Mathematical modeling for financial analysis of an enterprise: Motivating of not open innovation

Borodin, Alex et al. Article Mathematical modeling for financial analysis of an enterprise: Motivating of not open innovation Journal of Open Innovation: Technology, Market, and Complexity Provided in Cooperation with: Society of Open Innovation: Technology, Market, and Complexity (SOItmC) Suggested Citation: Borodin, Alex et al. (2021) : Mathematical modeling for financial analysis of an enterprise: Motivating of not open innovation, Journal of Open Innovation: Technology, Market, and Complexity, ISSN 2199-8531, MDPI, Basel, Vol. 7, Iss. 1, pp. 1-15, https://doi.org/10.3390/joitmc7010079 This Version is available at: https://hdl.handle.net/10419/241664 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ Journal of Open Innovation: Technology, Market, and Complexity Article Mathematical Modeling for Financial Analysis of an Enterprise: Motivating of Not Open Innovation Alex Borodin 1,* , Irina Mityushina 2, Elena Streltsova 3, Andrey Kulikov 4, Irina Yakovenko 3 and Anzhela Namitulina 5   Citation: Borodin, A.; Mityushina, I.; Streltsova, E.; Kulikov, A.; Yakovenko, I.; Namitulina, A. Mathematical Modeling for Financial Analysis of an Enterprise: Motivating of Not Open Innovation. J. Open Innov. Technol. Mark. Complex. 2021,7, 79. https:// doi.org/10.3390/joitmc7010079 Received: 18 January 2021 Accepted: 25 February 2021 Published: 1 March 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). 1Department of Finance, Plekhanov Russian University of Economics, 117997 Moscow, Russia 2Department of Finance, Belgorod National Research University, 308015 Belgorod, Russia; [email protected]u 3Department of Computer Software, Platov South Russian State Polytechnic University (NPI), 346428 Novocherkassk, Russia; [email protected]u (E.S.); [email protected] (I.Y.) 4Department of Organization of Medical Provision and Pharmacoeconomics, I.M. Sechenov First Moscow State Medical University (Sechenov University), 119991 Moscow, Russia; [email protected] 5Department of Finance, Financial University under the Government of the Russian Federation, 105064 Moscow, Russia; [email protected] *Correspondence: [email protected]u Abstract: The article develops economic and mathematical models as a tool for conducting factor financial analysis of the prospects for the development of an industrial enterprise. The functioning of the developed economic and mathematical models is based on the DuPont model, which allows analyzing the dynamics of the company’s profitability in the course of two-factor and three-factor financial analysis. The proposed model tools are based on the convergence of deterministic financial analysis methods embedded in the DuPont model and simulation methods that allow analysis under the influence of random factors. The constructed economic and mathematical models for forecasting profitability use the company’s retrospective data on its financial condition: the amount of profit, revenue, assets, and equity. The constructed simulation models are implemented in the OMEGA software product and included in the computer technology for predicting the profitability of an industrial enterprise. The architecture of the proposed tools is presented, and the results of simulation experiments performed on models are demonstrated. Keywords: financial analysis; DuPont model; simulation models; computer technology 1. Introduction At present, economic development and improving the competitiveness of the economy is a priority in shaping the policy of any country. The determinants of economic growth are inextricably and organically linked to economic development, among which the fundamental one is an increase in national production, which leads to an increase in the gross domestic product (GDP) and, as a result, to an increase in the welfare of society. Of course, the level of socio-economic development of the country is provided, first of all, by the economic growth of economic entities that contribute to the formation of GDP. A prerequisite for increasing the rate of growth of national production is the positive dynamics of profitability of the country’s leading enterprises as an indicator of their commercial activity. The business parameters that are directly associated with the resulting enterprise profit, the profitability indicators formally defined by the ratio of the resulting effect of the invested capital or resources and characterizing the efficiency of the resources used in economic activity. The study of these characteristics, as fundamental criteria for efficiency, is assigned one of the main roles in the system of analysis of enterprises’ activities. In this regard, in modern economic literature, considerable attention is paid to the development of methodological aspects of profitability analysis. Approaches to improving the efficiency of firm management in terms of financial coefficients were proposed by Ali, J. Open Innov. Technol. Mark. Complex. 