, methods for assessing its boundary conditions and recommendations for top managers and owners of such companies are formulated.

The principle of proportionality of the results of assessments (p. 271) obtained within the framework of various approaches was formulated and, on their basis, an approach was developed to derive a final judgment about the value of the value of the object of assessment, based on the results of assessments carried out by various assessment approaches (p. 265-2CE).

Concluding the work, the author expresses his conviction that the "adoption" of the provisions, models and methodological methods proposed in this study will help everyone interested persons obtain more informed and accurate views of the value of companies, businesses and interests in them, and make informed management decisions, taking into account their consequences for the value of their business.

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259. Woolridge, R., 1993, "Competitive Decline and Corporate Restructuring", in The New Corporate Finance, ed. D. H. Chew, Jr., New York: McGraw-Hill.

260. Zhu Y. and I. Friend "The Effect of Different Taxes on Risky and Risk-free Investment and on the Cost of Capital", Journal of Finance, 41 (March 1986, pp. 53-66).

Kozyr Yuri Vasilievich, Doctor of Economics, General Director of KOPART, Chairman of the Expert Council and Member of the Board of the Russian Society of Appraisers (ROO), partner, lecturer at the Department of Economics of Intellectual Property of the Faculty of Innovation and High Technologies of the Moscow Institute of Physics and Technology. Practical experience in the field of corporate finance and business valuation since 1994 (including in the oil, telecommunications and banking sectors). In March 2008, he was awarded the Order of Merit in Appraisal Activities, 1st Class.

Main media publications(1997-2008): magazines "Securities Market", "Evaluation Issues", " Banking Technologies", "Financier", mass media "Bulletin of the Appraiser", "Russian Appraiser", bulletins of "Rosbusinessconsulting" and the company "BARREL". Co-author and creator of the largest Internet portal of appraisers in the Russian Federation "Appraiser.Ru Virtual Club of Appraisers" (1999). Author methodologies, seminars and numerous publications on the valuation and management of the value of a business (assets) Author of the book Company Value: Valuation and Management Decisions (2009) Report at the international forum of appraisers in Bangkok (Thailand) - (2007) and (2008).

Key works/projects: Euroset, Ruspromavto, Apatity, Lebedinsky Mining and Processing Plant, Oskol Electrometallurgical Plant, Novokuznetsk Aluminum Plant, Shchekinoazot, AHC Tupolev, Dorogobuzh, Silvinit , "Akron", "Novoexport", "Promsyryeimport", "Selkhozpromexport", "Moscow People's Bank" (London), "K.B.S.E. Eurobank (Paris), Roskhimterminal, Irkutskenergo, Pechoraneft, Sibir Energy, Klinvolokno, Moscow Stud Farm No. 1, Rosneft, etc.

Some recent publications:

• Yuriy V. Kozyr. The Interest Rate Algebra // World Applied Sciences Journal, 28, 2013, pp.222-231. -
• Kozyr Yu.V. Should different appraisal approaches lead to a single value of appraised objects? -

Kozyr Yu.V. Valuation of receivables

When evaluating receivables, it is advisable to take into account the following main points.

1. Deadline limitation period for commercial transactions (excluding real estate transactions) is three years.

2. With long delays in payment accounts receivable (more than 3 years), accountants can write off bad debts to expenses of the current period (for example, on account 91 “Other income and expenses”), while reducing the taxable base of the corresponding period (for such write-offs, there must be a write-off decision). Information about such write-offs is reflected on the off-balance information account 007 “Write-offs at a loss of indebtedness of insolvent debtors”. The appraiser, when proceeding with the assessment of receivables, should find out whether write-offs were applied to overdue receivables, and, if applied, in what amount. In the event that accountants write off part of the receivables, the appraiser must express his opinion on whether he agrees with the amount of write-offs or not. In case of disagreement, the valuer must make its own adjustments to the receivables, starting from the full (nominal) amount of the receivables (an example of such adjustments is presented below). According to the logic of things, usually after a three-year period from the moment the debt arose, its value becomes practically zero, provided that before the expiration of this period a claim was not filed against the debtor to collect this debt.

3. What discount rate should be taken to adjust receivables?

The answer to this question seems to be the following.

If risk factors are taken into account in the amount of receivables, further adjustments to receivables that reflect the time factor (deferred payment) should be made by discounting (discounting) the amount receivable at the risk-free rate.

If risk factors are not taken into account in the amount of receivables expected to be collected, further adjustments to receivables that reflect both the time factor and the risks of receivables should be carried out by discounting (discounting) the amount of receivables expected to be collected at a rate that takes into account the risks of non-receipt of receivables.

The risk-free rate used to discount the risk-adjusted amount of receivables lies in the range of the deposit rate (or government bond yield rate) of the delivery rate at which the entity being valued is able to borrow from banks. The latter is justified in the following way. There are four possible situations:

1. the enterprise does not have the possibility of expansion;
2. there are opportunities for expansion, while the expected return on investment in expansion is lower than or equal to the value of the deposit rate in the bank.
3. Expansion opportunities are available, while the expected return on investment in expansion is higher than the deposit rate, but lower than the lending rate.
4. Expansion opportunities exist and the expected return on investment in expansion is greater than or equal to the lending rate.

In situations 1-2, obviously, the appropriate discount rate would be the bank's deposit rate (or government bond yield).

In situation 3, the appropriate discount rate would be the expected return on investment in the expansion (higher than the deposit rate but lower than the lending rate).

