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FEDERAL STATE EDUCATIONAL INSTITUTION

OF HIGHER EDUCATION

NATIONAL RESEARCH UNIVERSITY

HIGHER SCHOOL OF ECONOMICS

Saint Petersburg School of Economics and Management

Department of Management

Instruments of increasing enterprise value: undervalued stocks

Bachelor's thesis

In the field 38.03.02 `Management'

Educational programme `Management'

Gabaidulin Vitalii Vladimirovich & Zemskov Oleg Olegovich

Reviewer

Financial Analyst, Candidate of Economic Sciences,

G.V. Grachev

Saint Petersburg 2019

Abstract

In the thesis paper the we intend to disclose and discover the notion of investment in undervalued stocks. Authors endeavour to testify that amongst fundamental enterprise valuation models there is the very one which is, effectively, can suggest the most optimal strategy for equity trade focusing on undervalued stocks for portfolio investments. Hence, to propose investors a sufficient way to analyse the investment potential, forecast return and develop a strategy for efficient securities investment, in order to outperform the market. Assuming market frictions in terms of accounting anomalies and its inconsistency for estimating fair stock price creation in the secondary market, there is no such a model which is said to be the most accurate in the deal. To mitigate the differences between the market value added and fair or intrinsic stocks prices, investors use various valuation techniques: CAMP, Fama-French, DCF derivatives, NCAV and others. In our paper, we will focus on comparing these and other techniques, but stating that NCAV is a superior choice in diverse situations. The study deploys application of valuation models on the same pool of financial statements of multiple companies. The created sample of portfolios then will be put through CAPM to estimate the return on portfolios formulated with various fundamental models. Based on studies, revealing NCAV being the model with the highest return among time-series, we are looking forward finding similar results but in comparison with other valuation techniques, however in specifically controlled conditions. As a result, for the paper, NCAV does not outperform the market consistently, however in order to do so it recommended to use other valuation techniques. NCAV requires specific market conjunction and cannot be named universal.

Key words: valuation, undervalued stocks, NCAV, fundamental analysis, accounting anomaly.



Table of contents

Introduction

1.1 The Nature of the Firm

1.2 Comments of enterprise value

1.3 Research question and objectives

1.4 Relevance of the research

Literature review

2.1 The Nature of an Investor

2.2 Words on fundamental analysis and value investing

2.3 Intrinsic value and margin of safety of a stock

2.4 Enterprise Value & Accounting Anomaly

2.5 PEG ratio (Price to earnings to growth)

2.6 Valuation techniques

2.6.1 Discount Dividend Model

2.6.2 Residual Income (RI) model reference

2.6.3 Fama & French model & CAPM

2.6.4 Net Current Asset Value

2.6.5 Graham's Number (moderate ratio of price to assets)

2.6.6 FCF (Free cash flow)

2.7 Other factors influencing anomalous stock returns

2.7.1 Transaction Costs

2.7.2 PEAD (Post-earnings-announcement-drift)

Statement of research question

Methodology

4.1 Description of data collected on each stage of the research

4.1.1 First Stage: Raw data sampling

4.1.2 Second Stage: Model Application

4.1.3 Stage three: CAPM application

4.2 Tools used to perform analysis

Description of findings

5.1 Ratios estimation

5.1.1 DDM & NCAV

5.1.2 RI & NCAV

5.1.3 FCF and NCAV

5.1.4 Graham's number computations

5.2 Betas and Portfolio returns

5.3 CAPM calculation. Portfolio 1.

5.4 CAPM calculation. Portfolio 2.

5.5 CAPM calculation. Portfolio 3.

5.6 CAPM calculation. Portfolio 4.

Conclusion

6.1 Primary discussion

6.2 Limitations & Assumptions of the research

References

enterprise value income model



Introduction

1.1 The Nature of the Firm.

The enterprise or a firm, a company - the terms that are used as a reference to each other and which have the similar meaning, but what do they mean in their essence? Transaction Cost Economics and Ronald Coase as its founder suggest (Coase, 1937) that enterprises exist because of their relative efficiency in coordination of means of production, thus minimising transaction costs. The inspired Nobel prize winner Oliver Williamson extends the study in promoting the firm as a nexus of contracts (Williamson, 1989).

Veblen (1914) explains the essence of existence of enterprises as the fundamentally constituted nature of people within community. The agents of such community creatively response to their environment. Veblen (1923) insists as conventional economics takes important institutions such as private property or ownership relationships for granted. In addition, Veblen states that conventional economics fails to recognize how business environment has been transformed by technology and arrival of corporations.

Later on, historically, Edith Penrose creates resource based accounts of the firm in her 1959 work: “The Theory of the growth of the Firm”. The most critical question in this respect Penrose suggests is “How do firms perform variably in the same environment?” (Penrose, 1959). She explains as that firms should be viewed as the resource based approach. Firms are the bundles of resources, capabilities and competencies. They are seen as team embodied, tacit production and organisational knowledge that can be employed by team members for strategic use. All resources are potentials and differentiation amongst these create diversity. Out of such discussion Penrose suggests rationale: “Knowledge is a result of learning, but learning in form of experience; […] experience itself cannot be transmitted. It produces a change” (Penrose, p. 48). There is always a potential to use resources more efficiently.

