Peer selection using the SARD approach

To determine peers based on fundamentals using the SARD approach, a workflow has been created using the analytic software Alteryx (Appendix 17, Table 17.1). The algorithm developed is based on Equation 3.1 in Section 3.2 and is built in a series of steps, which ultimately seeks to

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minimize the SARD-score. The first step in the workflow is to rank all Danish firms from smallest to highest for each selection variable in each year from 2010 until 2019. Secondly, the difference in ranks between each target firm and the rest of the peers is calculated on a yearly basis. By summing the differences across all selection variables for each target, the SARD value is calculated. Peers are ultimately chosen based on the firms with the lowest SARD scores relative to a target. As the peer group size is set to four, the four closest firms to target for each selection variable are chosen, i.e. if a target has the 20^th highest ROE, the peer group would consist of those having the 18^th, 19^th, 21^st, and 22^nd highest ROE. Thus, the firms which are most similar to a target based on the chosen selection variables, are selected as peers. As the algorithm includes the target firm in the calculations, all SARD-scores equalling 0 are excluded from the estimation sample as a target cannot serve as a peer for its own multiple predictions.

In cases with identical summed ranks, the algorithm chooses peers randomly similar to how Knudsen et al. (2017) conduct their calculations. Since the calculation of SARD is based on relative rankings, peer groups change for each target, i.e. if company A serves as a peer to company B, company B does not necessarily serve as a peer to company A. Furthermore, as firms’ fundamentals change over time, peer groups are formed on a yearly basis, thus a target might have different peer groups each sample year.

When appointing peer groups based on the EU dataset, the same procedure is followed: the rankings of the selection variables are performed relative for all firms in the EU from smallest to highest each year. However, as the objective of this thesis is to determine how to find peers on a small market like Denmark, solely Danish targets are examined. Hence, SARD scores are only calculated for Danish targets while peers are selected among all firms in the EU.

4.3.1 Variable selection

As prescribed in Section 3.2, SARD has no restrictions for the number of selection variables used as opposed to other fundamental approaches. In Knudsen et al.'s (2017) study ROE, Net Debt/EBIT, Size, EPS growth, and EBIT margin are used as proxies for profitability, risk, and growth and provide the basis for their results and ultimately the arguments in favour of the SARD approach relative to industry affiliation. Hence, this study examines the peer selection for Danish targets using the same selection variables to reduce potential biases relative to the original study in order to compare results. The motivation of including these variables and how

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such fundamentals serve as proxies for profitability, risk, and growth will be examined in the following.

ROE is the first selection variable applied, as previous literature including Alford's (1992), Cheng & McNamara (2000), Bhojraj & Lee (2002), and Nel & le Roux (2015) has obtained appropriate results using ROE as a proxy for profitability. ROE reflects the return of the owner’s investment as it takes both profitability of operations and the effect of financial gearing into account as it denotes the return after debt is served (Petersen et al., 2017). However, since this study solely examines EV-based multiples, the theoretical derivation in Section 2.2 indicates that ROIC should be preferred as a proxy for profitability as it is independent of capital structure which corresponds to the Enterprise Value which reflects all value that flows to both equity- and debt holders. Despite the theoretical favouritism, none of the previous literature considered takes ROIC into account when using EV-multiples due to practical challenges of classifying Invested Capital for all target firms. Knudsen et al. (2017) achieve increased prediction accuracy using ROE for EV/EBIT while, similarly, Herrmann & Richter (2003) achieves it for both the EV/EBIT and EV/EBITDA multiple. Thus, ROE is also applied as a proxy for profitability in this study. Further motivation of using ROE is found from the close theoretical relationship to ROIC as Petersen et al. (2017) define it as follows, where NBC is net borrowing costs in percentage, NIBL is the (book) value of net interest-bearing liabilities and BVE expresses book value of equity:

ROE = ROIC + (ROIC - NBC) * ^NIBL

BVE (4.2) Besides underlining the relationship between ROE and ROIC, it also demonstrates that the cost of debt is already included in ROE. Consequently, ROE should be compared to the cost of equity rather than WACC, which is used as calculation rate to EV, since the cost of debt will otherwise be considered twice²⁴. Hence, Equation 4.2 both serves as an argument against and in favour of using ROE to simplify implementation. Ultimately, it is clarified to be a complex discussion between theory, practical implication, and empirical results. For this reason, ROIC will be applied later in the robustness checks to determine if applying a simplified, generic

24 Since both ROE and WACC takes cost of debt into account

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calculation of Invested Capital yields more accurate multiple predictions than ROE in order to challenge the literature’s assumptions.

