finexpert capital market report

Transcription

1 finexpert capital market report Volume 7 1 Preface & People 3 Current Research 15 Cost of Capital: Overview 20 CAPM: Beta Factor Development 42 Yield Curve: Svensson (1994)

2 Detailed Table of Contents Preface and People 1 Current Reseach 3 Target capital structure in WACC, Beta Un-Levering and Re- Levering in corporate valuation gross or net-debt? 4 Cost of Capital: Overview 15 Cost of Capital Q Cost of Capital Q Cost of Capital Q Cost of Capital Q CAPM: Beta Factor Development 20 DAX MDAX TecDAX Automobiles 24 Banks 25 Basic Ressources 26 Chemicals 27 Construction 28 Consumer 29 Financial Services 30

3 Detailed Table of Contents CAPM: Beta Factor Development (continued) Food & Beverages 31 Industrial 32 Insurance 33 Media 34 Pharma & Healthcare 35 Retail 36 Software 37 Technology 38 Telecommunication 39 Transport & Logistics 40 Utilities 41 Yield Curve: Svenson 42

4 Preface Dear finexpert members, we are pleased to release the 2017 finexpert capital market report. The report contains cost of capital developments over the last year, 1 and 2 Year Beta estimates since 2015 for the Prime All Share indices as well as Yield Curve estimates. The report is meant to be a comprehensive reference for cost of capital estimates where finexpert users can find sector-specific information for valuation purposes. We also provide an update about the newest academic research on cost of capital and related topics. The paper that we present discusses the use of gross versus net debt for unlevering/re-levering the beta factor. Enjoy reading! Best regards, Prof. Dr. Bernhard Schwetzler, Chair of Financial Management HHL - Leipzig Graduate School of Management 1

5 People Prof. Dr. Bernhard Schwetzler Capital market data Jun.-Prof. Dr. Alexander Lahmann Capital Market data, Yield Forecasts Dr. Benjamin Hammer Capital Market Data Sarah Hoy, cand. M.Sc. Technical Editing Malte Wolf, cand. M.Sc. Technical Editing 2

6 Current Research 3

7 Current Research on Cost of Capital Target capital structure in WACC, Beta Un-Levering and Re-Levering in corporate valuation - gross- or net-debt? 1 Bernhard Schwetzler For the valuation of unlisted companies cost of equity cannot be derived from observable market prices. Many practitioners work with industry betas that are adjusted for differences in the capital structure. The adjustment procedure (dubbed un-levering and re-levering ) is using a particular equation determining the impact of leverage upon the beta of a company. However it is not quite clear whether the equation should be used on the basis of gross debt or on the basis of net debt (i.e. the difference between gross debt and cash/financial assets). This note argues in favour of the use of net debt. I. The problem For the valuation of listed companies, the CAPM has prevailed as a model to derive the cost of equity in valuation practice. For unlisted companies, the transfer of estimated betas from a selected peer group or from the corresponding sector is recommended as an approximation. 2 Since betas are dependent on capital structure, a direct transfer of the estimated peer group -betas is only possible if the capital structures of the companies in the peer group or sector are equal to the one of the company to be valued. If this is not the case, an adaptation to different capital structures is recommended, referred as un- levering/re- levering. In this case, the following relationship between the beta of a levered firm (so-called equity -beta or levered beta β E ) and the beta of the same, but unlevered firm (so-called asset - beta or unlevered beta β Asset ) is assumed: (1) denotes the corporate tax rate and D/E the (target) leverage of the company. Equation (1) highlights on the one hand the additional financial leverage - risk arising from the risk-free payments to be made to the lenders. On the other hand, (1) assumes a tax system only considering corporate taxes. Interest is tax deductible, so that the company realizes an added value effect called tax shield from the proportional debt financing. In addition, the above equation implies a certain financing policy with a permanently constant debt level that is independent of the company's future development. 3 The dampening effect on the leverage risk given in (1) by the factor (1 - ) is explained by the fact that the appropriate tax savings occur without risk. Thus the increased risk from the proportional leverage is partly compensated. Finally, equation (1) assumes that the debt of the company is risk-free; technically speaking, the debt is - beta β D as a risk measure for the creditor is zero. The adjustment procedure proposed uses equation (1) first "backwards": The estimated equity - beta of the industry is "un-levered" thus deriving the asset beta as a measure of the overall risk of the companies in this industry. For this procedure, the aggregate capital structure in the industry (in market values) is used. In the second step, the re- levering the individual capital structure of the company is set to transpose the asset - beta of the industry into the equity beta of the firm. Fig. 1 highlights the adjustment procedure. 4