2021,7, 79. https://doi.org/10.3390/joitmc7010079 https://www.mdpi.com/journal/joitmc J. Open Innov. Technol. Mark. Complex. 2021,7, 79 2 of 15 H.F. and Charbaji, A. [ 1 ], Chen, L., Liaw, S., and Shin Chen, Y. [ 2 ], Tan, P.M.S., Chye Koh, H., and Chin Low, L. [ 3 ], Winand, M., Zintz, T., and Scheerder, J. [ 4 ], Tamuleviˇcien ˙ e, D., Mackeviˇcius, J. [5]. This article does not aim to consider formal expressions for many types of individual indicators of profitability, calculated in different areas and which include return on assets (ROA), return on sales (ROS), return on fixed assets (ROFA), return on investment (ROI), return on equity (ROE), etc. The use of these indicators for financial analysis undoubtedly has a number of advantages, including ease of calculation, understanding, compliance with accounting methods, and traditional application. However, traditional criteria for evaluating the profitability of an enterprise have a number of disadvantages. These include binding to conditional accounting values, non-additivity, and others. The authors of the article propose to use the factor analysis model developed by the management of the American company DuPont to assess profitability—the DuPont model, which allows determining the factors that account for the dynamics of profitability. However, the trend of digitalization of the economy put before financial analytics raises new challenges, not only related to the consideration of the current but also the future financial state of enterprises, changing under the influence of the external and internal environment (market, systems of decision-making, etc.). In this regard, forecasting profitability, as an important stage of financial planning, has aroused great interest among researchers. Recently, there are a number of works that raise this problem. Thus, the mechanisms for constructing forecasting models with adaptive and rational expectations were proposed in the article Timofeeva N. Yu. [ 6 ]. The article Deminova S. V., Suchkova N. A. is devoted to solving the issues of forecasting the profitability of a company using computer modeling [ 7 ]. All this actualizes the problem of forecasting the profitability of an enterprise based on computer modeling. This article proposes an approach to build modeling tools for financial analysis built-in to computer technology, enabling the study of the profitability of the company in the future. Within the framework of the proposed approach based on the DuPont model, the task of forecasting the financial condition of an enterprise is set based on the results of processing a set of time-varying indicators included in this model. The proposed model tools for financial analysis are based on the convergence of deterministic financial analysis methods embedded in the DuPont model and simulation methods. The methodological base of the research includes the basic elements of a systematic approach, contributing to the development of an effective strategy of research, system analysis as an applied aspect of the system approach, strategic management theory, financial analysis, theory of stochastic systems, and simulation modeling. The research uses methods of factor financial analysis (two-factor and three-factor), statistical modeling, and statistical data processing. 2. Literature Foundations Currently, profitability indicators are the most important performance characteristics of any organization, so the study of their changes in the future is of increased interest in the scientific community. The ability of an organization to adequately assess its potential state in the future allows not only to prevent risks in a timely manner but also to maintain competitiveness in the modern market. In this regard, the authors investigated forecasting methods used in various subject areas. A dynamic model linking the predictability of profitability with the factors of firm development was proposed by Alti A., Titman S [8]. The model generates forecasts of investment portfolio profitability depending on its characteristics. Addoum J. M’s research is devoted to the development of a theoretical measure of yield hedging [ 9 ]. It is shown that profitability can be represented by the aggregate parameter “high-minus-low demand” (HML). The theory of the profitability anomaly was developed in [ 10 ]. The authors suggested measuring the “stickiness of expectations” at the firm level and finding strong support for additional forecasts. The work of Weisbrod, E. [ 11 ] was devoted to solving the problems of unrealized shareholder returns. J. Open Innov. Technol. Mark. Complex. 