Going to the roots of conventional economics, we can trace a very comprehensive idea out of Adam Smith discussion around the invisible hand of the market. We would like to alternate the argument of his kind saying that each and every one who faced the enterprise, understands that it produces a value. Either we consider the value as a common wealth, or a moral satisfaction of some sort, we know that it is a value. So, the enterprises are famous for creating the value for its workers, its customers and society as a whole. So, is the enterprise value being a sum of all “values” gained by all stakeholders of the particular enterprise?

Answering for it, we shall look at the separate study started by Jensen & Meckling (1976) and continued in works by E. Fama (1983), J. Tirole (1986) and R. Gibbons (2013). According to the aforementioned papers, when one talks of the enterprise, he should not forget of its contractual nature. In each firm, there are principals and agents possessing different goals. Each side has its own intentions and incentives to fulfil its goal. The value for both sides represents different commodities. For principals, it is wealth in form of market capitalisation and stock prices; for agents, it is remunerations and various types of compensation. Interestingly, the value of the former is in somewhat dependency with latter, which makes the rules of balancing conflicting interests more complex task. Eventually, the finance does not formulate the enterprise value as stakeholders' benefits.

We would like to switch the dimensions we were discussing before, and emphasise that since now when we say enterprise value we mean the price of a company.

1.2 Comments of enterprise value.

The finance world has been changing throughout the years, in a way given that the concepts that were drastically popular a decade ago, now are not more than a bulk of headings in a corporate finance textbook. The basic term as a price, again, is a very good example of this tacit change. The management science now talks about the value of some sort instead of price. It might be the value of securities, such as stocks or options, it might be the enterprise value so needed in investment analysis, capital budgeting or mergers & acquisitions transactions. Value is much broader and at the same time more precise notion comparing to price. We shall avoid philosophical interrogations on the theory of value we follow in our discussion, but primarily we consider intrinsic theory of value as dominant later on.

Going back to enterprise value, it might be seen as two different scenarios:

1) enterprise value formed as asset pricing and (2) value per share as a measurement unit. Looking ahead, our field of interest is rationalization of valuation of enterprise exact in terms of value per share. The reasonable questions in this regard: who measures the value of the company per share? How is it performed? What if there is a mistake in valuation of an enterprise? The preliminary answers for these questions are that people do it, they use sophisticated models and, undoubtedly, they can be mistaken. Moreover, the information tends to lag or bias depending on the point of interest of specific groups. Such a phenomenon or better say market inefficiency in providing perfect share price information is usually called as an accounting anomaly. Financial analysts both external and internal for a company read accounting information, such as financial statements. Market in the face of analysts and special business machines responds to this information and corrects share prices, however only with immediate inputs, skipping underlying processes. Accounting anomaly in this paper is viewed as the undervalued and the overvalued stocks. It is common sense that investing in undervalued stocks in long-term perspective will exercise in higher returns in comparison with what benchmark would suggest. Some investment funds and great investors had made a fortune dealing with undervalued stocks.

Undervalued stocks, also known as value stocks, had been producing a return in a time-series, which is sufficiently higher than any other type of shares investments. Fama and French in a number of works, since 1988 up to 2018, had been proving that in the solution of stocks return a substantial role play its undervalued properties (book-to-market ratio) (Fama and French, 1988, 1989; Fama & French, 1992, 1993) ). In the spotlight of undervalued stocks, there is a number of various methods on looking at valuation of undervalued assets: NCAV (Net Current Asset Value), DDM (Discount Dividend Model), Fama-French three factor model, CAPM (Capital Asset Pricing Model), PEG (Price-to-earnings-to growth), DCF (Discounted Cash Flow). Interestingly enough for NCAV valuation for undervalued stocks method, according to Dudzinski & Kunkel (2014) in their "Ben Graham's NCAV (Net Current Asset Value) Technique in the 21st Century" the strategy produced an annualized geometric return of 24.7% from 2003 to 2010 that was unexplainable by either the capital asset pricing model (CAPM). "Ben Graham's Net Current Asset Values: A Performance Update" (Oppenheimer, 1986) also found that the strategy outperformed the benchmark. This study determined that this strategy produced a return of 33.7% compared to 12.1% for the benchmark between 1971-1983.

1.3 Research question and objectives

In this paper, we will give an account on the problematic of choice of appropriate valuation model to detect either the enterprise is undervalued and hence its shares do as well. In particular our goal is to clarify which model of valuation of intrinsic value of the company is most suitable for particular industry. We will compare the following models: NCAV, DDM, FCF, RI, Graham's Number.