8 Figure 1: From Industry-Beta to Firm- Beta: Un- levering and Re- levering INDUSTRY (Automotive) FIRM TO BE VALUED Equity beta Asset Beta Re-Adjustment for Firm-specific leverage Equity beta 1,26 1 Industry Firm 1, (1 0,35) 1,67 = 0,60 [1+(1 0,35) 2] = 1,40 un-levering" Gross Leverage Automotive Industry = 1,67 ASSUMPTION: Asset risk within industry is comparable "re-levering" Gross Leverage Firm = 2 The approach presented in equ. (1) uses the gross debt to equity ratio of the company and the industry for the un- levering and re levering procedure. The asset beta derived in the first step corresponds to the risk of all assets of the peer group - company or the aggregate sector; it also includes the risk of a possibly existing stock of financial assets, such as securities and cash. If the risk of these assets is significantly different from the risk of the operating assets then the asset beta derived for the industry is biased by different levels of financial assets. This leads to the question whether the procedure of un- levering and re- levering should be performed based on the net - or on the gross leverage ratio. This paper shows that as a rule using net - debt leverage ratios yields correct results. The (more common) application of the gross leverage ratios may result in significant deviations. II. The beta - decomposition One of the central (positive) features of the CAPM is the additivity principle: It states that, regardless of the correlation of the cash flows of two securities, the value of a portfolio of both companies simply results in the sum of the two individual values. The beta - factor is the weighted average of the betas of the two individual companies. 4 The corresponding result can also be applied on the beta of the assets and liabilities of the company: the beta of all assets is the weighted average of the betas of each asset or business line; on the liability side, the entire risk is split into the two positions of equity and debt. Again, the overall risk to be borne results in a weighted average over the shareholders' equity - and the debtholders debt beta. Differentiating between operating assets and financial assets on the assets side, this results in the following balance sheet identity: 5 (2) Here Fin and Op denote the respective market values of financial and operating assets and β Fin and β Op corresponding betas. Equation (2) shows how the asset risk "produced" by the assets is split into the risk of equity and debt. Equation (1) above assumes risk-free debt and thus β D = 0; thus the entire asset risk is projected into the share of the equity holders. On the other side, the entire asset - beta is the weighted average over the operating asset - beta and the beta of the financial assets; the weights correspond to the proportionate market values. 5

9 Crucial for the application of the equation (1) for the un- and the re levering procedure is thus the question of whether the two asset betas β Fin and β Op differ from each other. At least for the position "cash" there are good arguments for differences between the two betas: The company's flat cash holdings regularly achieve risk-free interest income; therefore they have a beta of zero. Theoretically, the risk effects of cash positions mirror those of risk-free debt: risk-free, state independent interest expenses are the counter part of risk-free, state-independent interest income. Assuming for simplicity identical interest rates for borrowing and lending, then cash can be considered as negative debt with respect to its risk and its cash flow effects. Considering the outstanding importance of the cash position within the financial assets, then there are good arguments for my opinion to set β Fin = β cash in equation (2) with a value of zero. Equation (2) would then look like this: 6 (2) It follows first (3) The market value of the operating assets Op is (4) This eventually results in (5) Equation (5) suggests that net debt is relevant when linking (operating) asset and equity betas. Equations (2) to (5) do not yet take into account taxes. Concentrating on corporate taxes and assuming a symmetric treatment of interest in the tax code, i.e. the tax deductibility of interest expenses corresponds to the taxation of interest income on corporate level, the tax benefit of (gross) debt is partly offset by a tax disadvantage of the interest income. The valuation of the (net) tax benefits finally requires an assumption about the financing policy of the firm. We assume the firm to follow a policy of a constant, state independent level of debt and cash over an infinite timeframe. The market value of the company s equity is regularly reflecting the net tax benefits stemming from cash and debt holdings. We assume the absolute debt to exceed the level of cash and thus a positive net debt. Under the above assumptions the present value of the entire net tax shield is positive: The risk equation extended for the tax effects looks like this: 7 (6) (7) Among the assumptions set above the positive and negative tax effects of cash and debt and therefore their balance are risk-free, i.e. set β Net Debt = 0. Assuming risk-free debt and risk-free cash β D = β Cash = 0, this results in the following relationship between the operational asset beta and the equity beta of the company: 6

10 Due to the balance sheet identity, for the market values is to hold. Taking into account the above equation for the determination of TS Net Debt this results in the following relationship between the operating asset - beta and the equity - beta: As (10) suggests, net debt is still relevant if we include corporate taxes. (8) (9) (10) III. The consequence for the un - levering and re - levering: net debt is relevant Comparing the two beta - equations (1) and (10) highlights the most important assumption for the potential choice between them: a) Applying equation (1) assumes that the risk of all assets (financial assets and operating assets) is comparable within the peer group or industry. b) Un-levering and re -levering in equation (10) is correct if the risk of the operating assets is comparable within an industry. Clearly the assumption behind equation (10) is more reasonable: The use of industry data as a benchmark in corporate valuation is based on the idea that the comparability of key variables such as growth, profitability and risk of listed corporations in an industry allows to compare listed and unlisted companies in the same industry. The classification of companies in different industries is always based on their operational activities. Thus the risk of operating assets within an industry should be comparable; the appropriate technical assumption is that the operating asset - beta is the same within an industry. The use of the total asset - betas however may yield incorrect risk assessments when companies are in the same industry and share the same operational risk properties, but display different financial assets and cash positions. Applying identical total asset - betas on all firms in an industry would only be justified if all companies do not only display comparable operating risks, but also have a comparable composition of operating and financial assets. As the fraction of financial assets of companies within the same industry shows significant dispersion, this can hardly be expected. The consequence of these considerations is that the un - levering and re - levering procedure should be performed with the leverage ratio based on the net debt, i.e. debt minus cash and financial assets instead of gross debt. IV. An example 1. The un- levering of industry - betas The procedure is highlighted using an example, based on real figures for the automotive sector of the fourth quarter of Table 1: Estimated beta Automotive Industry Q YR levered (equity) Beta β L D / E (Market Values) Unlevered (asset) beta β U (Based on MM) Net D / E (Market Values) Operating unlevered (asset) beta β U (Based on MM) vs. Previous vs. Previous vs. Previous YR vs. Previous YR vs. Previous YR YR YR ß L R 2 n % CAGR % CAGR % CAGR % CAGR % CAGR % % % 2.9% 0-1.8% - % % 2.7% 8 - % -0.2% 7

