Having presented the empirical findings of the study in the previous section, the purpose of this section is to carry out several robustness checks by varying a series of input in the performed analysis to test the consistency of the previous findings inSection 5.2. Unless stated otherwise, the default methodological setup using 10 peers for the methods without industry and five peers for methods with industry restrictions. Tests are performed for 1) different multiples (using forward multiples), 2) regions, 3) sectors, 4) size, 5) time, and 6) different numbers of peers.
5.3.1 Choice of Multiples
The analysis presented in Section 5.2 only includes multiples based on historical value drivers. This section aims to test if these findings are consistent when val-uations are based on one-year forward multiples rather than observed multiples.
Descriptive statistics for all multiples are presented in Section 5.1. As explained inSection 4.1, the forecasted financial items are based on the median of analysts’
consensus estimates from Bloomberg. For the comparison, Table 16 reports the me-dian valuation errors and the U-test results for the income statement-based multiple (i.e. EV/Sales, EV/EBITDA, EV/EBIT, and P/E) compared to the same results for the corresponding one-year forward multiple.
From Table 16, it is clear that most of the ranks and U-tests for the forward multiples support the results of the corresponding historical multiple. However, in a couple of specific cases, the implementation of one-year forward multiples would modify the results of the tested hypotheses. Additionally, all forward multiples show lower me-dian valuation errors across all selection methods, indicating that forward multiples
generally provide more accurate valuations.
First, in relation to the findings in Section 5.2.1 the U-test shows a significantly lower median valuation error for ‘Industry’ compared to ‘Fundamentals’ when ap-plying P/Et+1. For P/E, this difference was found to be insignificant. Furthermore, in relation toSection 5.2.2EV/EBITt+1 shows a lower median valuation error of
‘Industry & Fundamentals’ compared to ‘Fundamentals’, while the opposite is true for EV/EBIT. However, in both cases, the U-test shows no significance.
For Hypothesis 4 investigated inSection 5.2.3, the support of Hypothesis 4 found in terms of EV/EBITDA becomes less significant when using EV/EBITDAt+1 (from significance at the 1% level to significance only at the 5% level). The forward multiple has the opposite effect in terms of P/E, where P/Et+1 supports Hypothesis 4 at the 1% level of significance rather than only at the 5% level when using P/E.
In terms of Hypothesis 5, which was analysed in Section 5.2.4, when applying EV/EBITt+1rather than EV/EBIT the evidence in favour of Hypothesis 5 becomes statistically significant (even at the 1% level), which is not the case for EV/EBIT.
Conclusion
In general, the findings inSection 5.2prove to be independent on whether historical or forward multiples are applied. However, in relation to Hypothesis 1 ‘Industry’ is significantly better than ‘Fundamentals’ for P/Et+1, which was not the case for P/E.
Furthermore, when applying EV/EBITt+1 rather than EV/EBIT the evidence in favour of Hypothesis 5 becomes statistically significant. Finally, all forward multiples show lower median valuation errors across all selection methods, indicating that forward multiples generally provide more accurate valuations.
