Master Thesis
The Relationship between Enterprise Valuation Multiples and Size Effects.
Alexander Barge
July 2012
Abstract
This study analyzes whether enterprise valuation multiples should be adjusted for size effects. Three enterprise valuation multiples: EV/EBITDA, EV/EBIT and EV/Sales are researched for 2295 U.S. firms over the period 2000-2010. The results of the simple tests indicate a significant positive relationship between enterprise valuation multiple and size. However, the dated panel regression results and the results of the OLS regressions do not confirm the fundamental key value driver formula. As such, it is difficult to assess the validity of the relationship between size and enterprise valuation multiples.
The Relationship between Enterprise Valuation Multiples and Size Effects.
University of Groningen Faculty of Economics and Business
Department of Economics, Econometrics and Finance Msc Business Administration – Finance
Author: Alexander Barge
a.h.j.barge@student.rug.nl
Student number: 1545221
Supervisor: dr. ing. N. Brunia
Table of Contents
1. Introduction 4
2. Valuation background 8
2.1 Key concepts in valuation 8
2.2 Enterprise value and size 10
2.3 Valuation multiples and size 12
2.4 Hypotheses 17
3. Methodology 20
3.1 Bivariate analyses of the enterprise valuation multiples 20
3.2 Dated panel regressions 21
3.3 Yearly OLS regressions 23
4. Data 24
4.1 Sample selection 24
4.2 Dependent variables 25
4.3 Independent variables 26
4.4 How is dealt with outliers? 29
5. Results 31
5.1 Bivariate analyses 31
5.2 Dated panel regression results 35
5.3 Yearly OLS regression results 38
6. Conclusion 41
6.1 Summary and main findings 41
6.2 Limitations and suggestions for further research 42
References 44
Appendices
Figure A1 EV multiples and the U.S. Treasury Bill over the years. 47 Table A1 Descriptive statistics of the three multiples over
the years 2000 – 2010 and total sample. 48
Table A2 Descriptive statistics of the independent variables over the period 2000 – 2010 and total sample. 49 Table A3 Correlation matrices of the dated panel regressions 50 Table A4 Correlation matrices of yearly OLS regressions 51 Table A5 Results of yearly OLS regressions 52 Table A6 Dated panel regression results with size 53
measured as total assets
1. Introduction
Valuation based on multiples is a relative valuation metric often used by investment bankers and professionals operating in the corporate finance and M&A sector. The valuation metric is used to estimate the value of a company by comparing it to the values assessed by the market for similar or comparable companies, controlling for any differences between the company and the so-called peer group or benchmark that might affect the multiple. The search for comparable companies to include in a peer group is always a challenge since no two firms are identical and firms in the same business can still differ on, for example, size (e.g. market capitalization), profitability, leverage, risk and/or growth potential.
This study analyzes whether valuation multiples are related to size effects after controlling for expected profitability, growth and risk, by making use of simple tests and regression analyses. If this study shows a significant relationship between valuation multiples and size effects, then practitioners like Koller et al. (2010) should adjust their practices. Also, professionals in the industry should take size effects into account when selecting comparable companies.
The relationship between enterprise value and size effects has been researched extensively in the past, for example by Banz (1981), Titman and Wessels (1988), Reinganum (1990) and King and Segal (2008). The contribution to the existing literature is that this empirical study makes use of recent data. The use of recent developments (internet, increased regulation resulting in increased transparency and highly volatile stock markets) could have a significant impact on the relationship between size effects and enterprise value. This is because the investor community has increased access to (financial) information of public companies and information asymmetry in theory is thereby potentially reduced.
higher compared to enterprise multiples of both smaller and larger U.S. companies in terms of market capitalization.
Figure 1 – Enterprise Valuation Multiples versus Market Capitalization
Figure 1 shows the relationship between three different enterprise valuation multiples and firm size as measured by market capitalization (in USD million). Figure 1-A is based on the data provided by Damodaran on his website. This dataset includes 5928 U.S. firms with data as of January 2011. Figure 1-B is based on the dataset used in this study which included 2295 U.S. firms. Similar size classes as Damodaran are used. Multiples are calculated annually over the period 2000-2010. 0 5 10 15 20 25 < 1 0 10 -20 20 -40 40 -100 100 -250 250 -500 500 -1000 1000 -2500 2500 -10000 >10 0 0 0 Mutiple Value USD m
EV / EBITDA EV / EBIT EV / SALES
0 2 4 6 8 10 12 14 < 1 0 10 -20 20 -40 40 -100 100 -250 250 -500 500 -1000 1000 -2500 2500 -10000 >10 0 0 0 Mutiple Value USD m
EV / EBITDA EV / EBIT EV / SALES
Figure 1a Figure 1b
The two graphs in Figure 1 show a different relationship between various enterprise valuation multiples and market capitalization (as measure of firm size). Figure 1-A is based on the data of Damodaran’s website1 and shows that mid-sized companies earn
higher enterprise multiples compared to smaller and/or larger companies. Damodaran provides no explanation for this relationship. The question rises whether the peak in Figure 1-A is caused by size effects. If this holds, then practitioners should adjust their practices. Figure 1-B is based on the dataset compiled for this paper and provides a different view on the relationship between enterprise valuation multiples and size effects. This is because each of the three enterprise valuation multiples are positively related to market capitalization. The different results can be explained due to the usage of different datasets. The dataset of Damodaran includes 5928 U.S. firms measured on one specific moment in time while the dataset for this paper includes 2295 U.S. firms, measured over a multiple year period. The fact that the results, as shown in Figure 1,
are different does not affect the relevance of the research question. In both cases, the graphs indicate a relationship between enterprise valuation multiples and size effects.
In this research three Enterprise Valuation (EV) multiples are considered, which are: Enterprise Value/Earnings Before Interest Taxes Depreciation and Amortization (EV/EBITDA), Enterprise Value/Earnings Before Interest Taxes (EV/EBIT) and Enterprise Valuation/Sales (EV/Sales). The rationale to select these three valuation metrics is the frequent usage of these multiples in the industry and the opportunity to compare the result to the analysis of Damodaran since the input variables are similar.