11 The equity - beta of the Automotive Industry (15 companies) estimated via regression analysis is 1.26; the industry leverage based on gross debt is 1.67, based on net - debt Setting an absolute debt level of an aggregate balance sheet (measured in market values) for the automotive industry can be derived; for the liability side of the balance sheet this yields: For the asset side, first the cash balance is determined: The market value of the operational assets on the one hand can be calculated as "levered enterprise value" that is including of the net - tax benefit from the leverage or as "unlevered enterprise Value" without the net - tax benefit: 10 Table 2: Asset structure, capital structure and balance sheet in market values automotive industry Q Balance sheet total assets liabilities cash % equity % EV unlev % debt % TS net debt % Firm Value % Firm Value % The un-levering of the estimated industry s equity beta can now be based on the net-debt leverage of 1.32 of the industry; we obtain then the operating asset beta: β op.auto reflects the risk of an all equity financed company in the automotive - industry without any cash holdings, securities and other financial assets. The corresponding cash flow for the valuation of the company is the free cash flow from operations as "free cash flow to entity". If, however, the gross - debt ratio of the industry is used, un - levering yields the (total) asset beta: 8

12 β asset.auto reflects the risk of an all equity financed company with an average sector (risk-free) cash position of about 13% of its total firm value. The corresponding cash flow for the valuation of this company then must reflect the after - tax cash flows generated by all assets of the company: the free cash flow from operations (free cash flow to entity) plus the after - tax interest income generated by cash, securities and financial assets. Since the latter fraction of the total cash flows is riskless the total asset - beta (04) is lower than the operating asset - beta (78). 2. The re levering to the company - beta The asset - beta of the industry is the starting point for the valuation of the company in the same industry. We assume that DCF WACC approach is applied. The industry s - beta is the starting point for determining the cost of equity of the company to be valued. For the calculation of the WACC a target capital structure is needed, serving as weights for the cost of equity and the cost of debt. Here again, two options are available: a) The (target -) capital structure is based on the capital structure using gross debt. b) The (target -) capital structure is based on the capital structure using net debt. The following example shows that based on the operating asset beta of the industry the application of the capital structure based on net - leverage will yield the correct value for the firm s equity. For this, the net - debt ratio for both the re levering procedure and the calculation of the cost of equity as well as the weighting of equity and debt in the WACC is to be used. The WACC is then applied to discount the company's free cash flow to entity, thereby determining the company's levered enterprise value. In the last step of valuation, the net debt will be deducted from the firm s levered enterprise value and result in the value of equity. For our example the firm s leverage ratio based on net debt of and based on gross debt of is given. The firm s equity beta is then derived by re-levering the industry s operating beta: Table 3 shows the calculation of the (target -) capital structure and cost of capital of the company to be valued. Table 3: Calculation of the cost of capital and the corporate value using the net debt- (target) capital structure Risk-free interest rate 5% Market risk premium CAPM 5% Cost of equity company Cost of debt 5% Weight of debt (Net debt leverage) WACC company (Net debt leverage) Free cash flow (entity) 50,0 9

13 Based on this information, the "levered" enterprise value is determined as the value of the operating business of the company: Free cash flow to entity is defined before interest expenses, but also before interest income and other financial income. For this reason, the operating asset - beta is the correct starting point for the calculation of the equity - beta for the firm to be valued. By applying the net - debt-equity ratio for the calculation of the equity - beta and the weights of the WACC we assume that the operating business of the company is financed with a mix of equity and the net debt. The remaining "package" of cash and debt has net a value contribution of zero and therefore does not have to be considered further in the valuation procedure. 11 Net debt is finally deducted from the "levered" enterprise value to determine the equity value. Consequently, the enterprise value calculated includes the (net -) tax benefit from the corresponding (net -) debt financing. The gross level of debt for the firm to be can be determined using the two leverage ratios Net l net / (1-l net ) = and gross l / 1-l = based on the following two equations: (11) This results in the value of the debt (12) (13) and The cash level of the firm can be derived by The net debt is thus The value of equity is then 10

14 Table 4 displays the balance sheet of the firm to be valued in market values. Table 4: Asset structure, capital structure and balance sheet of the firm in market values Balance sheet total assets liabilities cash % equity EV unlev % debt Firm Value % Firm Value % We may use the adjusted present value (APV) approach to validate our result. Here, the enterprise value is calculated based on the assumption of all equity financing (unlevered), by discounting the free cash flow to entity with the cost of equity under (fictitious) all equity -financing and without cash / securities. Based on the industry s operating beta this cost of capital can be determined by: The enterprise value (unlevered) is then Adding the tax benefit from net - debt yields the levered enterprise value calculated above with the WACC model: The majority of the literature recommends un levering and re - levering based on the gross - debt leverage ratio. Thus the question is under which circumstances this procedure leads to correct results. 1. Determination of the WACC and of the enterprise value We start with the firm to be valued. The company's WACC will now be based on the gross debt leverage. If the corresponding cash flow definition is the sum over the free cash flow to entity and the after - tax interest income, then discounting with the WACC based on gross debt leverage will obtain the correct the firm value as the value of all assets of the company. The cost of capital of the total assets here correspond with the total cash flows generated by it. For the figures of the above example, the value of the firm is derived in Table 5. 11