We reckon our research question to be: To extent does NCAV (Net Current Asset Value) model show the return on portfolio among companies arranged by using different fundamental valuation models in varying industries? We believe that NCAV is the superior choice for undervalued investments and we reckon to study the question primarily on historical data. We are to observe different contexts including industry and period specification.

The relevance of this paper is reflected in elaborated guide for enterprises which is comprised of precise valuation technique of stocks with subsequent decisive focusing on undervalued ones. At this time, there have not been suggested alternative ways of enterprises' cash flow usage. Current investment strategy of most enterprises which follow the aim to increase their free cash flow is predominantly to invest in themselves, scaling properties, plants and equipment to generate more money. However, this business is not relevant for some enterprises which have already reached a point at which a future organic expansion does not seem lucrative or when the expansion even undermines overall company's performance because of market competition or other conditions. 

Throughout the entire research the authors set up the following objectives: 

1. Perform the extended literature review. Literature review will cover the most appropriate research papers to cover the whole field of study of undervalued stocks, enterprise value, securities investments, and so on. 

2. Detect valuation models: applicability to use with undervalued stocks. The research will also take in consideration the most popular and frequent models of stocks valuation in order to break them down, identify differences and peculiarities and applicable conditions to use them. 

3. Choice of variables for data set and modelling.

4. Elaborate on regression analysis for incoming potential results 

5. Conduct sampling. The authors will identify a pool of companies for future analysis, gather all needed information and data about performance of the companies, and then structurally prepare sample for computations. 

6. Utilise models for preliminary results 

7. Gain outcomes 

8. Explain outcomes and give comments 

9. Discuss limitations and future developments.

Some of the objectives denote to necessary quantitative methods which emphasize objective measurements and statistical analysis of numerical data gathered from the official sources (annual reports, The United States Securities and Exchange Commission, and others). The main instruments of analysis are computations of ratios and modelling.

1.4 Relevance of the research

The applicability and relevance of the results that were achieved during the course of this paper in the later sections are focused on elaboration of investment patterns and investment decisions when equity finance becomes the primary agenda for particular investor. Overall, we divide investors in two groups: 1) professional - which we assume are consisted of two subgroups: institutional and non-institutional investors and (2) non-professional investors. Specifically, we reckon that our findings would be rather applied by non-institutional and non-professional investors. Non-institutional agents can be seen as individual firms (corporations), which cannot be considered as any of economically institutional organisations, such as hedge funds, investments funds, pension funds and other similar structures. Individual firms are pursuing different goals, when in endeavour to prosper and thrive. Depending on strategy, various firms may not face the point when the question of increasing scale is solved by equity investing whatsoever. Effectively, firm's lucrative willingness may be achieved by becoming the object of investing rather than by investing in different assets itself. Originally, during fast development stage, firm increases scale by applying its own free cash flow to widen the business. However, in the situation when the capability of creating free cash flow becomes obsolete, firm usually faces the case of becoming public. Since that, the amount of investments firm will receive depends on its operational efficiency, profitability and other interrelated characteristics. Tracing this idea backwards, again we are talking about the significance of stock price and accuracy of manipulating with it. Investing in company's stocks by other company is essentially a method of increasing value on its own basis - by widening portfolio, and, at the same time, increasing the value of its own assets - by increasing cash flow. We believe that firms which are interested in diversifying will find the results promising to a certain extent. We also recognise individual investors as professional investors. By this we understand prosperous individuals, whose financial situations and lifestyle allows them to invest relatively impressive amount of money into private or public companies. The main reasons for it are similar to corporate investors (in comparison with institutional) - diversifying assets and improving cash flow. Eventually, non-professional investors are also considered as target audience for this paper. Most important difference between this subgroup and the previous is the amount of free cash flow that a person can allow him/herself to spend on stock's market and, of course, the possessed experience in decision-making on investments. Techniques and financial instruments are in the same list as well. We do not recognise institutional investors as our potential field of applicability primarily because of the nature of decision-making within these organisations. Investment and hedge fund central goal is to develop sustainable approach to gain return on very diversified portfolio of assets. That is way the interest of a fund is to find remunerative shares in short-term and middle-term rather than making predictions on either the company will significantly rise in long-term. Nonetheless, the biggest profit is made on long-term relations with undervalued companies.

The sample is consisted of different companies, varying in time periods and industries across US stock market. To assess the results and compare our estimations per model with the real information we are to base our research on historical data.

The paper will be finished with limitations and discussion.



Literature review

2.1 The Nature of an Investor.

The investment strategy does not have any common patterns with how to become rich faster and without any losses. Since people began investing in stocks, no one has been updated the ways of investments which promised both high and fast returns, minimum losses and maximum experience. However, since the essence of investing in stocks had been strengthened, both non-professional and professional investors divided themselves in two camps. Members of the first camp, to these days, are enthusiastic to

a. Invest lots of money in company' stocks

Talking about money, there are no doubts, the sum of investment is highly dependent on an investor's strategy, however, welfare the investors is ignored in this paper. The main point is that small amount of money cannot generate high return, hence it is not considered by them.

b. Wait up high return in a fast way.