As another proxy for profitability, EBIT margin is applied, since it achieves significant improvements when predicting EV/Sales multiples in previous literature (Knudsen et al., 2017).

This corresponds to the theoretical derivation shown in Equation 2.11, where EBIT margin must be included to uphold the reflection of the firm’s total value and achieve similar results as to earnings multiples. On the contrary, EBIT margin does not theoretically serve any improvements on valuation using EV/EBITDA and EV/EBIT, however, it will be included for all multiples applied in this study in order to uphold a basis for comparison. At the same time, EBIT has the advantage, opposed to ROE, that it is neither affected by capital structure nor taxes. As this thesis intends to both determine the optimal peer selection method while also comparing the accuracy using different peer pools for Danish targets, this makes up a great advantage since targets across country borders would likely be affected by different corporate tax rates and policies, which EBIT margin will not be subject to.

Net Debt/EBIT is applied as a proxy for financial risk since it implies whether a firm’s funds from operations are sufficient to meet debt obligations. Applying Net Debt/EBIT in Knudsen et al.'s (2017) study of SARD leads to significantly improved prediction accuracy for both EV/Sales and EV/EBIT indicating that the market’s perception of firm risk is correlated to its payback capacity. Knudsen et al. (2017) justify the choice of this selection variable by the general application of Net Debt/EBIT in credit analysis where a high ratio indicates great liquidity risk as a firm may not be able to pay off its debt by the available profits in the short-run. On the other hand, Bhojraj & Lee (2002) did not achieve improved predictions of EV/Sales multiples using book value of leverage, while Liu et al. (2002) concluded that adjusting for leverage did not improve valuation properties for neither EV/Sales nor EV/EBITDA, hence, debt-equity ratios are discarded as selection variables for risk.

Additionally, Size is applied as a second proxy for risk, as size and risk are theoretically linked as described in Section 2.3.2 since larger firms are better diversified in terms of e.g. projects and real options, while they also tend to have better access to capital markets, are more liquid and the information level and analyst coverage is greater, which overall reduces risk (Berk &

DeMarzo, 2017). Plenborg & Pimentel (2016) in fact perceive the impact of size as an

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implementation issue in itself when performing multiple valuation, which is linked to the empirical evidence first found by Alford (1992). As presented in Section 3.1.1, Alford (1992) found that valuation accuracy is highly correlated with firm size since larger firms yield greater valuation accuracy, as prediction errors in his study are halved for large firms compared to smaller firms. Both Cheng & McNamara (2000), Dittmann & Weiner (2005) as well as Knudsen et al. (2017) support these findings, which constitutes the empirical reasoning of including size as a proxy for operating risk. Knudsen et al. (2017) reflect firm size by applying Market Capitalization, i.e. the market value of equity, as opposed to the rest of literature using Total Assets as a proxy for size. To uphold the basis for comparison to the original SARD developed for the US, Market Capitalization will be applied in this study. It should be noted that an iterative challenge arises as it requires that market data are known to apply the selection variable, however, further discussion is outside the scope of this thesis.

Finally, a proxy for growth should be applied as it is the third value driver, besides profitability and risk, which is crucial for a firm’s value and the theoretical relationship to EV/Sales, EV/EBITDA, and EV/EBIT is demonstrated in Section 2.2. Growth can be reflected using both reported and forecasted numbers. However, as presented in Section 3.3.2, empirical ‘horse races’ suggests that forecasted earnings are preferred which corresponds to the fact that market prices reflect the expectation for future earnings rather than past performance. Hence, Knudsen et al. (2017) apply median analysts’ earnings forecasts from I/B/E/S as a proxy for future growth²⁵. However, in this study, it is not possible to apply future growth as a selection variable for Danish peers since a great portion of the companies in the dataset is smaller firms lacking such analysts’ forecast. Hence, in order to include growth in a selection variable rather than excluding it fully, a one-year historical revenue growth is applied. It is preferred to use more than one-year growth to avoid single-year fluctuations, however, this is prevented since a part of the sample is lacking such historic information, i.e. it would lead to exclusion of further observations. The application will be subject to discussion when the empirical results have determined the appositeness of the variable.