15 Table 5: Calculation of the cost of capital and the corporate value of the firm using the gross debt - (target -) capital structure. Risk-free interest rate Market risk premium Cost of equity firm Cost of debt firm Weight of debt (gross capital structure) firm WACC (gross capital structure) firm Free cash flow (entity) + interest income after taxes 5% 5% 5% Firm Value By deducting the gross - debt (199.46) we get the correct value of equity (498.66) using this way. For the valuation of the firm relying on the gross debt capital structure is not a problem if the WACC is applied on the total cash flows of all assets, i.e. the free cash flow to entity plus the (gross) interest income after taxes. 2. The derivation of the equity beta and cost of equity by un - and re - levering As we have seen, for the valuation of the company the WACC approach based on gross debt - capital structures may yield correct results, if applied on a modified cash flow. Unfortunately, this does not apply for the un- and re-levering procedure in order to derive the cost of capital for the firm being valued from industry betas. The reason for this is that even for the application of the gross debt leverage based WACC the correct cost of equity are necessary for the valuation of the company. 12 As shown above, the un- and re-levering procedure starting from the industry s equity - beta can be based on the respective net - debt ratio D/E net, Ind. of the industry D/E net, firm of the company. This yields the following relation : If the un - and re levering procedure is performed on the basis of the gross - debt leverage ratios D/E gross, Ind. and D/E gross, firm resp., we obtain the following relationship: Since the equity - betas of the industry and the company β E,Ind and β E,firm as being the starting and the end point of the process must be identical in both cases 12, the following relationship would have to hold for the correct valuation of the target. 12

16 (11) Equation (11) can easily be interpreted: gross - and net - gearing set the respective "lever" for the backward calculation of the un - levering and the forward calculation of re - levering. If the ratio of the two "forward -" and "reverse leverages" in the net debt - approach is the same as in the gross debt approach, one gets from the same starting point of the equity - beta in the industry to the same destination point of the equity beta of the firm to be valued. Another simple interpretation offers a simple conversion from (11): the ratio of gross - lever to net - lever must be the same for calculating backward at the industry level and forward at the enterprise level. This interpretation also leads to the conclusion that condition (11) will be satisfied only in very exceptional cases: Within a particular industry differences between the different firm s gross debt - and net debt leverage ratios exist; the difference between the industries average and the individual companies within the industry is precisely the reason for the un - and re levering procedure. Thus, in order to arrive at the correct result the deviation of the company s leverage from the industry s - average has to be identical for the gross debt - gearing with that for the net debt - gearing. That will be the case by chance at best. VI. Limitations The result derived here is based on some assumptions that are worth to be discussed (and certainly will). The most important assumption is that cash is equal to "negative" debt in all relevant properties. - The valuation equations assume a symmetrical tax treatment of interest income and interest expense. Correspondingly, the positive tax shield of debt is offset by a negative tax shield from the tax disadvantage of interest income at company level. This disadvantage results from the higher taxation of interest income at company level in the tax regime assumed here: the company has to pay taxes on the interest income, while at the shareholder level it is taxexempt. In the German tax system the balanced tax treatment of interest income and expenses is not given. - The model assumed for the cash the identical "Modigliani/Miller financing policy" as for debt. This financing policy is generally subject to criticism from several reasons: First, the assumed permanent debt position is not compatible with the definition of capital costs as oneperiod conditional returns. Secondly it does not seem very plausible to assume that the company is able to maintain a certain debt level permanently to t = independently from the future uncertain development of its cash flows. However, this objection is not relevant to the result derived here. The result derived here occurs even if another financing policy, such as a "value-based" financing policy according to Miles/Ezzel, is assumed. This would only change the tax shield on the net debt and the tax effect in the "leverage - equation" linking equity - beta and asset beta or operating asset beta. - The model assumed the same financing policy for the cash and debt; the adjustment of the cash level and the debt level following possible changes in the company's future value should be the same for both components of net debt. This is not very realistic: debt levels are regularly fixed by contractual agreements with creditors; premature repayment is often not possible. By contrast, cash and securities holdings can be used much easier and faster for investment, changed distributions, etc. without the need for contractual agreements. Empirical studies also show that management of the cash level by the company's management follows different rules than that of the debt level. This finding, however, does not fully invalidate the result derived here: Different 'policies' for cash and debt have different degrees of risk associated to the tax 13

17 effects and therefore result in different beta - factors of active and passive tax shields. The proposed procedure allows in principle different policies for cash and debt. VII. Endnotes 1 This is a shortened version of the German article Zielkapitalstruktur im WACC und Un-levern, Re-levern bei der Unternehmensbewertung Brutto- oder Netto-Verschuldung? in BewP 2/2017 pp publishes quarterly estimated industry betas since 2007; the procedure is based on the industry classification of Deutsche Börse AG. 3 The corresponding financial policy is also called MM - policy designated by Modigliani / Miller, 1961 who derived the corresponding evaluation equations. 4 Even in case of a negative correlation of the two payment streams and an associated risk reduction there will be no reduction in the relevant risk and cost of capital below the weighted average. The reason for this is that investors have already privately realized this benefit by portfolio formation. 5 The entire beta factor of all assets must be identical to the beta factor of all liabilities. 6 Equation (2) assumes ß D = 0 and cash being the only financial asset. 7 If cash > D with negative net debt, the corresponding risk of net tax disadvantage would be reported on the liabilities side of the risk equation. 8 The numbers are taken from the quarterly survey of industry betas of 9 At industry level only the ratios between the various positions are of interest. 10 The calculations are performed here and on with a corporate tax rate of 35%. 11 Since interest income and expense are exactly equal and have the same risk ignoring their impact is correct. If the tax treatment of interest income and expenses is symmetric then the net tax effects are zero. The remaining tax benefit of the (positive) net debt is included in the "levered" enterprise value. 12 The risk of equity does not dependent on whether the valuation is performed via the gross debt or the net approach. The equity beta and the cost of equity of the company therefore have to be identical in both approaches. 13 Equity Beta and cost of equity are identical in the gross debt and in the net debt valuation approach. Prof. Dr. Bernhard Schwetzler, CVA is Professor of Financial Management at HHL- Leipzig Graduate School of Management. 14