This research includes 2295 U.S. firms of the Russell 3000 index, which are analyzed over an 11-year historical period (2000-2010). The rationale to select these companies is because the Russell 3000 index provides the most complete picture of the U.S. economy.
Three types of tests are conducted to analyze the relationship between the selected enterprise multiples and size effects and are described below. Results for each test are briefly described as well:
1. Kruskal-Wallis tests are performed in which the dependent variables are split up into ten deciles for each of the independent variables, which are tested. Results of this test shows that the observed valuation multiples are significantly related to the market capitalization of companies.
2. Dated panel regressions are performed with the selected enterprise valuation multiples. Results of this test do not confirm a statistically significant relationship between enterprise valuation multiples and size after controlling for profitability, growth and risk.
Based on these results, even though the outcomes of the different tests are not supportive to one another, one could argue that from a practitioner’s point-of-view it is recommended to adjust the peer group for size effects in order to compile a better suited peer group, which should ultimately result in increased accuracy in the valuation of firms. The results also support the findings, up to a certain level, of Koller et al. (2010) who state that comparables should be selected based on the same industry with similar return on invested capital, growth, weighted average cost of capital and operating tax rate.
Although some evidence of a relationship between size and the value of enterprise multiples is found, these results should be interpreted with care. This, because the data used in this study does not confirm the fundamental key value driver formula. A possible explanation is that historical data is used, while the key driver formula requires forward looking data as input. A possible opportunity for future research in the area of valuation is therefore to mimic this study while making use of forward looking data.
2. Valuation Background
This section discusses relevant literature. In the first sub-section, some key concepts related to valuation will be outlined. Secondly, existing literature regarding enterprise value and size effects will be discussed.
2.1 Key concepts in valuation
Koller et al. (2010) demonstrate the so-called ‘key value driver formula’, an equation that captures the essence of valuation in practice. The key value driver formula is stated below (1):
(1)
Where NOPLAT denotes net operating profits less adjusted taxes, RONIC is the expected rate of return on new invested capital, G implies the rate at which the company’s NOPLAT and cash flows grow each year and WACC denotes rate of return that investors expect to earn from investing in the company, the weighted average cost of capital.
According to Koller et al. (2010) two value drivers exist: expected return on new invested capital and revenue growth. Comparing these drivers is only valid when you look at companies from similar industries and countries. This is due to the fact that peers in the same industry have similar risk profiles and consequently have a similar cost of capital. Companies in different countries face different legal and accounting rules, which make it hard to compare firms from different countries.
to understand and easier to present to the average investor compared to a valuation based on multiples. The last argument Damodaran (2002) mentions is that relative valuation is much more likely to reflect the current mood of the market, since it is an attempt to measure relative and not intrinsic value.
Two types of valuation multiples exist: enterprise valuation multiples and equity valuation multiples. Equity valuation multiples are not taken into account in this research, since equity multiples are affected by differences in capital structure. According to Koller et al. (2010), equity multiples are distorted by capital structure and non-operating gains and losses. Enterprise valuation multiples might be affected by capital structure, but this is only the case when capital structure affects operating performance and investment decisions. Although the focus of this research is on enterprise valuation multiples, there is relevant related research conducted in the field of equity valuation multiples, which will be discussed below.
The study of Kaplan and Ruback (1995) makes one other important distinction in multiples: practitioners often value companies using trading or transaction multiples. In a multiple valuation, a ratio or multiple of value relative to a performance measure is calculated for a set of guideline or comparable companies. First of all, the ‘comparable company analysis’, uses a multiple based on the trading values of the firms in the same industry as the firm is being valued. The second type of multiple analyses is the ‘comparable transaction analysis’, which uses a multiple from companies that were involved in a similar transaction to the company being valued. The third type is the ‘comparable industry transaction analysis’, which uses a multiple from companies in the same industry that were involved in a similar transaction to the company being valued. As stated in the introduction, in this research three enterprise valuation multiples are dealt with. In order to compare the results of this study with the findings of Damodaran: EV/EBITDA, EV/EBIT and EV/Sales are used as trading multiples. The reason to focus only on trading multiples originates from the data availability and the comparability with other studies.
between enterprise value and size. As such, the next sub-section will discuss relevant literature on the relationship between enterprise value and firm size. Thereafter, in sub-section 2.3, the focus will be on valuation multiples and firm size.
2.2 Enterprise value and size
The relationship between enterprise value and size has been researched extensively.
Some authors find that small firm are higher valued. For example, Banz (1981) examines the relationship between the stock returns and total market value of NYSE common stocks. The author finds that, over a forty-year period, smaller firms have had higher risk adjusted returns compared to larger firms. Furthermore, Banz (1981) states that the size effect shows a misspecification of the capital asset pricing model (CAPM). This limitation of the CAPM is underlined by the results of Fama and French (1992). With their study, Fama and French (1992) provide an overview of the limitations of the capital assets pricing model, which is characterized as a milestone within the research related to the CAPM. One of the limitations Fama and French (1992) find is that beta is unrelated to stock returns. Furthermore, the authors find that smaller firms provide relatively high returns and that returns are relatively high on stocks with low market to book ratios.
Moreover, Fama and French (1993) find that firm size, based on market capitalization of the equity, is a factor that explains differences in average stock returns and bonds. They conduct research into the U.S. stock market (NYSE, Amex and NASDAQ) the period 1963 – 1991. Taking their findings into account, one would expect that there might be a negative relationship between size and enterprise multiples.
In line with Banz (1981), Hawawini and Keim (2000) analyze the stock returns over a period of thirty years and measure size with the use of market capitalization. Hawawini and Keim (2000) confirm the finding of Banz (1981) that there is a clearly negative relationship between firm size and average stock returns. Similar to Banz (1981), Hawawini and Keim (2000) also argue that it is unknown whether size is responsible for the “size effect“.
