The paper is devoted to a conceptual approach to the construction of a set of models for identifying a class of peer companies when choosing multipliers in the process of assessing the market value of companies that are not listed on stock exchanges. The proposed approach is based on machine learning methods (clustering and classification) and implemented on data from 113 IT companies listed on the S&P500. The prognostic efficiency of machine learning methods is considered when constructing a class identification model based on "noisy" data. Models of identification of a class of peer companies have been developed, the choice of values of interval multipliers for the analyzed firms (which are not included in listings) has been substantiated, which makes it possible to improve the quality of assessing the market value of their business.
The modern conditions for the functioning of companies are characterized by a
post-crisis syndrome associated with the effect of the economic "shock" induced by
COVID-19. Unfortunately, the consequences of this "shock" turned out to be deeper
than predicted. In particular, the IMF has updated the forecast of the global economic
decline from 3% to 4.9% [
Undoubtedly, the impact of "shock" has an asymmetric effect on various sectors of the economy, spheres of activity, enterprises of various spheres of activity, forms a reverse impulse to reduce the level of stability of systems of a higher level of the hierarchy, in particular, of the banking system, certain elements of which have a concentration of assets in certain sectors. Under these conditions, the search for new methods and mechanisms of financial management, aimed at reducing both individual and systemic risks, becomes relevant in systems of different levels of the hierarchy.
One of the basic areas of financial management in corporate systems is market
value management. In particular, the priority of this area is confirmed by the fact that
maximizing the company's market value (maximizing the income of the company's
owners) is considered as the main criterion indicator of the effectiveness of financial
decisions [
a) S&P 500 Index dynamics (2020)
b) Euronext Index dynamics (2020)
The significant volatility of the value of financial assets due to the panic expectations of investors regarding the duration of the recovery of the level of business activity and the profitability of companies' activities forces us to look for new technologies for monitoring and of proactive management of the risk of loss of long-term financial stability, loss of financial security due to a decrease in market value, aimed at preventing crisis situations.
It must be said that managing the market value of a company involves solving a triad of such functional tasks as assessing and monitoring the dynamics of the company's market value; diagnostics of the factors that determine the change in the market value of the company; formation of a financial strategy aimed at ensuring sustainable development of the company and maximizing market value. Among the triad of identified tasks, the basic task, the quality of the solution of which largely impacts on the efficiency of managing the market value of the company as a whole, is the assessment and monitoring of the dynamics of the market value.
The problem of developing theoretical and methodological approaches to assessing
the market value of a company is widely considered in the scientific literature [
It should be noted that a large number of scientific works are devoted to the
analysis of factors affecting the market value of corporations, while the factors under
consideration reflect both financial and non-financial aspects of company policy. In
particular, work [
Noting the unconditional relevance and effectiveness of the topics and approaches touched upon by the authors of the above works, it should be noted that approaches to assessing the market value of companies with different scales of activity have not been fully considered. It should be noted that the use of the income approach, which requires the development of adequate forecasts of the financial flows of companies for the medium term in the context of the post-crisis syndrome and a high level of turbulence in the external environment, as well as the cost-based approach, which requires an expensive item-by-item assessment of the value of assets, is difficult for medium-sized companies.
As mentioned earlier, the market approach to business valuation involves the analysis of the value of similar companies, the data of market transactions for which are known. Estimating the value of a company using the market method includes the following main stages: 1) selection of peer enterprises; 2) financial analysis and comparison, recognition of the class of a peer enterprise; 3) selection and calculation of estimated multipliers; 4) application of multipliers to the evaluated enterprise; 5) amendment to the total value.
It should be noted that today the issues of developing a model for identifying a class of peer enterprises are poorly considered, the data of which can be used to calculate the values of the multipliers for the evaluated company, which is not listed on stock exchanges. This task can be effectively solved using machine learning methods, which are further discussed in this work.
The proposed methodological approach to assessing the market value of a company based on machine learning methods includes the following main modules: 1) module 1 – classification of peer companies; 2) development of a model for identifying a class of peer companies and the choice of multipliers; 3) recognition of the class of evaluated companies and assessment of market value (Table 1). The content of each module is considered below.
In the first module, the grouping of peer companies is carried out. The main tasks of this module are: formation of a system of indicators by which comparison is carried out, assessment of their information content; grouping of peer companies.