Fast way means a couple of hours/days/weeks/months. Here a key point is that the desire to have a high return (because of huge investments) in a fast way (because of the investors' nature) is called a short-term investment.

Regarding this way of investment, the main reason and explanation of such people's behaviour is their nature. According to Benjamin Graham (1940), this type of investors is decisively interested in speculative deals on the stock market. Indeed, a lot of people enthusiastically look for easy techniques and quick ways of increasing the welfare. However, both of these factors (easy techniques and quick ways) have the traps and pitfalls.

The second camp is absolutely different because people's nature can be described in the opposite side from short-term investment. In this paper, the authors will take into consideration only this kind of investors because undervalued stocks a priori can be regarded in long-term view on the stocks. Regarding Graham' philosophy of investment, the investors with long-term perspective are called intelligent investors. Moreover, Graham (Zweig & Graham, 2003) made a transparent comparison between two types of investors: “An investment operation is one which, upon through analysis promises safety of principal and an adequate return. Operations not meeting these requirements are speculative”.

In order to establish the final point in comparing two camps, this paper offers an instructive example of a blind speculation. Let the authors of this paper back to 1720, when Sir Isaac Newton owned shares of the South Sea Company (one of the most popular and hottest stocks at that time in England). Feeling that the market was getting out of hand, Isaak Newton dumped his South Sea shares, having a profit of Ј7000, but how it usually occurs in speculative markets, swept up in the wild enthusiasm of the market, Newton lost Ј20000. (Carswell, 1993)

2.2 Discussion on fundamental analysis and value investing

As defined by Abarbanell & Bushee (1998), the fundamental analysis is a practice that relies heavily on the analysis of current and past financial statement data to identify when underlying firm value differs from prevailing market prices. The better understanding of fundamental analysis might be explained through the comparison with another, absolutely opposite type of analysis - technical. On the one hand, the investor uses fundamental analysis when delves into financial statements (Balance sheet, Income statement, Cash flow statement), focusing on key lines of particular statement (earnings, liabilities, current assets, etc.) and constructing some ratios which, in a right combination, give a snapshot of company's performance. Moreover, the analysis of past and current situation gives a premise to predict future firm performance (its earnings, cash flows, etc.) (Abarbanell & Bushee, 1998). On the other hand, technical analysis is a methodology for forecasting the movement of prices through the study of past market data, primarily price and volume. The definition clearly says that there is no any link between technical analysis and financial statements, thus the research ignores any paths of technical analysis of investment.

With fundamental analysis, the research focuses on value investing which still remains one of the core ideas of fundamental analysis. Value investing is a practice of purchasing securities or assets for less than they are worth (Klarman, 2010) with a strong perception of buying not just a speculative instrument, but a part (regardless of significance) of a business, a fractional ownership in the underlying business.

Diving into the history, the first form of value investing derives from the Benjamin Graham's philosophy which focuses on fundamental valuation of stocks which are traded below their intrinsic value.

2.3 Intrinsic value and margin of safety of a stock

Before buying stocks of a company an investor has to understand whether the market price of the stocks is fair or not. By fare pricing the authors mean an adequate stock price which truly reflects a company's performance. If a company experiences decline, stocks also decline on the exchange, vice versa. In other words, “stocks do well or poorly because the businesses behind them do well or poorly” (Zweig & Graham, 2003). Thus, the main aim of intelligent investors is to find out such companies whose stocks are traded at a fair price, in any other outcome, there is a risk to overpay for a stock (Zweig & Graham, 2003):

No matter how careful you are, the one risk no investor can ever eliminate is the risk of being wrong. Only by insisting…margin of safety -never overpaying, no matter how exciting an investment seems to be-can you minimize your odds of error (p.13)

The above citation of the conceptual author of value investing, Benjamin Graham, who had made a great contribution to the security analysis, is a premise to introduction of crucial notions of value investing - margin of safety and intrinsic value. First of all, intrinsic value is identified as “that value, which is justified by the facts, e.g., the assets, earnings, dividends, definite prospects, as distinct, let us say, from market quotations established by artificial manipulation or distorted by psychological excesses” (Graham & Dodd, 1940). The second definition, margin of safety, means the difference between intrinsic value of a stock and its market price. The visual introduction of relationships between three basic definitions (market price, intrinsic value, margin of safety) can be regarded on the Figure 1

Figure 1. Relationship between market price, intrinsic value

Regarding the visual introduction, this becomes quite clear that when a stock market price is less than its intrinsic value, the investor receives the margin of safety that is calculated as:

There is no any precise estimation of the threshold of margin of safety, however the presence of this margin says that “the investor never overpays, no matter how exciting the investment seems to be…” (Graham & Zweig, 2003).