Besides a negative relationship between firm size and enterprise value, other authors argue that small firms, everything else being equal, have a relative lower value compared to larger firms. Titman and Wessels (1988), for example, dispute that the cost of capital is negatively related to firm size, which is measured by the natural logarithm of sales and quit rates, the percentage of the industry’s work force that voluntarily leaves their jobs. The authors include quit rates, because large firms often offer wider career opportunities to their employees, resulting that large firms have lower quit rates compared to small firms. Furthermore, Titman and Wessels (1988) share the opinion that small firms pay significantly more for their capital than large firms, because smaller companies face higher transaction costs of issuing long-term debt and equity compared to larger companies. Also, they find empirical evidence that small firms use significantly more short-term financing than large firms. Because of their short-term funding these small firms are highly sensitive to economic conditions that have less effect on larger firms, which are less leveraged and which have longer debt maturities. The preference for short-term financing for small firms would lead to a higher weighted cost of capital. Moreover, a higher required rate of return on equity for small firms, all other things equal, results also to a higher weighted average cost of capital for these firms. Nonetheless, assuming the situation where all other things are not equal, it has to be taken into account that multiples need to be adjusted for firm size. Therefore, it would be expected that small companies with a higher weighted cost of capital, all other things being equal, have lower valuation multiples.
projects that would have a positive net present value at a low weighted average cost of capital. Therefore, the expected return on new investments is not independent of the weighted average cost of capital.
2.3 Valuation multiples and size
This sub-section presents research conducted in the field of valuation multiples. Table 1 presents an overview of the relevant articles which will be discussed below.
Alford (1992) studies the P/E multiple by comparing the predicted stock price with the actual stock price, the use of the actual stock price relies on the assumption that market prices correctly reflect fundamentals. Alford (1992) finds that industry membership, or a combination of risk and earnings growth, are effective criteria for selection comparable firms. He states that portioning industries by risk or growth does not improve valuation accuracy. Alford (1992) uses firm size, measured by total assets, as proxy for risk, because risk characteristics are likely to differ between small, closely-held, companies and large, publicly-traded, companies. He empirically studies the years 1978, 1982 and 1986 and includes beta as a control variable for the risks of the firms in one part of their analysis.
Table 1 – Relevant literature related to valuation multiples
Which type Sample Regression Measure of Classification Size effects
Author (year) EV / Equity Multiple analysed (years) analysis? size (industry) significant? Relevant results
Alford (1992) Equity Price/Earnings 1978, 1982,1986 No
Total assets 2% of sample (30
firms)
SIC codes
3 digits Yes
Valuation accuracy increases with the inclusion of firm size
Bhojraj & Lee (2002) Both Market/BookEV/Sales 1982-1998 Yes Market capitalization SIC codes2 digits Yes
They develop a so called "warranted multiple" for each firm and and identify peer firms as those having the closed warranted multiple
Cheng & McNamara (2000) Equity Price/Earnings
Market/Book 1973-1992 No Total assets
SIC codes
4 digits Yes
Large firms enjoy more valuation accurcy to indentify comparable firms Dittmann & Weiner (2005) EV EV/EBIT 1993-2002 No Total assets
5 firms closest
SIC codes
4 digits No
Comparables should been chosen from same country only
Henschke & Homburg (2009) Equity Price/EarningsMarket/Book 1986-2004 Yes Log total assets SIC codes 4 digits Yes
Differences between firms lead to systematic errors in value estimates of different multiples, adequately controlling for differences improves valuation
Kaplan & Ruback (1995) EV EV/EBITDA 1983-1993 Yes Log of trans-action value SIC codes2 digits No
Compare market value of highly leveraged transactions to discounted value of corresponding cash flow forecasts, valuations preform at least as well as multiples
King & Segal (2008) Both
Market/Book Price/Earnings
Tobin's q EV/EBITDA
1989-2004 Yes Log total assets 4 industry
groups Yes
They find a negative relation between firm size and EV/EBITDA multiple
Lie & Lie (2002) Both
EV/EBITDA EV/EBIT EV/Sales EV/Book value Price/Earnings Forward price/Earnings
1998 No Total assets SIC codes 3 digits Yes
These results are specifically true for financial firms
- EV/EBITDA multiple yields better estimates than the EV/EBIT multiple -EV/Sales multiple least accurate
Lui, Nissim & Thomas (2002) Equity
Earnings/Price Operation cash flow/Price
1982-1999 Yes N/A classificationIBIS industry N/A
Focusing on the composition of peer groups for companies in different countries, Dittmann and Weiner (2005) test the EV/EBIT multiple over the period 1993 – 2002. The authors analyze which selection criteria for comparable firms should be used in order to come up with the most accurate peer group. They conclude that the comparable firms should be chosen from the same country. Furthermore, Dittmann and Weiner (2005) state that the peer-group is not improved by looking at the industry membership or size based on total assets. The use of total assets as a measure of firm size is in line with Alford (1992) and Cheng and McNamara (2000).
are equal to each other. Thus, at low levels of leverage, leverage increases value and at high levels of leverage, additional leverage reduces value.
A general approximation is provided by Bhojraj and Lee (2002) in order to select comparable firms within a market-based research. The authors develop a so called ‘warranted multiple’ for each firm. Furthermore, they indentify so-called peer firms, the firms that have the closest warranted multiple. Bhojraj and Lee (2002) select comparable firms based on industry, size, profitability, growth and risk characteristics. They test these five variables with the use of an Ordinary Least Squares (OLS) regression analysis for the EV/Sales and Market/Book multiples.
Henschke and Homburg (2009) study, in line with Lui et al. (2002), the problem of differences between firms and the impact of valuations based on equity valuation multiples. With their paper the authors focus on to what matter additional firm-specific information is ignored by using industry-based multiples. Furthermore, Henschke and Homburg (2009) state that it is complicated to compose a peer group with similar characteristics to the firm that is valued, taking into account all characteristics that are relevant (i.e. profitability, growth, risk and industry). Their research includes the price/earnings- and market/book multiples over the years 1986 to 2004. Henschke and Homburg (2009) show empirically that differences between firms lead to systematic errors in the value estimates of different multiples with regression analyses. Size is included as a proxy for risk, small firms are considered to be riskier, thus should trade at lower multiples. They measure size by the natural logarithm of total assets. Henschke and Homburg (2009) find that, by performing a regression analysis, size has a significant effect in the situation where valuations are based on multiples. In addition, the authors state that deviations in risk, measured by leverage and size, seems to be less essential compared to deviations in expected (book) return on equity or growth. Henschke and Homburg (2009) find that adding industry membership as a selection criterion does not significantly reduces valuation errors.
related highly leveraged transactions. Based on their sample of 51 highly leveraged transactions that have been executed between 1983 and 1989, they find empirical evidence of a well-established relationship between the market value of highly leveraged transactions and the discounted value of the corresponding cash flow forecasts. Kaplan and Ruback (1995) also consider the relationship between implied risk premiums and firm size (measured as the logarithm of the transaction value). They conclude that there is no significant relationship between these two variables.