2021,7, 79 3 of 15 The author demonstrated that an unrealized profit position of shareholders can cause both short-term returns and losses. In the context of the problem of forecasting the profitability of organizations, the work of Chiang C. [ 12 ] is interesting, which showed that measuring unexpected profits by calculating the consensus error (CE), represented as the difference between the actual profit and the average professional forecast, leads to inadequate results. The CE value is a poor approximation of a windfall. The best result when measuring unexpected profits is the percentage of misses. The article by Malloy C. J., Moskowitz T. J., Vissing-Jørgensen A. [ 13 ] deserves attention. Using data on household consumption at the micro-level, the authors showed that long-term risk in asset pricing significantly better reflects their average return than aggregate or non-stock risk. The work of Pástor L’., Stambaugh R. F. [ 14 ] is devoted to the development of a predictive system for estimating expected returns. The system proposed by the authors is based on establishing a correlation between unexpected returns and innovations in expected returns. Comparing the proposed approach with standard predictive regressions, the authors concluded that the proposed predictive system evaluates the expected results with higher accuracy. The impact of financial restrictions on risk and expected return was studied by Livdan D., Sapriza H., Zhang L. [ 15 ]. The study was conducted by observing an asset pricing system that “includes retained earnings, debt, expensive equity, and collateral restrictions on debt capacity” [ 15 ]. Research has shown that “more financially constrained firms are riskier and receive higher expected returns on shares than less financially constrained firms” [ 15 ]. The work of Fama E. F., French K. R. is devoted to the estimation of profit received by non-financial firms [ 16 ]. The internal rate of return is estimated based on the initial market value of their securities and the value of their investments. Research on stock returns was conducted by Harford J. [17]. The author claims that “cash-rich bidders destroy seven cents of value for every extra dollar of cash reserves.” Along with the conclusions of scientists about the effectiveness of forecasts, there are also opposite opinions. So, the authors Easterwood J. C., Nutt S. R. studied the behavior of analysts and divided them into two classes. The first class includes analysts who “immediately and without bias include information in their forecasts” [18]. The second class includes analysts who systematically underestimate the information of predictive systems. The result of research on the behavior of analysts is the author’s conclusion that “analysts do not react enough to negative information but overreact to positive information” [ 18 ]. Currently, the problem of improving the efficiency of profit management is of particular relevance. One of the management methods is to have multiple shareholders. Jiang F., Ma Y., and Wang X. found that “firms with multiple block holders, as a rule, have a higher level of profit management than firms with a single controlling shareholder” [ 19 ]. In other words, having multiple shareholders has a positive impact on the effectiveness of profit management if they are of the same type: public or private. In addition, according to authors Jiang F., Ma Y., and Wang X., the effectiveness of profit management increases with an increase in the number of large shareholders and “an increase in the relative ownership of other large shareholders to the controlling shareholder” [ 19 ]. Currently, the subject of research by many scientists is the widespread use of mathematical tools for predicting the performance of organizations. At the same time, an important problem is not only to predict the overall trend of the organization’s development but also to anticipate less repetitive events. For example, the works of Sanchis, R.; Duran-Heras, A., Poler, R. [ 20 ], as well as Cerna, S., Guyeux, C., Royer, G., Chevallier, C., Plumerel, G. are devoted to solving the problem of creating tools that allow predicting possible failures in the sustainable operation of an enterprise [ 21 ] and Vasilieva, T. Jurgilewicz, O., Poliakh, S., Tvaronaviˇcien ˙ e, M., Gidzik, P. [ 22 ], Hilkevics, S.; Semakina, V. [ 23 ]. In [ 20 ], a mathematical model of mixed linear integer programming was proposed to optimize the potential of readiness for non-standard situations. The model “optimizes the activation of preventive actions to reduce the propensity for violations.” The objective function of the linear programming problem being solved J. Open Innov. Technol. Mark. Complex. 