Private Equity Portfolio Management and Positive Alphas

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INOM

EXAMENSARBETE TEKNIK, GRUNDNIVÅ, 15 HP

STOCKHOLM SVERIGE 2020,

Private Equity Portfolio Management and Positive Alphas

RIKARD FRANKSSON

KTH

SKOLAN FÖR TEKNIKVETENSKAP

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Private Equity Portfolio

Management and Positive Alphas

Rikard Franksson

ROYAL

Degree Projects in Applied Mathematics and Industrial Economics (15 hp) Degree Programme in Industrial Engineering and Management (300 hp) KTH Royal Institute of Technology year 2020

Supervisor at KTH: Ximei Wang

Examiner at KTH: Sigrid Källblad Nordin

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TRITA-SCI-GRU 2020:107 MAT-K 2020:008

Royal Institute of Technology School of Engineering Sciences KTH SCI

SE-100 44 Stockholm, Sweden URL: www.kth.se/sci

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Abstract

This project aims to analyze Nordic companies active in the sector of Information and Communications Technology (ICT), and does this in two parts. Part I entails analyzing public companies to construct a valuation model aimed at predicting the enterprise value of private companies. Part II deals with analyzing private companies to determine if there are opportunities providing excess returns as compared to investments in public companies.

In part I, a multiple regression approach is utilized to identify suitable valuation models.

In doing so, it is revealed that 1-factor models provide best statistical results in terms of significance and prediction error. In descending order, in terms of prediction accuracy, these are (1) total assets, (2) turnover, (3) EBITDA, and (4) cash flow. Part II uses model (1) and finds that Nordic ICT private equity does provide opportunities for positive alphas, and that it is possible to construct portfolio strategies that increase this alpha. However, with regards to previous research, it seems as though the returns offered by the private equity market analyzed does not adequately compensate investors for the additional risks related to investing in private equity.

Keywords: Nordic private equity performance, private equity valuation, CAPM, port- folio optimization, multivariate linear regression, quadratic optimization

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Sammanfattning

Det här projektet analyserar nordiska bolag aktiva inom Informations- och Kommunika- tionsteknologi (ICT) i två delar. Del I behandlar analys av publika bolag för att konstruera en värderingsmodell avsedd att förutsäga privata bolags enterprise value. Del II analyserar privata bolag för att undersöka huruvida det finns möjligheter att uppnå överavkastning jämfört med investeringar i publika bolag. I del I utnyttjas multipel regressionsanalys för att identifiera tillämpliga värderingsmodeller. I den processen påvisas att modeller med enbart en faktor ger bäst statistiska resultat i fråga om signifikans och förutsägelsefel. I fallande ordning, med avseende på precision i förutsägelser, är dessa modeller (1) totala tillgångar, (2) omsättning, (3) EBITDA, och (4) kassaflöde. Del II använder modell (1) och finner att den nordiska marknaden för privata ICT-bolag erbjuder möjligheter för överav- kastning jämfört med motsvarande publika marknad, samt att det är möjligt att konstruera portföljstrategier som ökar avkastningen ytterligare. Dock, med hänsyn till tidigare forsk- ning, verkar det som att de möjligheter för avkastning som går att finna på marknaden av privata bolag som undersökts inte kompenserar investerare tillräckligt för de ytterligare risker som är relaterade till investeringar i privata bolag.

Nyckelord: nordiskt privatkapitals prestation, värdering av privatkapital, CAPM, port- följoptimering, multipel linjär regression, kvadratisk optimering

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Chapter 1 Introduction

Private equity has been receiving increasing attention over the past few years, reaching an all-time high in investor activity in 2018 [1]. In particular, the Nordic markets for private equity comprise a large portion of this activity, both in the European region and globally [2]. However, private equity is not as readily, or easily, accesible as publicly traded equity, caused by the lack of an official and regulated trading platform. Furthermore, private equity exposes investors to risks that are not commonly present at such an extent when considering public equity. Nonetheless, investor activity is booming and the question to be asked is: does private equity offer positive alphas?

1.1 Project Scope

The project aims to analyze Nordic medium sized companies active in the sector of ICT, Information and Communications Technology. More specifically, applicable companies should be registered with an activity code belonging to sector J - Information and Commu- nication, according to Eurostat’s statistical classification of economic activities [3]. The term “medium size” refers to at least one of the following criteria being fulfilled:

• 1m EUR ≤ Operating Revenue < 10m EUR

• 15 ≤ Number of employees < 150

• 2m EUR ≤ Total assets < 20m EUR

By looking at “medium sized” companies, there is some insurance of the companies’ busi- nesses being viable, or at least an indication of proof-of-concept having been established.

Thusly, the risks of unexpected short-term default and probabilities of explosive growth should be smaller. One might rather expect to find opportunities of managerial enhance- ments to boost growth. However, when considering the companies on their own, as op- posed to analyzing funds’ performance, attention is directed towards these companies’

abilities to enable growth. In other words, the project is not directed towards analyzing the performance of funds or the skills of their general partners, the attention, instead, lies upon what the market has to offer potential investors. Furthermore, the project does not aim to include macro-economical influencial factors but rather intends to investigate company characteristics and how to value equity with simple measures.

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2 CHAPTER 1. INTRODUCTION

Lastly, a dataset of deals made in the industry, with companies fulfilling the afore- mentioned critera, was not available at the time of the project writing. Thus, calculation of applicable discounts and premiums is deemed lying outside of the project scope and figures sampled from relevant research will instead be considered.

1.2 Research Question

With booming investor activity and a target market to analyze, the project intends to in- vestigate: Does the Nordic private equity market for medium sized companies active in the sector of Information and Communications Technology offer opportunities for unexpect- edly large returns, as compared to the corresponding public market?

By constructing some optimal portfolio of applicable assets the question can be an- swered depending on the performance of such a portfolio. In turn, the project also aims to answer: Does the Nordic private equity market for medium sized companies active in the sector of Information and Communications Technology offer opportunities for returns exceeding those of comparable public equity, and, if so, does the excess return compensate for additional risk?

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Chapter 2 Background

Private equity fundamentally refers to equity that is not publicly traded and is constituted by the shares of companies not publicly listed at any exchange. Public exchanges for equity trading impose rules and frameworks that listed companies must comply with. This includes standardized information handling and reporting procedures that specify the extent and details that press-releases, financial statements, and other public announcements must adhere to. Simply put, the goal is to ensure information symmetry, i.e., that all investors are equally well-informed. Furthermore, exchanges provide a unified platform for trading of the listed equity where investors gather to negotiate the prices of shares.

