УДК: 338.27

DOI: https://doi.org/10.36887/2415-8453-2021-3-7

Ihor Skvortsov
Doctor of Economics, Professor, Professor of the Department of Enterprise Economics and Investments, Lviv Polytechnic National University
Lilia Hrynash
PhD in Economics, Associate Professor of the Department of Economics and Marketing, Educational and scientific Institute of Entrepreneurship and Advanced Technologies of Lviv Polytechnic National University
Khrystyna Gorbova
PhD in Economics, Associate Professor of the Department of Finance, Accounting and Analysis, Educational and scientific Institute of Entrepreneurship and Advanced Technologies of Lviv Polytechnic National University

JEL classification: C52, O31, O40


Substantiation of differences between payback and break-even points in the production activities of enterprises is concerned. The method of modeling and research of economic phenomena and processes is offered. The methodological basis of this approach are two elements: the creation of a formalized economic categorical apparatus and the construction of mathematical models of economic processes. The essence of the formation of the categorical apparatus is as follows: three primary categories are proposed, on the basis of which all secondary ones are defined axiomatically. The application of this categorical apparatus makes it possible to solve the following main issues: to formulate the content of qualitative economic concepts (categories) of “stock” and “flow”; to introduce into economic practice such an important indicator as “economic acceleration”, as a result of which there is an opportunity to reasonably model and study nonlinear economic processes; change the understanding of many economic concepts – “value”, “price”, etc., because they become categories that have separate units of measurement, and therefore formed indicators that are significantly different from traditional (“cost”, “profit price”, etc.). But most importantly, it ultimately provides an opportunity to model and explore important economic processes and indicators.

The application of the proposed category apparatus is shown on the example of modeling and research of economic processes occurring at the enterprise in the implementation of operational activities – production and sale of manufactured products. The most important element of this activity is the substantiation of payback and break-even points that correspond to a given technological process.

The disadvantage of existing approaches to substantiate these indicators is that when describing these processes using traditional concepts, researchers often confuse which point they consider – payback or break-even, as the main indicators in the obtained models are almost the same – on the X-axis “production volumes ” are put, and on the Y axis -“ costs ”and“ sales ”. Therefore, the main difference between these points is not in the name of the elements of the study (their name is the same in both cases), but in their essence. In the first case, when the payback point is determined, these indicators are considered as a “stock”, and in the second – when determining the break-even point – in the form of flows. This means that in order to avoid mistakes, it is necessary to understand clearly in which space (stocks or flows) research should be carried out.

Keywords: economic categories, stock, flow, economic acceleration, payback point, break-even point, fixed and variable costs, one-time and current costs.


  1. Tsal-Tsalko, Yu. S. (2012). Vytraty pidpryiemstva. [Enterprise costs]. К Ukraine.
  2. Lipsic, I. V. (2011). Kommercheskoe cenoobrazovanie [Commercial pricing]. Izdatel’stvo BEK. Moscow. Russia.
  3. Holovko, T. V., Sahova S. V. (2002). Stratehichnyj analiz. [Strategic analysis]. In Kuzhel’noho M. V. (ed.). KNEU. К Ukraine.
  4. Moskvin, S.O. (2003). Proektnyj analiz. [Project analysis]. Vydavnytstvo Libra. К Ukraine.
  5. Kotsiuba, O. S. (2020). «Estimation of payback period of the investment project within the fuzzy-multiple statement of the problem». Biznes Inform, No 10, pp.173–179.
  6. Prokopenko, V. L. (2017). «Return on investment in electrical distribution networks (on the example of decisions on the reconfiguration of 0.38-10 kV networks)». Enerhetyka ta elektryfikatsiia. No 10/11,46-53.
  7. Shemaiev, V. V. (2014). «Assessment of financial efficiency of investment projects supported by international financial organizations». Finansy Ukrainy. No 5,96-105.
  8. Skvortsov, I. B. (2003). Efektyvnist’ investytsijnoho protsesu: metodolohiia, metody i praktyka. [The efficiency of the investment process: methodology, methods and practice]. Vydavnytstvo NU “Lvivska politekhnika”. Ukraine.
  9. Kuchta, D. (2000). Fuzzy capital budgeting. Fuzzy Sets and Systems, Vol. 111, Issue 3, pp. 367–385.
  10. Kahraman, C., Ruan, D., Kacprzyk, J., Fedrizzi, M. (2001). «Capital Budgeting Techniques Using Discounted Fuzzy Cash Flows Soft Computing for Risk Evaluation and Management». Physica-Verlag, pp. 375–396.
  11. Makarova, M. S. (2015). «Fuzzy methods for estimating the discounted payback period». European research, No 3, pp. 42–46.
  12. Tyschuk, T.A. (2001) Ekonomikomatematychne modeliuvannia protsesiv upravlinnia proektamy na osnovi teorii nechitkykh mnozhyn. [Economic and mathematical modeling of project management processes based on the theory of fuzzy sets]. Abstract of Ph.D. Thesis. 08.03.02. Donetsk.
  13. Karachyna, N. P., Vityuk A. V. (2013). «Methodical space for evaluating the economic efficiency of investment projects». Ekonomichnyi chasopys-XXI. No 5/6, pp. 92-95.
  14. Klepikova, O. A., Sil’vestrova, Yu. S. (2015). «Modeling of break-even point of the enterprise taking into account restrictions». Naukovyi visnyk Khersonskoho derzhavnoho universytetu. Issue 1. Part1. pp. 167-171.

The article was received 15.06.2021