Lie and Lie (2002) research multiples that are used to estimate enterprise value. Their research includes only the year 1998. The authors find that the market to book value usually generates more precise and less biased estimates compared to the sales or earnings multiples. Precision is the standard deviation of the estimator. On the other hand, bias is the average difference between the estimator and the true value. Furthermore, Lie and Lie (2002) find that the EV/EBITDA multiple holds more precise and less biased estimates than the EV/EBIT multiple, except for the pharmaceutical companies.
Lui, Nissim and Thomas (2002) study the earnings to price multiple. They conclude that forward-looking earnings explain stock prices remarkably well. They make use of COMPUSTAT, CRSP and IBES summary files to collect data of the U.S. market (NYSE, AMEX and NASDAQ) over the years 1982 – 1999. For this reason, forward-looking data would be preferred to historical data. This finding is in line with the earlier work of Kim and Ritter (1999), who also use forward looking data in their analysis of the Market/Book and Price/Earnings multiples.
In addition, both Cheng and McNamara (2000) and Lui, Nissim and Thomas (2002) show that the use of earnings as a basis for multiples leads to more precise estimates than book values or sales.
(i.e. production methodology, distribution channels and research and development). By applying these recommendations the peer group will have similar ROIC, growth, weighted average cost of capital and operating tax rate. In addition, Koller et al. (2010) recommend to use the median above the average of the peer group when a multiple is chosen, in order to reduce the impact of outliers within the peers.
As can be seen above, many studies on enterprise valuation multiples have been performed. From the results of these studies can be concluded that the relationship between size effects and enterprise valuation multiples is, in some cases, significant. However, some other studies show no significance within the relationship between these variables.
2.4 Hypotheses
To summarize, existing literature shows that, when adequately controlling for differences between firms, valuation accuracy is improved considerably. It is important to note that the components of the key value driver formula are related to each other, but could also be related to differences in size. Based on the available literature the following research question is derived:
Are enterprise valuation multiples related to size after controlling for expected profitability, growth, firm’s risk and industry?
This research question leads to the following hypotheses:
H0: Enterprise valuation multiples do not depend on size after controlling for
profitability, growth, firm’s risk and industry.
H1: Enterprise valuation multiples do depend on size after controlling for
profitability, growth, firm’s risk and industry.
According to Koller et al. (2010), two key value drivers exist: Return On New Invested Capital (RONIC) and growth. These two value drivers will be used as independent variables in the regression analysis. As mentioned in the previous section, the findings of Banz (1981) and Titman and Wessels (1988) suggest that all valuation multiples should be adjusted for firm size. For this reason size is also included as an independent variable.
Moreover, Shalit and Sankar (1977) state that there is no ideal measure of firm size. They state that the decision for a certain size measure mainly depends on the purpose of the study. The authors provide three considerations for the selection of the most appropriate size measure. The first consideration is based on a priori economic information. Secondly, the authors mention practical considerations of data availability. The third consideration is related to statistical and estimation problems of the dataset. Taking into account these considerations and other empirical research related to enterprise valuation multiples, the market capitalization and total assets have been chosen as measures of firm size in this study. So, in line with both Damodaran2 and
Fama and French (1993) market capitalization is used as a measure of size. In addition, based on King and Segal (2008) a second measurement of size is used for the dated panel analysis, which is total assets.
Furthermore, for the dated panel regression analysis also the risk free rate is included as an independent variable. This is because a higher risk free rate leads to a higher cost of capital, which results in a lower valuation multiple.
According to Alford (1992), beta is used as a proxy for firm’s risk where King and Segal (2008) use leverage as a proxy for risk. For this reason both variables will be independently included into the regression, since beta and leverage could be correlated which will be further explained in section 3 of this paper.
Based on the key value driver and the other existing literature, the following relations between the enterprise valuation multiples and the different independent variables would be expected, as denoted in Table 2.
Table 2 – Expected signs for the regressions analysis of the three enterprise valuation multiples
Variable Expected sign Intuition
ROIC + Higher return on new invested capital leads to a
higher value, if growth is larger than zero.
Growth +
Higher sales growth, leads to higher revenues, when return on net invested capital is larger than the weighted average cost of capital
Size
+/-Inconclusive
(+) Koller et al. (2010) indicate large firms have higher credit rating, so less probability of default (-) King and Segal (2008)'s findings predict a negative relation between size and EV multiples
Risk free rate - Higher risk free rate, leads to a higher cost of capital, hence lower value.
Beta - Higher beta, means more risk, thus less value
Leverage
+/-Trade off theory:
3. Methodology
This section describes the methodology that is used to empirically test the hypotheses as mentioned in the previous section. The methodology section consists of three sub-sections. In the first sub-section, the sample will be split into ten groups that are tested to find possible significant differences related to size. The second and third sub-sections will show how the dataset is tested in the dated panel regressions and the yearly OLS regressions, respectively.
3.1 Bivariate analyses of the enterprise valuation multiples
In order to test whether differences in size have an impact on enterprise valuation multiples (EV/EBITDA, EV/EBIT and EV/Sales), the dataset is divided into ten size deciles. For each decile the corresponding median multiple is reported. Besides the size variable, the data is also split into ten deciles for four other variables (i.e. ROIC, growth, beta and leverage). These variables are known to be related to enterprise multiple values and allows to verify whether the results confirm the findings from prior empirical literature. As an example, growth is divided into ten deciles with decile 1 being the group with the lowest growth and decile 10 being the group with the highest growth.
Secondly, consistent with Banz (1981), the effect of size on the other variables is tested. The sample is divided into ten size deciles (based on market capitalization) and for each decile the corresponding median value of each variable is reported.
