Finding Peers for Multiple Valuation of Danish listed ﬁrms

(1)

17 May 2021

Finding Peers for Multiple Valuation of Danish listed firms

Danish title: Identificering af peers til multiple værdiansættelse af danske, børsnoterede selskaber

Camilla Mie Hørsholt (110404)

Signe Bøgelund Bøgholm Kristensen (101756) Supervisor: Thomas Correll

Master Thesis

M.Sc. in Finance and Accounting / M.Sc. in International Business

COPENHAGEN BUSINESS SCHOOL

No. of characters: 261,441 No. of pages: 120

(2)

Page 2 of 177

Resumé

En af de centrale udfordringer ved anvendelse af multiple værdiansættelse i praksis relaterer sig til identificering af sammenlignelige virksomheder (peers). Den grundlæggende antagelse bag relativ værdiansættelse er, at perfekte substitutter skal handles til samme pris. Således kræver det, at de valgte peers har identiske attributter i rentabilitet, risiko og vækst, da dette betegnes som de teoretiske faktorer, der driver virksomheders værdi. I takt med at industrier er i konstant udvikling og virksomheder i stigende grad fokuserer på at differentiere sig, er det i højere grad udfordrende at identificere sammenlignelige virksomheder. Formålet i denne afhandling er at afdække, hvor anvendelig en fundamental-baseret metode baseret på finansielle nøgletal er til udvælgelse af peers for danske virksomheder, som er særligt udfordret af at operere på et lille marked. Til dette formål benyttes SARD-metoden (’Sum of Absolute Rank Differences’). For at afgøre anvendeligheden, sammenlignes metodens præcisionsgrad med udvælgelse baseret på brancheklassifikation, samt en kombination af disse tilgange. Endeligt undersøges det, hvorvidt danske selskaber bør udvide til at finde peers i EU fremfor blot på et lille hjemmemarked.

Analysen baseres på at sammenligne estimerede multipler med de observerede, for selskaber på NASDAQ Copenhagen i perioden fra 2010 til 2019. Resultaterne indikerer, at peerudvælgelse baseret på SARD opnår mere præcise værdiansættelsesestimater end brancheklassifikation. Der foreligger ikke entydige resultater for, hvorvidt en kombination af disse metoder foretrækkes fremfor SARD, da det varierer alt efter hvilke udvælgelsesvariable og multipler, der benyttes.

En mulig forklaring på tvetydigheden er, at brancheklassifikationer på den ene side reflekterer aspekter af værdiskabelsen, som ikke fanges af nøgletal, mens anvendeligheden samtidig påvirkes af, at Danmark er et lille marked, hvor udvalget af peers indskrænkes markant af brancheklassifikation og efterlader lille forklaringskraft til SARD. Desuden kan resultaterne være negativt influereret af, at branchekoderne er generiske og ikke afspejler differentierede forretningsmodeller. Afslutningsvis peger resultaterne på, at peer grupper for danske selskaber med fordel kan udvides til at indeholde virksomheder fra EU-lande, dog med modifikationer alt efter hvilke nøgletal, der benyttes i SARD. Det tyder på, at der opstår en afvejning mellem et større udvalg af peers, mens der modsætningsvis kan være lande-specifikke karakteristika, der ikke fanges i EU. Overordnet afspejler resultaterne, at det er afgørende hvilke nøgletal, der benyttes i SARD, og at disse tilpasses til multiplen, de søger at estimere, samt efter det enkelte selskab, da anvendeligheden afhænger af virksomheders størrelse og branchen, de opererer i.

(3)

Page 3 of 177

Firm valuations are conducted regularly in a broad range of situations including cases of M&A, restructurings, Initial Public Offerings, and for general investment decisions. For this purpose, different valuation methods exist including a generally acknowledged approach of applying multiples with the objective of determining the market value relatively. Thus, if firms generate identical future cash flows, the value of a firm (target) can be determined by observing the value of a comparable firm (peer). Hence, the underlying assumption for the relative valuation method is based on the basic economic concept, the Law of One Price, which assumes that perfect substitutes should sell at the same price (Rossi & Forte, 2016). However, the relative valuation method does not capture the intrinsic value of a firm as opposed to the present value approach such as the discounted cash flow model (DCF), which is generally perceived to give the most accurate reflection of firm value since it considers forecast and risk directly. As the assumptions related to such intrinsic valuation make the DCF model harder to conduct, practitioners prefer multiple valuations in different cases to overcome complexity. Often, multiples are applied complementary as a market benchmark or on a standalone basis, for instance in order to analyse if a public firm is either over- or undervalued (Lie & Lie, 2002; Rosenbaum & Pearl, 2009).

Notwithstanding the less complex features of the relative valuation method, the Law of One Price assumption leads to a range of implementation issues of applying multiples for firm valuation in practice. Such issues relate to which accounting figures reflect normal cash generation and to different aspects of constructing the multiples including which firm characteristics are essential in order to attain the greatest comparability between firms in the underlying value drivers, and how to identify and select comparable firms for peer groups. Namely, the choice of peer groups is the central area of investigation in this study, as it is decisive to the outcome of firm valuation, hence practitioners and previous empirical studies, in general, agree that this specific issue is a central element in relation to applying multiples in practice (Plenborg & Pimentel, 2016).

The two schools of thought

The current literature reflects two schools of thought in the matter of peer selection. The first school selects firms based on industry affiliation and was initially introduced by Alford (1992).

The underlying idea of identifying peers based on industry membership rests upon the

(6)

Page 6 of 177

expectation of industries reflecting similarities in profitability, risk, and growth, which essentially are the underlying value drivers in firm valuation (Berk & DeMarzo, 2017). When investigating peer selection based on industry affiliation, literature applies internationally recognized classification systems such as the Standard Industry Classification system (SIC) or the Global Industry Standard (GICS) as the selection criterion for comparable firms. On the contrary, the second school of thought constitutes an alternative approach to peer selection as it argues that no theoretical component directly relates profitability, risk, and growth to industry affiliation (Damodaran, 2011). Hence, the second school of thought challenges the premise of industries by definition sharing similarities in these three underlying value drivers which essentially legitimize peer selections. Thus, this school suggests that proxies should rather be derived directly from a firm’s financial fundamentals to ensure similarity in the three key indicators.

