As introduced in Section 3.1, and as described by Dittmann & Maug (2008), re-searchers that compare valuation methods need to consider carefully before choosing between percentage and logarithmic errors as the valuation error measure. They argued that, mathematically, percentage errors penalise overvaluations more than undervaluations. While undervaluations exceeding 100% are impossible, overvalua-tions are not limited and will, in several cases, be more extreme than 100%. This issue creates a positive skewness, which is also observed in the data sample used in this thesis. To illustrate this, as an example Figure 2 shows the distribution of valuations errors for P/E when applying various selection methods. In contrast, logarithmic errors create more symmetric distributions of valuation errors, because, for each overvaluation, there exists an undervaluation of equal absolute size. Sta-tistically, logarithmic error distributions are thus closer to satisfying the normality assumptions often made for statistical inference.
Figure 2: Density Plot of Valuation Errors for P/E
0.0 0.5 1.0 1.5 2.0 2.5
0.0 0.5 1.0 1.5
Absolute percentage error
Density
colour
Fundamentals Industry
Industry & Fundamentals Region & Fundamentals Region & Industry
Region, Industry & Fundamentals
However, none of the comparable studies of peer group selection methods have ap-plied logarithmic errors, while by contrast, percentage errors have been widely used (Alford, 1992; Cheng & McNamara, 2000; Dittmann & Weiner, 2005; Nel et al., 2014; Knudsen et al., 2017). Thus, to increase comparability with previous liter-ature, this thesis employs absolute percentage errors as the measure of valuation errors. Furthermore, the absolute percentage errors provide a straightforward eco-nomic interpretation. As a result, the term ‘valuation error’ is used to refer to absolute percentage errors going forward. The valuation error for a companyi be-tween the predicted value, ˆVi, and the actual value, Vi, is, therefore as follows:
Valuation errori =| Vˆi−Vi Vi
| (24)
As a solution to the skewness issue, the overall accuracy of peer group selection methods is primarily evaluated on the basis of the median (as a measure of
cen-tral tendency) and interquartile range (as a measure of dispersion) of the absolute percentage errors, since these measures are less sensitive to the distribution of the inputs than the mean and standard deviation. This method of evaluating central tendency has been widely used in related literature (Alford, 1992; Cheng & McNa-mara, 2000; Dittmann & Weiner, 2005; Nel et al., 2014; Knudsen et al., 2017). The Mann-Whitney U test is employed to test for significance in the difference of the me-dian of two sets of valuation errors (i.e. valuation errors for two different peer group selection methods). The Mann-Whitney U test is a non-parametric test and does not require the assumption of normal distributions, unlike the t-test. The Wilcoxon signed-rank test provides the same advantages as the Mann-Whitney U test, but as the Wilcoxon signed-rank test requires two paired samples, it would exclude a large number of observations when methods generating numerous observations are tested against a method generating few observations.
To support and check the evaluation based on the median and the Mann-Whitney U test. The mean and a related t-test with heteroskedasticity-robust standard errors is performed to test for differences in the mean of valuation errors. However, it is important to stress that the conclusions of the empirical analysis are drawn from the results of the Mann-Whitney U test. Furthermore, the valuation errors are tested cross-sectionally across observations for all years in the sample.
Figure 3: Research Design
5 Empirical Findings
This section presents the empirical findings of this study carried out as outlined in the Data and Methodology section. First, Section 5.1 provides a short overview of the variables in the data sample. Next, the empirical results of the study are presented and examined in Section 5.2 to evaluate the hypotheses of this thesis.
Finally, various robustness checks are performed in Section 5.3 to validate the findings. Throughout this section the selection methods defined inSection 4.5are referred to in single quotation marks (e.g. ‘Industry’).
5.1 Descriptive Statistics
This section aims to provide an overview of the key variables in the data sample applied for this analysis. Table 6 presents summary statistics for these variables in terms of central tendency (mean and median) and dispersion (interquartile range).