18 Cost of Capital: Overview 15

19 Prime All Share Industries, DAX 30, TecDAX 30, MDAX 50 Cost of Capital Q as of year Equity Beta R² 2 year Equity Beta R² 5 year Equity Beta R² n Cost of Equity (based on 1y beta) Debt - Equity ratio (market values) Asset beta Prime All Share Industries Asset Beta Miles Ezzell debt beta = Net-Debt - Equity ratio (market values) Operating Asset beta Operating Asset beta Miles Ezzell debt beta= Automobiles 1,27 0,79 1,24 0,80 1,43 0, ,2% 1,71 0,60 0,61 1,35 0,68 0,67 Banks 1,78 0,55 1,37 0,54 1,36 0, ,0% Basic Resources 1,07 0,39 0,95 0,40 0,89 0,38 4 6,1% 0,78 0,71 0,70 0,47 0,82 0,81 Chemicals 0,97 0,82 1,06 0,89 1,01 0, ,5% 0,32 0,80 0,79 0,28 0,82 0,81 Construction 1,09 0,69 1,01 0,69 1,11 0,62 4 6,2% 0,44 0,85 0,83 0,25 0,94 0,92 Consumer 0,70 0,62 0,78 0,71 0,81 0, ,0% 0,03 0,68 0,68 0,01 0,69 0,69 Financial Services 0,68 0,52 0,75 0,64 0,68 0, ,9% Food & Beverages 0,66 0,20 0,48 0,07 0,33 0,02 1 3,8% 0,55 0,48 0,50 0,42 0,52 0,53 Industrial 1,01 0,85 0,97 0,88 0,97 0, ,7% 0,42 0,79 0,78 0,26 0,86 0,85 Insurance 1,08 0,77 0,94 0,79 0,95 0,70 4 6,1% Media 0,79 0,57 0,77 0,64 0,77 0, ,5% 0,22 0,69 0,69 0,14 0,72 0,72 Pharma & Healthcare 0,87 0,62 0,92 0,70 0,65 0, ,9% 0,33 0,72 0,71 0,29 0,73 0,73 Retail 0,85 0,58 0,74 0,60 0,87 0, ,8% 0,29 0,71 0,71 0,10 0,79 0,79 Software 0,85 0,70 0,84 0,74 0,86 0, ,9% 0,12 0,79 0,78 0,03 0,84 0,83 Technology 1,13 0,63 1,08 0,59 0,97 0, ,4% 0,19 1,01 0,99 0,04 1,10 1,09 Telecommunication 0,91 0,67 1,02 0,74 0,81 0,46 8 5,2% 0,72 0,62 0,62 0,63 0,64 0,64 Transport. & Logistics 1,00 0,77 0,91 0,73 0,93 0, ,6% 0,55 0,73 0,72 0,39 0,79 0,78 Utilities 1,24 0,43 1,13 0,41 1,04 0,30 8 7,0% 1,73 0,58 0,60 1,05 0,73 0,72 Prime All Share 1,00 1,00 1,00 1,00 1,00 1, ,7% 0,54 0,74 0,73 0,41 0,79 0,78 DAX 30 1,04 0,99 1,04 0,99 1,05 0, ,9% 0,66 0,73 0,72 0,53 0,77 0,76 TecDAX 30 0,91 0,73 0,89 0,77 0,69 0, ,2% 0,13 0,84 0,83 0,05 0,88 0,88 MDAX 50 0,90 0,89 0,87 0,90 0,84 0, ,1% 0,15 0,83 0,82 0,08 0,86 0,86 Median ROE (Return on Equity) Median Non-cash ROE (Return on Equity) Median ROC (Return on Capital) Median Non-cash ROC (Return on Capital) Median Capex / Depr. Median Dividend payout Prime All Share Industries Automobiles 0,22 0,11 0,09 0,09 1,02 0,36 Banks 0,82 0,09 Basic Resources 0,05 0,05 0,05 0,05 1,13 0,51 Chemicals 0,20 0,09 0,10 0,11 0,92 0,41 Construction 0,07 0,05 0,06 0,06 1,01 0,18 Consumer 0,07 0,05 0,06 0,08 1,00 0,35 Financial Services 0,04 0,04 2,87 0,28 Food & Beverages 0,05 0,02 0,03 0,03 1,34 1,19 Industrial 0,14 0,08 0,09 0,10 0,84 0,34 Insurance 2,37 0,50 Media 0,15 0,11 0,11 0,12 0,48 0,59 Pharma & Healthcare 0,04 0,04-0,01 0,05 0,68 0,28 Retail 0,01 0,05 0,03 0,02 0,91 0,26 Software 0,19 0,11 0,14 0,18 0,52 0,29 Technology 0,10 0,03 0,06 0,08 0,69 0,30 Telecommunication 0,09 0,06 0,07 0,07 0,48 0,63 Transport. & Logistics 0,19 0,10 0,08 0,09 0,85 0,48 Utilities 0,05 0,05 0,04 0,05 1,20 0,40 Prime All Share 0,11 0,07 0,08 0,09 0,85 0,34 DAX 30 0,21 0,11 0,08 0,12 0,97 0,38 TecDAX 30 0,16 0,10 0,13 0,17 0,52 0,28 MDAX 50 0,18 0,10 0,09 0,12 1,12 0,35 16