2.4 Enterprise Value & Accounting Anomaly

There are two ways financiers and investors can observe the enterprise value. It is either (1) asset pricing or (2) value per share. The obvious difference is in how we form each one? Basically, assets pricing approach creates the cash equivalent that might be used as a financial resulting number. Summing the prices for all assets will give the simple price of a company. Intangible assets are calculated as well, in the example, regardless of impairment or other depreciation.

The value per share is able to be discussed only after the company had become public. At IPO underwriting banks create the face value of the stocks of a company, dividing the asset pricing value on the number of shares outstanding. The first day the enterprise becomes public - its value is a subject to change. The uniqueness of the stock price phenomenon is a very complicated polemic. In 1930s a stock price was formed based on the financial results of companies, disclosed to publicity, analysed by financiers at banks, exchanges and funds and then modified based on demand and market conjuncture. Definitely, nowadays the stock prices are changing every second using business processing machines which incorporate analysts' forecasts, demand and supply, central banks operations and exceedingly more at the same time. No less important position play assurance and audit procedures that keep financial results of public corporation being statistically significant and corresponding, thus trustworthy.

However, there are situations that cannot be explained by market efficient analytics in general sense. For example, it is a situation of undervalued or overvalued enterprise, hence undervalued or overvalued stocks. Phenomena like those were called accounting anomalies. It is accounting because of its financial statement nature. Investors and financiers build forecasts deciding either to invest into enterprise or not, based on accounting information disclosed by it. Interestingly, as argued in Kothari (2001) we perhaps should not retain the anomaly argument upon market inefficiencies, as investors might try to assume. Building forecasts on enterprise future performance has to stay on the basis of accounting information, hence stock prices efficiency must be the null hypothesis. Otherwise, is there any sense in financial statement in helping to forecast future return and stock earning if it is inefficient initially? The fair question in this regard would be: why do stock prices fail to provide unbiased information timely? However, this one is a subject for deep previous? and future developments.

2.5 PEG (Price to earnings to growth) ratio.

The traditional metric of the relationship between the market price of a share and its earnings, the so-called price to earnings ratio, has been considered as one of the basic and fundamental metrics of fair value of a stock. Breaking down this ratio, it becomes clear that the lower price to earnings ratio (P/E) of a company, the more attractive this company appears in front of an investor. Indeed, if the market price of a share is higher than its value calculated as net income (after preferred stocks subtraction) divided by number of outstanding shares, this share seems to be overestimated, and vice versa. For instance, Lakonishok, Shleifer & Vishny (1994) claimed that stocks with low P/E ratio tended to outperform the stocks with high P/E. One of the possible reasons of that phenomenon might be the overestimation of the length of time that high growth would continue, overvaluing high growth stocks. However, this simple and quite transparent ratio does not provide any profound evidence whether a stock is overestimated or not.

The future implementation of P/E ratio led to some improvements, the second version of ratio includes the growth of earnings in a particular period. This additional index makes a ratio more precise and practical because it takes into account growth which can revert overestimated shares to underestimated. The time horizon of earnings per share growth might be chosen on the investor's behalf.

Generally, the PEG ratio is



One of the greatest investors, Peter Lynch, expressed his opinion about PEG ratio in the following way (Lynch, 1989):

The P/E ratio of any company that's fairly priced will equal its growth rate ... If the P/E of Coca-Cola is 15, you'd expect the company to be growing at about 15 percent a year, etc. But if the P/E ratio is less than the growth rate, you may have found yourself a bargain. A company, say, with a growth rate of 12 percent a year...and a P/E ratio of 6 is a very attractive prospect. On the other hand, a company with a growth rate of 6 percent a year and a P/E ratio of 12 is an unattractive prospect and headed for a comedown...In general, a P/E ratio that's half the growth rate is very positive, and one that's twice the growth rate is very negative.

The opinion of Peter Lynch has logical paths which seem to be the arguments for huge weaknesses of the obsolete P/E ratio because PEG delves deeper, covering both internal and external features.

The controversial argument of weak effectiveness of P/E and PEG ratios is reflected by Voss (2011) which stated that these ratios are applicable to the extremely narrow and rare circumstances which “ever met in the investment market place.” Testing the ratios, the author finds out that price to earnings to growth ratio does not account for the investors required rate of return. Voss (2011) assumes that if an investor hopes for at least 10% of return, overall returns fall from 107,51% to 89,02%, and if he hopes for a 40% return, the overall return falls to 49,78%, respectively.

Effectively, out of such presupposition of inconsistent usage of PEG and P/E ratio, as the simplest and straightforward metrics, there had been constant attempts to alternate the most common metric.



2.6 Valuation techniques.

In this section, we will look at various valuation and forecasting models which are to be applied in estimation of undervalued stocks, hence recognising the accounting anomaly through fundamental analysis.

2.6.1 Discount Dividend Model.

To start our discussion on forecasting returns on undervalued securities with various models, it is useful to start with a traditional approach used in almost all papers on accounting anomalies and fundamental analysis as reference point - discount dividend model.