All initial 13,001 observations are included; however, the number of observations for each peer selection method in Section 5.2 varies according to the number of negative multiples and lack of enough firms within the same industry. Therefore, Table 6 also reports the fraction of negative values for each variable. As explained in Section 4.1, income statement figures are on a trailing 12-month basis, while balance sheet figures are based on the last available balance sheet on March 31st each year. The market capitalisation is observed at closing March 31st each year.
Generally, all variables have higher means than medians, indicating that the vari-ables are positively skewed. This can be explained by the composition of the firms in the S&P Global 1200 Index. As a large cap index, the S&P Global 1200 includes the largest listed firms in the world, which are extremely positive outliers. On the other hand, since no small- and mid-cap firms are included in the sample, the extent of dispersion on the negative side is limited.
Table 6: Summary Statistics for Variables applied in the Study
Variable Mean Median IQ Range Negative, %
Sales 22,109 10,281 18,525 0.001
EBITDA 3,815 1,699 2,917 0.007
EBIT 2,656 1,202 2,142 0.032
Net Income 1,703 747 1,433 0.060
E[Salest+1] 22,314 10,324 18,332 0.000
E[EBITDAt+1] 3,883 1,767 2,912 0.004
E[EBITt+1] 3,007 1,329 2,328 0.017
E[Net Incomet+1] 1,915 822 1,498 0.028
Equity 14,692 6,618 11,705 0.014
Market Cap 27,804 13,641 21,301 0.000
Net Debt 13,256 2,931 9,124 0.204
Enterprise Value 34,998 17,146 27,703 0.001
ROIC 0.154 0.087 0.101 0.032
ROE 0.183 0.128 0.132 0.060
EBIT-margin 0.161 0.142 0.155 0.032
E[4EBIT] 0.104 0.092 0.106 0.099
E[4E] 0.095 0.103 0.120 0.107
Net Debt/EBIT 6.65 2.41 5.17 0.196
Net Debt/Equity 1.28 0.50 1.06 0.204
EV/Sales 3.97 1.87 2.16 0.001
EV/EBITDA 11.91 9.66 5.72 0.007
EV/EBIT 24.62 14.23 8.01 0.032
P/E 28.18 16.84 11.09 0.060
P/B 4.46 2.00 2.25 0.014
EV/Salest+1 2.85 1.79 2.07 0.000
EV/EBITDAt+1 20.49 9.13 4.74 0.004
EV/EBITt+1 16.37 13.04 6.55 0.017
P/Et+1 22.43 15.40 8.44 0.028
Note: The summary statistics are based on the gross data sample of 13,001 observations, including firms in the S&P Global 1200 Index at March 31st each year from 2008 to 2018.
Only observations for firms included in the index with several share classes are excluded. All financial statement items are in USD millions.
For the P/E multiple, 6% of observations are excluded due to negative earnings. For EV/EBIT this is 3.2% and for EV/EBITDA only 0.7%. Analysts generally expect higher net income, EBIT, EBITDA, and Sales in the coming year compared to the last historical 12 months. Therefore, only 2.8% of P/Et+1 observations, 1.7% of EV/EBITt+1 observations and 0.4% of EV/EBITDAt+1 observations are excluded due to negative earnings.
To provide an initial understanding of the fundamental factors used as input in the selection of peers through the SARD approach as well as the observed valuation multiples, Table 7 shows the median of these values when observations are grouped by sector (Panel A) and by region (Panel B).
First, it is clear that the most frequent sector in our sample is Financials, followed by Consumer Discretionary, Industrials, and Materials. Technology firms are the most profitable in terms of ROIC, while Consumer Staples is the most profitable in terms of ROE. Utilities are the least profitable in terms of ROIC, as are Financials in terms of ROE. Energy firms have the highest expected growth in both EBIT and net income followed by the Materials sector. Utilities, Communications, and Consumer Staples sectors have below median expected growth in EBIT and net income. The Technology sector appears to carry the lowest risk measured by Net Debt/EBIT and Net Debt/Equity.
