The impact of the stage of the company's life cycle on the cost of equity through the coefficient β

Shatakishvili Klimentii Emzarievich Postgraduate student, Department of Finance, Money Circulation and Credit, Financial University under the Government of the Russian Federation 123458, Russia, g. Moscow, ul. Tallinskaya, 3k1 klim17cool@gmail.com

Introduction

The main way to estimate the cost of equity is the CAPM model, created in the 60s by Jack Trainor, Ian Mossin, William Sharp and John Litner independently of each other ^[1]. This model is widely used not only to estimate the cost of equity, but also to determine the required level of profitability for financial assets.

Re=Rf+?*(Rm-Rf),                                                                                                    (1)

where Re is the cost of equity;

Rf – profitability of a risk-free asset;

 Rm – average market yield;

 ? is the coefficient ?.

The coefficient ? is a measure of market risk, reflecting the variability of the profitability of an asset in relation to the profitability of another portfolio, which often plays the role of an average market portfolio. Thus, a regression of the profitability of the company's shares is built relative to the profitability of the market portfolio. Note that, as a rule, when using the CAPM model, the ? coefficient is taken based on the industry in which the company operates. That is, the model is based on the premise that for all enterprises of a certain industry, the influence of market dynamics on the value of shares is the same.

Financiers Koloucheva and Novak conducted research, finding out that among those who use the CAPM model when assessing the cost of equity (52% of respondents), 76% use the industrial beta ^[2]. Later, KPMG consulting company confirmed this conclusion, claiming that among the appraisers using the CAPM model (83% of respondents), 79% use the industrial beta (initially – leverless, leading it to an indicator that takes into account leverage). Note that there are other models for evaluating stock returns. In particular, the three-factor model of Pham and French, as well as the four-factor model of Pham-French-Carhart, which differs from the three-factor by adding the momentum factor and has the following form:

 (Ri- Rf) = ?i+ ?i(Rm- Rf) + hiHML + siSMB + miMOM + ?i,                              (2)

where Ri is the profitability of the portfolio;

 Rf – risk-free rate (the yield of a one-month US Treasury bond in this study);

 ? i is the four–factor alpha of the portfolio (an additional factor to the Fama-French model, momentum);

 HML (High Minus Low) is a factor based on the assumption that undervalued companies perform better than overvalued ones);

 SMB (Small Minus Big) is a factor suggesting that small companies show better results than large ones in the long term;

 MOM (momentum effect) is an additional factor added by Fama, French and Carhart to more fully reflect the systematic risk, which will allow controlling the possible bias of estimates;

Hi, si and mi weights of these factors taken from French's study (2018);

 ?i is a random error.

 To create these variables HML, SMB and MOM, the Fama–French method is used: in June of each year, all stocks in the sample are ranked by capitalization and divided by median value into groups with small capitalization (Small, S) and large capitalization (Big, B). Then the shares are sorted by the ratio of book value to market value (Book-to-market equity, BE/ME). To obtain BE/ME, the book value of equity of the t – 1st year is divided by the capitalization of ordinary shares calculated at the end of December of the year t - 1. According to this indicator, the shares are divided into three groups: 30% of shares with a lower ratio (Low, L), 40% with an average value (Medium, M) and 30% with the highest BE/ME score (High, H). As a result of the data manipulations, six portfolios are built (S/L, S/M, S/H, B/L, B/M, B/H). The S/L portfolio includes securities that are small in size, and Low in BE/ME. The S/M portfolio is formed from shares in the small and medium groups, etc. HML is calculated as the difference between the average return on shares of companies in groups with a high and low ratio of book value to market BE/ME. The weighted average return of portfolios is calculated from July of the year t to June of the year t + 1, after which the portfolios were balanced.

The study analyzes the four-factor model due to the fact that it is less researched, but at the same time newer than its analogues.

The main part

The life cycle of a company consists of various and identifiable stages that the organization goes through as a result of key changes in internal factors that determine the results of the organization (strategy, financial planning, managerial skills, experience, organizational structure) and/ or external factors that affect the development of the market in which the company operates (level of competition, macroeconomic, social and technological factors) ^[3]. Recently, the life cycle model has attracted considerable attention as a way of conceptual understanding and analysis of various aspects of the company's development ^[4].

The concept of the corporate life cycle arose as an analogy of the development of living organisms, that is, they are born, grow, mature and eventually decline ^[5]. However, this analogy oversimplifies the real cycles of companies, since, unlike living organisms, organizations do not go through their life cycle in the same chronological order from birth to death, as, for example, a person.  The analogy with the development of a living organism is closer to the life cycle of various products or industries, but companies often work in several industries, and, accordingly, their life cycle depends on the totality of the life cycles of several products ^[6].

Back in 1984, financiers Miller and Friesen analyzed 36 businesses that have existed for at least 20 years, using 54 variables to describe their market position, organizational structure and strategy ^[7]. They found that organizations, although they go through a certain chronological order of the stages of the life cycle, often deviate from the standard path. For example, companies can be reorganized, revived, split up, or go bankrupt soon after creation, without even starting to show revenue growth.

There is no consensus among financiers regarding the theoretical classification of the various stages of the life cycle (or the number of these stages). Each model has a strong theoretical justification, so researchers usually choose any of the various classifications ^[8]. There is also no single methodology for determining the life stage of a company. Commonly used indicators such as age, size, revenue growth rates, propensity to pay dividends, the size of capital investments, capitalization.  However, all these indicators require a preliminary assumption about the underlying distribution of the various stages of the life cycle. For example, if we take the rate of income growth, we must determine the cut-off points by comparing which level of the variable corresponds to each of the stages of the life cycle.