20 Prime All Share Industries, DAX 30, TecDAX 30, MDAX 50 Cost of Capital Q as of year Equity Beta R² 2 year Equity Beta R² 5 year Equity Beta R² n Cost of Equity (based on 1y beta) Debt - Equity ratio (market values) Asset beta Prime All Share Industries Asset Beta Miles Ezzell debt beta = Net-Debt - Equity ratio (market values) Operating Asset beta Operating Asset beta Miles Ezzell debt beta= Automobiles 1,32 0,79 1,23 0,80 1,45 0, ,4% 1,73 0,62 0,63 1,36 0,70 0,69 Banks 1,78 0,51 1,41 0,53 1,28 0, ,0% Basic Resources 1,02 0,37 0,96 0,40 0,87 0,37 4 5,8% 0,82 0,66 0,66 0,50 0,77 0,76 Chemicals 1,00 0,79 1,05 0,89 1,00 0, ,7% 0,34 0,82 0,81 0,27 0,85 0,84 Construction 1,03 0,57 1,01 0,68 1,02 0,55 4 5,9% 0,59 0,75 0,74 0,39 0,82 0,81 Consumer 0,71 0,52 0,78 0,69 0,86 0, ,1% 0,03 0,69 0,69 0,01 0,70 0,70 Financial Services 0,57 0,36 0,74 0,61 0,64 0, ,3% Food & Beverages 0,58 0,12 0,49 0,09 0,43 0,03 1 3,4% 0,62 0,42 0,44 0,47 0,45 0,47 Industrial 1,01 0,82 0,98 0,88 1,00 0, ,7% 0,40 0,80 0,79 0,24 0,88 0,86 Insurance 1,15 0,75 0,96 0,79 0,87 0,65 4 6,5% Media 0,81 0,51 0,76 0,62 0,75 0, ,6% 0,18 0,72 0,72 0,10 0,76 0,75 Pharma & Healthcare 0,81 0,54 0,92 0,71 0,73 0, ,6% 0,30 0,68 0,67 0,23 0,70 0,70 Retail 0,76 0,47 0,76 0,62 0,92 0, ,4% 0,19 0,67 0,67 0,03 0,75 0,74 Software 0,85 0,67 0,84 0,74 0,81 0, ,9% 0,08 0,80 0,80 0,03 0,83 0,83 Technology 1,15 0,53 1,09 0,57 0,93 0, ,5% 0,17 1,03 1,01 0,03 1,12 1,12 Telecommunication 0,83 0,57 1,01 0,73 0,95 0,60 8 4,7% 0,76 0,55 0,57 0,66 0,58 0,59 Transport. & Logistics 0,98 0,74 0,92 0,75 0,93 0, ,6% 0,57 0,72 0,71 0,41 0,78 0,77 Utilities 1,13 0,39 1,16 0,43 1,04 0,28 7 6,4% 1,22 0,63 0,63 0,65 0,79 0,78 Prime All Share 1,00 1,00 1,00 1,00 1,00 1, ,7% 0,51 0,75 0,74 0,37 0,80 0,79 DAX 30 1,07 0,99 1,04 0,99 1,05 0, ,1% 0,59 0,77 0,76 0,47 0,82 0,80 TecDAX 30 0,78 0,67 0,90 0,77 0,69 0, ,5% 0,13 0,72 0,72 0,03 0,77 0,76 MDAX 50 0,84 0,85 0,87 0,90 0,83 0, ,8% 0,16 0,76 0,76 0,07 0,80 0,80 Median ROE (Return on Equity) Median Non-cash ROE (Return on Equity) Median ROC (Return on Capital) Median Non-cash ROC (Return on Capital) Median Capex / Depr. Median Dividend payout Prime All Share Industries Automobiles 0,19 0,10 0,08 0,10 1,10 0,39 Banks 1,31 0,41 Basic Resources 0,05 0,05 0,05 0,06 1,02 0,25 Chemicals 0,17 0,07 0,10 0,11 0,91 0,47 Construction 0,08 0,04 0,07 0,09 0,96 0,52 Consumer 0,10 0,07 0,09 0,10 0,94 0,38 Financial Services 0,05 0,04 7,98 0,25 Food & Beverages 0,05 0,02 0,03 0,03 1,34 1,19 Industrial 0,14 0,09 0,08 0,11 0,85 0,30 Insurance 1,32 0,53 Media 0,19 0,11 0,10 0,17 0,55 0,43 Pharma & Healthcare 0,06 0,05 0,01 0,08 0,64 0,31 Retail 0,07 0,06 0,07 0,04 0,67 0,43 Software 0,23 0,11 0,16 0,22 0,67 0,40 Technology 0,10 0,07 0,07 0,09 0,65 0,12 Telecommunication 0,10 0,04 0,07 0,08 0,50 0,92 Transport. & Logistics 0,20 0,12 0,09 0,10 0,81 0,33 Utilities -0,13-0,06 0,01 0,00 0,93 0,65 Prime All Share 0,12 0,08 0,08 0,10 0,85 0,36 DAX 30 0,20 0,12 0,10 0,12 0,93 0,38 TecDAX 30 0,14 0,09 0,11 0,14 0,69 0,27 MDAX 50 0,13 0,10 0,08 0,12 0,95 0,43 17