Thirdly, the dataset is divided into industry sectors, in order to investigate whether industry is an important variable to consider. Literature is inconclusive on the effect of industry with respect to enterprise valuation multiples. (i.e. Alford (1992), King and Segal (2008), Cheng and McNamara (2000) and Henschke and Homburg (2009)).
Appendix. If data is characterized by non-normality, a non-parametric test such as the Kruskal-Wallis test is more powerful in detecting subsample differences. This, because the test assumes that the population shapes are identical (i.e. originate from the same distribution), though not necessarily normal. When the Kruskal-Wallis test statistics are significant, the different variables could have a significant influence on enterprise valuation multiples. The use of the Kruskal-Wallis test is in line with the earlier research of Alford (1992).
3.2 Dated panel regressions
The above bivariate analysis is insufficiently accurate, because a bivariate analysis cannot explain whether the independent variables simultaneously have a significant influence on the dependent variables (i.e. the three enterprise valuation multiples). As such, to investigate whether size can explain differences in enterprise valuation multiples, a dated panel regression will be performed.
The dated panel regression model is as follows:
Where
α is the intercept term, β is a matrix with independent variables and control variables and ω being the random error term. The cross sectional error term, , has zero mean and is independent of an individual observation error term. , has a constant variance and is independent of the explanatory variables.
In order to test whether size has a significant impact on the enterprise valuation multiples, three different dated panel regressions are performed. The first model includes return on invested capital, growth and size (based on market capitalization). The second, adds the risk-free rate and either beta or leverage. In the third model the industry dummies are included.
The control variables that are used as a proxy for firm’s risk in the models are beta and leverage, which is in line with the existing literature. Beta is used in the study of Alford (1992) and leverage is used in the study of King and Segal (2008). The control variables beta and leverage are not simultaneously included in any model in literature. This is because beta and leverage could be correlated, since beta is partly dependent on the leverage of a firm3. Hence, when the leverage rises the company’s equity beta will rise.
Note that beta and leverage are estimated separately. This is done in order to prevent multicollinearity, despite the low correlation between the variables leverage and beta, as can be seen in Appendix Table A3.
Other concerns arise since the variables within the matrix βi might be (unexpectedly)
correlated. Table A3 in the Appendix reports correlations among the variables used in the regressions. None of the correlation coefficients exceeds the 0.7 ‘rule of thumb’ threshold level. The variables are low or moderately correlated and suggest that
multicollinearity is unlikely to bias the regression coefficients. In order to prevent perfect multicollinearity, Brooks (2008) argues that it is needed to exclude one of the dummies. This study excludes the industry dummy Telecommunications. This means that the coefficients of the dummies are all relative to Telecommunications. The correlation matrix for the dated panel regressions is depicted in Appendix Table A3.
Although, all variables used in the regressions will be defined in the Data section (Section 4), the use of the industry dummy will be explained below. Industry dummies are included, since industry is an important factor to consider with the use of multiples (i.e. Cheng and McNamara (2000) and Koller et al. (2010)). According to Cheng and McNamara (2000) different industries face different degrees of operating advantages that result in excess profitability. Therefore, a dollar invested in an industry is not independent of the industry in which it is earned. For this reason industry dummies are included.
3.3 Yearly OLS regressions
High yearly stock market volatility and volatility in profit (EBIT and EBITDA) of firms result in highly volatile multiples within the sample period (2000-2010). In order to remove all the time effects, yearly OLS regressions are used to test whether the results of the dated panel regression analysis hold through time. The use of regression analysis is in line with Bhojraj and Lee (2002). The OLS regressions are estimated by using the following specification. Yearly OLS regression model:
4. Data
This section discusses the data that is used. Firstly, the sample selection is outlined. Subsequently, sub-section two and three describe the dependent and independent variables. Finally, the elimination of outliers is explained in the fourth sub-section.
4.1 Sample selection
In order to test the hypothesis, the constituents of the Russell 3000 index, as of December 31st 2010 are used. The Russell 3000 index is built in 1984 to create a more
accurate and comprehensive set of equity indexes for the United States than there was before. The list of constituents is received from Russell. DataStream is used to collect annual financial information for each constituent. According to Koller et al. (2010) it is very important that every multiple is calculated in a consistent manner. The numerator (enterprise value) and denominator (EBITDA, EBIT or Sales) are based on the same underlying assets.
According to Lie and Lie (2002) the assets of financial firms are relatively liquid and are easier to value than nonfinancial companies. Combining financial and nonfinancial companies could bias the results. Therefore, financial companies are excluded from the dataset. The period 2000-2010 is selected since data availability before the year 2000 is limited. Although practitioners and scientific researchers prefer to make use of forward-looking financial data, this data is difficult to retrieve from the available resources. As such, this study makes use of historical data. When the data for a particular firm for a specific year variable is missing, the firm is included in the sample resulting in an unbalanced dated panel set. Table 3 shows how the dataset has been constructed. The total number of firms used in this research is 2295.
Table 3 – Data selection procedure
Table 3 - the number of constituents of the Russell 3000 index is equal to 2952 at 31/12/2010
Russell 3000 index Number of firms included
Total number of constituents at 31/12/2010 2952
Financial firms 600
No name and industry classification available 46
No enterprise valuation data available over the whole period 11
4.2 Dependent variables
In order to prevent misunderstandings of definitions of the three enterprise valuation multiples, each element of the multiples will be defined according to the definitions of DataStream4, [in the bracket the exact code in DataStream is displayed].
Enterprise Value is defined as Market Capitalization at the end of the fiscal year plus Preferred Stock plus Minority Interest plus Total Debt minus Cash. [WC18100]
Earnings before Interest, Taxes, Depreciation and Amortization (EBITDA) represents the earnings of a company before interest expense, income taxes, depreciation and amortization. It is calculated by taking the pre-tax income and adding back interest expense on debt and depreciation, depletion and amortization and subtracting interest capitalized. [WC18198]
Earnings before interest and taxes (EBIT) represents the earnings of a company before interest expense and income taxes. It is calculated by taking the pre-tax income and adding back interest expense on debt and depreciation and amortization and subtracting interest capitalized. [WC18191]
Sales represents gross sales and other operating revenue less discounts, returns and allowances. [WC01001]
These definitions are used when referred to the EV/EBITDA, EV/EBIT and EV/Sales multiples. These three multiples are used in the regressions for the four different models.