Under the fundamental school of thought, a peer selection method by Knudsen, Kold, and Plenborg (2017) is developed, based on the ‘Sum of Absolute Difference’ between firms, namely SARD. This approach is built on the idea of reflecting the three underlying value drivers through a range of selection variables. The authors apply five selection variables namely ROE, Net Debt/EBIT, Size, Growth, and EBIT margin, which peers are identified by in relation to the target firm. Their study is based on a large sample of US firms, whereto the approaches of the two schools of thought are investigated, i.e. the accuracy of SARD compared to industry affiliation. Furthermore, the authors propose an alternative method of using SARD within industries, which bridges the fundamental and industry schools of thought. Ultimately, the SARD approach’s advantage lies within the option of choosing an infinite number of proxies.

Thus, Knudsen et al. (2017) propose future research to examine the method on a small market, as the option of infinite proxies is advantageous when a limited number of observations is apparent, since the number of available peers will not be reduced by the methodological approach unlike other fundamental approaches.

Similar to Knudsen et al. (2017), prior literature presents discrepancies in which peer selection method is the superior, thus creating a ‘horse race’ between the two schools of thought. The studies favouring an industry-based peer selection are Alford (1992) and Cheng & McNamara (2000) who find that using an industry classification system for identifying comparable firms leads to more accurate valuation predictions than using fundamentals. On the contrary, Bhojraj

& Lee (2002), Herrmann & Richter (2003), Dittmann & Weiner (2005), Nel & le Roux (2015),

(7)

Page 7 of 177

and Serra & Fávero (2018) all agree that the greatest accuracy is found within fundamentals.

However, from a practical perspective, peer selection is not limited to either solely applying industry or financial fundamentals. To find the optimal peer groups, practitioners apply many selection criteria besides the ones constituting the two schools of thought, and such criteria are understood to be prioritized differently depending on the target (Rosenbaum & Pearl, 2009).

The objective of the thesis

Multiple valuation is crucial for firm valuation and dependent on the peer selection method’s ability to find the best comparable firm. It could be presumed that the larger a peer pool is, the higher the possibility of identifying a good peer. A small market with few listed firms challenges the peer selection, making it more difficult to find the best candidates for a peer group. Thus, this thesis seeks to understand what the optimal peer selection method is for multiple valuation of Danish listed firms, which are subject to a small home-country market. To examine the overall research topic, the framework of this thesis will be based on the ‘horse race’ between the fundamental- and the industry approach similar to previous literature. Knudsen et al. (2017) propose for future research that SARD could be examined on a small market, as it is a beneficial method for the fundamentals approach when a few observations is apparent. Hence, the SARD method will be applied in this study to reflect the fundamental approach, while GICS classifications will constitute the industry approach. With the understanding from a practical perspective of peer selection not being limited to using either a fundamental or an industry approach, a combination of the two approaches will be examined, similar to the approach applied by Knudsen et al. (2017). However, peer selection for Danish listed firms could presumably benefit from a larger underlying peer pool. Hence, it will be examined if Danish targets benefit from expanding the home-country peer pool to a cross-border peer pool, which in this study will consist of firms from countries within the European Union. Thus, this thesis intends to create an understanding of how to find comparable firms for Danish listed firms by establishing an interface between academia and practice.

(8)

Page 8 of 177

1.1 Research question

From the initial considerations of optimal peer group selection, the purpose of this thesis can be formulated into the following research question:

With the objective to achieve the most accurate multiple predictions, how does a fundamental approach perform in the identification of peers for Danish listed companies which are subject to a small home- country market?

In order to procure the required knowledge to answer the research question, three separate postulations are formulated into the following hypotheses:

Hypothesis 1: Peer selection based on the SARD approach yields more accurate multiple predictions than applying an industry classification using a home-country peer pool

Hypothesis 2: Peer selection based on a SARD approach within industries yields more accurate multiple predictions than applying SARD across industries using a home-country peer pool

Hypothesis 3: Peer selection based on an EU peer pool yields more accurate multiple predictions than applying a home-country peer pool

To assess the performance of peer selection based on fundamentals, an industry-based approach will be applied as a benchmark. Thus, Hypothesis 1 addresses whether a selection method based on SARD predicts more accurate valuation estimates for Danish targets, compared to a selection method based on industry classification when applying a Danish peer pool. In continuation of assessing a fundamental-based peer selection approach, its performance is compared to a combination of fundamentals and industry, as it is known that common practice includes both schools. Thus, Hypothesis 2 addresses whether a selection method based on SARD within industries yields higher multiple prediction accuracy compared to SARD across industries. The intention of investigating the two stated hypotheses is to gain a comprehension of which is the superior selection method for Danish targets when using a home-country peer pool. However, with the understanding of Denmark being a small market it is expected that a larger peer pool could improve the possibility of finding better comparable firms for multiple valuation of Danish targets, thus, the third hypothesis is formulated. Hypothesis 3 addresses whether the investigated peer selection methods with an underlying EU peer pool yield higher

(9)

Page 9 of 177

prediction accuracy than applying a Danish home-country peer pool. The three hypotheses stated above will guide the structure and analysis of this thesis, with the aim to support the understanding of how peers for Danish listed firms should be identified when the objective is to achieve the highest prediction accuracy. The following section will provide the reader with the overall structure of the thesis.

This chapter will continue with an outline of the applied scientific method, the overall quality of the empirical results, and the undertaken delimitations. In Chapter 2, the theoretical framework in relation to multiple valuation and peer selection will be described. Chapter 3 provides a literature review of prior research on the topic of peer selection methods, i.e. the two schools of thought. Chapter 4 outlines the research design and the methodological approach applied to address the research question. Chapter 5 presents the empirical results with the aim to address the stated hypotheses orderly. Chapter 6 outlines the interpretation of the obtained findings and a discussion of these and additionally addresses the limitations of the study in relation to the empirical findings. Furthermore, the implications of the results and discussion will be outlined in relation to a practical application. Finally, Chapter 7 will conclude the thesis.

1.2 Scientific method

In order to examine the research question of this thesis regarding how a fundamental-based approach performs in peer selection for Danish listed firms, three hypotheses have been constructed and presented in the previous section. The postulations formed in these hypotheses are based on literature related to peer selection and the theoretical understanding of underlying value drivers for multiple valuation. Hence, the underlying scientific method in this thesis relates to critical rationalism, as the hypotheses are examined deductively by interpreting observations leading to a consideration of falsification (Holm, 2018). This scientific method is central to bear in mind, as the conducted analyses related to each of the three hypotheses can potentially be rejected based on the findings obtained, while verification of general causality cannot be achieved based on this one case of investigation. Hence, the scientific method allows for greater knowledge about peer selection for Danish listed firms, while it simultaneously urges for potential new hypotheses to be investigated in the future as the method’s epistemology is rationalistic i.e. acknowledging the fact that a definite verity of the research topic cannot be conducted (Holm, 2018).