2.1 Private, Not Public, Equity

Private companies are not required to follow the policies of exchanges and, inherently, often comply with more lax policies regarding information transparancy. Consequently, investments in private equity are riskier than investments in publicly traded equity, stemming from the challenges of

• illiquidity,

• information assymetry, and

• lack of intermediary.

2.1.1 Illiquidity Decreases Investor Autonomy

With no official marketplace for trading, there are generally a lot less actors looking to trade private equity. Moreover, private companies are often characterized by few and large own- ers. In effect, finding counterparties for trades is difficult and investors can find themselves in a position of not being able to enter a position of interest or exit an overdue position.

Sorensen, Wang, and Yang [4] find that the cost of illiquidity constitutes 50% of limited partners’ total present value costs, in the case of limited partnership funds investing in private equity. Furthermore, Franzoni, Nowak, and Phalippou [5] find that the risks of illiquidity advocates a liquidity risk premium of 3% per annum.

With less market participants being present, the risk of not being able to exit a position when required is substantial. Being overinvested in private equity thus increases the risk of

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4 CHAPTER 2. BACKGROUND

not being able to meet capital requirements from other undertakings due to cash shortage and might cause involuntary liquidation at discounts [6].

Generally, the transaction costs of trading increases as the liquidity of the underlying asset decreases and with an assumed relationship between transaction costs and the liquidity of an asset it follows that if transaction costs can be quantified then the cost of illiquidity should be possible to estimate. Damodaran [7] suggests an estimate of an illiquidity discount of asset valuations in the range of 25-35%, where the valuation is performed assuming the asset is liquid. Thus, illiquidity can be conceptualized by considering

• bid-ask spreads,

• price impact of trading, and

• opportunity cost.

Bid-Ask Spreads

The bid-ask spread refers to the difference in price market participants are willing to sell and buy assets from the perspective of a prospective investor. With less investors trading an asset there is implicitly less market concensus of what the fair price of the asset should be.

With more trading activity more investor assumptions and estimates are aggregated, along with other information present, to form market prices. Consequently, less liquid assets, and private companies in particular, have less aggregate information tied to its market prices. With less information, uncertainty regarding the fair value increases and, in turn, the bid-ask spread widens, increasing the price paid to acquire the asset while decreasing the price at which the asset can be sold.

Price Impact of Trading

The price impact of trading refers to when an investor either exits a position or enters a new position in a way that directly affects the available market prices. For example, a buyer enters a position of large volume and acquires all volume present of sellers at certain price levels. As a result, offers to sell at such price levels no longer exist and (1) the bid-ask spread widens, as well as (2) the total cost of acquisition is greater than if all volume was acquired at the previously availabile most beneficial price level.

Opportunity Cost

The opportunity cost of trading refers to the timing of investment. An investor might wait to enter or exit a position, hoping for a more profitable opportunity. In doing so, the investor might instead be faced with the opposite situation causing reduced profits. Naturally, this is difficult to measure and expectations vary. However, the situation is a consequence of differences in public and private information, the time horizon of investments, trading style of the investor, and so on, and is therefore indeed relevant.

2.1.2 Information Assymetry Increases Uncertainty

Since private companies do not have to adhere to the rules and directives of regulated equity markets or MTFs the requirements of information transparancy are less extensive – for

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CHAPTER 2. BACKGROUND 5 more information see EUs MiFID II. As a result, most private equity investors are significantly less well-informed when compared to investors targeting public equity. Moreover, large actors in private equity investment make use of personal and professional networks established over many years of experience. Thus, information assymetry warrants con- cern since the selling party of any trade of private equity is likely to possess more detailed information of the underlying company and its business.

2.1.3 Lack of Intermediary Decreases Availability

The lack of a market place for trading reduces the availability of investment opportunities and thus increases the effort required to find suitable investments. This, in turn, decreases the potential returns of the investments due to the increased cost of identifying opportunities. Furthermore, often no immediate intermediary is available to increase capital mobility and encourage investments in private equity. The intermediaries that do exist are mostly constituted by private equity funds and venture capitalists. These intermediaries do facitilitate access to the private equity markets, but at a cost. Sorensen, Wang, and Yang [4], Franzoni, Nowak, and Phalippou [5], and Phalippou and Gottschalg [8] all find that the performance of these intermediaries, net of fees, is quite poor and that the cost of the services is high. So, finding investment opportunities requires effort and therefore is expensive while intermediaries performing this service demand costly compensation, resulting in decreased availability of investment opportunities at an increased cost.

Note, though, that while private equity fund and venture capital funds act as intermediaries in gathering capital and deploying it on the market of private equity they provide additional services. Alongside providing capital to business ventures these actors also provide expertise and experience to aid business development. They provide companies with managerial skills and aspects commonly combined with profound industry knowledge. As a result, investors often invest in the funds general partners’ abilities to leverage private companies’ innovations and solutions in order to enable growth and, in turn, returns.

2.2 Risk Compensation

Clearly, private equity investments impose risks to an extent that is not commonly present on the markets for public equity. Corporate finance theory states that the increased risk should be compensated with a larger risk premium to incentivize investors to carry it.

Sorensen, Wang, and Yang [4], Franzoni, Nowak, and Phalippou [5], and Phalippou and Gottschalg [8], again, suggest that this, in fact, is not the case for limited partners in a private equity fund when looking at fund performance net of fees. Lopez-de-Silanes, Phalip- pou, and Gottschalg [9] state that one in 10 investments provides no return at all while one in four investments provides an internal rate of return exceeding 50%.

Thus, there are indications that the market of private equity provides opportunities of high returns, with significant risks, and that providers of capital, or limited partners, to existing funds are not adequately compensated with larger returns for the risk they carry.

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2.3 The Value of Equity

Private equity is further characterized by a lack of continuous equity valuation. In the case of publicly listed companies the value of the equity is continuously adjusted by traders so that expectations and predictions are always included in the valuation of the companies’

shares. The liquidity provided by being publicly listed aggregates the public opinion of companies thus yielding valuations of equity that are “agreed upon” by every interested party. Private companies, on the other hand, are not subjected to these pricing processes and an intrinsic valuation of the equity must be calculated. Naturally, this is a subjective process. Any intrinsic valuation will include expectations of future performance and, sometimes, expectations of performance increases resulting from the additional knowledge and expertise provided by the investor.