In situation 4, the appropriate discount rate would be the loan rate, because if, for example, the return on investment in expansion is expected to be 25%, and the loan rate is 14%, then if the payment of receivables is delayed, the company can take a loan at 14% from the bank and continue their investment in expansion. In this case, its costs due to the delay in payment of receivables will be fixed at the level of the lending rate (14%).

Accordingly, summing up, we conclude that the value of the appropriate discount rate for receivables applied to debts that does not raise doubts about the completeness and timeliness of payment is in the range of values ​​from deposit to credit rates.

Regarding the discount rate problem debt or a debt that raises doubts about the completeness and timeliness of its payment, the following expression can sometimes be used to evaluate it:

where:

rf - risk-free rate, the value of which in relation to the assessment of receivables, as previously indicated, is in the range from the deposit rate to the lending rate,

pd - probability of default (non-payment of debt) in the amount of k, 0

kpd - expectation of the level of possible losses (average losses in the event of a default).

where:

rc is the current market return, cov(kpd,rc) is the covariance of the current market return and the expected loss level, a is the risk price: a = pr/σ2, where pr is the market risk premium, σ2 is the variance of the market return (the return of the market index).

Note. If a pronounced relationship is found between the state of the market cycle phase (growth, decline) and the expected probability of losses, the first assessment method presented in the example should also be adjusted to take into account this dependence in the amount of debt receivable (in the example presented in the text, the amount is 95 million rubles should be adjusted by a cov(kpd,rc)).

Let's bring example.

Let there be accounts receivable = 100 million rubles, the repayment of which is expected to occur in a year. However, there are certain doubts about this, the quintessence of which is the allowable level of losses (not full and / or late payment) of 10%, and in the event of an unfavorable outcome, the probability of which (pd) is estimated at 10%, as expected, the amount of non-payment will be 50% (k = 0.5). Let it be known that, as a result of the analysis, the appraiser came to the conclusion that a suitable risk-free rate in relation to the receivables of the company being valued is a rate equal to 12%. We will evaluate this receivable in two ways - by reflecting risks directly to the amount of debt (method 1) and by reflecting risks in the value of the discount rate (method 2).

Method 1.

It follows from the conditions of the problem that the expected level of collection of receivables is 95% (100% - 10% * 50% = 95%), which in absolute terms is equivalent to receiving 95 million rubles. Discounting this amount at a risk-free rate of 12% for a period of one year would give the following estimate of the market value of the receivable:

95 / (1 + 0.12) \u003d 84.82 million rubles.

Method 2.

In accordance with expression (1), the discount rate that takes into account the risks of repayment of this debt is:

Discounting the full amount of receivables at the above-determined rate, we obtain one more estimate of the market value of receivables:

100 / (1+ 0.179) = 84.82 million rubles

As can be seen, both evaluation methods lead to the same result.

4. If one or more debtors are in bankruptcy it is necessary to determine the value of the bankruptcy estate of creditors of each of such debtors, determine the possibility of repaying this bankruptcy estate, as well as the number of the queue of creditors to which the assessed enterprise belongs (the company whose receivables are being assessed). Usually, if the receivable of a legal entity is a business receivable, the enterprise falls into the fifth (last) queue of creditors.

The repayment of accounts payable by bankrupt companies in accordance with the Bankruptcy Law is carried out in order of priority: first, creditors of the first priority are satisfied, then the second, and so on. until there are enough funds to pay off. At the same time, those on the waiting list of the first stages can receive a full refund, those on the waiting list of medium priority (for example, the third stage) receive partial reimbursement, and those on the waiting list of the last groups (for example, the fourth and fifth) receive nothing. If, after full satisfaction of creditors of a higher priority queue, there are not enough funds to repay the next priority in full, repayment occurs according to the principle of proportionality. For example, the total debt claims of fourth priority creditors amount to 10 million rubles, while the bankrupt company has only 4 million rubles to satisfy their claims. (40% of the amount of claims within this queue of creditors), each of the creditors of this queue will receive 40% of the amount of their claims.

Below is the content of Article 64 of the Civil Code of the Russian Federation (Satisfaction of creditors' claims), which regulates the procedure for payments to creditors upon liquidation of legal entities.

Article 64. Satisfaction of creditors' claims

1. Upon liquidation of a legal entity, the claims of its creditors shall be satisfied in the following order:

first of all, the claims of citizens to whom the liquidated legal entity is liable for causing harm to life or health are satisfied through the capitalization of the corresponding time payments;

in the second place, settlements are made for the payment of severance pay and wages with persons working under an employment contract, including under a contract, and for the payment of remuneration under copyright agreements;

in the third place, the claims of creditors for obligations secured by the pledge of property of the liquidated legal entity are satisfied;

in the fourth place, debts on obligatory payments to the budget and extra-budgetary funds are repaid;

in the fifth place, settlements with other creditors are made in accordance with the law.

5. When measuring receivables under the procedures of the adjusted net assets method appropriate adjustments should be made in relation to accounts payable, as well as to all other obligations of the company. Here you should not forget, at least, about such moments:

• the same principle of corporate finance applies to a company's obligations to its creditors as applies to its own receivables: money received or paid tomorrow is worth less than money received or paid today;
• accounts payable overdue for more than 3 years are written off to the income of the organization, which, ceteris paribus, causes an increase in income tax;
• The market value of a company's liabilities cannot exceed the market value of its assets.

The last remark is often ignored, which in some cases (when valuing companies whose market value of assets is lower than the book value of assets) may lead to inadequate valuation results using the adjusted net assets method.