Table 4, at the end of this section, provides descriptive statistics of the three multiples, as well as the descriptive statistics of the other variables. The significant Jarque-Bera probabilities indicate that the data is non-normally distributed. As described in the methodology section, also non parametric tests are performed. Appendix Table A1 presents the annual descriptive statistics for each multiple.
4 DataStream Global Equity Manual
4.3 Independent variables
This sub-section describes the definitions of the independent variables used in this study.
Return on invested capital (ROIC)
Although Koller et al. (2010) recommend to use NOPLAT/Invested Capital in order to calculate the return on new invested capital (RONIC), those two variables are not available in the DataStream database. Therefore, RONIC will be proxied using the return on invested capital (ROIC), based on equation (2) of Damodaran (2002)5:
(2)
The EBIT [WC18191], and the book values of Net Debt [WC18199] and Equity [WC03995] are obtained from DataStream. The term, , in the above formula refers to the operating tax rate. Because tax rates should be related to the operating activities of each company, it is useful to calculate operating tax rates. These operating tax rates have been calculated for each firm for each year making use of this equation (3).
(3)
Reported Taxes (RT) [WC01451] and EBIT are retrieved from DataStream. Given that the following equation (4) should hold:
(4)
The term Interest & Other can be calculated and used in equation (3). The marginal tax rate is based on the U.S. Central Government Corporate Income Tax rate of the Organization for Economic Co-operation and Development (OECD). According to the OECD website6, this rate is 35 percent for the period 1997-2010. However, the tax rates
5 This equation is also available on the website of Damodaran: http://pages.stern.nyu.edu/~adamodar/. Section Background, Extended Glossary of Financial Ratios and Measures.
6 The website of the OECD:
differ across the different states of the U.S., which makes it even more difficult to obtain information for each firm, each year and each state specifically. To reduce complexity, it is assumed that the margin tax-rate is equal to 35%.
The ROIC that is used in the analysis is a historical three-year average. Thus the proxied ROIC for 2000, is based on the average ROIC’s of the years 1997-1999. If there is only one or two year of data available, then the available data is used (e.g. average of two years if only two observations are available over a period of three years).
Growth
In order to proxy the growth of each firm, the historical three-year average growth of sales [WC01001] is used. According to Koller et al. (2010) three-year average sales growth is used. When there is only one or two year(s) of sales data available these data are used, following King and Segal (2008). The use of historical data is not in line with the recommendations of Koller et al (2010) that use a consensus forecast of revenue growth. However, these consensus forecasts are not available in DataStream.
Size
Risk free rate
The historical U.S. Treasury bill rate with a maturity of 10 years is derived from the Federal Reserve website.7 This is in line with the recommendations that Damodaran
makes at his website.8 The pattern of the U.S. Treasury bill rate over the period
2000-2010 is presented in Appendix A1 (Figure A1.4). Beta
The annual raw beta for each firm is estimated by making use of weekly returns of each firm and the MSCI world index total return. The period 2000-2010 is used to estimate the betas for each year. In some cases there was no data available covering the whole year period. In such case, the beta is estimated over the period for with data availability. The Bloomberg’s adjustment has been applied over these raw betas in order to smooth the betas. The smoothing reduces the impact of extreme observations toward the overall average. The following equation (5) of Bloomberg is used to adjust the betas:
Adjusted Beta = 1/3 + 2/3 * (Raw Beta) (5)
This type of smoothing mechanism is applied because of Blume’s (1975) observation that betas revert to the mean.
Leverage
Leverage is defined as net debt/market capitalization of the equity at the end of the fiscal year. Both net debt [WC18199] and market capitalization of the equity [WC03995] are obtained from DataStream. Net debt is given in terms of book value while market capitalization is given in terms of the market value of equity. Financial theory suggests that the relationship between leverage and firm value follows an inverse u-shaped relation. As such, a squared term for the leverage variable is included to test for a non-linear relation.
In order to classify the different firms into industries, the Industry Classification Benchmark system is used.9 The Industry Classification Benchmark is a classification
7 The website of the Federal Reserve: http://www.federalreserve.gov/releases/h15/data.htm.
system categorizing companies and securities worldwide, in order to compare companies across the levels of classification and national boundaries. The classification for the different firms is derived from DataStream [ICBIC]. Although, literature frequently makes use of Standard Industrial Classification (SIC) codes, DataStream is not able to provide this type of classification.
4.4 How is dealt with outliers?
In this research, there has been dealt with outliers. Taking into account the existing literature and based on general economic sense, the following steps are taken to deal with the outliers in the dataset.
First, companies which make a loss (i.e. negative profit) are excluded from the dataset, because negative EBITDA and EBIT values would lead to negative multiples that do not make sense. According to Bhojraj and Lee (2002) it is very difficult to value loss making firms. In line with these authors and in line with Dittmann and Weiner (2005), negative EBIT and EBITDA firm-year observations are excluded from the dataset.
Secondly, only positive NET SALES are used. DataStream sometimes sets the value of NET SALES at zero, because they have no information on sales available. In order to deal with this issue, only the sales data with values larger than 0 have been used.
Thirdly, the upper value of the three multiples is limited to 30, in order to cope with a possible upward bias of the data set due to the removal of the negative values of EBITDA, EBIT and NET SALES. The limit is in line with the Damodaran website10 and
Macabacus website11.
Lastly, in line with prior research of Dittmann and Weiner (2005) and Liu, Nissim and Thomas (2002), both the multiples and all variables in the regressions are winsorized at a 1% - 99% interval over all observations for each variable in order to reduce the impact of outliers, within the dataset.
The descriptive statistics of the dependent and independent variables of the entire sample are presented in Table 4. The descriptive statistics of the dependent variables per year can be found in the Appendix (Table A1) The descriptive statistics of the independent variables per year are presented in the Appendix (Table A2).
Table 4 - Descriptive statistics of the dependent and independent variables of the entire sample
5. Results
In this section, the results of the research will be discussed. In the first sub-section, the results of the bivariate analyses are described. In the second sub-section, the outcomes of the dated panel analyses are presented. Finally, the results of the yearly OLS-regressions are discussed.