Table 16: Robustness Check - Choice of Multiples
Industry & Region & Region & Region, Industry Industry Fundamentals Fundamentals Industry Fundamentals & Fundamentals EV/Sales+1 0.362 (5) 0.526 (6) 0.311 (3) 0.313 (4) 0.269 (1) 0.280 (2)
EV/Sales 0.376 (5) 0.528 (6) 0.322 (3) 0.324 (4) 0.270 (1) 0.294 (2)
Industry + ** - ** - ** - ** - **
Fundamentals - ** - ** - ** - ** - **
Industry & Fundamentals + ** + ** + - ** - **
Region & Industry + ** + ** - - ** - **
Region & Fundamentals + ** + ** + ** + ** + **
Region, Industry &
Fundamentals + ** + ** + ** + ** - **
EV/EBITDA+1 0.205 (4) 0.220 (6) 0.190 (3) 0.184 (2) 0.214 (5) 0.174 (1) EV/EBITDA 0.232 (4) 0.242 (6) 0.218 (2) 0.221 (3) 0.235 (5) 0.204 (1)
Industry + ** - ** - ** + * - **
Fundamentals - ** - ** - ** - * - **
Industry & Fundamentals + ** + ** - + ** - **
Region & Industry + ** + ** + + ** - *
Region & Fundamentals - + ** - ** - ** - **
Region, Industry &
Fundamentals + ** + ** + ** + * + **
EV/EBIT+1 0.227 (6) 0.181 (5) 0.177 (2) 0.180 (4) 0.179 (3) 0.162 (1)
EV/EBIT 0.236 (6) 0.201 (2) 0.204 (4) 0.209 (5) 0.202 (3) 0.187 (1)
Industry - ** - ** - ** - ** - **
Fundamentals + ** - + - - **
Industry & Fundamentals + ** - + - - **
Region & Industry + ** - ** - ** - * - **
Region & Fundamentals + ** + + + ** - **
Region, Industry &
Fundamentals + ** + + * + ** +
P/E+1 0.208 (4) 0.219 (6) 0.187 (3) 0.181 (2) 0.210 (5) 0.170 (1)
P/E 0.255 (5) 0.264 (6) 0.239 (3) 0.236 (2) 0.254 (4) 0.215 (1)
Industry + ** - ** - ** + - **
Fundamentals - - ** - ** - ** - **
Industry & Fundamentals + ** + ** - + ** - **
Region & Industry + ** + ** - + ** - **
Region & Fundamentals + + * - ** - ** - **
Region, Industry &
Fundamentals + ** + ** + ** + ** + **
Note: Table 16 reports the median valuation error for the each of the multiples EV/Sales, EV/EBITDA, EV/EBIT, and P/E based on various peer group selection methods. Furthermore, it reports the significance between the selection methods based on the Mann-Whitney U test. The lowest triangle contains test results for the historical multiple and upper triangle contains test results for the forward multiple. A ”+” indicates that the method in the row is more accurate than the method in the column.
* significance at 5% level. ** significance at 1% level.
5.3.2 Regions
The purpose of the regional robustness check is to evaluate the empirical findings when examining each of the five regions individually. It is worth noting that the results presented in this section take those results from the empirical findings and group them differently; no new calculations have been performed. The robustness check for forward multiples is provided in Appendix A.1.5.
From Section 5.1 it is clear that the weights of each region differ. A robustness check is therefore relevant to observe if the over/underweight among regions distorts the empirical findings.
To give the reader an understanding of how Table 17 is evaluated in this robustness check an example will follow. The example will focus on EV/Sales by comparing the method ‘Industry’ to the method ‘Fundamentals’. By looking at the total rank, it appears that ‘Industry’ (5) is ranked better than ‘Fundamentals’ (6). This appears to be true for all regions why five out of five regions supports the overall rank.
Section 5.2.1finds that ‘Industry’ is a more precise method compared to ‘Funda-mentals’ for EV/Sales and EV/EBITDA. This is supported by the regional robust-ness check where five out of five regions for EV/Sales and four out of five regions for EV/EBITDA achieve a lower valuation error for ‘Industry’ compared to ‘Funda-mentals’. Furthermore, it is found that ‘Fundamentals’ performs significantly better than ‘Industry’ for EV/EBIT and P/B. This is again supported in the regional ro-bustness test where five out of five regions for EV/EBIT and five out of five regions for P/B achieve lower valuation errors for ‘Fundamentals’ compared to ‘Industry’.
For P/E there is no significant difference between ‘Industry’ and ‘Fundamentals’.
The robustness check shows three out of five regions in favour of ‘Industry’.
Section 5.2.2 finds that applying fundamentals within an industry significantly reduces the valuation error for EV/Sales, EV/EBITDA and P/E compared to the two methods alone. This is supported by the regional robustness check which shows
either five out of five for these multiples except P/E for ‘Fundamentals’, which scores four out of five. Furthermore, for EV/EBIT and P/B valuation errors are reduced significantly going from ‘Industry’ to ‘Industry & Fundamentals’. This is again supported with five out of five regions for both multiples. ‘Industry & Fundamentals’
is significantly worse than ‘Fundamentals’ for P/B, which is supported by five out of five regions. There is no significant difference for EV/EBIT for ‘Fundamentals’
which is supported by this robustness check. There is no significant difference for P/E between ‘Fundamentals’ and ‘Industry & Fundamentals’. The robustness check shows three out of five in favour of ‘Fundamentals’.
