Relation to previous literature

The initial paper by Knudsen et al. (2017) introducing SARD as a fundamental peer selection method forms the basis for this study as no other published research papers apply their approach. Thus, the empirical results from this thesis will initially be compared directly to the original study in Section 6.1.1. Subsequently, a comparison to literature approaching the ‘horse race’ between industry and a fundamentals approach will be conducted in Section 6.1.2 followed by a comparison to the literature addressing a combination of fundamentals and industry in Section 6.1.3. Finally, the literature addressing cross-border impacts on prediction accuracy will in Section 6.1.4be related to the findings in this thesis applying both a Danish and a cross-border EU peer pool.

6.1.1 The original SARD paper

The initial paper by Knudsen et al. (2017) found that selecting peer groups based on SARD, i.e. applying a fundamentals approach, leads to greater multiple prediction accuracy compared to peer selection by industry affiliation for the S&P 1500 index. As presented in Section 3.2, Knudsen et al. (2017) suggest that SARD can be useful outside the US where the number of observations is less plentiful. This open research question is examined in this thesis when applying SARD to the Danish market. Overall, the findings obtained for Danish targets are similar to Knudsen et al.'s (2017) results as SARD yields more accurate predictions than industry does. Furthermore, the results in this thesis indicate a progressive improvement in valuation accuracy when adding a selection variable in the SARD model similar to the original study,

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although the proxy for growth varies from Knudsen et al. (2017) as Historic Revenue Growth is applied in the methodological approach of this thesis as a substitute for missing EPS growth.

However, differences appear in the results’ significance levels when investigating SARD on a small market, i.e. Denmark, compared to the original research paper. The findings for EV/Sales are shown to be significant, while the results for two earnings multiples, EV/EBITDA and EV/EBIT, indicate a pattern of improvement when adding more selection variables despite somewhat insignificant results. However, once the peer pool is expanded to include all EU firms, the progressively improvements of adding more selection variables more significant for the two earnings multiples as well. Furthermore, Knudsen et al. (2017) argue that their findings indicate a significant improvement applying the EBIT margin in relation to the EV/Sales multiple.

Similar, it is evident throughout this analysis that adding the EBIT margin as a selection variable in SARD significantly reduced median errors from 0.588 to 0.436 for EV/Sales.

Moreover, Knudsen et al. (2017) find that using SARD within industries leads to increased accuracy of valuation estimates. In contrast, a rather ambiguous pattern for the INDSARD method is found in this thesis for the Danish peer pool. Expanding the peer pool to EU does not reduce the ambiguousness between INDSARD’s performance relative to SARD, however, it is seen that certain combinations of INDSARD including ROE, Net Debt/EBIT, and Size overall leads to the most accurate predictions for EV/EBITDA and EV/EBIT. Further, it is revealed that when SARD includes enough selection variables INDSARD does not yield better prediction accuracy than a pure fundamental approach. For EV/Sales, however, a significant improvement is seen when using INDSARD, but similar to Knudsen et al. (2017), SARD5 including EBIT margin ultimately outperforms all INDSARD combinations. The differences to the original study related to the results of INDSARD with an underlying Danish peer pool can stem from different factors related to the overall methodology. Firstly, Knudsen et al. (2017) apply INDSARD using a GICS 6-digit layer as industry affiliation while the broadest layer, i.e.

GICS 2-digit, is applied in this thesis due to too few observations in the more specific 6-digit layer. This leads to the second differentiating factor between the two studies: the Danish market used in this thesis is substantially smaller than the S&P 1500. Using a pure Danish peer pool leads to inefficiency of using INDSARD as too few observations exist per industry, hence, peer pools are predetermined by the industry as described in Section 5.2.2. However, despite expanding the quantity of inputs for the selection methods by using a cross-border peer pool with EU, this thesis does not find similar findings as Knudsen et al. (2017), since combining

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SARD with an industry criterion does not consistently yield higher prediction accuracy.

Whether this result is related to the underlying peer pool being affected by cross-border differences or the fact that the industry criterion is a GICS 2-digit layer will be discussed when interpreting the results further in Section 6.2.