Ultimately, this leads to the application of five selection variables: ROE, EBIT margin, Net Debt/EBIT, Size, and growth. Knudsen et al. (2017) identifies peers from an incrementally

25𝔼[EPS_t+2]⁄𝔼[EPS_t+1]

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increasing ladder of combinations, first applying one selection variable up to all five (p.93). The authors determine the sequence by performing a univariate analysis, which denotes that ROE yields the most accurate valuation predictions while Net Debt/EBIT yields the second-best accuracy etc. Based on the findings for all five selection variables, the following order is applied by Knudsen et al. (2017) for both EV/Sales and EV/EBIT, and the same is used for all three multiples in this thesis to uphold the basis for comparison, however, a univariate test will be performed in robustness checks to determine the optimality of the sequence:

SARD1: ROE

SARD2: ROE + Net Debt/EBIT

SARD3: ROE + Net Debt/EBIT + Size

SARD4: ROE + Net Debt/EBIT + Size + Growth

SARD5: ROE + Net Debt/EBIT + Size + Growth + EBIT-margin

Table 4.2 provides an overview of each selection variable and the related definitions of data items extracted from Capital IQ using the Excel formula plug-in. The calculations of each selection variable follow Knudsen et al.'s (2017) definitions and the data is extracted from Capital IQ. ROE is calculated as net income divided by the book value of equity. Net Debt/EBIT is based on the net debt²⁶ calculated by Capital IQ divided by the disclosed EBIT. Size is found by extracting Market Capitalization directly from Capital IQ based on the total number of shares

26 By default, net debt is set by Capital IQ to be total interest-bearing liabilities deducted by total cash &

short-term investments and long-term marketable securities.

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outstanding multiplied by the share price on the specific date. Growth is calculated as (Total Revenuet⁄Total Revenuet-1)-1 as it is based on historical revenue growth rather than earnings forecasts. Lastly, the EBIT margin is defined as Total Revenue divided by EBIT. Both financials and market data are identically defined and extracted for both Danish targets and the extended peer pool of EU firms.

To illustrate the procedure of the SARD approach and summarise the above sections, an example is shown in Table 4.3. For illustrative purposes, the sample is assumed to solely consist of 10 companies and peer selection is for the sake of simplicity based on the first two selection variables, i.e. ROE and Net Debt/EBIT. Panel A shows the first step of the SARD approach where each of the ten firms is ranked from smallest to highest (1-10 in this case) relative to the sample based on ROE and Net Debt/EBIT, respectively. Coloplast A/S is for instance ranked the highest (10) with a ROE of 39% while ranked sixth (6) out of ten with a Net Debt/EBIT ratio of 0.85. In Panel B, the next step is presented as the rank differences are calculated relative

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to a target firm (here: Ambu A/S). Hence, the absolute rank differences are calculated for each of the selection variables and summed in the SARD-score. As an example, serving as a natural peer to Ambu, Coloplast yields a SARD-score of 6: /r_{ROE, Ambu} - rROE,Coloplast/ + /rND/EBIT, Ambu - rND/EBIT,Coloplast/ = |5-10|+|7-6| = 6. Ultimately, based on SARD-scores relative to the target firm, the peer group can be identified. Ambu yields a SARD-score of 0, and is, as explained, excluded from the estimation sample as it cannot serve as a peer to its own multiple predictions. As the peer group size is set to be four, the four firms with the lowest SARD score, i.e. the most similar in terms of ROE and Net Debt/EBIT are selected as peer group. In this case, the peer group consists of Enalyzer A/S, North Media A/S, and A.P. Møller Mærsk A/S while the fourth peer could be either Coloplast A/S or Gyldendal A/S as both yields a SARD-score of 6. Hence, this illustrates how SARD has an element of randomness, as the choice between Coloplast A/S and Gyldendal A/S is not settled by the model.

In this illustrative example, the level of such random component is significantly larger than on the applied sample, since the probability of companies having the same SARD scores decreases with the number of firms. However, variation in empirical results is still arising due to this random component and impacts the relative performance of selection methods as it depends on each simulation. Thus, to ensure robustness in the empirical findings, all selection methods for both the Danish and EU peer pool are simulated until no variations occur in the generated results whereto the average of these results are used in this study.

4.3.2 Cross-validation of SARD

In order to insure the validity and reliability of this study’s results, the SARD algorithm developed in Alteryx is cross-validated to confirm it is corresponding to the original model developed by Knudsen et al. (2017). The authors have provided this study access to the dataset on which the SARD model originally was built upon. This makes it possible to assess how the prediction accuracy of the developed workflow in Alteryx will generalize to other datasets unbiased of the model itself. As seen in Appendix 2, the prediction errors for EV/Sales and EV/EBIT corresponds to what Knudsen et al. (2017) achieve which enhances the reliability of this study’s empirical results.

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