InSection 5.2.3it is found that the valuation error for all multiples12 for both the fundamentals-based method and the industry-based method is reduced when select-ing peers within a region; the only exception is EV/EBIT as there is no significant difference between ‘Fundamentals’ and ‘Region & Fundamentals’. The robustness check generally supports the results in regard to Hypothesis 3; EV/EBITDA is an exception where only two out of four regions support the results.
For Hypothesis 4 the robustness check shows quite weak support with three out of five regions for EV/EBITDA, P/E and P/B, and only two out of five for EV/EBIT.
The significant results in the empirical findings for Hypothesis 4 are mainly driven by improvements in valuation accuracy for Japanese and North American compa-nies, while the fundamentals-based approach generally seems to perform better in a global context for European companies.
Section 5.2.4 finds that when combining region, industry, and fundamentals the valuation error is significantly reduced for EV/EBITDA and P/E, when compared to ‘Region & Industry’ and ‘Region & Fundamentals’. This is confirmed by the robustness check which shows that three out of three regions for EV/EBITDA and four out of five regions for P/E support the findings for ‘Region & Industry’. For
‘Region & Fundamentals’ the robustness check also support with two out of three regions for EV/EBITDA, and five out of five regions for P/E. Furthermore, it is
12except EV/EBIT for ‘Fundamentals’ compared to ‘Region & Fundamentals’.
shown that the valuation errors for EV/Sales and P/B are reduced from ‘Region &
Industry’ to ‘Region, Industry & Fundamentals’. From ‘Region & Fundamentals’
to ‘Region, Industry & Fundamentals’ it is the other way around, as the median valuation error for EV/Sales and P/B increases. This is also confirmed by the robustness check with two out of three regions for EV/Sales and four out of five regions for P/B in favour of ‘Region, Industry & Fundamentals’ when compared to
‘Region & Industry’. Furthermore, three out of three regions for EV/Sales and three out of five for P/B are in favour of ‘Region & Fundamentals’ compared to ‘Region, Industry & Fundamentals’.
The primary regions that show conflicting results compared to the overall findings are Japan and Latin America. It should be noted that the results in Latin America are based on only 385 observations: this corresponds to 35 observations a year. In the robustness check Japan makes up approximately 35% of the conflicting results, and Latin America accounts for approximately 25%. In contrast, North America and Asia-Pacific only make up approximately 10% of the conflicting results. Europe accounts for approximately 20%.
Conclusion
In general, the regional robustness check supports the conclusions presented in Sec-tion 5.2. The only weakness in the regional robustness check can be found in regard to Hypothesis 4 as the results are mainly driven by improvements in valua-tion accuracy for Japanese and North American companies, while the fundamentals-based approach generally seems to perform better in a global context for European companies. Generally, it can be concluded that Japan and Latin America are the commonest regions in regard to offer conflicting observations. Excluding these two regions might have changed the results of the empirical findings.
Table 17: Robustness Check - By Region
Industry & Region & Region & Region, Industry Industry Fundamentals Fundamentals Industry Fundamental & Fundamentals EV/Sales
Asia-Pacific ex. Japan 0.382 (2) 0.607 (5) 0.363 (1) 0.455 (3) 0.467 (4) N/A Europe 0.389 (5) 0.510 (6) 0.326 (2) 0.358 (4) 0.281 (1) 0.333 (3) Japan 0.398 (5) 0.482 (6) 0.363 (4) 0.309 (2) 0.287 (1) 0.317 (3)