A preliminary list of indicators by which the comparison of analogous companies
is carried out is formed on the basis of a review of literary sources. To assess the
information content and filter the generated list of indicators, various methods can be
used: methods based on auto-information criteria; methods focused on the assessment
of information content based on the analysis of cause-and-effect relationships. The
first group of methods makes it possible to assess the informational significance of
indicators, to reveal hidden properties and patterns in large volumes of raw data, in
the case when the structure of the input and output data set is unknown. The
advantage of the second group of methods is the ability to reduce the dimension of the
information space of attributes based on the analysis of cause-and-effect relationships
of a set of input and output indicators. The choice of the method is determined by the
complete or incomplete provision of information, the sample size, the structure of the
set of input and output indicators, and the presence of a training sample. Taking into
account the limitations on the information security of indicators, the methods of
expert analysis are used in the work to form a system of diagnostic indicators. More
detailed procedures for filtering the system of indicators are given in [
The resulting system of indicators is the basis for grouping peer companies using
cluster analysis methods [
In the second module, a model for identifying a class of peer companies (M2) is
developed. To solve this task with the subsequent selection of the best one,
discriminant analysis models, probit-logit analysis models, and neural network
modelling are used [
The content of the third module is the identification of the class of the evaluated companies and the choice of the multiplier for assessing the market value. In this
In accordance with table 1 in the 1st module a list of indicators is formed, and a model for the classification of IT companies is built using the methods of hierarchical agglomerative and iterative cluster analysis. To compare the evaluated companies and their peers, based on the proposed filtering procedures, the following indicators were selected: х1 – Profit Margin, %; х2 – Operating Margin, %; х3 – Current ratio; х4 – Total Debt / Equity; х5 – Short ratio. Fragment of the initial data is presented in table 2. No. 1 2 3 4 … 113 module, based on the financial data of the evaluated company, the class of peer companies is recognized, the shares of which are quoted on the stock exchange. Identification of a class of similar companies allows you to select a multiplier and apply it to the financial base of the evaluated company (a company that is not included in the listing) to determine the real market value based on the M3 model.
Thus, the methodological approach proposed above makes it possible to develop a set of models for identifying a class of peer companies and increases the validity and quality of management decisions regarding the choice of a price multiplier used to assess the value of a business.
The proposed approach has been tested on data from 113 IT companies listed on
the S & P500 [
To construct the grouping at the initial step, one of the methods of hierarchical clustering was used - the Ward method, which allows minimizing the total intraclass variance. The Euclidean metric was considered as a measure of distance. The classification dendrogram obtained using the program “Statistica” is shown in Fig. 2.
Analysis of the data shown in Fig. 2, allows us to conclude that it is expedient to have 2 or 3 cluster partitioning of the initial set of IT companies. Since the minimum value of the classification quality functionals is typical for a 3-cluster partition, the results of this grouping are presented below.
The found value of the number of clusters was specified as an exogenous parameter when determining the composition of clusters using the iterative algorithm of the "k-means" method. The results of analysis of variance, reflecting the significance of the variables for classification, are shown in Fig. 3.
The data in Fig. 3 shows that the hypothesis of significant differentiation of clusters is accepted with a 99% confidence level. The mean values of the indicators are given in Fig. 4.
As can be seen from Fig. 4, cluster 3 was formed by IT companies with a high level of corporate sustainability. Companies in this cluster are characterized by high gross and operating margins, low levels of debt for companies of the analyzed industry focus, and an average level of current liquidity. That is these are profitoriented companies with a sufficient level of sustainability. Cluster 1 includes companies with an average level of both gross and operating margins, a high level of current and absolute solvency, and a low level of debt. This cluster was formed by companies with a sufficient level of corporate stability. Cluster 2 companies have the worst characteristics: there is a significant gap in the level of marginality in comparison with companies in cluster 3 and cluster 1, the highest level of debt in the surveyed set of companies, the average level of absolute liquidity, but its lowest shortterm level. Thus, this cluster was formed by companies with a low level of corporate sustainability.
Analysis of the composition of the clusters made it possible to conclude that the classification obtained is correct. In particular, companies in the cluster with a high level of corporate stability (cluster 3) included such companies as FACEBOOK INC (С_75), NVIDIA CORP (С_98), TWITTER (С_108), etc (Fig. 5). Companies with a high level of corporate stability account for 24% of companies in the analyzed population.