(10)

Page 10 of 177

To examine the quality of the findings in this study, reliability and validity must be considered (Carmines & Zeller, 1979). Validity relates to whether a measuring instrument is valid to be applied relative to a certain phenomenon, i.e. alignment should appear between the subject to investigate and the empirical data applied. To establish a premise for validity in this thesis, three hypotheses are constructed to assure alignment between the analysis performed and the research question. To ensure a connection between the measuring instruments applied and these hypotheses, the multiples used within this study are derived theoretically to understand which selection variables reflect the underlying value drivers, and how empirical data should be applied and linked to the selection methods being tested. Simultaneously, the methodological setup is based upon previous empirical studies, i.e. relies on critical tradition within this field of research. However, some limitation of objectivity exists in the application of the datasets, as manipulation is performed through the exclusion of negative values and missing data, thus, restricting the data and affecting validity. However, the sample of Danish targets, being the primary focus in the thesis, has not been prone to the same level of exclusions as the EU dataset, indicating that the overall validity is not highly affected by the manipulation.

Reliability is an indicator for the overall credibility of the findings, thus, researchers should be able to attain identical results if replicating the study (Carmines & Zeller, 1979). The SARD method which is applied as the fundamental approach is formulated mathematically, thus, when applying the model on an equivalent dataset, the results can be replicated. To ensure that no systematic biases to such reliability occur, the developed algorithm within this study is applied to the original dataset used by Knudsen et al. (2017) and shows identical results as seen in Appendix 2, indicating high reliability. However, in the pure industry approach peer groups are chosen randomly within industry groups, i.e. the results vary somewhat each time the developed model is simulated. In order to mitigate this matter and secure reliable findings, the model is simulated until no variation appears in the results. Moreover, various robustness checks are conducted in the second part of the analysis to examine factors affecting the peer selection methods, thus increasing the reliability of the obtained results.

Finally, addressing the generalizability of this study, the deductive approach within critical rationalism increases the ability to generalise the results since it is the most severe scientific test as once a hypothesis is falsified, the postulation cannot be perceived as valid in general (Flyvbjerg, 2006). However, the data selection and the selection methods used within this study

(11)

Page 11 of 177

challenge the generalisability, as the findings are not universal and might alter if applying an alternative fundamental approach than SARD or another peer pool than EU. This is though acknowledged by the critical rationalistic approach as the aim is not to create general verifications but solely enlarge knowledge that evolves continuously (Holm, 2018).

1.3 Delimitations

The following section will outline the designated topics to be excluded from the performed investigation of the research question. The empirical analysis is restricted to the time period from 2010 until 2019 whereto the newest market data will be applied. To examine fundamentals’ performance in the research question both a home-country and cross-border peer pool is tested in hypothesis 3, however, solely an EU peer pool is applied for this purpose as the alternative peer pool. Furthermore, SARD will constitute the fundamental approach.

Thus, to the greatest extent possible, the methodology and analytical approach of the original SARD method will be followed. The SARD approach is not limited by the number of fundamentals and can in general encompass all possible selection variables and valuation multiples. This analysis will consider ROE, Net Debt/EBIT, Size, Growth, and EBIT-margin similar to Knudsen et al. (2017). Regarding the multiples used, EV/Sales and EV/EBIT will be applied in the analysis similar to the original study of SARD, however, price-multiples will not.

As an addition, the EV/EBITDA multiple will be included. The selection method based on industries is restricted to using a GICS classification system, thus, no other industry affiliation approach will be examined. The motivation and decision behind these methodological delimitations will be further described in Chapter 4. Finally, it is noteworthy, that rather than evaluating the fundamental-based selection method’s performance through the level of prediction accuracy, this study is focused on examining the performance relative to an industry approach and a combination of the two. All specific decisions related to these delimitations will be further described in Chapter 6.

(12)

Page 12 of 177

2. Theoretical foundations

This chapter aims to establish a theoretical framework for the analysis. Hence, Section 2.1 will initially present the underlying assumptions which multiple valuation is built upon to justify why two uncertain cash flows should sell at the same price. Second, the derivation of the applied multiples from the DCF is presented in Section 2.2 in order to understand the theoretical underlying value drivers of the multiples. Subsequently, the theoretical reasoning as to why the two schools of thought, i.e. industry affiliation and fundamentals, are appropriate peer selection methods. In Section 2.3, the definition of industry is introduced alongside the theoretical link to the underlying value drivers for multiples.

2.1 Underlying assumptions

Multiple valuation is a relative methodology where a firm’s value is determined by the comparison of assets between firms as opposed to absolute valuation methodology in which the value of a firm is found intrinsically (Damodaran, 2007). The central assumption for the relative valuation approach is the basic economic concept, the Law of One Price, which states that perfect substitutable assets should sell at the same price (Rossi & Forte, 2016). This concept is transferred to an enterprise context in which comparable firms that are expected to generate the same cash flows in the future should be valued at the same price today. Thus, the value of a company can be derived from observing the value of a comparable firm.

In order for the Law of One Price to hold for multiple valuation, the general assumption of efficient markets has to be met. This means that market prices should “fully reflect all available information”

(Fama, 1970, p. 383). Hence, the risk-adjusted stock price (P) at time t is a function of the expected uncertain future cash flows (𝐶𝐹# ), ultimately, contingent on the available information at the time (Φ):

P_t=∑ E"^CF^!^t+i

(1+r)ⁱ|Φ_t$

∞i=1 (2.1)

The efficient market hypothesis builds upon the assumption of Random Walk, which states that past movement or trend of a stock price do not influence the future price. Only new information will affect future movements since the market already reflects full information at the time. Thus,

(13)

Page 13 of 177

multiple valuation can be used for valuing a firm today based on expectations about the future and will change when new information appears (Fama, 1970). Hence, multiples are estimated on a yearly basis in this thesis to reflect the new information given to the market when firms are publishing financial statements. Furthermore, relative valuation is based on the assumption that firm value is linearly proportional to the identified value driver(s) and such proportionality should hold for all the identified comparable firms (Rossi & Forte, 2016). It should be noted that the outlined assumptions rest on an average consideration, as the market can misprice stocks in the short run or on an individual basis. Among other things, behavioural economics can influence prices which for example can be reflected in ‘the earnings puzzle’ where over- or undervaluation will occur after the announcement of financial statements. However, the market prices are assumed to be correct on average (Berk & DeMarzo, 2017).