For funds looking to invest in private equity, Ewens, Jones, and Rhodes-Kropf [10]

state that higher discount rates are used to account for risk that includes the funds’ idiosyn- cratic risk. Plenborg and Pimentel [11] state that the risk of illiquidity on its own warrants a discount between 15-46%, wider than a spread of 25-35% suggested by Damodaran [7].

They continue by mentioning the inclusion of a control premium, referring to the difference between status quo value and optimal value stemming from the assumption that more experienced management are better equipped to leverage the assets and core business of the company to generate value. Furthermore, the control premium reflects the fact that when valuing private equity using multiples the acquired valuation reflect minority shares while valuations should include the benefit of controlling shares, as it is more common for investors to acquire majority stakes in target companies. This control premium is found to lie between 26-45%. Following findings related to illiquidity discounts, Emory Jr., Den- gel, and Emory Sr. [12] investigate the difference in transaction prices pre- and post-IPO of 543 transactions. They find a mean pre-IPO discount of 30-55%, based on transaction timing pre-IPO. Officer [13] finds the discount rate of unlisted targets in the range of 15-30%. Further, Silber [14] finds that the illiquidity discount to exceed 30%.

Valuation of equity is usually performed by either, or both, of two methods, namely

• forecasting and discounting cash flows, and

• multiples.

2.3.1 Cash Flow-Based Approach

Valuing equity with a cash flow-based approach requires forecasting the future performance of the target company, in terms of cash flows. This allows for specific and detailed assumptions to be made regarding the components of the cash flow calculations. These cash flows are then evaluated in present value terms and specific discount rates can thus be applied to account for the riskiness of the cash flows.

2.3.2 Comparable Multiples-Based Approach

Valuation with multiples is based upon finding a comparable company to the target company. For the comparable company it is assumed that it is similar to the target company in terms of risk and business development such that the valuation procedure would highlight

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CHAPTER 2. BACKGROUND 7 minor differences in assumptions and characteristics. As such, multiples of financial figures of the comparable company is calculated, e.g., Enterprise Value

EBITDA , which allows for simple estimation of any comparable target company valuation. Reasearch shows that accrual- based multiples outperform cash flow-based multiples, and that multiples excluding bias in accounting information, such as EBITDA in favor of EBIT, provide better estimates of value. Furthermore, combining value estimates has been found to increase the accuracy of value estimates, reasoning that each value estimate provide information, and forward measures provide better accuracy than current measures [11], [15], [16], [17], [18]. Eberhart [19] finds a negative relationship between the information available concerning comparable firms and the volatility of the target company’s expected returns close in time to corporate events, supporting the fact that comparable companies provide analysts with useful information.

Identifying Comparable Companies

When considering private equity, finding comparable firms can prove difficult and finding related financial statements is another challenge in itself. This is why the illiquidity discounts and control premiums are useful. The underlying assumptions of applying these factors entails valuing companies as if they are liquid and investments represent minor shares. Thus, identifying comparable companies requires less effort since publicly traded companies can be used. On the other hand, the uncertainty of comparable companies increases as the dynamics and complexities of public companies differs from that of private companies. Stakeholder pressure and expectations affect managerial decisions, investment horizons, and business practice. Thus, using multiples based on public companies provides benefits in terms of effort but introduces a new dimension of uncertainty. With valuations being inherently subjective and varying in accuracy, this uncertainty is likely surpressed by the availability of public companies and the extent of their financial reports.

Dittmann and Weiner [20] find that comparable companies in Europe should be identified by considering companies with similar return on assets across European countries, as op- posed to regarding industry classification. Herrmann and Richter [21], on the other hand, construct a factor-based approach to finding comparable companies based on measures of performance. They find that this approach also outperform industry classification in finding comparable companies. Even though research suggests more thorough screening approaches for finding comparable companies, industry classification constitutes an approach much more viable in terms of effort, considering that this project aims to value a large set of companies based on comparables.

2.3.3 Approach Trade-Off

When determining the valuation of a single company both approaches are practically identical, as no comparable company need be identified. However, usually many target companies are to be valued and, consequently, the effort required to utilize a cash flow-based approach increases significantly. The multiples-based approach requires dramatically less effort to apply but suffers from reduced ability to make qualified assumptions of each target company of interest. Thus, there is a trade-off between the efforts of analyzing each company individually and finding comparable companies to base the valuation upon. While the cash flow-based approach does allow for more control of the valuation it is nonetheless

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difficult to accurately forecast performance and it does not guarantee more precise valuations when compared to the multiples-based approach. In fact, Plenborg and Pimentel [11]

find that more than 90% of professionals utilize the multiples-based approach, indicating that many professionals find the practicality of the multiples-based approach is extensive enough to make it the preferred approach. Using a multiples-based approach introduces another trade-off regarding which multiples to use. With research favoring forward measures one must determine if the effort required to find the forward measures is worth the increased accuracy. This trade-off is difficult to quantify or argue due to the subjectivity of valuations and measurement of accuracy, since a “true” valuation estimate does not need to exist, and, thus, the choice depends on the opinion of the analyst and the availability of data. However, when using the relative valuation approach, i.e., valuation through multiples of comparable companies, one should be aware of the fact that any relative valuation will inherit certain characteristics of the comparable companies. Basing multiples on an industry that is overvalued will likely cause any consequent valuation to be overvalued as well [22]. This could be seen as a strength of consistency, and a fallacy of problem inheritance.

2.4 The Nordics and Private Equity Activity

Creandum [2] states that the Nordics account for approximately 50% of European private equity exits and approximately 7% globally, in monetary figures. In 2016 the average annual sum of exit values exceeded 4b USD and Information technology is highlighted as the most valuable sector. Høegh-Krohn [1] supports these figures and continues to state that in 2018 approximately 24b EUR was raised by buyout- and venture capital funds, and that more than 13b EUR was invested. The amount of invested capital in Nordic private equity has more than doubled, on average, between 2016 and 2018, denoting an all-time high. Moreover, 59% of all venture investments in 2018 were attracted by the tech sector and mainly in ICT, Information and Communications Technology [1].