In the second module, a model for recognizing a class of analogous companies was built. Input variables (training sample) are: х1 – Profit Margin, %; х2 – Operating Margin, %; х3 – Current ratio; х4 – Total Debt / Equity; х5 – Short ratio, and the resulting variable is the class of the company that is listed on the stock exchange: 1st class – average level of corporate stability, 2nd class – low level of corporate stability, 3rd class – high level of corporate stability. To build a model, as mentioned above, with the subsequent selection of the best one, the methods of discriminant analysis, logistic regression, methods of neural network modelling were used.
The results of estimating the discriminant power of variables are shown in Fig. 6.
The values of the Wilkes λ-statistic, the F statistic indicates the significance of the variables for recognition. The strongest discriminator is the variable x5 – absolute liquidity, x3 – current liquidity. The criteria for the static significance of the canonical discriminant variables are shown in Fig. 7.
a) criteria for the static significance of discriminant canonical functions
b) factorial structure of canonical variables
Fig. 7 allows to conclude about the statistical significance of the canonical discriminant functions. The first canonical discriminant function has a higher information load, the factor structure of which makes it possible to conclude that it reflects the level of short-term and medium-term financial stability of the company. Negative values of factor loadings indicate that the lower the value of the first canonical discriminant variable – the higher the level of the company's stability. The second variable has a much lower discriminant power and is “responsible” primarily for the level of marginality. Negative values also allow us to give the following interpretation: the lower the value of the canonical variable – the higher the level of profitability of the company.
The distribution of objects in the space of canonical variables is shown in Fig. 8.
Fig. 8 shows the higher discriminant power of the first canonical variable, which "distinguishes" the companies with aggressive and conservative financial management models. The boundaries of cluster 2 and cluster 3 are not clear-cut; nevertheless, most of the objects in cluster 3 are characterized by a high level of margins in comparison with companies in cluster 2 and cluster 1.
The parameters of the classifying discriminant functions are shown in Fig. 9. a) parameters of classifying discriminant functions b) classification matrix
Fig. 9 show the acceptable recognition quality for the system of discriminant functions as a whole: the percentage of correct classification is 81.41%. However, the quality of recognition of the elements of the 3rd cluster is low. To improve the quality of the model, the “outliers” points were removed from the initial sample; a fragment of their identification is shown in Fig. 10.
The parameters and quality criteria of the classifying functions built on the truncated data are shown in Fig. 11. a) parameters of classifying discriminant functions b) classification matrix
As can be seen from Fig. 11, the recognition error is 0%, which allows us to conclude that it is possible to use the constructed system of models for a class recognition of peer companies in the process of assessing the market value of companies that are not listed on stock exchanges.
It should be noted that the data in Fig. 8 indicates the presence of a significant array of "noisy" data, therefore, models of neural networks were considered as an alternative model for class recognition. The neural network modelling results are shown in Fig. 12.
The construction of the model was carried out in the interactive computer decision
support system «Methods of nonlinear estimation in multicriteria problems of robust
optimal design and diagnostics of systems in the conditions of parametric a priori
uncertainty" ("ROD & IDS") [
As a result of training the neural network, the classification error was less than 7%.
In the third module, based on the built set of models, the recognition of a class of analogous companies for 5 IT companies operating in the Ukrainian market was carried out. The results of class recognition are shown in Fig. 13.
a) based on discriminant functions b) based on distances to cluster centroids c) based on posterior probabilities
As can be seen from Fig. 13, the analyzed companies belong to cluster 2. The mean values of the multiples for each cluster of peer companies are shown in Table 3.
Cluster Cluster 3 Cluster 1 Cluster 2
Thus, when assessing the market value of the analyzed companies, the following values of the interval multipliers should be used: Enterprise Value / Revenue – 4.19; Enterprise Value / EBITDA – 14.56. It should also be noted that the proposed set of models can be useful in the formation and calibration of the strategy for managing the market value of the analyzed companies, since it allows one to determine the target values of the variables that determine the company's transition to a higher cluster.
The conducted research led to the following conclusions: a conceptual approach to the construction of a set of identification models for a class of peer companies is proposed, which, based on the use of machine learning methods, makes it possible to increase the validity of management decisions regarding the choice of interval and moment multipliers when assessing the value of companies that are not listed on stock exchanges;
models for classifying IT companies by the level of corporate sustainability have been developed;
models of class identification of peer companies have been developed. The use of models for recognizing the class of evaluated companies made it possible to justify the choice of multiplier values that should be applied to the financial base of the analyzed companies.
As areas for further research, it is necessary to highlight the analysis of the combinatorial application of the proposed conceptual approach and methods of simulation modelling, system dynamics, scenario modelling for the formation of a risk-resistant strategy for managing the company's market value.