21 Prime All Share Industries, DAX 30, TecDAX 30, MDAX 50 Cost of Capital Q as of year Equity Beta R² 2 year Equity Beta R² 5 year Equity Beta R² n Cost of Equity (based on 1y beta) Debt - Equity ratio (market values) Asset beta Prime All Share Industries Asset Beta Miles Ezzell debt beta = Net-Debt - Equity ratio (market values) Operating Asset beta Operating Asset beta Miles Ezzell debt beta= Automobiles 1,15 0,66 1,22 0,78 1,44 0, ,8% 1,71 0,55 0,59 1,35 0,61 0,65 Banks 1,73 0,36 1,50 0,53 1,26 0, ,0% Basic Resources 0,94 0,26 0,99 0,39 0,87 0,35 4 5,7% 0,76 0,63 0,65 0,49 0,71 0,72 Chemicals 1,07 0,75 1,03 0,87 1,01 0, ,4% 0,34 0,87 0,87 0,27 0,91 0,90 Construction 1,08 0,47 1,02 0,66 1,00 0,53 3 6,5% 0,59 0,78 0,79 0,39 0,86 0,86 Consumer 0,87 0,51 0,77 0,65 0,86 0, ,3% 0,17 0,78 0,78 0,06 0,83 0,83 Financial Services 0,49 0,19 0,71 0,58 0,65 0, ,2% Food & Beverages 0,70 0,09 0,56 0,11 0,42 0,03 1 4,3% 0,71 0,48 0,51 0,49 0,53 0,55 Industrial 1,08 0,74 1,00 0,87 0,99 0, ,5% 0,40 0,86 0,86 0,24 0,94 0,94 Insurance 0,96 0,58 0,96 0,78 0,85 0,64 4 5,8% Media 0,79 0,37 0,76 0,58 0,76 0, ,8% 0,23 0,69 0,69 0,14 0,72 0,73 Pharma & Healthcare 0,95 0,50 0,92 0,69 0,74 0, ,7% 0,29 0,80 0,80 0,23 0,83 0,83 Retail 0,75 0,33 0,79 0,61 0,94 0, ,6% 0,31 0,63 0,64 0,10 0,71 0,71 Software 0,88 0,53 0,86 0,73 0,83 0, ,4% 0,08 0,84 0,84 0,03 0,86 0,86 Technology 1,18 0,42 1,12 0,56 0,94 0, ,0% 0,17 1,06 1,05 0,03 1,16 1,16 Telecommunication 0,82 0,41 0,98 0,69 0,97 0,57 8 5,0% 0,75 0,55 0,58 0,65 0,58 0,60 Transport. & Logistics 0,95 0,56 0,93 0,72 0,91 0, ,7% 0,52 0,71 0,72 0,37 0,77 0,77 Utilities 0,90 0,23 1,20 0,41 1,04 0,27 7 5,5% 1,16 0,52 0,56 0,62 0,65 0,66 Prime All Share 1,00 1,00 1,00 1,00 1,00 1, ,0% 0,61 0,72 0,73 0,44 0,78 0,78 DAX 30 1,06 0,99 1,04 0,99 1,05 0, ,3% 0,73 0,72 0,73 0,57 0,78 0,78 TecDAX 30 0,87 0,60 0,90 0,75 0,71 0, ,3% 0,11 0,82 0,82 0,02 0,86 0,86 MDAX 50 0,84 0,79 0,88 0,90 0,84 0, ,1% 0,35 0,68 0,69 0,17 0,75 0,76 Median ROE (Return on Equity) Median Non-cash ROE (Return on Equity) Median ROC (Return on Capital) Median Non-cash ROC (Return on Capital) Median Capex / Depr. Median Dividend payout Prime All Share Industries Automobiles 0,20 0,11 0,08 0,10 1,09 0,40 Banks 1,21 0,34 Basic Resources 0,06 0,05 0,06 0,06 0,98 0,38 Chemicals 0,17 0,07 0,10 0,11 0,91 0,47 Construction 0,06 0,04 0,06 0,06 1,06 0,35 Consumer 0,10 0,06 0,09 0,11 0,91 0,35 Financial Services 0,05 0,04 26,56 0,25 Food & Beverages 0,11 0,05 0,07 0,07 1,15 0,54 Industrial 0,14 0,09 0,09 0,11 0,85 0,29 Insurance 1,32 0,53 Media 0,12 0,09 0,08 0,09 0,64 0,28 Pharma & Healthcare 0,05 0,05 0,01 0,08 0,64 0,32 Retail 0,02 0,05 0,02 0,01 0,91 0,51 Software 0,24 0,11 0,17 0,20 0,69 0,39 Technology 0,09 0,06 0,07 0,09 0,71 0,04 Telecommunication 0,09 0,03 0,04 0,04 0,50 0,87 Transport. & Logistics 0,20 0,12 0,09 0,10 0,81 0,33 Utilities -0,13-0,06 0,01 0,00 0,93 0,65 Prime All Share 0,12 0,08 0,07 0,10 0,87 0,34 DAX 30 0,21 0,11 0,09 0,12 0,90 0,36 TecDAX 30 0,15 0,09 0,12 0,15 0,68 0,28 MDAX 50 0,13 0,10 0,08 0,11 0,97 0,43 18