2.5 Project Goal

This project aims to analyze private companies in the Nordics acting in the sector of ICT in an attempt to provide insights regarding the state of the market and the presence of fi- nancially beneficial investment opportunities. In particular, this project aims to investigate whether or not these companies provide investment opportunities with positive alphas. In the process of finding such opportunities, the project further aims to develop a simple valuation procedure based on a combination of “common” multiples for valuation. As such, the project will cover an investigation of what multiples are most significant in valuing Nordic private equity within ICT and the magnitude of these multiples.

Hopefully, this project will provide insights that can be used to gain an increased un- derstanding of the Nordic private equity market, the risks investors are exposed to, and the basic differences to public equity investments. Lastly, this project will make an attempt to describe the performance of Nordic private equity and explain any unexpected differences in returns.

In effect, this report hopefully aids in strengthening the trend of previous years with

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CHAPTER 2. BACKGROUND 9 increasing investor activity in private equity, which is a key component to continue nur- ture the entrepreneurially spirited founders and employees that shape the landscape of economic growth and technical innovation, and that characterizes private equity.

The report is divided in two parts where Part I regards the construction of the valuation model required to estimate the value of private companies. Part II is based on the estimated values of private companies resulting from Part I and contains the market and portfolio analysis answering the questions of whether or not private equity offers investment opportunities with positive alphas.

In effect, to answer the research questions listed in the introduction the following must first be considered:

• How can the value of private companies be estimated, and what are the parameters needed to do so?

• How is the alpha of private equity calculated?

• What is an appropriate portfolio strategy and how does it perform?

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Part I

Building a Valuation Model

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Chapter 3 Theoretical Considerations

3.1 Defining Valuation Measures

The project will utilize regression analysis to calculate measure loadings to be used for combining multiple measures of companies’ performance and state to estimate their value.

But, before defining the model of regression such measures must be considered and defined.

Available research considered unanimously find that forward measures improve the accuracy of valuation [11], [15], [16], [17], [18]. However, finding or calculating forward measures for the 7,834 companies to be analyzed is simply not feasible given the scope of the study. Regarding other types of measures there is less consensus of their rank- ing in valuation accuracy. Nonetheless, different measures provide proxies for underlying information regarding a company’s state and performance. As long as this underlying information is not identical for two measures, using more measures increases the extent of the information basis provided by the measures at hand. Measures to be considered can be categorized according to measures based on figures found in:

• income statements,

• statements of financial position,

• cash flow statements,

• other types of statements.

3.1.1 Income Statement Measures

Consider the measures from the income statement, turnover and EBITDA. A company’s turnover indicates the amount of business being generated and maintained. Per annum it measures outcomes of activities – such as product launches, market expansion, direct sales, etc. – often performed prior to the year investigated. As such, it can include information of long-term strategy performance, short-term sales initiatives, and more. Thus, evaluated independently on a per annum basis reveals little more than the size of currently conducted business. The yearly growth of turnover, on the other hand, provides a measure

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12 CHAPTER 3. THEORETICAL CONSIDERATIONS

of how well implemented strategies and initiatives perform in terms of growing the business. Furthermore, EBITDA then provides a measure of the company’s ability to generate profits, excluding accounting policies, from the business activities.

In conclusion, measures as provided by the income statement that should be consid- ered in a model of company value entail (1) turnover, (2) yearly turnover growth, and (3) EBITDA.

3.1.2 Statement of Financial Position Measures

In the case of the statement of financial position, companies disclose information regarding their asset portfolio and capital structure, among other figures. Measures of leverage and asset distribution provides useful information in terms of a company’s structure. Due to system imperfections caused by e.g., taxes, companies are incentivized to maintain a capital structure where debt is prevalent. Seemingly high proportions of debt in a firm’s capital structure implies a managerial belief of steady rates of income streams and a ro- bustness of business that can support debt in a sustainable manner, as well as incentivizes managers to actively supervise the financial health of the firm. This means that measuring relative debt in a company can potentially provide information concerning the stability of a company’s revenues, managerial belief and confidence, and manager’s financial attention.

Moreover, the distribution of investments in different asset types can reveal the direc- tion of interest and intent of a company. Especially in the industry of ICT, where tangible assets, apart from investments in offices and similar, is generally dominated by investments in computers and other technical assets. Acquiring large amounts of hardware will not necessarily boost long-term competitiveness as a large portion of the investments will be obsolete in just a few years. Investments in intangible assets such as software systems and solutions, research projects, etc., on the other hand, provide opportunities for nurtur- ing the long-term growth of the company and, in effect, its value. While intangible assets, just like tangible assets, are exposed to the risk of becoming obsolete, it represents an asset class that often can be more easily updated and extended to increase its usability and life span.

Apart from intangible assets, the total book-value of assets provides an accounting valuation of the basis of the business. As such, it provides a measure of company size useful to relate the performance of companies of similar, and differing, size.

So, measures that can be extracted from the statement of financial position and that should be included in a valuation model include (4) relative level of debt (leverage), (5) relative level of intangible assets and (6) total assets.

3.1.3 Cash Flow Statement Measures

The statement of cash flows is generally highly regarded by valuation analysts. Current valuation practice and research regards a company’s cash flows as the basis of valuation.

Shortly put, the sum of a company’s future cash flows, in present value terms, equals the value of the company. However, as previously stated it is not feasible to estimate these cash flows for all the companies considered. Instead, consider the fundamental information mediated by the bottom line of the cash flow statement: does the company generate a surplus of cash flow and, if so, how much?

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CHAPTER 3. THEORETICAL CONSIDERATIONS 13 Thus, the single measure based on the cash flow statement that should be included in a valuation model is (7) cash flow.

3.1.4 Other Measures

Other measures to be considered, that are not included in the statements mentioned, include number of employees. The number of employees provides a measure of company size as well as some indication of limitation in the amount of business that can be conducted.

Whether or not the company is publicly listed could be applicable in a valuation regression model to incorporate information of related deals and acquisitions which would allow for direct incorporation of illiquidity discounts and control premiums. Though, since the calculation of such factors is not included in the scope of the project, such factors are dis- carded from the regression model and instead applied using figures from research at a later stage.

Consequently, other measures to be included in a valuation model is simply constituted by (8) number of employees.