Health Care firms trade at the highest multiples, except in terms of EV/EBIT where Materials and Utilities trade at slightly higher EV/EBIT multiples. This is in line with the fact that Health Care is among the most profitable sectors in terms of both ROIC and ROE while carrying the second lowest risk in terms of both Net Debt/EBIT and Net Debt/Equity. In terms of growth, Health Care firms are close to the overall median across all sectors. Firms in Communications, Health Care, and Utilities sectors trade at high median EV/Sales multiples due to high median EBIT-margins. The opposite is true for Consumer Discretionary, Industrials, Materials, and Consumer Staples. Communications trade at the lowest valuation in terms of
both EV/EBITDA and EV/EBIT, while Financials trade at lowest P/E and P/B multiples, which is the only meaningful multiples for firms in this sector.
Panel B shows that the sample includes the most observations for North American firms (46.1% of the total observations) followed by European firms (30.0%). Japan accounts for 12.7%, and the rest of Asia-Pacific accounts for 8.3%. Finally, Latin America only accounts for 2.9% of observations. This distribution is in line with the composition of the S&P Global 1200 Index as explained in Section 4.1.
Furthermore, North American firms seem to be the most profitable, while Japanese firms seem to be the least profitable. Firms in the last three regions appear to have median ROICs and ROEs close to the overall median. As expected due to the emerging markets status, Latin American firms have the highest expected growth in both EBIT and net income. The expected earnings growth of firms in all other regions is close to the overall median for these variables.
The above median EV/Sales multiples in Asia-Pacific ex. Japan, Latin America, and North America can be explained by their above median EBIT-margin. The low ROE can partly explain the low median P/B in Japan compared to other regions. The distortion in the relationship between EV/EBITDA and EV/EBIT (e.g. the fact that Japan has the lowest median EV/EBITDA, but the second-highest EV/EBIT) might be explained by differences in accounting policies affecting depreciation and amortisation. Furthermore, there might be differences in the concentration of sectors across regions.
Table7:SummaryStatisticsbySectorandRegion PanelA:MedianbySector EBIT-E[4E[4NetNetDebt/NetDebt/EV/EV/EV/ nROICROEmarginEBIT]Income]EBITEquitySalesEBITDAEBITP/EP/B Communications7940.0940.1460.1790.0690.0843.000.762.267.9612.7315.792.30 ConsumerDiscretionary1,8610.1130.1610.1000.0980.1101.750.431.289.1713.3416.732.39 ConsumerStaples1,1260.1120.1670.1140.0770.0882.200.591.7310.9414.5418.392.88 Energy9100.0730.1040.1390.1490.1542.720.462.258.3914.0317.361.64 Financials2,578N/A0.0920.203N/A0.0984.310.57N/AN/AN/A13.721.22 HealthCare9880.1240.1630.1790.0920.1041.050.242.7611.1414.9920.032.98 Industrials1,4530.1030.1570.1090.0970.1102.390.571.4610.2414.1217.532.51 Materials1,3700.0760.1040.1100.1190.1383.160.561.609.3015.0817.111.64 Technology1,1800.1350.1500.1560.1160.108-0.61-0.152.279.8114.2119.402.90 Utilities7410.0510.1040.1720.0610.0687.401.482.509.5015.5514.791.49 PanelB:MedianbyRegion EBIT-E[4E[4NetNetDebt/NetDebt/EV/EV/EV/ nROICROEmarginEBIT]Income]EBITEquitySalesEBITDAEBITP/EP/B Asia-Pacificex.Japan1,0740.0810.1200.1810.0950.0992.240.312.1210.2815.4315.791.73 Europe3,8960.0930.1360.1280.0890.1062.540.561.619.2913.9415.701.96 Japan1,6500.0520.0770.0710.0880.0912.780.401.028.2914.7716.671.17 LatinAmerica3850.0980.1360.1590.1230.1432.630.602.039.6213.6616.702.09 NorthAmerica5,9960.0940.1470.1660.0920.1012.230.522.3410.2814.1617.842.48