2021,7, 79 4 of 15 minimizes the expected annual costs of preventive actions that lead to destructive events. The advantage of the constructed model is its ease of use, which does not require the involvement of highly qualified mathematical staff. Methods for detecting operational failures embedded in mathematical models were developed in [ 24 ]. Questions about predicting stock prices using deep learning are covered in Shahi, T., Shrestha, A., Neupane, A., Guo, W. [ 24 ]. The authors developed a deep learning architecture in the form of an expert system. The article Espinoza-Audelo, L., Olazabal-Lugo, M., Blanco-Mesa, F., León-Castro, E., Alfaro-Garcia, V. is devoted to the application of mathematical modeling methods to assessing the impact of the external environment on the state of an organization [25]. Analyzing the effectiveness of traditional methods for obtaining information about the future, the authors proposed the use of a probabilistic ordered weighted average Bonferroni operator for estimating changes in prices for agricultural products. Recently, there has been an intensive use of fuzzy multiple approaches to modeling decision-making processes based on forecasting performance indicators of economic entities. Borodin A. et al . discussed the issues of creating intelligent modeling tools to support decision-making when evaluating projects submitted for funding [26,27]. The tools are based on mathematical models constructed using the mathematical apparatus of the theory of fuzzy logic. The work of Begam S., Selvachandran, G., Ngan, T., Sharma, R. [ 28 ] is devoted to the application of soft computing theory tools to the construction of information and predictive systems operating under uncertainty. For forecasting problems, the authors proposed a similarity measure on a complex multi-valued soft set that is used to support decision-making. The application of deep learning techniques for solving digital currency forecasting problems is proposed in the articles by Lamothe-Fernández, P., Alaminos, D., et al. and Szetela, B., Mentel, G., Mentel, U., Bilan, Y. [29,30]. The authors were faced with the task of predicting changes in the price of bitcoin. The use of recurrent convolutional neural networks for this purpose demonstrated the adequacy of the constructed model, which functions under conditions of uncertainty and its usefulness for evaluating cryptocurrency assets. The article Meng, Y., Qasem, S., Shokri, M. is devoted to the application of artificial neural networks [ 31 ]. The authors carried out a study of various forecasting models on the basis of machine learning with big data. Artificial neural network (ANN) and adaptive neuro-fuzzy inference system (ANFIS) models were used for long-term forecasting. The authors’ research of various variations of the ANN and ANFIS models that differ in combinations of input variables is valuable. When creating the tools, the goal of reducing the dimension of the “artificial neural network/adaptive neuro-fuzzy inference system” (ANFIS/ANN) model system was achieved while reducing computational costs and at the same time, increasing the reliability of forecasts. Machine learning methods for solving forecasting problems were used in studies by Popkov, Y., Popkov, A., Dubnov, Y., Solomatine, D. [ 32 ]. In [ 32 ], a new randomized hierarchical dynamic regression model with random parameters, measurement noise, and random input was proposed. Based on the constructed model, the entropy-randomized machine learning technology was developed, which successfully passed the test for predicting the daily load of the regional power system. The article Chiu, M., Chen, T., Hsu, K.-W. is devoted to solving the problem of developing tools based on machine learning for predicting labor productivity in an enterprise [ 30 ]. The authors proposed a new approach to modeling performance training as an indeterminate process “based on the interval fuzzy number (IFN) of mixed binary quadratic programming (MBQP) with an ordered weighted average (OWA)” [ 33 ]. Experiments carried out on the constructed model demonstrated its advantage over existing methods in terms of prediction accuracy. The use of artificial neural networks for solving forecasting problems is reflected in the article Jiang, P., Hu, Y., Wang, W., Jiang, H., Wu, G. [ 34 ]. Using a synthesis of neuro-network and regression modeling methods, the authors managed to achieve high prediction accuracy. Various traditional forecasting models for demand management, such as autoregressive integrated moving average (ARIMA), as well as soft computing methods, such as J. Open Innov. Technol. Mark. Complex. 