3.1.5 Summary of Measures to be Considered

Summarizing considerations and conclusions regarding measures and information results in the following list of measures that should be included in a regression model aimed at estimating the value of companies:

1. turnover,

2. yearly turnover growth, 3. EBITDA,

4. relative level of debt,

5. relative level of intangible assets, 6. total assets,

7. cash flow, and

8. number of employees.

These 8 measures can be categorized according to the type of information they provide concerning the companies analyzed, namely:

• Company size

◦ turnover

◦ total assets

◦ number of employees

• Financial efficiency

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14 CHAPTER 3. THEORETICAL CONSIDERATIONS

◦ yearly turnover growth

◦ EBITDA

◦ cash flow

• Financial structure

◦ relative level of debt

◦ relative level of intangible assets

Consequently, it can be argued that the measures this project aims to analyze are not only selected based on rational arguments, but also constitute measures widely used by industry professionals [20], [16], [15], [11].

3.2 Valuation Based on Periodical Measures

Industry professionals usually utilize either, or both, of the multiples-based approach and discounting cash flows when estimating the value of a company. The multiples-based approach is fundamentally dependent on an assumption of a linear dependence between company valuation and some particular multiple. Discounting cash flows, on the other hand, can be represented as follows

V₀ =

∞

X

t=1

CF_t

R^D_t . (3.1)

Where V0is the estimated value of the company, CFtis the cash flow generated in the t:th period of time, and R^Dt the discount rate used for t units of time. Clearly, such an approach requires explicit assumptions of future cash flows, appropriate discount rates, and treating cash flows in perpetuity. Forecasting cash flows entails estimating future revenues, costs, and asset allocations. As such, the methodology of the discounted cash flows approach entails invastigating (1) company size, (2) financial efficiency, and (3) financial structure as core parts of the valuation procedure.

3.2.1 Measure Observations Are Not Independent

Note that equation 3.1, like the multiples-based approach, in fact is of linear nature if CF^t treated as given. However, in forecasting cash flows of firms a common approach bases the forecast on assuming some exponential growth in revenue – growth of relevant market constitutes a popular baseline of growth – and determining other variables as fixed portions of the revenue. Assumptions can be made complex and extensive – this constitutes an argument of magnitude used both in favor and opposition of the valuation approach – with many variables being included. The key issue, though, results from the fact that practically every financial measure is heavily dependent on past performance of said measure. In the discounted cash flow approach this is illustrated by forecasting e.g., revenue based on exponential growth – any type of relative growth, or recession, inherits this problematique – making the time-dimensionality dependency explicit.

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CHAPTER 3. THEORETICAL CONSIDERATIONS 15 To explicitly define this dependence between yearly observations, let I(St) define the sum of revenues in period t generated by a set of revenue streams, i.e.,

I(S_t) = I(ω₁) + I(ω₂) + ... + I(ω_k), (3.2)

S_t = {ω₁, ω₂, ..., ω_k}. (3.3)

Let the individual revenue stream ωi correspond to revenue generated by some business activity. Next, consider the revenue streams of period t + 1, S^t+1, and define it as

S_t+1= (S_t\LS_t) ∪ N S_t+1, (3.4) where LStrefers to the revenue streams lost in period t and N St+1refers to the new revenue streams of period t + 1. Thus, we can formulate the revenue generated in period t + 1 as a function of the revenue generated in period t,

I(S_t+1) = I(S_t, LS_t, N S_t+1) = I(S_t) − I(LS_t) + I(N S_t+1). (3.5) We can further extend the formula for any number of years, such that

I(S_t+2) =I(S_t) − I(LS_t) + I(N S_t+1) − I(LS_t+1) + I(N S_t+2), (3.6) I(S_T) =I(S_t) − I(LS_t) + I(N S_t+1) − I(LS_t+1) + I(N S_t+2) (3.7)

+ ... − I(LS_{T −1}) + I(N S_T).

For the revenue streams of period k ∈ {t + 1, t + 2, ..., T } to be independent of those of period t it must be that St ∩ S_k = ∅ or, equivalently, LSt = S_t. In practice, this infers that a company must lose all of its business every period of time and generate new business for the following period, independent of the business previously terminated, for the revenues of multiple periods in sequence to be independent in this regard. Such a scenario is highly unlikely, particularly when considering companies of the size present in this project’s analysis. Of course, the same line of arguing is applicable for most other financial measures. In conclusion, multiple observations regarding a single company must be treated as dependent.

Returning to the discussion regarding forecasting cash flows, it should be noted that when estimating future revenues a common approach is to assume current business activities will grow or be complemented. In the notations of this section we denote this:

S_t+1= S_t∪ N S_t+1. Again, the inter-period dependency becomes transparent.

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Chapter 4 Methodology

4.1 Data Collection

The dataset used in this project can be acquired through Orbis [23] and entails 7,822 companies, of which 102 are public, that fulfill the following criteria:

• Size classification: At least one of...

◦ 1m EUR ≤ Operating Revenue (turnover) < 10m EUR

◦ 15 ≤ Number of employees < 150

◦ 2m EUR ≤ Total assets < 20m EUR

• Geographical region: the Nordics

• Activity code (NACE Rev.2): Section J (58-63)

• Other: Operating revenue available for last year of time period investigated

Bureau van Dijk [23] states that the data provided by Orbis is standardized to account for differing legal filing obligations and accounting differences across countries. Furthermore, figures are presented in EUR thousands using exchange rates as of each period’s closing date. Thus, no further treatment or standardization of the figures acquired is made, except for basic formatting.

The dataset covers the time period 2011-2018 and contains the following variables:

• Income statement

◦ Turnover

◦ EBITDA

• Statement of financial position

◦ Intangible fixed assets

◦ Cash & cash equivalents

◦ Total assets

16

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CHAPTER 4. METHODOLOGY 17

◦ Long-term debt

◦ Loans

◦ Total shareholder funds and liabilities

• Cash flow statement

◦ Cash flow

• Other

◦ Number of employees

◦ Public (last observed year)

In other words, the dataset contains 62,576 observations of annual financial data, in groups of 8 observations related to a specific company.

4.2 Asset Valuation - Multiples and Regression

This project aims to construct a regression model for estimating the Enterprise Value of companies – see Investopedia [24]. In short, the enterprise value of a company is a proxy of the cost of acquiring the company in its entirety – although, a controlling premium is usually present in an actual takeover – and can be denoted

Enterprise value = Market capitalization + Long-term debt + Loans

− Cash & cash equivalents.