Latin America 0.483 (3) 0.517 (4) 0.452 (2) N/A 0.341 (1) N/A
North America 0.352 (5) 0.539 (6) 0.294 (3) 0.309 (4) 0.238 (1) 0.275 (2) Total 0.376 (5) 0.528 (6) 0.322 (3) 0.324 (4) 0.270 (1) 0.294 (2) EV/EBITDA
Asia-Pacific ex. Japan 0.300 (3) 0.326 (5) 0.284 (2) 0.283 (1) 0.321 (4) N/A Europe 0.226 (3) 0.250 (5) 0.210 (1) 0.236 (4) 0.253 (6) 0.218 (2) Japan 0.274 (4) 0.250 (3) 0.235 (2) 0.341 (6) 0.234 (1) 0.331 (5)
Latin America 0.252 (2) 0.268 (3) 0.246 (1) N/A 0.307 (4) N/A
North America 0.214 (5) 0.227 (6) 0.206 (3) 0.198 (2) 0.209 (4) 0.186 (1) Total 0.232 (4) 0.242 (6) 0.218 (2) 0.221 (3) 0.235 (5) 0.204 (1) EV/EBIT
Asia-Pacific ex. Japan 0.301 (5) 0.274 (4) 0.240 (2) 0.228 (1) 0.274 (3) N/A Europe 0.225 (6) 0.202 (3) 0.189 (2) 0.208 (4) 0.209 (5) 0.187 (1) Japan 0.315 (4) 0.207 (2) 0.252 (3) 0.411 (6) 0.178 (1) 0.386 (5)
Latin America 0.304 (4) 0.246 (1) 0.263 (2) N/A 0.277 (3) N/A
North America 0.214 (6) 0.187 (2) 0.192 (3) 0.200 (5) 0.194 (4) 0.177 (1) Total 0.236 (6) 0.201 (2) 0.204 (4) 0.209 (5) 0.202 (3) 0.187 (1) P/E
Asia-Pacific ex. Japan 0.297 (6) 0.273 (4) 0.269 (3) 0.245 (2) 0.279 (5) 0.215 (1) Europe 0.238 (4) 0.261 (5) 0.221 (2) 0.233 (3) 0.263 (6) 0.210 (1) Japan 0.307 (6) 0.301 (5) 0.279 (4) 0.265 (2) 0.270 (3) 0.264 (1) Latin America 0.284 (3) 0.360 (6) 0.306 (4) 0.226 (1) 0.330 (5) 0.271 (2) North America 0.245 (5) 0.249 (6) 0.228 (2) 0.235 (3) 0.238 (4) 0.215 (1) Total 0.255 (5) 0.264 (6) 0.239 (3) 0.236 (2) 0.254 (4) 0.215 (1) P/B
Asia-Pacific ex. Japan 0.429 (6) 0.282 (3) 0.321 (5) 0.274 (2) 0.301 (4) 0.250 (1) Europe 0.381 (6) 0.267 (1) 0.296 (4) 0.364 (5) 0.272 (2) 0.293 (3) Japan 0.449 (6) 0.295 (2) 0.347 (5) 0.346 (4) 0.263 (1) 0.338 (3) Latin America 0.511 (6) 0.350 (3) 0.393 (5) 0.282 (1) 0.371 (4) 0.333 (2) North America 0.365 (6) 0.266 (2) 0.291 (3) 0.349 (5) 0.262 (1) 0.304 (4) Total 0.393 (6) 0.274 (2) 0.303 (4) 0.350 (5) 0.271 (1) 0.300 (3)
Note: Table 17 reports the median valuation error for various selection methods grouped by regions.
5.3.3 Sectors
The purpose of performing a robustness check across sectors is to evaluate to what degree the overall rank of median valuation errors is truly individual for each sector and therefore conclude how robust the empirical findings are. Looking at Table 7 in Section 5.1 it is clear that there is a difference between the weight of each sector.
This supports the importance of this robustness check. It should be highlighted that this section does not perform new calculations but simply divides the empirical findings into different sectors. Table 18 contains results for the enterprise value-based multiples, and Table 19 contains results for the equity-value-based multiples. Both tables summarize the median valuation error and ranks for each of the 10 BICS2 sectors.13 The robustness check for forward multiples is provided in Appendix A.1.6.
The robustness check will evaluate how many individual sector ranks that supports the total rank. Each multiple is evaluated by looking at all 10 sectors and test in what degree they individually support the five hypotheses, which gives a total of 72 different combinations for EV-based multiples and 80 combinations for equity-based multiples (See Figure 1 inSection 1.1).
An example is first given in order to understand how Table 18 and 19 are evaluated in this robustness check. The example will be focused on EV/Sales by comparing the method ‘Industry & Fundamentals’ to the method ‘Region, Industry & Fun-damentals’. The total rank implies that ‘Region, Industry & Fundamentals’ gives a better rank (2) than ‘Industry & Fundamentals’ (3). This is, however, not true for the following sectors: Communications, Health Care, Industrials, and Materials.