2.2 Derivation of multiples

To value assets on a relative basis, prices must be standardized. A multiple indicates the market price of a single unit (here: firms) while the substitutability is reflected in a standardized conversion of prices in terms of a key statistic (Damodaran, 2012). Such key statistic is often a financial measure from either the income statement or the balance sheet, e.g. revenue or book value of equity. It can also be an operating measure such as the number of customers or subscribers. In theory, any key indicator can potentially be used, however, in order to ensure substitutability between firms and constitute a benchmark for the target firm, the chosen metric should reflect the profitability, risk, and growth potential as academics agree those are the factors of most influence and in line with the firm value (Damodaran, 2012; Rossi & Forte, 2016). As stated later in Section 4.2.1,this thesis will be based on generic enterprise multiples using universal measures of financial performance in the denominator (Sales, EBITDA, and EBIT) as those are widely used and can reflect value across the sample (Rosenbaum & Pearl, 2009). Hence, to understand the mathematical relationship between value drivers for profitability, risk, and growth and the value of a firm, the derivation of EV/Sales, EV/EBITDA, and EV/EBIT multiples from the present value approach will be demonstrated.

Initially, it should be noted that while the Equity Value (market capitalization) reflects the market price of the owner’s capital, the Enterprise Value (EV) is a measure of the total firm value as a sum of all ownership interests in a company and claims on its assets from both debt

(14)

Page 14 of 177

and equity holders. Therefore, using EV-based multiples, the fundamentals used should also reflect the value that flows to both equity- and debt holders (Rosenbaum & Pearl, 2009).

In order to discover the fundamentals behind the EV-multiples, the DCF will be the pivotal point as it determines the firm value based on the expected after-tax free cash flows to the firm (FCFF). Since the FCFF can be used to pay both dividends or debt or be retained for future activities, FCFF is including cash flows to both equity- and debt holders (Damodaran, 2012).

FCFF can be expressed as the remaining part of NOPAT (the net operating profit after tax, t) at time 𝜏, after cash are withdrawn to investments in the firm:

FCFF = NOPAT - Δ Invested Capital (2.2) Where

NOPAT = EBIT * (1-t) (2.3) The change in Invested Capital (IC) equals investments made in Net Working Capital (NWC) and CAPEX, which means it is a reflection of the change in operating assets net of operating liabilities. On the other hand, IC can be denoted as the change of total equity and net interest- bearing liabilities, as it constitutes the financial side of the net operating assets (Petersen, Plenborg & Kinserdal., 2017).

The DCF model determining the Enterprise Value based on FCFF can be expressed as:

EV_τ=∑^∞_{τ =1}FCFF_τ * )1+g_τ*^N* (1+WACC_τ)^-N → EV_τ=_WACC-g^FCFF (2.4) WACC, the weighted average cost of capital, is the discount rate representing the required return on invested capital from both equity- and debt holders and is dependent on the capital structure as equity and debt components, in general, have significantly different risk profiles and tax ramifications (Rosenbaum & Pearl, 2009). The DCF assumes a constant growth rate (g) for the cash flows in perpetuity, which must be lower than the required return WACC in order for the model to serve (Berk & DeMarzo, 2017). The DCF also makes the assumption, that both the capital structure, tax rate, and reinvestment rate, 𝜃_!, are constant, where the reinvestment rate constitutes the change in Invested Capital as a share of NOPAT from Equation 2.2:

(15)

Page 15 of 177 θ =∆Invested Capital

NOPAT (2.5) The DCF in Equation 2.4 can now be restated based on the definition of FCFF in Equation 2.2 followed by the relation between reinvestment rate and Invested Capital in Equation 2.5 to:

EV_τ = NOPAT - ΔInvested Capital

WACC - g → EV_τ=NOPAT * (1-θ)

WACC - g (2.6) Furthermore, NOPAT is directly coherent with the return on Invested Capital (ROIC) after- tax since it is expressed as (Petersen et al., 2017):

ROIC =Invested Capital^NOPAT (2.7) Also, growth (𝑔) is dependent on ROIC as well as by what is reinvested in the firm (𝜃) and can be expressed as g = θ * ROIC. Hence, the reinvestment rate can be denoted as a function of ROIC and growth: θ =_ROIC^g (Berk & DeMarzo, 2017). Subsequently, the Enterprise Value in Equation 2.6 can be rewritten to a multiple as a function of ROIC:

EVτ

NOPAT = ^(1-θ)

WACC-g = ^%1-

g ROIC&

WACC-g = ^ROIC-g

WACC-g *_ROIC¹ (2.8) Finally, the EV/EBIT multiple can be derived, based on the coherence shown between NOPAT, EBIT, and the tax rate (t) initially in Equation 2.3:

EV_τ

EBIT=_WACC-g^ROIC-g * _ROIC¹ * (1-t) (2.9) As EBIT represents EBITDA * (1 - depreciation rate) the equation can be rewritten, and the expression of EV/EBITDA is obtained:

EV_τ

EBITDA=_WACC-g^ROIC-g * _ROIC¹ * (1-t) * (1-depreciation rate) (2.10) Further, EBITDA (or EBIT) could also be replaced by Sales, as it is a function of Sales * EBITDA margin (or EBIT margin). Thus, the EV/Sales multiple takes the following theoretical form:

(16)

Page 16 of 177 EVτ

Sales= ROIC - g WACC - g* 1

ROIC * (1-t) * (1-depreciation rate) * EBIT margin (2.11) From the examined derivation of EV/EBIT, EV/EBITDA, and EV/Sales from the DCF model, it is clarified how these multiples are functions of ROIC, WACC, and g representing profitability, risk, and future growth, respectively. All things being equal, the EV-based multiples will increase with higher ROIC while it will decrease with higher WACC as a result of the mathematical formulation. As the growth rate, g, is a product of ROIC and the reinvestment rate, 𝜃, an increase in g will, all things being equal, lead to higher multiples.

Also, the derivation shows, that all three EV-based multiples are negatively impacted by the tax rate, while the Sales- and EBITDA multiple also are negatively linked with the depreciation rate. Additionally, the EV/Sales multiple is a function of the EBIT margin, which has a positive impact, i.e. higher margins lead to higher multiple. These interconnections are a result of the fact that the multiples do not intrinsically take corporate tax rates, depreciation rates, and EBIT margins into account, respectively. Hence, in order for both the absolute valuation- (DCF) and the relative valuation methodology (all three multiples) to result in the same firm value, there must be no differences in those fundamental parameters between the identified comparable firms and the target.