5.1 Bivariate analyses
Table 5 presents the results of bivariate analyses of the enterprise valuation multiples and their potential determinants. In Table 5, the variables return on invested capital, growth, size, beta and leverage are split up into ten deciles (from small to large). For each decile the valuation median multiple is shown. For each variable, the ANOVA test and the Kruskal-Wallis test are performed. The tests statistics of the ANOVA and Kruskal-Wallis tests are significant and consistent with each other. This means that the median multiple for each variable differs across the dataset.
Table 5 – Each variable classified in ten deciles.
In this table, each variable is split into deciles, ranked from smallest group to largest group. The median of the multiples are given for each decile. In the last two columns the ANOVA and Kruskal-Wallis test statistics are presented together with their significance.
As can be seen in Table 5, the return on invested capital (ROIC) does not have the predicted positive relationship with EV/EBITDA and EV/EBIT. The relationship between ROIC and these two multiples is a u-shaped relationship where a positive linear relationship is expected. For the EV/Sales multiple, the predicted positive relationship is confirmed. The second key value driver, growth, has the predicted relationship with each enterprise valuation multiple. However, for the EV/EBIT multiple the differences between groups are not significant. Focusing on the size variable, the value of the multiples increases with size. This finding is in line with Koller et al. (2010) who state that large firms have a higher credit rating and thus a smaller probability of default. The beta variable has a u-shaped relationship with respect to all three multiples. No theoretical foundation was found in literature that can explain this relationship. Finally, leverage has an inverted u-shaped relationship with all three enterprise valuation multiples. This is in line with the trade-off theory that at low levels of leverage, an increase in leverage increases the enterprise value, while at high levels of leverage the cost financial distress is value destroying.
To conclude, based on these bivariate results, mixed evidence for relationships is found between the enterprise valuation multiple and their determinants; some relationships are consistent with the existing literature while others are not. Importantly, size has a consistent positive relationship with all three enterprise valuation multiples. However, a more detailed analysis is required to determine the statistical significance of this relationship (particularly since the data is non-normally distributed)
Table 6 shows the relationship between size (based on market capitalization) and the four other variables. The return on invested capital increases as the size of firms increases.
Table 6 – Size versus other variables.
In this table, each variable is classified according to ten size groups. For each group, the median of each variable is given. In the last two columns the ANOVA and Kruskal-Wallis test statistics are given together with their significance.
The average growth rate is relatively high, and not in line with the observation of Koller et al. (2010) that large firms struggle growth. However, the growth rate declines after the seventh size decile. Moreover, the absolute growth values are not in line with Koller et al. (2010). The median beta is relatively low, despite the Blume’s adjustment for betas. The beta for the smallest size group is the lowest. This finding is not in line with literature, that large companies are more diversified than small ones and hence have a lower beta. The findings on the leverage variable with respect to size are in line with the findings of Titman and Wessels (1988). The relationship between leverage and size follows a u-shape relationship.
To sum up, based on Table 6, the findings on the relationship between size with the other variables (ROIC, growth and beta) are not in line with the predicted relationships from existing literature. However, the variable leverage has the predicted relationship.
Below, in Table 7 the dataset is categorized in industries, based on the Industry Classification Benchmark system. The significant results of the Kruskal-Wallis tests in Table 7 shows that for all the three multiples the median enterprise valuation multiple differs across industries. Thus, the company’s industry is an important variable to consider when a company is valued. This finding is in line with the earlier work of Koller et al. (2010), Alford (1992), King and Segal (2008) and Cheng and McNamara (2000). However, it does not confirm the results of Henschke and Homburg (2009) who find that industry membership as criteria does not significantly reduce valuation errors. Because literature is inconclusive about the inclusion of industry dummies, the regression analysis is performed with and without the inclusion of industry dummies.
Table 7– Differences in multiple value between industries
In this table the dataset is classified into different industries. For each industry the number of firms in the sample is given. Also, the mean and the median of Market capitalization, EV/EBITDA, EV/EBIT and EV/Sales are given. Furthermore, the test statistics of the Kruskal-Wallis tests are presented together with their significance.
5.2 Dated panel regression results
The results of the dated panel regression analysis are presented in Table 8. The focus on the discussion of the results will be on models A,B and C, where market capitalization is used as proxy for size. Furthermore, an additional dated panel regression is performed where the identical specifications have been used with the substitution of beta for leverage.
Panel A presents the results for the inclusion of the independent the dependent variable is EV/EBITDA variable. Contradictive to the key value driver formula return on invested capital (ROIC) has an insignificant negative relationship with the EV/EBITDA multiple. Growth is marginally significant in model A. However, in the other two models (B and C) the value becomes insignificant and the sign changes. This is inconsistent with the predictions of the key value driver formula. The size coefficient is positive and highly significant. This implies that as the market capitalization increases the valuation multiple EV/EBITDA increases as well, which again implies that large companies have higher valuations.
The positive significant sign on the risk-free rate is contradictive to the prediction that a higher interest rate leads to a higher cost of capital, which will ultimately lead to a lower valuation multiple. It might be that the risk-free rate is not accurate enough to approximate the cost of capital. The coefficient of the beta in models B and C is significantly positive, which is also in contrast with the expected relationships from literature.
Focusing, on industry dummies the technology industry has the highest coefficient and is statistically significant. This finding is in line with the findings from Table 7.
Table 8 – Dated panel regression results.
They explain this finding with the mean reversion of earnings, meaning that firms with above-average profitability in one period can encounter a decline in earnings in the next period. This decline is due to new entrants entering their business such that profit margins are reduced by increased competition.
Similar to panel A, size is significantly positive in all three models. For the risk-free rate and the beta the coefficients are again positive and significant.
Finally, in panel C EV/Sales is regressed against the independent variables. In line with the key value driver formula, ROIC has a positive and significant sign. However, again growth fails to confirm the prediction of the key value driver formula. Size is again positive and significant. The sign and significance levels of the risk-free rate coefficient and beta coefficient are similar to the outcomes in panel A and panel B.
The results of the regression where the EV/Sales is used as the dependent variable (Panel C) gives the best approximation of the key value driver formula. Compared to sales, the accounting values EBITDA en EBIT are more volatile over time which could be an explanation for the relatively high R2 - value within Panel C.