This means that four sector-ranks out of nine are conflicting with the total ranks.
In terms of EV/Sales, it appears that all sectors support the total ranks to an excellent extent. Only 7 out of 72 sector-ranks do not support the total ranks. Four of the non-supportive ranks can be limited to ‘Industry & Fundamentals’ compared to ‘Region, Industry & Fundamentals’. Moving on to EV/EBITDA, it appears that
13nine sectors for EV based due to the exclusion of companies within ’Financials’.
all sectors to a reasonable extent support the total ranks. 18 out of 72 sector-ranks do not support the total ranks. Five of the non-supportive ranks can be limited to Consumer Discretionary. Four non-supportive ranks can be limited to ‘Industry’
compared to ‘Fundamentals’. Looking at EV/EBIT, it appears that all sectors to a great extent support the total ranks. 14 out of 72 sector-ranks do not support the total ranks. Four of the non-supportive ranks can be limited to Health Care.
For P/E it appears that all sectors to a great extent support the total ranks. 15 out of 80 sector-ranks do not support the total ranks. Five of the non-supportive ranks can be limited to ‘Industry’ compared to ‘Fundamentals’. Furthermore, four can be limited to Consumer Staples. Lastly, it appears that for P/B all sectors to a great extent support the total ranks. 14 out of 80 sector-ranks do not support the total ranks. Five of the non-supportive ranks can be limited to ‘Industry &
Fundamentals’ compared to ‘Region, Industry & Fundamentals’.
Looking in general across all multiples no specific sector stands out negatively;
however, Consumer Staples, Health Care, and Technology were the most distorting sectors with 9 conflicting ranks out of 40.14 Furthermore, looking in general across the eight combinations, ‘industry and fundamentals’ compared to ‘region, industry, and fundamentals’ stands out with 16 non-supportive ranks out of the total for this combination of 47.15
Conclusion
In general, this robustness check supports the empirical findings by identifying a pattern in that each sector has the same rank among the different valuation methods as the overall ranks. With this concluded, there is one problematic finding in the robustness check: ‘Industry & Fundamentals’ compared to ‘Region, Industry &
Fundamentals’ has 16 non-supportive ranks out of a total of 47. This corresponds to an error percentage of 34%, and it can, therefore, be concluded that the findings
14Five different multiples and eight different combinations.
15Five different multiples and 10 different sectors for two equity-based multiples and nine different sectors for three EV-based multiples.
in relation to this specific combination are questionable following the robustness check.
Table 18: Robustness Check - By Sector (1)
Industry & Region & Region & Region, Industry Industry Fundamentals Fundamentals Industry Fundamental & Fundamentals EV/Sales
Communications 0.270 (4) 0.454 (6) 0.250 (3) 0.189 (1) 0.239 (2) 0.294 (5) Consumer Discretionary 0.408 (5) 0.503 (6) 0.379 (4) 0.367 (3) 0.265 (1) 0.358 (2) Consumer Staples 0.370 (5) 0.543 (6) 0.286 (3) 0.333 (4) 0.268 (1) 0.281 (2) Energy 0.409 (5) 0.638 (6) 0.383 (4) 0.339 (2) 0.350 (3) 0.300 (1)