Consequently, from the examined derivation, it has been shown that the classic present value approach forms the basis for the thought of peer selection. Namely, that in case the market value of both equity and debt approaches the present value of the expected FCFF based on the profitability, risk, and growth of the firm, such variables will explain a significant part of the variation in EV/Sales, EV/EBITDA, and EV/EBIT across firms. Therefore, it is these fundamental metrics, which peer groups should be selected upon. For that purpose, two different schools of thought related to peer selection are dominating the literature. The first approach argues that comparable firms should be found within similar industries, while the second approach argues that peers should rather be identified through similar financial key indicators. In the following section, the theoretical frame of the first schools of thought will be presented, while the second school of thought relates to the theoretical derivation illustrated in the above section.

(17)

Page 17 of 177

2.3 Industry approach

To assess the first school of thought, comparability based on industry-peers, this section will first clarify definitions of what constitutes an industry in theory. Secondly, the theoretical arguments of the interconnection between industry affiliation and profitability, risk, and growth will be outlined in order to interpret the relationship between industry and multiple valuation and why such affiliation could be used for peer selections.

2.3.1 Definition of industries

One of the most prevailing definitions of an industry originates from Michael E. Porter. He determines an industry as a set of firms related in terms of their products or services, thus, they constitute close substitutes serving the same customer needs. Such substitutability between products or services leads customers to be indifferent. Hence, cash is placed fairly randomly between firms within the same industry (Porter, 1979, 1998, 2008). However, such theoretical definition of industries can be perceived as rather vague as there is no clear distinction of to what degree firms must be substitutes, nor how substitutability is measured, which leads to blurred industry boundaries. Thus, when using empirical industry classifications, one should bear such limitation in mind: industry classifications do not fully reflect company information in terms of for example geography, various business activities nor distinctive competitive strategies serving different segments among firms with the same basic products or service offerings (Nightingale, 1978).

Numerous empirical industry classification systems have been developed by private and public organisations and are most often numeric schemes built hierarchically from broad to narrow classifications. Some of the most commonly known are SIC, NAICS, ICB, BICS, and GICS¹. Such standards for industries provide analysts, strategists, and investors with a joint and convenient basis for comparing companies (MSCI, 2020). Several studies have been conducted to compare some of the different industry schemes and determine which layer of industry codes accumulates the most comparable multiples. Consequently, various studies conclude that a more specific level of industry classifications is recommended as it has proven to yield the greatest comparability among peers. However, in 4-layer industry schemes, no significant

1SIC: Standard Industry Classification System, NAICS: North American Industry Classification System, ICB:

Industry Classification Benchmark, BICS: Bloomberg Industry Classification Standard, GICS: Global Industry Classification Standard

(18)

Page 18 of 177

improvements are found in the most specific layer compared to the second most specific (Alford, 1992; Cheng & McNamara, 2000; Liu et al., 2002; Weiner, 2005). The GICS is determined by (Bhojraj, Lee & Oler, 2003) as the most accurate industry scheme for valuation purposes compared to Fama French, SIC, and NAICS. First of all, rather than being focused on production and technology as SIC and NAICS, GICS has the advantage of being developed directly for professional investors based on a combination of business descriptions, revenues split, earnings analysis, and market perception (MSCI, 2020). Secondly, the categorization of firms in GICS is centralized and fulfilled by the credit rating agency Standard & Poor’s jointly with the finance company MSCI, whereas other industry schemes assign various data vendors to categorize firms which leads to less consistency (Bhojraj et al., 2003).

GICS is built on the classic hierarchical structure and consists of four industry levels ranging from (10) Sectors, (24) Industry Groups, (64) Industries, and ultimately (139) Sub-industries as the most specific categorization. All companies are assigned to a Sub-industry in terms of an 8- digit GICS code, which per definition belongs to the three levels above through composition of the code as seen in the illustrative example in Table 2.1. All firm’s GICS classifications are reviewed at least once a year to ensure no major redefinitions of a firm’s line of business have been made through a range of smaller steps (MSCI, 2020).

2.3.2 The interrelation between industry and value drivers for multiples

Industry affiliation reflects similarities in firms’ profitability, risk, and growth. That is ultimately the theoretical reasoning as to why peer selection can be based on industries. Generally, such inference is built upon the assumption, that firm’s performance is a function of the external environment it operates in.

The Structure-Conduct-Performance (SCP) paradigm developed in Industrial Organization Economics is the fundamental theory presenting causality between industries and firm performance in the long run (Bain, 1959). The fundamental line of thought is that the ‘Structure’

(19)

Page 19 of 177

of an industry determines a firm’s ‘Conduct’ i.e., how firms behave in terms of pricing, marketing, investments, and so on. Subsequently, this behaviour affects a firm’s ‘Performance’

in terms of market power, which determines the firm’s ability to set prices above marginal costs i.e., setting prices higher than under perfect competition². Thus, the industry structure is ultimately determining a firm’s profitability. Porter (2008) later elaborated on such causality as he bases the theory of ‘five forces’ on the premises of the SCP paradigm. He argues that five different features determine the industry structure: (1) the threat of new entrants and (2) of substitutable products, along with the bargaining power of both (3) suppliers and (4) buyers, which ultimately affects the (5) rivalry within an industry. For instance, entry barriers, like economies of scale, lower the threat of new entrants due to the necessity of large initial investments. Such industry structure affects the profitability, as economies of scale directly lower the production costs per unit, while it also limits rivalry in the industry, leading to more favourable competitive conditions with less pressure on prices. Hence, Porter (2008) concludes causality between the concentration of competition in industries, reflected in rivalry, and the gap between a firm’s revenues and costs.

Furthermore, risk factors are also convergent for firms within industries. In general, it is assumed that firms operating in the same industry are influenced by the same external risk factors, which cannot be controlled by the firm (Petersen et al., 2017). Examples of such could be political instability, GDP growth, social-cultural trends, technological development, or environmental conditions. Similarities arise within industries as some are more exposed to certain risks than others. For instance, depending on price elasticity, purchasing power influences industries differently as it is positively correlated to firms in industries related to luxury goods, negatively correlated to inferior goods while it is hardly correlated to normal goods (Berk & DeMarzo, 2017). Hence, within industries firm’s outputs are largely influenced by the same external risk factors as revenues show correlated tendencies in case of demand shocks, leading to somewhat similar uncertainty in future cash flows. Correspondingly, such similarity also shows on the input level as e.g. prices on raw materials or labour lead to convergent levels of costs. For instance, labour heavy industries are highly affected by the wage level, while capital-intensive industries are highly influenced by interest levels³. Thus, it is recognized in economic theory that the required return must vary across industries as reflected in industry betas (Damodaran, 2021).