The left part of the formula denotes that price of a stock is expressed as function of earnings, dividend per share of the next accounting period divided by expected return. In its basic form is replaced with (Discount Rate-Dividend growth). However, as some companies reviewed in the later parts of this report do not have dividends and some do, we decided to change it to what we have right now. Having roots in Gordon Growth model (GGM) (Gordon & Shapiro, 1956) DDM reflects that stocks price could be observed as discounted sum of all future dividends (net present value of future dividends). This approach in its core form has some significant disadvantages. First, there are situation when company does not have a steady growth, thus discounting by one year with decreasing growth will exhibit negative stock price, while we can have negative income (e.g. in mining and extraction companies), which again will turn model into negative sign product. Henceforth, it is obvious to say that stock price seeking with the model is sensitive to growth that is to be used. Second, when company does not pay dividends, we assume that model makes no sense whatsoever. The solution for such case is to rewrite the formula using other substituting indicators as we describe next.

In the right part of the equation there is a simple transformation, which as developed by Ohlson (1995) and Kothari (2001), the price (P) is expressed as function of earnings (E), expected return (r) and delta change in book value. D is net dividends which are Y (income) less BV (change in book value). Y and BV are forecasted future variables, based on accounting information. Using this transformation, we can solve no dividends case using the cash flow which should have been used for dividend pay otherwise. We can also switch dividends per share (DPS) with earnings per share (EPS), however in this case we have to retain from growth stock search with DDM, to value stock search, using exactly earnings growth. Hence, such a model reflects that it is vital to forecast earnings, returns and book growth to understand the potential for securities investment. Taking a step further, such a transformation is an essential feature of residual income model.

2.6.2 Residual Income (RI) model reference.

Undoubtedly, residual income approach to finding intrinsic value is more appropriate than discount dividend model or discounted cash flow when firm is either does not pay dividends or exhibits unpredictable pattern for dividend payments. As was mentioned above, residual income helps to manage situations when company has negative FCF (free cash flow) during several years. What is special about the model is that it assumes value of the stock rather than a price initially. The syntax of the formula please find below:

The formula is similar to DDM, however, as was pointed out with important adjustments. It the syntax of residual income ( we use Net income less Equity charge (Equity capital multiplied by Cost of Equity). Basically, as with DDM the meaning of RI stands behind calculating value of company's stock as the sum of BV (book-value) and the present value of its expected future residual income.

Going back to Discount Dividend Model, Fama & French (1993) suggested and empirically tested the soundness of the similar approach, helped out the model with understanding that expected returns as realised returns are positively related to forecasted profit and negatively related to book growth (Richardson, Tuna & Wysoski, 2010). “If investors' expectations of future earnings are higher (lower) than actual future earnings, current prices will be too high (low), and future returns will be low (high)” (Richardson, Tuna & Wysoski, p. 420).

Summarising the insights which investor can gain out of discount dividend model, we may trace a very influential idea. Forecasting expected returns can give us intrinsic value of the enterprise if either the growth of the company is steady. The figure of estimated intrinsic value is then might be compared with market price, and if the following guideline is fulfilled then we may face the market accounting anomaly, thus gaining undervalued or overvalued stocks with excess return opportunity:

1. Stock price + forecasts of accounting information lead to noticing expected return, as it has impact on dividends (or e.g. EPS)

2. ROR + (1) lead us to intrinsic value (V) of company, with assumption that prices can be inefficient.

3. If Intrinsic value (V) of stock divided by market price (P) of stock do not equals to 1, then we have a situation with accounting anomaly. It means that difference between V and embedded P gives us excess return. (Richardson, Tuna & Wysoski, 2010)

2.6.3 Fama & French model & CAPM

Starting off as the critic of the paradigmatical Capital Asset Pricing Model (CAPM) developed by Sharpe (1964), Lintner (1965) and Black (1972), Fama and French (1993) in their paper on common risk factors in pricing of stocks and bonds suggest a potentially more effective approach when looking on stock returns as a risk function. But before we deepen into Fama and French we ought to explain some of the most important features of Capital Asset Pricing model.

In CAPM, the variable which determines the risk component thus return properties of a security was market в (market return) in comparison with stock or portfolio risk.

Figure 2. CAPM graphical interpretation

Above you can find the graphical interpretation and a syntax of CAPM in its paradigmatically proven form. Generally, the model describes interrelation between expected return of an asset and its risk (i.e. risk of investing in this particular security). The central logic in CAPM is that the return on asset consists of risk-free return and risk-premium.

As a modification, Fama and French proposed adding 3 factors into the model. The choice of the factors was motivated by the most intriguing stocks constantly appearing on the market. Mentioning more than 549 enterprises were becoming public in period after 1980 - 2001 (Fama and French, 2004), the 10% of all companies were newly created. Setting like this had showed emergence of large amount of value stocks, known as (1) small companies' stocks (small caps) and (2) high book-to-market (HBM or HML - High [book-to-market ratio] Minus Low) ratio firms. HBM can be explained as intrinsic value exceeding market value of a share, so that V/P >1.