Ultimately, the main distinction to Knudsen et al.'s (2017) study is the level of accuracy obtained in the empirical results as they are significantly higher in this study regardless of using an underlying peer pool of Danish or EU firms. As mentioned in Section 4.5, the SARD model developed in this study corresponds one-to-one with the model developed by Knudsen et al.

(2017). Thus, differences between this thesis and the original paper should predominantly be attributed to the characteristics of the sample. In general, the absolute percentage errors of the median range from 0.40 to 0.20 in the original study compared to 0.71 to 0.36 within this thesis revealing a significant difference in the level of accuracy. However, the pattern of multiples’

relative performance is the same in both studies as EV/Sales in general leads to higher prediction errors than EV/EBIT indicating that the earnings multiples provide a more accurate valuation estimation. The large differences in the level of valuation errors can be explained by the smaller sample, consisting of Danish targets, as just described. Additionally, the quality of the datasets, i.e. the liquidity of the firms, can presumably be another explanation of the difference. When comparing the sample used in this study and Knudsen et al. (2017), respectively, it is evident that the original paper of SARD uses a sample composed of the S&P 1,500 index. The S&P 1,500 is a stock market index tracking tradeable companies in the US. It includes all stocks from the S&P 400, S&P 500, and S&P 600 ensuring a sample distribution of 400 Mid Cap companies, 500 Large Cap companies, and 600 Small-Cap companies, overall covering 90% of the market capitalization of US stocks, thereby being an appropriate approximation of an entire market. The S&P 1,500 index tracks high-quality stocks which are calculated based on ROE, accruals ratio, and financial leverage, ensuring tradeable and liquid firms (S&P Global, 2021). In comparison, the two datasets of Danish and EU firms applied in this thesis constitute entire markets with no adjustment for illiquid firms. This can interrupt the prediction accuracy as illiquidity discounts are obtained to compensate for the risk cost of holding inventory, i.e. such illiquid stocks are not valued on the same terms as large, liquid stocks which hamper the multiple valuation based on peer selection with fundamentals (Damodaran, 2006).

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6.1.2 Literature on fundamentals- versus industry peer selection

Returning to the two schools of thought of comparing industry affiliation to a fundamental selection method, the overall findings of this study indicate that SARD, i.e. a fundamentals approach, for selecting peers for Danish targets, yield greater prediction accuracy than industry does on its own. Several studies addressing the ‘horse race’ between the two schools of thought obtain similar results. Bhojraj & Lee (2002), Knudsen et al. (2017), Nel & le Roux (2015), Herrmann & Richter (2003), Dittmann & Weiner (2005), and Serra & Fávero (2018) all favour a fundamental approach and thereby conform to the findings of this thesis. Contrarily, Alford's (1992) and Cheng & McNamara's (2000) findings are disagreeing as they suggest that industry on a stand-alone basis achieves higher prediction accuracy than ROE and Total Assets for P/E and P/B valuation. This is inconsistent with the findings of this thesis as greater accuracy for all combinations of SARD, including ROE on a stand-alone basis, is obtained compared to industry affiliation. This result is apparent for all the multiples applied including EV/Sales, EV/EBITDA, and EV/EBIT as they in general all achieve a significance level of 1% both using a Danish and EU peer pool.

Dittmann & Weiner (2005) applies a similar research design as Alford (1992) and Cheng &

McNamara's (2000), however, covering a broad global sample of OECD countries including Denmark, in a newer time perspective, and applies an EV/EBIT multiple. Despite using the same research design as Alford (1992) and Cheng & McNamara (2000), they obtain different findings as higher prediction accuracy is achieved by ROA on a stand-alone basis and a combination of ROA and Total Assets, compared to industry affiliation alone. Those findings conform to the results in this thesis where all the combinations of SARD outperform industry.

Hence, this implies that the different findings from Alford (1992) and Cheng & McNamara (2000) compared to Dittmann & Weiner (2005) and this thesis, relate to their application of equity multiples, i.e. P/E and P/B, rather than EV-based multiples.