Financials N/A N/A N/A N/A N/A N/A
Health Care 0.290 (2) 0.602 (6) 0.273 (1) 0.307 (4) 0.312 (5) 0.303 (3) Industrials 0.348 (3) 0.470 (6) 0.305 (2) 0.389 (5) 0.250 (1) 0.356 (4) Materials 0.395 (5) 0.497 (6) 0.346 (2) 0.372 (4) 0.265 (1) 0.366 (3) Technology 0.436 (5) 0.583 (6) 0.384 (3) 0.403 (4) 0.317 (1) 0.381 (2) Utilities 0.422 (5) 0.479 (6) 0.269 (3) 0.276 (4) 0.187 (1) 0.234 (2)
Total 0.376 (5) 0.528 (6) 0.322 (3) 0.324 (4) 0.270 (1) 0.294 (2)
EV/EBITDA
Communications 0.192 (4) 0.251 (6) 0.190 (3) 0.138 (2) 0.238 (5) 0.129 (1) Consumer Discretionary 0.263 (4) 0.235 (1) 0.246 (3) 0.309 (6) 0.238 (2) 0.305 (5) Consumer Staples 0.183 (3) 0.242 (6) 0.187 (4) 0.180 (2) 0.239 (5) 0.175 (1) Energy 0.285 (4) 0.303 (5) 0.277 (3) 0.260 (2) 0.323 (6) 0.240 (1)
Financials N/A N/A N/A N/A N/A N/A
Health Care 0.196 (4) 0.266 (6) 0.194 (3) 0.191 (2) 0.253 (5) 0.189 (1) Industrials 0.226 (6) 0.218 (4) 0.219 (5) 0.185 (1) 0.203 (3) 0.195 (2) Materials 0.242 (5) 0.232 (4) 0.217 (2) 0.272 (6) 0.217 (1) 0.232 (3) Technology 0.291 (3) 0.292 (4) 0.282 (2) 0.334 (5) 0.264 (1) 0.356 (6) Utilities 0.212 (6) 0.180 (5) 0.164 (4) 0.163 (3) 0.157 (2) 0.149 (1)
Total 0.232 (4) 0.242 (6) 0.218 (2) 0.221 (3) 0.235 (5) 0.204 (1)
EV/EBIT
Communications 0.197 (6) 0.165 (2) 0.187 (5) 0.167 (3) 0.177 (4) 0.157 (1) Consumer Discretionary 0.285 (6) 0.206 (1) 0.229 (3) 0.265 (5) 0.211 (2) 0.265 (4) Consumer Staples 0.161 (4) 0.178 (5) 0.145 (1) 0.148 (3) 0.190 (6) 0.148 (2) Energy 0.339 (6) 0.264 (2) 0.273 (4) 0.317 (5) 0.272 (3) 0.231 (1)
Financials N/A N/A N/A N/A N/A N/A
Health Care 0.221 (2) 0.239 (5) 0.199 (1) 0.222 (3) 0.240 (6) 0.225 (4) Industrials 0.199 (6) 0.170 (4) 0.190 (5) 0.162 (3) 0.162 (2) 0.153 (1) Materials 0.279 (6) 0.215 (2) 0.233 (4) 0.267 (5) 0.210 (1) 0.232 (3) Technology 0.293 (4) 0.266 (2) 0.277 (3) 0.359 (6) 0.259 (1) 0.330 (5) Utilities 0.211 (6) 0.125 (2) 0.136 (4) 0.163 (5) 0.125 (3) 0.115 (1)
Total 0.236 (6) 0.201 (2) 0.204 (4) 0.209 (5) 0.202 (3) 0.187 (1)
Note: Table 18 reports the median valuation error for various selection methods grouped by sectors.
Table 19: Robustness Check - By Sector (2)
Industry & Region & Region & Region, Industry Industry Fundamentals Fundamentals Industry Fundamental & Fundamentals P/E
Communications 0.235 (6) 0.227 (3) 0.214 (2) 0.234 (5) 0.232 (4) 0.196 (1) Consumer Discretionary 0.272 (5) 0.276 (6) 0.261 (3) 0.209 (2) 0.266 (4) 0.203 (1) Consumer Staples 0.188 (2) 0.228 (5) 0.199 (4) 0.182 (1) 0.242 (6) 0.198 (3) Energy 0.354 (6) 0.334 (5) 0.302 (2) 0.317 (4) 0.311 (3) 0.292 (1) Financials 0.278 (4) 0.315 (6) 0.243 (2) 0.258 (3) 0.302 (5) 0.216 (1) Health Care 0.232 (3) 0.264 (6) 0.212 (1) 0.235 (4) 0.264 (5) 0.227 (2) Industrials 0.212 (5) 0.220 (6) 0.200 (3) 0.164 (1) 0.201 (4) 0.165 (2) Materials 0.278 (6) 0.268 (4) 0.271 (5) 0.255 (3) 0.248 (2) 0.239 (1) Technology 0.307 (5) 0.284 (3) 0.277 (2) 0.334 (6) 0.272 (1) 0.299 (4) Utilities 0.221 (6) 0.217 (5) 0.213 (4) 0.164 (1) 0.192 (3) 0.173 (2)
Total 0.255 (5) 0.264 (6) 0.239 (3) 0.236 (2) 0.254 (4) 0.215 (1)
P/B