2 In perfect competition firms do not have the power to influence prices, thus, P = MC in economic theory

3 Assuming high debt ratios

(20)

Page 20 of 177

Finally, industry affiliation also shows similarities related to growth. Pioneering industries such as technology or biotechnology are characterized by a high growth level in general, while mature industries with large tangibles such as real estate and utilities often yield lower growth (Berk & DeMarzo, 2017). Also, external risk factors are affecting growth differently depending on industries. For instance, firms operating in renewable energy are highly affected by environmental legislation and socio-cultural trends as consumer awareness. Regardless of industries, it is generally accepted in theory that no firms can outperform the total growth in the world economy in the long run (Petersen et al., 2017).

With that, there are evidently numerous theoretical arguments interpreting the coherence between industry on one side and profitability, risk, and growth and thereby ultimately future cash flows leading to correlated valuations on the other side. However, it should be noted that many counterarguments also exist as firms are not only affected by industries but also the specific markets and segments they are serving, as well as company-specific conditions (Petersen et al., 2017). For instance, such acknowledgment is seen in economic theory, as the required return is not only dependent on an industry beta but also alpha⁴ which on the other hand reflects the risk related to the specific firm (Damodaran, 2021). Furthermore, industry betas are ultimately adjusted for firms’ capital structures as debt yields higher risk than equity, hence, higher required returns. Several theories discuss such capital structures and whether they depend on the industry or the specific firm. The general arguments are that firms within the same industries can converge towards similar debt ratios in the long run as for instance industries characterized by high R&D are likely to have lower debt levels as opposed to capital- intense industries with high debt levels. However, capital structure is also argued to be firm- specific as loan terms such as maturities and interest varies as well as exposure to e.g. currencies vary from firm to firm. Better loan terms could for instance be related to factors such as the company size, as large firms are less risky due to greater diversification in projects and real options. Also, large firms tend to have better access to capital markets and are more liquid (Berk

& DeMarzo, 2017).

4 Industry beta is industries’ sensitivity to market changes, while alpha is the excess return which cannot be

explained by the market or random fluctuations

(21)

Page 21 of 177

3. Literature review

In this chapter, literature assessing peer selection methods for multiple valuation will be presented, since this constitutes the main implementation issue examined in this study. In Section 3.1, the two schools of thought which are dominating the literature, as described in the theoretical foundation, will be presented. To assess the first school of thought, the two empirical studies by Alford (1992) and Cheng & McNamara (2000) are examined initially in Section 3.1.1 as both studies argue in favour of peer selection based on industry. On the other hand, Section 3.1.2 exhibits the second school of thought which argues in favour of a fundamental approach since industry do not necessarily capture the underlying value drivers properly (Bhojraj & Lee, 2002; Dittmann & Weiner, 2005; Herrmann & Richter, 2003; Nel & le Roux, 2015; Serra &

Fávero, 2018). Subsequently, the original paper from Knudsen et al. (2017) proposing the SARD approach as a fundamentals-based selection method is presented in Section 3.2. Finally, Section 3.3 shortly presents literature assessing other implementation issues, besides peer selection, related to multiple applications in practice.

3.1 Literature on peer group selection

3.1.1 Evidence in favour of peer group selection on industry

Alford (1992) empirically examined the accuracy of the equity-based multiple P/E (price- earnings) when peers are selected based on industry, risk, and earnings growth. The quoted paper performs a cross-sectional analysis in the years 1978, 1982, and 1986 on NYSE, ASE, and OTC firms by comparing the predicted stock price from peer groups to its actual observed price in the market. For such predictions, Alford (1992) identifies peers based on SIC codes, ROE and Total Assets applied both as individual and as pairwise selection variables. SIC codes are required to include at least six firms per industry to generate peer groups, while for ROE and Total Assets 2% of the firms closest to the target is chosen as peers for the variables individually while 14% is selected when the variables are used pairwise, corresponding to 30 peers in total.

Based on absolute percentage errors, Alford's (1992) empirical research suggests that industry alone or a combination of ROE and Total Assets yields the most accurate results for peer

(22)

Page 22 of 177

selection. Application of ROE or Total Assets (as proxies for growth and risk, respectively) is non-beneficial on an individual basis as neither of them by themselves captures as much information as industry classification does. Also, neither of them is marginally useful when they are combined with industry. Thus, Alford (1992) concludes that while ROE and Total Assets are able to explain cross-sectional differences in P/E multiples when they are combined, industry is capable of catching the same information on its own.

Additionally, the study examines long-term growth forecasts by I/B/E/S⁵. Combined with industry, such growth forecasts are indistinguishable from using industry alone, hence, it does not contain information not already captured by industry classification. The accuracy of industry is examined further, as Alford's (1992) results suggest that 3-digit SIC-codes are as accurate as 4-digit. However, both 3- and 4-digit codes yield significantly more accurate valuation predictions compared to using fewer digits, i.e. broader industry classifications are less accurate. Finally, the study implies that valuation accuracy increases with firm size, as prediction errors are reduced for all selection variables when larger firms are examined compared to smaller firms.

Cheng & McNamara (2000) performed a similar empirical study as Alford (1992) since they examine how much cross-sectional variance in P/E multiples is explained by industry, ROE, and Total Assets, individually and combined. However, as opposed to Alford (1992) they applied 4-digit SIC codes and performed the valuation on a larger scale using data from 1973 to 1992 for all US-listed firms leading to 30,310 observations. Furthermore, Cheng &

McNamara (2000) introduced the P/B (price-to-book) multiple to investigate the importance of book value, both examined individually and combined as a P/E-P/B valuation approach.

Based on absolute percentage errors, Cheng & McNamara (2000) support Alford's (1992) findings as industry is the best performing selection variable on a stand-alone basis for both P/E and P/B multiples. However, opposed to Alford's (1992) results, both multiple’s accuracies are significantly improved when industry is combined with ROE. Hence, ROE captures information upon growth which is not reflected in the industry. Further, it is suggested in the quoted empirical study that P/E multiples yield better benchmarks for valuation compared to P/B multiples, indicating that earnings are more important than book value as a single number

5 Institutional Brokers Estimates System

(23)

Page 23 of 177

firm valuator. However, the examination of a P/E-P/B valuation approach shows that a combined multiple is the most accurate, which implies that both earnings and book value contain relevant information for firm valuation, thus, they are not perfect substitutes. For the combined P/E-P/B method, industry affiliation alone performs the most accurate predictions as neither a combination with ROE nor Total Assets yields distinguishable results.