Similar to Dittmann & Weiner (2005), Nel & le Roux( 2015) find in the majority of their results, that fundamentals outperform a pure industry approach. However, the quoted study investigates 16 different price-multiples and shows for some specific multiples that an industry selection achieves higher prediction accuracy than on a single fundamental. Evidently, their findings show a clear outperformance of industry when combining more than one fundamental.

Such results conform to the findings in this thesis, which suggest that by adding a relevant

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selection variable for the multiple in subject, an improvement in valuation accuracy is seen, hence, the improvement in the SARD combinations in Section 5.2.2 and 5.3.2. Similar to the rest of the literature, Nel & le Roux (2015) suggests that no single multiple is superior. However, a pattern is observed in the quoted studies as the EV/Sales multiple in general leads to a higher level of prediction errors compared to EV/EBIT, P/E, and P/B (Herrmann & Richter, 2003;

Knudsen et al., 2017). Similarly, the analysis in this thesis finds that the median prediction errors for EV/Sales range between 0.71 to 0.39, compared to the two earnings-multiple which ranges between 0.50 to 0.33, supporting this particular finding. Thus, both Dittmann & Weiner (2005), Nel & le Roux (2015), and Herrmann & Richter's (2003) overall results conform to the main finding of the analysis conducted in Section 5.2-5.4, as a fundamentals-based peer selection outperforms a pure industry-based. However, variations are seen in the methodological choices compared to this study as the applied sample, underlying peer pool, peer group size, choice of multiples, and selection variables are dissimilar, which must be kept in mind when comparing the findings of this study to previous literature.

Furthermore, Bhojraj & Lee (2002) also align with the fundamental school of thought but applies a different research methodology compared to the rest of the literature. The authors conduct a regression approach of a ‘warranted multiple’ and similarly find that fundamentals lead to higher prediction accuracy than industry. However, the selection variables used as proxies for estimating the ‘warranted multiple’ are not solely financial fundamentals as some are in fact adjusted for industry. In contrast to this thesis, Bhojraj & Lee's (2002) methodological approach provides them with information on which variables are more appropriate for each multiple applied, hence, such setup allows them to customize the applied selection variables for each specific multiple. On the contrary, the model used in this thesis is not constructed to fit a specific multiple as the same selection variables are applied for EV/Sales, EV/EBITDA, and EV/EBIT. The obtained findings also suggest that selection variables’ appropriateness depends on the multiple in use. For instance, as seen in Section 5.2.2 and 5.3.2 a strong interrelation between the EBIT margin and EV/Sales is evident as it improves the prediction accuracy of the multiple significantly, while improvements are insignificant when adding the EBIT margin to the EV/EBITDA and EV/EBIT multiple. Furthermore, the univariate tests performed also suggest that customisation of selection variables to the applied multiples yields greater accuracy which will be further interpreted in Section 6.2.

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Finally, the findings in this thesis suggest that the pure SARD method leads to greater accuracy the more selection variables are added regardless of whether the underlying peer pool is Danish or consists of EU firms. This aligns with Bhojraj & Lee (2002) and Nel & le Roux (2015) who find that a combination of fundamentals is better than solely using one single proxy when applying a home-country peer pool. Furthermore, Herrmann & Richter (2003) draw similar conclusions while also Dittmann & Weiner (2005) find that even though ROA outperforms industry alone, a combination of ROA and Total Assets yields even greater prediction accuracy for EV/EBIT. Their findings hold regardless of whether the peer pool comprises firms from a home-country or from across borders similar to this thesis. The only contradicting research paper to the obtained findings is Alford (1992), as he finds that ROE on a single basis is more accurate than a combination with Total Assets, however, these results are solely based on equity multiples using a US sample.