So, the factors that were implemented were: a) size as market capitalisation and (b) book-to-market ratio. The renewed formula look as follows:

As in Fama and French (1992), statistically, the univariate relations between return and size, E/P (earnings to price) and book-to-market equity are very strong. Exactly book-to-market equity and average return show positive relation in the presence of other variables (Fama and French, 1992). In terms of size and average return, time-series regression in Fama and French (1993), based on portfolios mimicking risk factors related to size and book-to-market equity, shows that these two parameters can effectively proxy for “sensitivity to common risk factors in stock return” (Fama and French, 1993, p. 5).

Later on, the most recent Fama and French (2018) has touched upon instead of three-factor-model, five-factor one, developed in Fama and French (2015), including in Eq. 3 profitability and investments. What is worth mentioning is that Fama and French (1995) showed that profitability, investments and book-to-market are significantly correlated. In regard to this, we shall avoid using 5-factor model, focusing our efforts on 3-factor one.

2.6.4 Net Current Asset Value.

Benjamin Graham was an investor who not only introduced such definitions as value investing, margin of safety, but also offered some instruments how to identify the stocks traded below their intrinsic value, or having margin of safety. One of those instruments is NCAV (Net Current Asset Value):

As the current assets include cash and cash equivalents (the most liquid asset), after deduction of all liabilities and preferred stocks (which Graham considered as liability) the investor has only net liquid asset that has no any chance to be overestimated. Non-current assets are excluded from the calculation, the investors “would pay nothing at all for the fixed assets - building, machinery…, or any good-will items that might exist.” (Graham & Zweig, 2003). Overall, Graham's homily was to buy the stocks which price is no more than two-thirds of its NCAV (Graham & Zweig, 2003). Graham and Dodd checked the effectiveness of NCAV by themselves - the portfolio of undervalued stocks gained 75% for two years (between 1957 and 1958) against 50% for S&P 425 industrials (Graham & Zweig, 2003). Moreover, none of undervalued companies showed significant losses.

The significance and importance of NCAV can be proven by some studies which have already tested the effectiveness of this instrument. The authors will consider some results of the researches of NCAV:

1. Between 1970 and 1983, a portfolio which was comprised of companies which had a share price no more than two-thirds of their working capital, had 28,3% growth rate in comparison with the benchmark portfolios from the NYSE (the growth rate was only 10,7%) (Oppenheimer, 1986);

2. Between 1999 and 2012, a portfolio of 126 selected securities with NCAV > market price showed the average return slightly greater than 18% when the market return (S&P 500) was only 2,91% (Bildersee & Cheh, 2015);

3. Between 2003 and 2010, the strategy of NCAV produced the annual return of 24,7% in comparison with benchmark. It was also unexplainable by both the CAPM (Capital Asset Pricing Model) and the Fama-French-Carhart model (Dudzinski & Kunkel, 2014).

Overall, there are a lot of other indexes and instruments which are aimed at finding out the undervalued stocks which have a positive margin of safety. Some of the techniques are criticized by researches, investors and financiers because of difficulty and complexity of suggested models, another camp of researches and investors finds them too diffused and unclear because are closely related to forecasts and, sometimes, expert estimations. However, all the investors and researches who focus on long-term investment, have been seeking for a unique and reliable model to estimate the intrinsic value of the shares.

2.6.5 Graham's Number (moderate ratio of price to assets).

Another test for identifying intrinsic value is called “Graham's Number”:

The first fraction in the formula is EPS (earnings per share), the second one is BVPS (book value per share). More interestingly, the numbers 15 and 1.5 are not random - Benjamin Graham believed that market price should not be more than 1.5 times the book value last reported in financial statement. “However, a multiplier of earnings below 15 could justify a correspondingly higher multiplier of assets. As a rule of thumb, we suggest that the product of the multiplier times the ratio of price to book value should not exceed 22.5” (Graham & Zweig).

Graham's formula. "Our study of the various methods has led us to suggest a foreshortened and quite simple formula for the evaluation of growth stocks, which is intended to produce figures fairly close to those resulting from the more refined mathematical calculations." - Benjamin Graham (Graham, 2006).

Graham suggested another indicator for growth stocks:

Breaking down the formula, EPS equals to earnings per share, g - reasonably expected growth rate (from 7 to 10 years), V - intrinsic value, x - the average yield of AAA corporate bonds in particular year, Y is a current yield of AAA corporate bonds. According to Graham, the formula resulted from a study of various valuation methods and considered an effective way of estimating the intrinsic value of shares. This formula should go with Graham's number for better valuation of intrinsic value. However, Graham claimed by himself that both formula and number were not perfect to make an investment decision.