Communications 0.429 (5) 0.248 (1) 0.285 (3) 0.433 (6) 0.249 (2) 0.309 (4) Consumer Discretionary 0.396 (6) 0.294 (2) 0.345 (4) 0.380 (5) 0.294 (1) 0.336 (3) Consumer Staples 0.442 (6) 0.249 (1) 0.316 (3) 0.403 (5) 0.260 (2) 0.364 (4) Energy 0.331 (6) 0.325 (5) 0.293 (2) 0.299 (4) 0.295 (3) 0.288 (1) Financials 0.374 (6) 0.310 (3) 0.265 (2) 0.317 (5) 0.313 (4) 0.256 (1) Health Care 0.401 (5) 0.282 (1) 0.323 (3) 0.419 (6) 0.287 (2) 0.396 (4) Industrials 0.367 (6) 0.227 (2) 0.319 (3) 0.355 (5) 0.217 (1) 0.355 (4) Materials 0.415 (6) 0.275 (2) 0.322 (3) 0.378 (5) 0.257 (1) 0.324 (4) Technology 0.428 (6) 0.297 (2) 0.388 (4) 0.420 (5) 0.282 (1) 0.379 (3) Utilities 0.337 (6) 0.221 (4) 0.213 (3) 0.294 (5) 0.195 (1) 0.210 (2)
Total 0.393 (6) 0.274 (2) 0.303 (4) 0.350 (5) 0.271 (1) 0.300 (3)
Note: Table 19 reports the median valuation error for various selection methods grouped by grouped by sectors.
5.3.4 Size
The purpose of performing a robustness check for the size of companies is to evaluate to what degree the findings in Section 5.2 is truly independent of company size (measured by market cap). Silber (1991), Bajaj et al. (2001), and Officer (2007) investigate the liquidity risk and find that larger companies have a lower risk due to a higher liquidity. Their findings indicate that the impact of size is relevant to test in this thesis. To perform this robustness check the companies in the sample are grouped in thirds depending on the market cap size (i.e. the largest third, the medium third, and the smallest third) for each year. It is worth noting that the results presented in this section simply take those results from the empirical findings and group them differently; no new calculations have been performed. The robustness check for forward multiples is provided in Appendix A.1.7.
Generally, Table 20 illustrates to a substantial degree that the findings of this thesis are independent of company size. Worth noticing is also the fact that the largest third of companies to have the lowest valuation error across most multiples as well as selection methods.
Only the findings concerning Hypothesis 1 are slightly unclear. The fact that ‘Indus-try’ yields significantly lower valuation errors than ‘Fundamentals’ for EV/EBITDA, which was found in Section 5.2.1, seems to be driven by the results for compa-nies in the largest third of the sample, since the smaller compacompa-nies (i.e. medium third and smallest third) indicate slightly more accuracy when using ‘Fundamentals’
rather than ‘Industry’. Moreover, in terms of P/E, the largest third and the medium third seems to provide evidence in favour of ‘Industry’, whereas the smallest third seems to provide evidence in favour of ‘Fundamentals’.
Finally, the insignificant result for EV/EBIT concerning Hypothesis 5 found in Section 5.2.4 seem to be questionable, since ‘Region, Industry & Fundamentals’
proves to be the most accurate selection method for all groupings according to size.
Conclusion
In general, the findings inSection 5.2prove to be independent from company size.
However, in a couple of specific cases, the consistency can be discussed for some size groupings. Most substantial is it that results for Hypothesis 1 for EV/EBITDA and P/E seem to be driven by one or two size groupings rather than all three.