6.1.3 Literature combining fundamentals and industry

Lastly, combining fundamentals with industry affiliation in this thesis, i.e. INDSARD, is compared to the reviewed studies that touch upon this topic. The studies in favour of an industry approach, i.e. Alford (1992) and Cheng & McNamara (2000) also investigate the prediction of combining industry with one or two fundamentals. Alford (1992) finds that neither ROE nor Total Assets are marginally useful when they are combined with an industry criterion. As the results of the SARD versus INDSARD methods are rather ambiguous in this thesis, since they are dependent on the number of selection variables, neither a pure fundamental approach nor a combined method is superior. However, when looking at the results of the combination method INDSARD1, it outperforms a pure fundamental approach. This is contradicting with Alford (1992), as INDSARD1 solely consists of ROE and outperforms SARD1 across industries and is evident for both a Danish and EU peer pool. Hence, ROE is useful in this thesis when combined with industry as opposed to Alford's (1992) suggestion. The differences between the results can stem from the choice of multiples and other methodological decisions undertaken as discussed in Section 6.1.2. Contrarily, Cheng & McNamara's (2000) findings indicate that a combination of ROE and industry in fact lead to better prediction accuracy than a pure industry selection method, which conforms to the findings of this study.

The literature which favours fundamentals shows somewhat ambiguous results when investigating a combined approach between industry and fundamentals which corresponds to

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the findings obtained in this thesis. The studies by Bhojraj & Lee (2002) and Herrmann &

Richter (2003) are in opposition to each other. Bhojraj & Lee (2002) find that when adding an industry selection criterion to peer selection based on the ‘warranted multiple’, an increase in prediction accuracy is achieved, thus, favouring a combined approach. However, the increase is marginal while the significant improvement from the benchmark, i.e. a pure industry selection method, stems from solely applying fundamentals rather than combining those with the industry. This corresponds to the findings of the thesis as the improvement of a combination method for INDSARD1 and INDSARD2 from SARD1 and SARD2, is marginal when observing the general level of prediction accuracy compared to the improvement achieved from fundamentals rather than industry affiliation. Contrarily, Herrmann & Richter (2003) find that industry classification does not contain superior information to what is already controlled for when adding enough fundamentals, which conforms to the findings from this study, as SARD combinations with enough proxies are not outperformed by a combination with industry as seen from Section 5.2.3 and 5.3.3. However, the combination method, INDSARD, outperforms a pure fundamental approach when less than three or four selection variables are applied (dependent on the multiple used), agreeing with the findings of Bhojraj & Lee (2002). Ultimately, the different results in whether a combined method or a pure fundamental approach yields the most accurate predictions must stem from the methodological set-up between the two reviewed research papers, and this thesis. Overall, the superior method is dependent on the selection variables used as seen in both the findings of this thesis and literature.

6.1.4 Literature on the underlying peer pool

When examining the relative performance between each of the selection methods, (1) Industry (2) SARD and (3) INDSARD, the same pattern appears regardless of the peer pool applied.

This corresponds to the findings of Dittmann & Weiner (2005) who suggests that for 312 Danish target firms from 1999 until 2002, the performance of Market, Industry, Total Assets, ROA, and a combination of ROA and Total Assets stays the same relative to one another regardless of the peer pool containing home-country, EU, or OECD firms.

In relation to Hypothesis 3 of this study, the underlying peer pool’s influence on prediction accuracy for Danish targets suggests that when applying the most accurate combinations of SARD and INDSARD, an expended cross-country peer pool of EU firms yields more accurate results than home-country peers for EV/EBITDA and EV/EBIT. For EV/Sales, combinations

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of SARD and INDSARD are indeed more accurate when using cross-border peers, however, solely until the EBIT margin is applied, where the most optimal combination performs better using a pure Danish peer pool. Similar, Dittmann & Weiner (2005) overall find that European countries obtain more accurate valuation predictions for EV/EBIT once peers are found among European Union member states or within OECD countries. However, as one of only four exceptions, the quoted study’s findings do not hold for Danish targets, as their study suggests that valuation errors are minimized when peers are in fact found using home-country firms. The differences to this thesis’ findings can be related to several factors. While this study investigates SARD and INDSARD with several fundamentals, Dittmann & Weiner (2005) solely considers ROA and Total Assets as selection variables. Furthermore, their sample of Danish targets solely covers the period from 1999 until 2002, i.e. there is no overlap in the time period. An important attribute to the sample applied in this thesis relates to the accounting standard as all firms adapted IFRS in 2005. Thus, dissimilarities in accounting standards are presumably affecting ROA and Total Assets in Dittmann & Weiner's (2005) research, unlike in this thesis, when finding peer cross-border.