2.6.6 FCF (Free cash flow).

Free cash flow is another important indicator of company's performance. The essence of FCF reflects all cash available to all the stakeholders. However, in terms of investment indicator, FCF should be considered as a measure of profitability.

The formula presented below allows to make some important conclusions about the links between free cash flow and intrinsic value.

Breaking down the above formula, the first three consecutive indices are calculated on the standard Statement of Cash flows. Abbreviation of D&A means depreciation and amortization reported by a company, change in working capital shows a deficit or a surplus between current assets and current liabilities. CAPEX, or capital expenditures, counts for all the expenses attributed to a company's property, plant and equipment.

Finally, how is FCF related to the indicator of a company's intrinsic value? The crucial point here is an accepted postulate - cash flows are used to pay dividends to the shareholders. And if the total free cash flow is divided by number of stocks outstanding, the result will be equal to a company's intrinsic value. However, as the FCF model takes into consideration CAPEX, it can be quite uneven over time (but it does not mean that FCF shows distorted information). For instance, if a company reported EBITDA of $ 100,000, and then bought new equipment worth $80,000, the company reported $20,000 (EBITDA - CAPEX) on $100,000 of EBITDA that year. And if there was an assumption that everything else remained the same and without additional purchases, both EBITDA and FCF would be equal again the next year. Undoubtedly, an investor would have to take into account why free cash flow is decreased.

Applicable to the investors, the intrinsic value of a company is calculated as the net present value (NPV) of the sum of free cash flows the company generates throughout its existence.

The introduction of FCF might seem to be done, however, the free cash flow model has been studied with different angels, and one of them is agency theory, which should be discussed in this paper. According to Vogt & Vu (2000), both free cash flow and managerial decisions over its use have significant implications for shareholder value in long-term period. Moreover, findings of Vogt and Vu (2000) imply that the excess returns of high free cash flow firms are more significant for the follow companies:

1. They have high BM (book to market ratio), that is also compatible with Fama and French (1992);

2. They have Tobin's Q ratio below unity

Moreover, regarding Jensen's hypothesis, the agents of companies with high free cash flows, work in an effective way to utilize free cash flow in a value-maximizing way. Another finding demonstrates the same outcome - the study of Vogt and Vu (2000) showed that the enterprises with high free cash flow and high capital spending are regarded as with low level of excess returns. And conversely, enterprises with high paid remunerations (predominantly dividends) are associated with large free cash flows and returns. Consequently, taking into the FCF model, the investors should bear in mind that a positive and huge free cash flow might be effective in terms of payments to shareholders, only if the agents' behaviour is focusing on value-maximizing, however (Jensen 1986):

Free cash flow is cash flow in excess of that required to fund all projects that have positive net present values when discounted at the relevant cost of capital. Conflicts of interest between shareholders and managers over pay-out policies are especially severe when the organization generates substantial cash flow. The problem is how to motivate managers to disgorge the cash rather than investing it at below the cost of capital or wasting it on organization inefficiencies. (p. 323)

That is why the expected free cash flow might be higher because the real (or stated) one includes the losses the principal inherit due to information asymmetry or other mitigations of agency problem.

2.7 Other factors influencing anomalous stock returns

2.7.1 Transaction Costs

One of the most sophisticated and rather neglected sides of stock returns is transaction costs. Basically, transaction costs are somewhat of costs which go along any economic transaction ever been performed. Oliver Williamson (1989) as the founder of Transaction Cost Economics (TCE), and as the direct descendant of Ronald Coase, explained transaction costs nature as:

Transaction costs are the economic equivalent of friction in physical systems. The manifold successes of physics in ascertaining the attributes of complex systems by assuming the absence of friction scarcely require recounting here. Such a strategy has had obvious appeal to the social sciences. Unsurprisingly, the absence of friction in physical systems is cited to illustrate the analytic power associated with `unrealistic' assumptions .... But whereas physicists were quickly reminded by their laboratory instruments and the world around them that friction was pervasive and often needed to be taken into account, economists did not have a corresponding appreciation for the costs of running the economic system (p. 19).

So, the analogy for transactions costs within equity market has been known as trading costs. However, it is not only the direct costs, such as commissions, tax or bid-offer spread with time lag. It is also indirect costs affecting prices. As an example, Stoll (1993) suggests that there was “round trip transaction cost” for investing in high capitalisation common shares as about 1%. During last 10 years this number has been steadily decreasing reaching 0,3% by the end of the period.

Overall, there are continuing discussions on the basis of the topic of transaction costs in recent literature on accounting anomalies and fundamental analysis. Stoll (1993), as an example, links it to sufficient lack of well quality information, which could be used to quantify transaction costs. Instead, trading costs are associated as somehow similar to transaction costs. Another point, which is quite often met within recent literature on the following topic is that researchers are trying to crystalize either anomalous returns are within the bounds of the market frictions or not (Richardson, Tuna & Wysoski, 2010). An example of these type of logic is arbitrage risk or other stocks market transaction costs that can estimate subnormal returns (Pontiff, 2006).