Focusing on the R-squared in model C, the statistical fit of the regression models is significantly improved by the inclusion of industry dummies. This is line with the findings of Cheng and McNamara (2000) who state that industries are an important variable to consider in multiple analyses.
Additionally, as mentioned earlier, the same regression has been applied with squared leverage substituting the beta variable. The results show a negative sign for all of the three panels (Table 8). However, these negative signs are not significant for all of the panels (i.e. for the EV/Sales multiple no significant values are found).
also be forward looking. However, as noted, the forward-looking data on ROIC and growth are not available. Therefore, historical data is used to measure ROIC and growth. Thus, although the coefficients of ROIC and growth have not the expected signs, this could be due to the backward looking nature of the data. The statistical results therefore do not reject the key value driver formula. There is no theoretical basis that predicts that past ROIC and growth are good estimators for the long term ROIC and growth rate. In other words, today’s winners could be tomorrow’s losers.
Comparing the results of the bivariate tests (Table 5) with the results of the dated panel regression analyses (Table 8) it reveals that the relationships found in Table 5 are in line with the outcomes of the regression analyses. For example, the relationship between size and the enterprise valuation multiples is in both situations positive.
As can be seen in section 2 of this paper, several previous studies use ‘total assets’ as a measure of firm size. In accordance with this literature, the different regressions and tests are also performed with ‘total assets’ as input for the size variable. The results of these dated panel regression analyses are presented in Table A6 in the Appendix and are insignificant. This weakens the results regarding size effects for enterprise valuation multiples. Also, R2 - value in Table A6 (with total assets as measure of size) is lower
compared to the model in Table 8 (with size measured as market capitalization). Thus, the statistical fit the models in Table A6 is lower.
5.3 Yearly OLS regression results
Table 9 presents the results of the yearly OLS regressions, the significant annual results are summed in the table. A more detailed table with OLS regression results for each of the three multiples with all coefficients is presented in Appendix Table A5.
The variation of the signs of ROIC and growth between the different years can be an explanation for the insignificant results in the dated panel regression results.
Table 9 – The aggregated results of the yearly OLS regressions.
The aggregated results of the yearly OLS regressions are presented in this table. For each multiple the total number of significant (at least 10% significance) variables are shown in this table. A minus before a number means that the relationship is negative and significant. The analysis contains 11 years, so 11 in the highest possible amount in the table. (For example: 2/-4 means that from 11 year observations, two were significant and positive and four were negative with the remaining five year observations being insignificant). Also, the average R-squared and the average number of observations are given over the observed 11 years.
Based on the results of the analyses, the key value driver cannot be confirmed. A possible reason for this could be the fact that for the regression inputs backward looking data for ROIC and growth is used, where forward looking data is preferred. Since the key value driver cannot be confirmed, it is difficult to come up with a valid conclusion about the influence of the size effect on the EV multiple taking the key value driver into account. However, if the key value driver formula is ignored, size has a positive influence on EV multiples.
To summarize, the results show no significant relationship between size effects and valuation multiples, when controlling for profitability, growth, firm risk and industry. These findings do not provide enough evidence to reject the H0
hypothesis, which states that enterprise valuation multiples do not depend on size after controlling for profitability, growth, firm risk and industry.
6. Conclusion
In this section the main findings will be discussed followed by identified limitations of this study and suggestions for further research.
6.1 Summary and main findings
This study examines the relationship between three enterprise valuation (EV/EBITDA, EV/EBIT and EV/Sales) multiples and size effects. This relationship is analyzed by performing tests on 2295 U.S. firms using data over an 11-year period (2000 – 2010).
Enterprise valuation multiples are frequently used by academics and professional working in the Mergers & Acquisition industry to estimate the value of a company. A company is valued by comparing it’s own multiples (e.g. EV/EBITDA) to the values assessed by the market for similar companies, controlling for any differences between the company and the so-called peer group that might affect the multiple. The search for similar companies to include in a peer group is always a challenge since no two firms are identical. This research studies whether one should control for firm size, based on market capitalization, when selecting comparable companies.
The relationship between enterprise value and size effects has been researched extensively in the past, for example by Banz (1981), Titman and Wessels (1988) and Reinganum (1990)). However, this empirical study makes use of recent data. This is important as recent developments such as the development of the internet, increased transparency and highly volatile stock markets could have a significant impact on the relationship between size effects and enterprise value.
The dated panel regression results confirm the results of the Kruskal-Wallis tests which show positive significant size effects. However, when looking at the key value driver the predicted signs of the variables are not confirmed by the empirical findings of this study. When looking at the different variables used in the regression analysis it cannot be concluded that size effects need to be taking into account. Thus, based on the dataset used, it is not possible to state that practitioners should take size into account when selecting comparable companies.
Furthermore, simple annual OLS-regressions are performed in order to test whether the results hold for individual years. The results of these regressions show that the variation of the signs of ROIC and growth can be an explanation for the insignificant results in the dated panel regression results. Again, for these regressions, the key value driver can not be confirmed.
Overall, given the results of both regression analyses, the dataset used does not validate the key value driver formula. The finding that this dataset does not confirm the key value driver, makes it difficult to interpret the results on the relationship between size effects and enterprise valuation multiples. This could be due the fact that the data used for this paper is backward looking data where the key value driver requires forward looking data. (i.e. Koller et al. 2010)
6.2 Limitations and suggestions for further research
There are some limitations with regard to this research. Research by Kim and Ritter (1999) and Lui, Nissium and Thomas (2002) documents that forward looking multiples increase predictive accuracy and decrease the variance of multiples within an industry. It would be interesting to perform the same research with forward looking data and verify whether the same results hold. DataStream does not have forward looking data available, so one should obtain data from another source. So, the return on invested capital as well as growth should be based on forward looking data.
Industrial Classification (SIC) codes. Unfortunately, DataStream is not able to provide this classification system. In order to improve the comparability with other studies, it would be useful to conduct this research using SIC codes.
Furthermore, the results of this study may differ across different geographies/countries. Therefore, one could perform the same analysis in different countries for robustness, for instance in the EU or the Asian market.
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