2021,7, 79 5 of 15 fuzzy logic, genetic algorithms, and neural networks, were considered in Suganthi L., Samuel A. A. [ 35 ]. The authors also paid attention to ant and swarm algorithms [ 35 ]. The article Ediger V., Akar S. [ 36 ] is devoted to forecasting energy demand in emerging markets based on econometric modeling. The author suggested using the ARIMA and seasonal ARIMA (SARIMA) methods for forecasting energy demand. A new forecasting method based on the mathematical apparatus of artificial neural networks was developed by Gonzalez P. and Zamarreno J. [ 37 ]. The proposed method involves training an artificial neural network using a hybrid algorithm. A method for predicting the future based on the synthesis of the seasonal autoregressive iterative moving average (SARIMA) and nonlinear autoregressive artificial neural network (NARANN) methods was proposed by Tutun S., Chou C., Canıyılmaz E. [ 38 ]. An effective planning tool is not only long-term but also short-term forecasting. Bayesian methods for short-term forecasting based on a neural network model were proposed by Lauret P. et al. [ 39 ]. Currently, evolutionary forecasting methods have become very popular. In this regard, the article Wang C., Hsu L. [ 40 ] is of interest. The researchers proposed using the synthesis of gray’s theory and genetic algorithms, which allowed us to obtain accurate results. A similar approach using the gray function was applied in studies by Cui J. et al. [41]. The authors developed a new gray prediction model that improves the accuracy of forecasting data with the characteristics of a non-uniform exponential law. The article Hu Y., Tseng F. is devoted to the development of a mathematical model for predicting bankruptcy [ 42 ]. The authors developed a functionally-connected network with fuzzy integral for bankruptcy prediction. A hybrid approach to forecasting based on the method of differential evolutionary gradient accelerated regression tree was developed by Garcia Nieto, P., García Gonzalo, E., Sanchez Lasheras, F., Bernardo Sánchez, A. [43]. Based on the method of differential evolution proposed by the authors of the article, a prediction model was constructed that allows “ranking the significance of independent input variables” [ 40 ]. The advantage of the model is high performance and simplicity. The idea of hybridization of the quantum genetic algorithm (QGA) with the support vector regression model (SVR) formed the basis of research by Zhou, Y., Zhou, M., Xia, Q., Hong, W. [44]. Using the empirical mode decomposition (EMD) method, the authors solved the convergent hybridization problem, which significantly improved the prediction accuracy. A combined forecasting system based on the use of artificial neural networks was built by Shih, P., Chiu, C., Chou, C. [ 45 ]. The system uses a dynamic parameter adjustment algorithm (DANGHS), which solves the problem of accurate forecasting. The application of the econophysics methodology by obtaining results derived from the Einstein evolution equation for forecasting in the framework of the fractal market hypothesis is shown in the studies of Blackledge, J., Kearney, D., Lamphiere, M., Rani, R., Walsh, P [46]. The authors obtained a number of results that are fundamental for stochastic modeling. Recently, in the study of complex systems and processes, interest in simulation has increased. The use of simulation modeling methods in forecasting tools makes it possible to conduct numerous experiments without threatening the functioning of the organization [ 47 – 49 ]. In Ermakov S., Leora S. [ 47 ], a modified Monte Carlo method was proposed for a wide class of applied problems. Recognizing the high significance of the research presented in the scientific literature, it should be concluded that the problem of building a model tool for predicting the profitability of a firm requires further study. Solving the problem of constructing mathematical models for predicting the profitability of an organization requires the use of an interdisciplinary synthesis of knowledge in the field of factor financial analysis and simulation. The article offers a tool that allows you to forecast the financial condition of an organization based on the synthesis of the DuPont model and simulation modeling. This article offers a tool that allows you to forecast the financial condition of an organization based on the synthesis of the DuPont model and simulation modeling. J. Open Innov. Technol. Mark. Complex. 