Table 20: Robustness Check - Size
Industry & Region & Region & Region, Industry Industry Fundamentals Fundamentals Industry Fundamental & Fundamentals EV/Sales
Largest third 0.343 (5) 0.539 (6) 0.286 (3) 0.295 (4) 0.255 (1) 0.268 (2) Medium third 0.378 (5) 0.520 (6) 0.335 (3) 0.347 (4) 0.274 (1) 0.309 (2) Smallest third 0.411 (5) 0.524 (6) 0.361 (3) 0.371 (4) 0.280 (1) 0.321 (2) Total 0.376 (5) 0.528 (6) 0.322 (3) 0.324 (4) 0.270 (1) 0.294 (2) EV/EBITDA
Largest third 0.211 (4) 0.244 (6) 0.200 (2) 0.202 (3) 0.232 (5) 0.191 (1) Medium third 0.239 (6) 0.235 (5) 0.220 (2) 0.228 (3) 0.231 (4) 0.212 (1) Smallest third 0.248 (6) 0.248 (5) 0.233 (2) 0.237 (3) 0.240 (4) 0.213 (1) Total 0.232 (4) 0.242 (6) 0.218 (2) 0.221 (3) 0.235 (5) 0.204 (1) EV/EBIT
Largest third 0.214 (6) 0.192 (3) 0.185 (2) 0.201 (5) 0.195 (4) 0.183 (1) Medium third 0.234 (6) 0.204 (5) 0.204 (4) 0.203 (2) 0.203 (3) 0.185 (1) Smallest third 0.266 (6) 0.209 (3) 0.229 (5) 0.228 (4) 0.206 (2) 0.193 (1) Total 0.236 (6) 0.201 (2) 0.204 (4) 0.209 (5) 0.202 (3) 0.187 (1) P/E
Largest third 0.222 (4) 0.248 (6) 0.209 (2) 0.211 (3) 0.238 (5) 0.196 (1) Medium third 0.258 (4) 0.275 (6) 0.247 (3) 0.244 (2) 0.265 (5) 0.223 (1) Smallest third 0.300 (6) 0.272 (5) 0.270 (4) 0.263 (2) 0.265 (3) 0.238 (1) Total 0.255 (5) 0.264 (6) 0.239 (3) 0.236 (2) 0.254 (4) 0.215 (1) P/B
Largest third 0.361 (6) 0.261 (1) 0.276 (4) 0.322 (5) 0.263 (2) 0.274 (3) Medium third 0.391 (6) 0.283 (2) 0.313 (4) 0.357 (5) 0.276 (1) 0.313 (3) Smallest third 0.423 (6) 0.275 (2) 0.338 (3) 0.378 (5) 0.274 (1) 0.340 (4) Total 0.393 (6) 0.274 (2) 0.303 (4) 0.350 (5) 0.271 (1) 0.300 (3)
Note: Table 20 reports the median valuation error for various selection methods grouped by size.
5.3.5 Across Years
To test the performance of the analysed peer group selection methods further, the median absolute percentage errors are plotted for each year from 2007 to 2017 in Figure 4. The purpose of this is to analyse whether the relative performances of the methods found and tested in Section 5.2 are consistent throughout the entire sample period. The robustness check for forward multiples is provided in Appendix A.1.8.
Generally, the conclusions of the hypotheses investigated in Section 5.2 are con-sistent across the years in the data sample, especially for Hypothesis 3 in Section 5.2.3. However, in some cases the choice of sample period might have impacted the findings. In addition, Figure 4 illustrates substantial fluctuations in valuation errors over time.
First, in Section 5.2.1 ‘Fundamentals’ was found to be performing significantly worse than ‘Industry’ when using EV/EBITDA. However, this is only true from 2014 onwards. In the period from 2007 to 2013 the difference in the performance of ‘Industry’ and ‘Fundamentals’ was indistinct. This indicates that extending the sample period further historically might have made the overall difference less sig-nificant. In the same section no significant difference was found for P/E. Figure 4 shows that ‘Fundamentals’ yielded lower valuation errors in the period 2007 to 2009, while ‘Industry’ performed better in the period from 2014 to 2017. From 2010 to 2013 the performance was close between the two. Thus, the relative performance of ‘Industry’ and ‘Fundamentals’ in terms of P/E seems to depend on the sample period.
In relation to the investigation of Hypothesis 2 in Section 5.2.2, in terms of EV/EBIT the median valuation error of ‘Fundamentals’ compared to the combi-nation ‘Industry & Fundamentals’ was found to be insignificant when considering the entire sample period. This finding seems to vary for different sub-periods as
‘Fundamentals’ performed the best until 2011; whereas ‘Industry & Fundamentals’