Hence, both Alford (1992) and Cheng & McNamara (2000) concludes that industry affiliation is the most accurate selection variable to identify peer groups for multiple valuation. However, Cheng & McNamara's (2000) extended study confines the sovereignty of industry as it is the most accurate approach using a combined P/E-P/B multiple, while a combination with ROE yields lower prediction errors for P/E and P/B individually.

3.1.2 Evidence in favour of peer group selection on fundamentals

As opposed to Alford (1992) and Cheng & McNamara (2000) various studies find that comparable firms based on fundamentals lead to more accurate valuations than industry. In the following, Bhojraj & Lee (2002) and Nel & le Roux (2015) will be presented initially in Section 3.1.2.1 as both studies examine peer selection methods on an individual market. On the contrary, both Herrmann & Richter (2003), Dittmann & Weiner (2005), and Serra & Fávero (2018) all investigate how the selection methods perform relative to one another when applied on cross-country peer pools. Those studies will be presented in Section 3.1.2.2.

3.1.2.1 Individual market approach

Similar to Knudsen et al. (2017) examining the SARD approach, which will be presented in Section 3.2, Bhojraj & Lee (2002) investigate peer selection methods on a sample solely consisting of US firms, i.e. an individual market. Similarly, Nel & le Roux (2015) investigates optimal peer group selection on an individual market, however, their sample consists of South African firms, a relatively small market compared to the US.

Bhojraj & Lee (2002) revise the idea of selecting peers based on industry affiliation and develops an approach for selecting firms based on proxies for expected profitability, risk, and growth.

Their study is based on US firms from S&P 1500 in the period from 1982 to 1998. Through cross-sectional regressions based on eight proxies, including industry-adjusted growth forecasts, book leverage, ROA, and ROE, they regress a ‘warranted multiple’ for EV/Sales and P/B.

(24)

Page 24 of 177

The ‘warranted multiple’ is predicted for each target firm and subsequently used to select peers based on the relative closeness to the target. The estimations of regressions show that the six strongest variables for predicting the multiples are Indevs, Adjpm, Losspm, Adjgro, Rnoa, and R&D⁶. Bhojraj & Lee (2002) find, contrarily to Alford (1992) and Cheng & McNamara (2000), that peers selected based on ‘warranted multiples’ offer significant improvements in the valuation compared to peers selected on industry affiliation and size respectively. Furthermore, they test whether combining a model using industry constrained peers selected on the basis of their ‘warranted multiple’, i.e. a combination of fundamentals and industry, lead to more accurate valuation predictions. The quoted study finds that the prediction errors are marginally lower for a combined approach. Hence, the main improvements found, stems from the pure industry compared to a fundamental approach, as the inclusion of the ‘warranted multiple’

increases the predictive power by far.

Furthermore, Nel & le Roux (2015) also examine the ‘horse race’ between selection methods based on fundamentals compared to industry affiliation. The sample consists of firms in South Africa in the period from 2001 until 2010. The fundamentals applied are ROE, Total Assets, and Historic Revenue Growth which serve as proxies for profitability, risk, and growth. The variables are used individually as well in combinations of two. The industry peer groups are created from four different layers of industry classification. The model is based on Principal Component Analysis biplots and monoplots, which assess multiple valuation performances for 16 price-multiples within five categories including earnings, assets, revenue, dividends, and cash flow. The empirical results of the quoted study support the findings of Bhojraj & Lee (2002), as the prediction accuracy is greater for the majority of the applied multiples when comparable firms are selected based on fundamentals rather than industry. When assessing whether a single fundamental variable, i.e. ROE, Total Assets, or Revenue Growth, is better than industry membership the results show a rather ambiguous pattern across all 16 multiples. However, by combining the fundamental variables by groups of two, the valuation accuracy significantly increases, outperforming industry, but still dependent on the specific multiple in use. Evidently, the empirical results from the research show that valuation precision depends on the peer group variables applied to a specific multiple, hence, a consistently superior selection method is not

6 Description of the variables in the listed order: Indevs: harmonic mean of EV/Sales for all the firms with the same two-digit SIC code. Adjpm: the industry adjusted profit margin. Losspm: a dummy, where DUM is 1 if Adjpm is less than or equal to zero, and 0 otherwise. Adjgro: industry/adjusted growth forecasts. Rnoa:

return on net operating asset. R&D: total research and development expenditure divided by sales.

(25)

Page 25 of 177

found. Thus, the fundamentals applied as selection variables should be chosen based on the multiple used for valuation.

3.1.2.2 Cross border approach

Conversely to the above-mentioned studies, Herrmann & Richter (2003), Dittmann & Weiner (2005), and Serra & Fávero (2018) examine methods of selecting comparable firms across country borders, rather than considering individual markets. Herrmann & Richter (2003) investigate the accuracy between selecting comparable firms chosen by industry, fundamentals, and a combination of the two. The sample is based on 524 largest US firms supplemented with the 830 largest European firms⁷ with the period of analysis ranging from 1997 to 1999. The variables used in the fundamental approach are based on the theoretical appropriate factors derived for each of the multiples applied including P/E, P/B, EV/IC, EV/EBIT, EV/EBITDA, and EV/Sales. The quoted study shows that higher prediction accuracy can be achieved if peers are selected based on relevant fundamentals, in contrast, to solely industry classifications by SIC codes. For instance, it is seen for the P/E multiple that comparable firms selected solely on the basis of long-term growth forecasts for EPS or ROE lead to significantly higher prediction accuracy than peers selected by SIC codes alone. The quoted study also tests a combination approach but finds, in contrast to Bhojraj & Lee (2002), that an additional control for industry membership does not increase the precision of the multiples. This indicates that when applying SIC codes, industry classification does not contain superior information to what is already controlled for by the fundamentals. This finding also holds for less theoretically appropriate fundamentals, such as historic revenue growth which is similarly better on a stand- alone basis rather than combined with industry. Furthermore, when Herrmann & Richter (2003) examine the relative accuracy of the different multiples, the results suggest that EV/EBIT, EV/EBITDA, and P/E lead to better prediction accuracy than P/B, EV/IC, and EV/Sales under the fundamentals approach. Additionally, EV/Sales appear to be meaningless if only an industry criterion is used.