2021,7, 79 6 of 15 3. Results 3.1. The Architecture of the Toolkit the Factorial Financial Analysis The architecture of the factor financial analysis tool is shown in Figure 1. J. Open Innov. Technol. Mark. Complex. 2021, 7, x FOR PEER REVIEW 6 of 16 itability of a firm requires further study. Solving the problem of constructing mathematical models for predicting the profitability of an organization requires the use of an interdisciplinary synthesis of knowledge in the field of factor financial analysis and simulation. The article offers a tool that allows you to forecast the financial condition of an organization based on the synthesis of the DuPont model and simulation modeling. This article offers a tool that allows you to forecast the financial condition of an organization based on the synthesis of the DuPont model and simulation modeling. 3. Results 3.1. The Architecture of the Toolkit the Factorial Financial Analysis The architecture of the factor financial analysis tool is shown in Figure 1. DATABASE Statistical data Preparation of initial data COMPLEX OF ECONOMIC AND MATHEMATICAL MODELS Simulation model for forecasting net profit Revenue forecasting simulation model A simulation model for predicting the value of assets Simulation model for forecasting equity capital DuPont two-factor model DuPont three-factor model Profit Revenue Assets Equity Figure 1. The architecture of the Toolkit the factorial financial analysis. Figure 1. The architecture of the Toolkit the factorial financial analysis. The tool of factor financial analysis proposed by the authors uses the following information about the company’s financial condition for the past period of its operation as input data: the amount of profit, revenue, assets, and equity. These data are perceived by the tools as samples from General populations that are accumulated in the database. The information accumulated in the database undergoes appropriate statistical processing (the process of statistical processing of sample data is described below). The results of statistical processing of sample data are input to a set of mathematical models that predict the above-mentioned parameters, considered as random variables. The data obtained as a result of forecasting are used by deterministic models of two-factor and three-factor J. Open Innov. Technol. Mark. Complex. 2021,7, 79 7 of 15 analysis-DuPont models. Based on the results of factor analysis, the company’s financial condition is assessed in the future by determining the return on equity KROE and asset ratios KROA . Thus, the proposed tools for conducting factor financial analysis implement the integration of deterministic and stochastic approaches, which allows you to assess the future state of the company based on the analysis of retrospective data on the financial condition of the company. 3.2. Complex of Economic and Mathematical Models of Factor Financial Analysis The models included in the tools of factor financial analysis are aimed at obtaining the coefficients of return on assets KROA and return on equity KROE calculated in accordance with the well-known deterministic analytical expressions for two-factor and three-factor Du Pont models obtained as a result of elementary mathematical transformations: KROA =Bene f it Activ =Bene f it Income ×Income Activ (1) KROE =Bene f it Equaity =Bene f it Income ×Income Activ ×Activ Equity (2) where Bene f it is the company’s net profit; Activ is the average value of assets; Income is the amount of revenue; Equity is the amount of equity. To implement the integration of deterministic and stochastic approaches, this article proposes to calculate KROA and KROE using the predicted parameters Bene f it , Activ , Income , Equity and evaluate the company’s activity in the planned period. The evaluate indicators in the planned period based on retrospective data accumulated in the database is proposed. The prediction of randomly changing values Bene f it , Activ , Income , Equity is proposed to be carried out on the basis of simulation modeling using the method of statistical tests. For this purpose, the authors built a set of economic and mathematical models. Ω=< 4 ∪ i=1Wi,4 SIMi i=1 ,DP2,DP3>(3) In a complex of models Ω , the components W1 , W2 , W3 , W4 are mathematical models that perform statistical processing of randomly varying values, respectively, Bene f it , Activ , Income , Equity . As a result of statistical processing, the laws