4.2.1 Model Specification

The regression model will, initially, contain the following variables:

• Dependent variable: enterprise value

• Independent variables:

◦ turnover

◦ total assets

◦ number of employees

◦ yearly turnover growth

◦ EBITDA

◦ cash flow

◦ leverage

◦ technical leverage

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18 CHAPTER 4. METHODOLOGY

Where the two measures of leverage are defined as

Leverage = Long-term debt + Loans Total shareholder funds & liabilities

,

Technical leverage = Intangible fixed assets Total assets

.

4.2.2 Training Data

The regression model will be trained on a subset of the dataset described in section 4.1.

This subset contains the companies that are, or have previously been, publicly listed.¹ This subset is, in turn, split in 8 sets by each observation’s respective reporting year to avoid observation co-dependence as described in section 3.2.1. These sets will further on be referred to as F Y¹ through F Y⁸, where F Y¹ refers to observations of 2011, F Y² observations of 2012, and so on.

Note that F Y1cannot provide data of yearly turnover growth, as this measure is calculated and not provided. Thus, F Y1 will not be present in the model selection process and the model evaluation process. However, if the model selected based on these processes does not contain yearly turnover growth as an independent variable the model will be used to predict valuations of observations from 2011 – that would otherwise correspond to F Y1.

4.2.3 Model Assumptions

Training the regression model with data on publicly traded companies will cause assumptions and properties of publicly traded companies to be implicitly included in the model.

This includes assumptions of liquidity, accessability, absence of control premium, and more.

Furthermore, the model is based on assumptions following standard multi-variate regression, i.e.,

y = Xβ + , (4.1)

∼ N(0, σ²I_n),

where y denotes the observations of the dependent variable, X observations of the independent variables – including ones for the intercept. β denotes loading for the independent variables, the error terms, and Inthe n-dimensional identity matrix. X and β are treated as given variables, such that

E[y] = Xβ, Var(y) = σ²I_n.

1The analysis includes previously listed companies to avoid survivorship bias resulting from companies being unlisted.

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CHAPTER 4. METHODOLOGY 19

4.2.4 Fitting Model

In the process of fitting the regression model every possible submodel of the full model will also be considered to investigate if they offer improved prediction performance. Thusly, the approach that will be followed can be outlined as:

1. evaluating the full model and every submodel, 2. choosing one candidate model, and

3. evaluating the candidate model.

Evaluating Every Model

To evaluate every possible model based on the choice of independent variables an all possible regression approach will be utilized. Let k be the number of independent variables present in a model. Then, for every k = 1, 2, ..., 8 there are ⁸_k

models to be analyzed.

Montgomery, Peck, and Vining [25, pp. 334–337] state that when a regression equation is used for prediction purposes we, generally, want to minimize the mean squared prediction error (MSPE). Hence, for every such model, the models’ respective MSPE will be cross-validated to form a measure of prediction performance. That is, for every model the measure

MSPE = E hX⁸

i=2 8

X

j=2

1^{j6=i}· (yF Yj− ˆyF Yj,F Yi)² i

(4.2)

is calculated, where 1 denotes the indicator function, yF Yidenotes observations of the dependent variable from set F Yi, and ˆy_{F Y}_j_{,F Y}_idenotes the predicted values of the dependent variable in set F Y^j of a model trained on set F Yⁱ.

That is, for every model, the model is trained on set F Yi and its mean prediction error calculated on sets F Yj, where j = 2, 3, ..., 8 and j 6= i. Then, the model’s performance is cross-validated for every possible training set, so that i = 2, 3, ..., 8.

Recall that F Y¹ is omitted due to lack of yearly turnover growth.

Choosing and Evaluating the Candidate Model

The candidate model will be chosen based on minimizing the MSPE. Then, it will be evaulated by considering the statistical significance of the model and its parameters, as well as considering three types of residuals as defined by Montgomery, Peck, and Vining [25, pp. 130–135], namely:

• unscaled residuals - denoted ei,

• standardized residuals - denoted di, and

• studentized residuals - denoted rⁱ.

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20 CHAPTER 4. METHODOLOGY

Here,

e_i = y_i− ˆy_i, (4.3)

d_i = e_i

√M S_Res, (4.4)

r_i = e_i

pMSRes(1 − h_ii), (4.5)

M S_Res = Pn

i=1e²_i

n − p , (4.6)

h_ii= (X(X^>X)⁻¹X^>)_ii, (4.7) and p is the number of independent variables present in the model.

4.2.5 Estimating Enterprise Value of Private Companies

The approved valuation model will be trained on F Y8 and used to estimate the enterprise value of every private company present in the dataset. The results of the estimation must be analyzed to ensure a reasonably stable valuation model has been constructed such that further analysis of the private company valuations yield acceptable results in terms of reliability, as will be presented in Part II.

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Chapter 5 Results

5.1 Training Data

Figure 5.1 shows a correlation plot of the independent variables and the dependent vari- able, based on observations in FY8. Clearly, the observation for which enterprise value exceeds 3b EUR – figures are presented in EUR thousands – is far from the main cloud of datapoints. This observation represents a company of vastly different size than any other observation in the training set. In fact, this observed company is more than 10 times as large, in terms of enterprise value, as any other observed company of the training set. Con- sequently, it seems as though there are too few observations in the range spanned by this observation and the main cloud of datapoints to properly analyze the data. The influence and leverage of this observation is of unreasonable magnitude to allow for any conclusions to be made regarding the other observations of the training set. As such, this observation will be removed with figure 5.2 showing the results of elimination. Observations of vari- ables total assets, cash flow, turnover, EBITDA, and number of employees does indicate that there is a linear relationship with enterprise value.

As regards yearly turnover growth, there are observations of companies that have ex- perienced a dramatical increase in turnover which inherently yields observations of high influence – in a linear model setting. Apart from the unusually large deviations in yearly turnover growth, these observations do not significantly differ from any other observations and will not be eliminated.

5.2 Asset Valuation Regression Model

In the following results and analysis, results of model comparisons use statistics based on cross-validation using FY2-FY8. However, when analyzing a single model the results are based on training the model on FY8 as this is the procedure that will be utilized when applying the model for Part II. Hence, the reader is advised to consider that model statistics might differ depending on context.