Dittmann & Weiner (2005) similarly investigates the valuation accuracy between selection methods based on fundamentals compared to industry affiliation for the EV/EBIT multiple but extend their study covering firms from a broad global sample of OECD countries. Their analysis

7 Based on market capitalization at the end of 1998

(26)

Page 26 of 177

covers the period from 1993 to 2002 and considers three comparable pools: country, region⁸ , and OECD. Five comparable selection variables are examined: market⁹, industry¹⁰, ROA, Total Assets as well as a combination of ROA and Total Assets. For each possible combination of the peer pools and selection variables, absolute prediction errors are calculated for all firms in the respective years. These prediction errors are pooled across years to identify the optimal selection method for each individual country. The empirical results find that selecting peers based on ROA on a stand-alone basis outperforms both industry affiliation and Total Assets, respectively. Whether it is ROA or a combination of ROA and Total Assets yielding the most accurate predictions depends on the specific country and comparable pool. However, for the US, UK, and Ireland, ROA and Total Assets combined lead to the smallest prediction errors on average compared to solely using ROA. Contrarily, for the remaining countries, the improvement is only marginal and insignificant, reflecting that a combination of fundamentals is not superior to using a single fundamental. This suggests that the significancy of selection variable might change across country borders. Furthermore, Dittmann & Weiner (2005) evaluate the optimal peer pool, and their findings suggest that peers should be chosen within the same country for the US, UK, Denmark, and Greece. However, for the remaining European countries, cross-border peer pools yield more accurate multiple predictions.

Evidently, the quoted study finds that the accuracy of selecting comparable firms by industry deteriorates during the ‘new economy boom’, indicating that the SIC industry classification cannot separate the firms from the ‘new economy’ from the ‘old economy’¹¹ firms.

Similar to Nel & le Roux (2015), Serra & Fávero (2018) examines a small market, Brazil, however, they apply a cross-border perspective for peer selection rather than examining a single market peer pool. The study examines the variances between multiples of firms in a range of scenarios including variance over time, within the same industry, between different industries, and lastly between different countries. The analysis period ranges from 2011 until 2014 with peer pools consisting of firms from Brazil (home-country) and the US (cross-border).

Furthermore, the quoted analysis is based on two different selection criteria: industry affiliation

8 Defined as 15 European Union member states

9 All sample firms except target

10 Based on SIC

11 New economy: high-growth industries that are on the cutting edge of technology and believed to be the driving force of economic growth and productivity. Old economy: blue-chip sector that enjoyed substantial growth during the early parts of the last century as industrialization expanded globally (Nel & le Roux, 2015)

(27)

Page 27 of 177

(using SIC) and similarities in fundamentals. The study examines eight different multiples including EV/Sales, EV/EBITDA, EV/EBIT, P/E, and P/B. The empirical results show that there are no single selection criteria that favours all multiples. The fundamental- versus industry- based affiliation is analysed in the fourth quarter of 2014, to where it is found that higher prediction accuracy for valuating Brazilian firms is achieved through a fundamental approach.

Looking at peer pools from the US and Brazil, the study finds that the same variables are not significant in both countries, which evidently makes it more difficult to form peer groups across borders with economic fundamentals. Thus, Serra & Fávero's (2018) findings suggest that the explanatory power of fundamentals for firm valuation is country-specific.

Summary of literature in favour of fundamentals

Common for all the preceding studies examined in Section 3.1.2.1 and 3.1.2.2 is that applying fundamentals in peer selection provides significantly better prediction accuracy in valuations compared to a selection based on industry alone. The fundamentals used across the quoted studies are all proxies for the three key value drivers, i.e. profitability, risk, and growth stemming from valuation theory. The distinguishable factors between the quoted studies are the samples examined and the combination of fundamentals and valuation multiples. Bhojraj & Lee (2002) and Herrmann & Richter (2003) commonly address the valuation accuracy when selecting peers based on a combination of fundamentals and industry, as opposed to solely investigating the difference between those two approaches. The studies show somewhat different results, however, the methodology between them differs as well. Bhojraj & Lee (2002) find that a combination approach achieves a higher level of prediction accuracy, contrarily to Herrmann

& Richter (2003), who find that an approach based on fundamentals with an industry criterion does not capture additional information in valuations when the economic fundamentals already reflect profitability, risk, and growth. Following the topic of fundamentals, the best performing variable somewhat varies in between the preceding studies. Evidently, what stands out, is that a combination of fundamentals is better than only using one single proxy (Bhojraj & Lee, 2002;

Herrmann & Richter, 2003; Nel & le Roux, 2015). No specific recurring fundamental outperforms others, however, Bhojraj & Lee (2002) find that growth forecasts are among the more important variables when predicting valuations. The evidence is supported by Herrmann

& Richter (2003), who also suggests that long-term growth forecast variables perform better.

Finally, when comparing the results from an individual market to cross-border, it is evident that

(28)

Page 28 of 177

the same fundamentals are not significant across borders, thereby making the selection of comparable firms more difficult across borders, when using a fundamentals approach, compared to an individual market (Serra & Fávero, 2018).

3.2 The SARD approach

Knudsen et al. (2017) endorse the favouring of fundamental peer selection since valuation estimates SARD using ROE, Net Debt/EBIT, Size, EPS growth, and EBIT margin as proxies for profitability, risk, and growth yields more accurate predictions compared to using industry affiliation as a proxy.

The SARD approach is a peer selection method that determines how similar companies are based on a range of selection variables consisting of optional fundamentals. First, all companies are ranked for each variable from highest to lowest relative to each other based on the chosen fundamentals. Subsequently, the differences between each target and the peer pool’s ranks are calculated and summed across all selection variables. Lower SARD values indicate fewer differences between a target and a peer, i.e. greater similarities among the chosen fundamentals, thus peers are selected based on the least sum of rank differences. As SARD is based upon rank differences relative to the sample rather than a specific target, and as the rank differences are measured in absolute values, several peers can appear with the same score relative to a target.

In those cases, when the model uses a fixed peer group size, the peer is selected randomly between those with the same SARD scores. This will be illustrated later in the methodology section. In its general form, the matrix for each target and potential peers can be expressed as:

SARD_i,j = /r_X,i- r_X,j/ + /r_Y,i - r_Y,j/+…+/r_Z,i - r_Z,j/ (3.1) Equation 3.1 indicates the sum of absolute rank differences between company 𝑖 and company 𝑗, with 𝑟_",$ representing the rank of company 𝑖 for the selection variable X, while 𝑟_",% is the corresponding rank of company 𝑗 for variable X, and so forth (Knudsen et al, 2017).

In Knudsen et al.'s (2017) study and derivation of SARD, the authors examine its usefulness on a cross-sectional sample of US firms from the S&P 1,500 index with valuations performed on a yearly basis from 1995 until 2014. SARD’s performance is measured on four different multiples:

P/E, P/B, EV/EBIT, and EV/Sales, where a randomly selected peer group within GICS