of distribution of the studied quantities are constructed in the form of distribution series. The components SIM1 , SIM2 , SIM3 , SIM4 are simulation models that generate possible values of random variables Bene f it,Activ,Income,Equity according to given distribution laws. Let us consider the algorithm for the functioning of models W1 , W2 , W3 , W4 in a generalized form, considering the samples as X={x1,x2, . . . , xn} . Determining the boundaries of variation of the values xi , i=1, n as xmin , xmax (where xmin the minimum, −xmax maximum values xi , i=1, n ), the full range (xmax −xmin) of models W1 , W2 , W3 , W4 can be decomposed into m identical intervals, each of which is determined by the relative frequency of falling values xi , i=1, n . In view of the triviality of calculations, a detailed algorithm for determining the relative frequencies of hit values xi , i=1, n in each of the decomposed intervals is not given. The result of the algorithm for the functioning of models W1 , W2 , W3 , W4 are the laws of the probability distribution of random variables Bene f it,Activ,Income,Equity formed as a series of distributions (Table 1). R(Bene f it):{Bene f iti}n i=1→P(Bene f itj)m j=1; (4) R(Activ):{Activi}n i=1→P(Activj)m j=1; (5) R(Income):{Incomei}n i=1→P(Incomej)m j=1; (6) R(Equity):{Equityi}n i=1→P(Equityj)m j=1. (7) J. Open Innov. Technol. Mark. Complex. 2021,7, 79 8 of 15 Table 1. Laws of distribution of random variables Bene f it,Activ,Income,Equity. R(Benefit) Intervals Ben1Ben2. . . Benm Relative frequency P(Benefit1) P(Benefit 2 ) . . . P(Benefitm) R(Activ) Intervals Ac1Ac2. . . Acm Relative frequency P(Activ1) P(Activ2) . . . P(Activm) R(Income) Intervals In1In2. . . Inm Relative frequency P(Income1) P(Income 2 ) . . . P(Income m ) R(Equity) Intervals Eq1Eq2. . . Eqm Relative frequency P(Equity1) P(Equity 2 ) . . . P(Equitym) In Table 1, the variables Benj , Acj , Inj , Eqi , j=1, m denote the coordinates of the centers of the decomposed intervals of random variables Bene f it , Activ , Income , Equity and the variables P(Bene f itj) , P(Activj) , P(Incomej) , P(Equityj) are the relative frequencies of hits of the corresponding random variables in the designated intervals. The constructed distribution laws in the form of interval series are used by simulation models SIM1 , SIM2 , SIM3 , SIM4 performing the functions of playing out possible values of values Bene f it,Activ,Income,Equity by the method of statistical tests. The generated values of the values Bene f it , Activ , Income , Equity are used by factor financial analysis models DP2,DP3, in accordance with the algorithm shown in Figure 2. The algorithm works as follows. Generation of possible values of random variables Bene f it , Activ , Income , Equity at a time according t to the given distribution laws is implemented by simulation models SIM1 , SIM2 , SIM3 , SIM4 . A loop t is organized by a variable. At the end of the cycle, the generated values are summed in variables ∑(Bene f it) ; ∑(Activ) ; ∑(Income) ; ∑(Equity) . At the beginning of the cycle, these variables are assigned zero values: ∑(Bene f it) =0, ∑(Activ) =0, ∑(Income) =0, ∑(Equity) =0. The accumulated amounts are used to calculate the average values Bene f it =∑(Bene f it) n , Activ =∑(Activ) n , Income =∑(Income) n , Equity =∑(Equity) n , involved in determining the coefficients KROA and KROS. 3.3. Computer Implementation of a Complex of Mathematical Models of Factor Financial Analysis The proposed set of economic and mathematical models Ω=< 4 ∪ i=1Wi , 4 SIMi i=1 , DP2 , DP3> was implemented in the OMEGA software product. The user interface of the OMEGA software package contains menu items: “Input Statistical Data” and “DuPont Model”. When you click the “Input Statistical Data” button, a drop-down list of “Net Profit”, “Own Capital”,“Revenue”, and “Assets” items appear and activating them invites the researcher to enter statistical data for the corresponding parameters. Pressing the “DuPont Model” button activates the simulation models SIM1 , SIM2 , SIM3 , SIM4 and models DP2 , DP3 The algorithm for the functioning of factor financial analysis models based on the application of the developed software product OMEGA presents the results of financial analysis of the operation of the company PJSC Gazprom. The initial data used in the financial analysis process is shown in Table 2. J. Open Innov. Technol. Mark. Complex. 2021,7, 79 15 of 15 52. Jeong, H.; Shin, K.; Kim, E.; Kim, S. Does Open Innovation Enhance a Large Firm’s Financial Sustainability? A Case of the Korean Food Industry. J. Open Innov. 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