The methodology of Victoria Dickinson, Professor at the University of Mississippi, was chosen for the study. In her article "Cash flows as an indicator of the stage of a company's life cycle", she describes the behavior of cash flows of companies in various periods of their existence:

Table 1. Classification of companies by stages of the life cycle through cash flows

·        Formation – at this stage, the company has a small customer base, and the level of profitability is often low or even negative. To improve the company's market share, it has to invest. Given that organizations at the initial stage usually have low profits (or none at all), there is a need for constant capital injections. As a result, operating cash flows (CFO) and cash flows from investing activities (CFI) will be negative, while cash flow from financing activities (CFF) will be positive.

· Growth – at this stage, enterprises are passing the break-even point (CFO > 0), but additional investments are still needed to strengthen positions (CFI < 0). According to Miller and Friesen, this cycle is characterized by high rates of revenue growth, and profits are often insufficient for investment, so at this stage organizations often have a high debt burden (CFF > 0).

· Maturity – companies consistently have a positive financial result (CFO > 0), as well as a strong market share. Despite the fact that the potential for growth still exists, investment flows from asset sales often exceed new capital investments (CFI >0), and dividend payments, share repurchases and debt servicing, combined with a lower need for external financing, lead to a negative flow on financial transactions (CFF<0).

·        Shake–up - sales continue to grow at this stage, but the pace slows down due to market saturation or the appearance of new competitors on the market. Sales peak at this stage, profitability decreases. Cash flows can behave in a variety of ways.

·        Decline – revenue growth rates are falling, which ultimately leads to a decrease in revenue and negative CFOs. Profitability is also declining due to the lack of innovation. At this stage, organizations sell part of their assets for further operation and payment of debts (CFI > 0). Cash flows from financial transactions can be both negative and positive.

Before formulating the hypothesis of the study, let's pay attention to the formula of the coefficient ?:

? =  = ,                                                                                          (3)

where Re is the expected return on the asset;

 Rm – market profitability;

 pem – correlation between the expected returns of an asset and the market;

 ?e is the standard deviation of the return on the asset.

The relationship between the volatility of the return on equity and the stage of the life cycle was touched upon in the study of Hassan and Habib (2017). Our approach focuses entirely on changes in the firm's contribution to the systematic risk of a diversified portfolio that occur as the firm goes through various stages of the enterprise lifecycle. Economists Cincarini, Kim and Moneta, investigating the same problem, come to a similar conclusion: the higher the age of the company, the lower the required return on equity. However, age is not always the right sign of a company's life cycle: firstly, companies often work in more than one industry and, ultimately, represent a set of life cycles of various products and/or services. Secondly, companies from different industries, as a rule, have different business cycle durations ^[10].

In our study, we will not consider individual companies, but their clusters, united according to the criterion of the life cycle. The hypothesis is based on the assumption of a decrease in the ? index from the initial stage to the final one.

The sample consists of public American companies traded on the NYSE, AMEX and NASDAQ.  The shares of American companies were chosen for the study due to the availability of an extensive amount of information. The period covered by the study includes 30 years (1989-2019). In total, the list includes 3,113 companies, financial organizations are not included in the sample due to their specifics.

Clusters of companies are used, not individual companies, since, according to the study by Pham and French, in this case the margin of error is lower. In addition, the Dickinson methodology was validated precisely on the basis of clusters of organizations.

Thus, 5 portfolios were built. Note that portfolios are dynamic: if in 1989 the company was at one stage, then next year it could be attributed to another stage. After the clusters were created, monthly returns for each of the companies were calculated to calculate the profitability and portfolio ratio weighted by market capitalization.

To estimate the coefficient ?, as indicated above, a four-factor Carhart model was used, the results obtained:

Table 2. Results of econometric analysis

According to the above information, the ? coefficient of mature companies (0.92) is lower than that of those at the stages of formation (1.47) and growth (1.15). However, further growth of this indicator is observed. Perhaps this is due to the fact that the maturity stage is the most reliable for all stakeholders and, possibly, the longest. Thus, the hypothesis was partially confirmed. Also note that the premium for excess profitability is insignificant for mature companies and companies in decline. The premium for the momentum effect is insignificant for all stages. The negative sensitivity of the portfolio of mature companies to SMB and the positive sensitivity for organizations in the stages of formation and loss are explained by the fact that companies in the first and last stages usually have low market capitalization, while mature companies have capitalization above average values. The negative sensitivity of companies at the stages of formation and growth with HML demonstrates that a smaller part of them belong to undervalued companies, which is logical, since they have the greatest potential for growth.

To check the statistical significance of the obtained coefficients ?, the White test was used. According to the results shown in the table below, all estimates are significant.

Table 3. White's test results

Conclusion

The results obtained indicate that there is a relationship between the company's ? coefficient and various stages of its life cycle. The observed indicator grows during 3 stages: the formation stage, followed by the growth stage, after – maturity. The lowest cost of equity is observed precisely at the last of these stages. Then the coefficient decreases. These findings partially confirm the assumptions of other researchers.

Based on the above, it can be concluded that for a more rational assessment of the cost of equity, it is necessary to take into account the life period of the company being evaluated. To do this, it is recommended to either create an analog of CAPM, or upgrade this model.  This article can be useful to all persons evaluating business (investors, appraisers, etc.), as well as for the further development of this theoretical aspect.