5.2.1 All Possible Regression

Table 5.1 lists the top three performing submodels, based on minimizing the MSPE, compared to the full model. Appendix A presents a more extensive table of model performance.

21

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22 CHAPTER 5. RESULTS

Figure 5.1: Correlation plot of FY8

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CHAPTER 5. RESULTS 23

Figure 5.2: Correlation plot of FY8 with eliminated influencial observation

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Table 5.1: Top 3 performing (sub)models and full model comparison, with index based on the minimum of MSPE

p Independent variables Index MSPE

8 TA TECH.LEV LEV CF TURNOVER YTG EBITDA NOE 3.947 3.68e+09

4 TA TECH.LEV LEV CF 1.007 9.389e+08

3 TA TECH.LEV LEV 1 9.324e+08

2 TA LEV 1.005 9.374e+08

The 3-factor model with independent variables total assets, leverage, and technical lever- age represents the model with minimum MSPE.

5.2.2 Multi-Factor Candidate Model

The results of fitting the 3-factor candidate model are presented in table 5.2. At a 95% level of confidence, only total assets and the intercept are statistically significant. Furthermore, the parameter sum of squares of leverage and technical leverage are significantly smaller than those of the intercept and total assets, indicating that their inclusion in the model might provide little aid in explaining the variation in the dependent variable.

The 2-factor model with independent variables total assets and leverage performs less than a percent worse than the 3-factor model, as seen in table 5.1. Thus, following the insignificance of terms in the 3-factor model, technical leverage is eliminated, yielding the 2-factor model with statistics presented in table 5.3.

Again, the statistics of the 2-factor model highlight issues with statistical insignificance of model parameters. Leverage is not statistically significant at a confidence level of 95%.

Looking back at figure 5.2, it is not to surprising given the sporadic nature of the relation between leverage and enterprise value. As as result of this, we turn to the 1-factor models.

5.2.3 1-Factor Candidate Models

Table 5.4 present the performance of the 1-factor models, with an index comparison versus the best performing model – that is, the 3-factor model previously mentioned. Further- more, table 5.5 presents a comparison between these models based on R². These tables agree on the following points:

• number of employees and yearly turnover growth perform the worst,

• total assets outperform turnover, which outperforms EBITDA, that outperforms cash flow, and

• technical leverage performs poorly.

The 1-factor model with leverage as independent variable does perform best in terms of minimizing MSPE, but has an R²value of less than 3%. With such a low value of R²the model is ruled out for further analysis. Hence, models to be analyzed entail the 1-factor models with independent variables total assets, turnover, EBITDA, and cash flow.

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Table 5.2: 3-factor model statistics

Multiple R² 0.535

Adjusted R² 0.514

Parameters

Term Estimate Std. Error t-value Pr(> |t|)

(Intercept) 1.19e+04 3.58e+03 3.33 0.0014

TA 8.75e-01 1.10e-01 7.96 2.9e-11

LEV -1.23e+04 1.48e+04 -0.83 0.4085

TECH.LEV -9.70e+03 7.51e+03 -1.29 0.2009

Analysis of Variance

Term Df Sum Sq Mean Sq F-value Pr(> F )

TA 1 1.44e+10 1.44e+10 74.24 1.9e-12

LEV 1 2.00e+08 2.00e+08 1.04 0.31

TECH.LEV 1 3.23e+08 3.23e+08 1.67 0.20

Residuals 67 1.30e+10 1.93e+08

Table 5.3: 2-factor model statistics

Multiple R² 0.523

Adjusted R² 0.509

Parameters

(Intercept) 8.48e+03 2.42e+03 3.51 0.0008

TA 8.97e-01 1.09e-01 8.22 8.9e-12

LEV -1.50e+04 1.48e+04 -1.01 0.3146

TA 1 1.44e+10 1.44e+10 73.52 2e-12

LEV 1 2.00e+08 2.00e+08 1.03 0.31

Residuals 68 1.33e+10 1.95e+08

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Table 5.4: 1-factor models

p Independent variables Index MSPE

1 LEV 1.344 1.254e+09

1 TA 1.706 1.59e+09

1 TURNOVER 1.713 1.597e+09

1 EBITDA 1.874 1.747e+09

1 CF 1.896 1.768e+09

1 TECH.LEV 2.109 1.966e+09

1 NOE 2.134 1.99e+09

1 YTG 4.593 4.282e+09

Table 5.5: 1-factor models with R²comparison

p Independent variables Index R²

1 TA 1 0.3649

1 TURNOVER 0.8522 0.311

1 EBITDA 0.5603 0.2045

1 CF 0.3821 0.1394

1 TECH.LEV 0.1207 0.04404

1 LEV 0.0585 0.02135

1 NOE 0.04451 0.01625

1 YTG 0.01392 0.005081

Total Assets

In the 1-factor model with independent variable total assets, the variable is statistically significant.

Multiple R² 0.516

Adjusted R² 0.509

Parameters

(Intercept) 7.07e+03 1.98e+03 3.58 6.4e-04

TA 9.18e-01 1.07e-01 8.57 1.8e-12

TA 1 1.44e+10 1.44e+10 73.5 1.8e-12

Residuals 69 1.35e+10 1.95e+08

Furthermore, figure 5.3 presents the residuals of this model. The figure indicates that the residuals do not show any apparent systematic behaviour and that residuals are of

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CHAPTER 5. RESULTS 27 Figure 5.3: Residuals of 1-factor model with total assets

reasonable scale. Hence, there is no indication of severe issues with the model and data.

Turnover

The second 1-factor model to consider is based on turnover as its independent variable.

The table below shows that the variable is statistically significant.

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Multiple R² 0.564

Adjusted R² 0.557

Parameters

(Intercept) 8.17e+03 1.79e+03 4.56 2.2e-05

TURNOVER 8.39e-01 8.89e-02 9.44 4.8e-14

TURNOVER 1 1.57e+10 1.57e+10 89.1 4.8e-14

Residuals 69 1.22e+10 1.76e+08

Figure 5.4 presents the residuals of this model. Again, the figure indicates that the residuals do not show any apparent systematic behaviour and that residuals are of reasonable scale.

Hence, there is no indication of severe issues with the model and data.

EBITDA

The third 1-factor model to consider uses EBITDA as its independent variable. Like the previous two 1-factor models, the independent variable is statistically significant.

Multiple R² 0.348

Adjusted R² 0.338

Parameters

(Intercept) 1.78e+04 1.94e+03 9.15 1.6e-13

EBITDA 4.59e+00 7.57e-01 6.07 6.2e-08

EBITDA 1 9.69e+09 9.69e+09 36.8 6.2e-08

Residuals 69 1.82e+10 2.63e+08

Figure 5.5 presents the residuals of this model. The figure indicates a presence of model insufficiency. The residuals are showing signs of systematic behaviour with a clustering

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Figure 5.4: Residuals of 1-factor model with turnover

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Figure 5.5: Residuals of 1-factor model with EBITDA

of observations with negative residuals. Furthermore, the residuals show some non-linear tendencies with an upwards sloping curve with minimum at the most dense cluster of points. Consequently, the model is deemed unreliable and is eliminated from the set of candidate 1-factor models.

Cash Flow

The last 1-factor model to consider is based on cash flow as its independent variable. The table below shows that the variable is statistically significant.

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Multiple R² 0.336

Adjusted R² 0.326

Parameters

(Intercept) 1.81e+04 1.97e+03 9.21 1.2e-13

CF 4.68e+00 7.93e-01 5.90 1.2e-07

CF 1 9.34e+09 9.34e+09 34.9 1.2e-07

Residuals 69 1.85e+10 2.68e+08

Figure 5.6 presents the residuals of this model. The figure reveals the same kind of patterns as for the model with EBITDA as independent variable. There are indications of systematic behaviour and non-linearity. Again, the model is deemed unreliable and it is eliminated from further analysis.

5.2.4 Choice of Final Model - Total Assets

Of the two remaining candidate models, namely the ones with independent variables total assets and turnover, their rankings based on performance, in terms of R² and MSPE, is not unanimous. Total assets performs best in terms of MSPE and turnover in terms of R². However, the models’ purpose is prediction and, hence, the model with independent variable total assets is more suitable in this regard, as the results indicate that it provides superior prediction performance.

5.3 Predictions Using Model

Using the 1-factor model with total assets as independent variable to estimate the enter- prise value of the private companies present in the dataset yields the plot for F Y1-F Y8

presented in figure 5.7.

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Figure 5.6: Residuals of 1-factor model with cash flow

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Figure 5.7: Plot of model predictions with training set observations in black, modelled relationship in red, and 95% prediction interval in blue

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Chapter 6 Discussion

6.1 Dataset

The dataset acquired contained many observations with missing values. As a result, there were less observations that could be used for model training. As stated in section 5.1, the data showed promise for identification of linear relationships, but some observations were too extreme to be considered suitable for the analysis. The extent of the problem with missing data is made clear when considering the fact that out of 1,088 observations of public, or previously public, companies only 328 observations are extensive enough to be usable in the project. Then, considering the fact that approximately one in 8 observations can be used for training purposes, due to observation dependency issues, this figure is further reduced to less than 90 observations for the largest subset.

Regarding the reliability of the data, Bureau van Dijk [23] states that it is standardized to eliminate accounting differences. Nonetheless, accounting principles and regulation allow for two companies with identical financial situations to report slightly different figures in their financial statements. As such, standardizing the data in terms of currency, report dates, calculation formulas, etc., does increase the reliability of the data in a setting such as the one of this project, but it can not account for every practice maintained at companies and, thus, can not be completely standardized. Consequently, when dealing with financial figures of companies one must be aware of the inherent presence of noise in the data.

This project relies on Bureau Van Dijk to provide accurate data of companies’ finan- cials. As an internationally large actor it seems reasonable that Bureau Van Dijk would work hard to ensure the quality of their data. But, to quickly validate the correctness of the data 20-30 observations of the 1,088 observations of public, or previously public, companies was sampled. With these samples, the figures were cross-referenced with those reported by the companies in annual reports as well as with historical exchange rates to arrive at the conclusion that the data seemed to be precise and correct.

6.2 Asset Valuation With Regression

Modelling company valuation with a multiple regression model does not seem to be straight- forward. The results do indicate that multiple regression models offers potential for smaller prediction errors. That is, however, at the expense of statistical significance and explain- ability. Since the best 1-factor model is, in fact, approximately 1.7 times worse at predic-

34

Private Equity Portfolio Management and Positive Alphas

Private Equity Portfolio Management and Positive Alphas

RIKARD FRANKSSON

Private Equity Portfolio

Management and Positive Alphas

Rikard Franksson

Abstract

Sammanfattning

Contents

I Building a Valuation Model 10

II Estimating Risk and Returns of Private Equity 38

Chapter 1 Introduction

1.1 Project Scope

1.2 Research Question

Chapter 2 Background

2.1 Private, Not Public, Equity

2.1.1 Illiquidity Decreases Investor Autonomy

2.1.2 Information Assymetry Increases Uncertainty

2.1.3 Lack of Intermediary Decreases Availability

2.2 Risk Compensation

2.3 The Value of Equity

2.3.1 Cash Flow-Based Approach

2.3.2 Comparable Multiples-Based Approach

2.3.3 Approach Trade-Off

2.4 The Nordics and Private Equity Activity

2.5 Project Goal

Part I

Building a Valuation Model

Chapter 3

Theoretical Considerations

3.1 Defining Valuation Measures

3.1.1 Income Statement Measures

3.1.2 Statement of Financial Position Measures

3.1.3 Cash Flow Statement Measures

3.1.4 Other Measures

3.1.5 Summary of Measures to be Considered

3.2 Valuation Based on Periodical Measures

3.2.1 Measure Observations Are Not Independent

Chapter 4

Methodology

4.1 Data Collection

4.2 Asset Valuation - Multiples and Regression

4.2.1 Model Specification

4.2.2 Training Data

4.2.3 Model Assumptions

4.2.4 Fitting Model

4.2.5 Estimating Enterprise Value of Private Companies

Chapter 5 Results

5.1 Training Data

5.2 Asset Valuation Regression Model

5.2.1 All Possible Regression

5.2.2 Multi-Factor Candidate Model

5.2.3 1-Factor Candidate Models

5.2.4 Choice of Final Model - Total Assets

5.3 Predictions Using Model

Chapter 6 Discussion

6.1 Dataset

6.2 Asset Valuation With Regression