22 Prime All Share Industries, DAX 30, TecDAX 30, MDAX 50 Cost of Capital Q as of year Equity Beta R² 2 year Equity Beta R² 5 year Equity Beta R² n Cost of Equity (based on 1y beta) Debt - Equity ratio (market values) Asset beta Prime All Share Industries Asset Beta Miles Ezzell debt beta = Net-Debt - Equity ratio (market values) Operating Asset beta Operating Asset beta Miles Ezzell debt beta= Automobiles 0,98 0,55 1,21 0,77 1,45 0, ,8% 1,70 0,47 0,52 1,35 0,52 0,56 Banks 1,79 0,37 1,61 0,50 1,27 0, ,3% Basic Resources 1,00 0,22 1,03 0,34 0,79 0,29 4 5,9% 0,77 0,67 0,68 0,49 0,76 0,76 Chemicals 1,11 0,76 1,03 0,83 1,02 0, ,5% 0,32 0,92 0,91 0,25 0,96 0,95 Construction 1,16 0,46 1,08 0,65 1,00 0,53 3 6,8% 0,62 0,83 0,82 0,41 0,92 0,91 Consumer 0,87 0,46 0,77 0,60 0,84 0, ,2% 0,17 0,79 0,78 0,07 0,84 0,84 Financial Services 0,49 0,19 0,69 0,52 0,63 0, ,1% Food & Beverages 0,74 0,09 0,65 0,13 0,41 0,03 1 4,5% 0,77 0,50 0,53 0,54 0,55 0,57 Industrial 1,14 0,74 1,03 0,85 1,01 0, ,7% 0,38 0,92 0,91 0,23 1,00 0,99 Insurance 0,97 0,60 1,00 0,75 0,85 0,63 4 5,7% Media 0,84 0,32 0,76 0,51 0,77 0, ,0% 0,25 0,73 0,73 0,15 0,77 0,77 Pharma & Healthcare 0,94 0,45 0,90 0,65 0,73 0, ,6% 0,31 0,78 0,78 0,24 0,81 0,81 Retail 0,75 0,36 0,82 0,57 0,95 0, ,5% 0,30 0,63 0,64 0,09 0,71 0,71 Software 0,87 0,53 0,85 0,70 0,83 0, ,2% 0,07 0,83 0,83 0,03 0,85 0,85 Technology 1,22 0,41 1,13 0,54 0,96 0, ,1% 0,15 1,11 1,10 0,03 1,20 1,20 Telecommunication 0,79 0,35 0,92 0,64 0,97 0,57 8 4,7% 0,71 0,54 0,57 0,62 0,56 0,58 Transport. & Logistics 0,98 0,54 0,98 0,70 0,91 0, ,8% 0,45 0,76 0,76 0,32 0,81 0,81 Utilities 0,75 0,16 1,16 0,39 0,99 0,24 7 4,5% 1,01 0,45 0,50 0,54 0,56 0,58 Prime All Share 1,00 1,00 1,00 1,00 1,00 1, ,9% 0,59 0,72 0,73 0,44 0,78 0,78 DAX 30 1,05 0,98 1,04 0,99 1,05 0, ,2% 0,57 0,76 0,76 0,45 0,81 0,81 TecDAX 30 0,93 0,59 0,90 0,72 0,71 0, ,5% 0,09 0,88 0,88 0,02 0,92 0,92 MDAX 50 0,87 0,79 0,89 0,88 0,84 0, ,2% 0,39 0,70 0,70 0,21 0,77 0,77 Median ROE (Return on Equity) Median Non-cash ROE (Return on Equity) Median ROC (Return on Capital) Median Non-cash ROC (Return on Capital) Median Capex / Depr. Median Dividend payout Prime All Share Industries Automobiles 0,21 0,11 0,08 0,10 1,10 0,39 Banks 1,21 0,34 Basic Resources 0,06 0,05 0,06 0,06 0,98 0,38 Chemicals 0,17 0,07 0,10 0,11 0,91 0,47 Construction 0,06 0,04 0,06 0,06 1,06 0,35 Consumer 0,09 0,06 0,08 0,09 0,91 0,40 Financial Services 0,05 0,04 44,04 0,19 Food & Beverages 0,11 0,05 0,07 0,07 1,15 0,54 Industrial 0,14 0,09 0,09 0,12 0,85 0,29 Insurance 1,32 0,53 Media 0,12 0,08 0,08 0,09 0,64 0,10 Pharma & Healthcare 0,05 0,05 0,01 0,08 0,64 0,32 Retail 0,01 0,05 0,02 0,00 0,88 0,51 Software 0,23 0,11 0,16 0,20 0,67 0,39 Technology 0,10 0,06 0,07 0,09 0,73 0,00 Telecommunication 0,09 0,03 0,04 0,04 0,50 0,87 Transport. & Logistics 0,20 0,12 0,09 0,10 0,81 0,33 Utilities -0,13-0,06 0,01 0,00 0,93 0,65 Prime All Share 0,12 0,07 0,07 0,09 0,86 0,34 DAX 30 0,20 0,12 0,09 0,12 0,91 0,38 TecDAX 30 0,15 0,09 0,12 0,15 0,68 0,28 MDAX 50 0,12 0,09 0,08 0,11 0,98 0,43 19

23 CAPM: Beta Factor Development 20

24 Development of CAPM Beta Factors - DAX 30 1 year vs. 2 year CAPM Equity Beta 1.10 Betas - Equity Beta DAX30-1y Equity Beta DAX30-2y Equity Beta 1 year vs. 2 year CAPM R² 00 Betas - R² DAX30-1y R² DAX30-2y R² 21

25 Development of CAPM Beta Factors - MDAX 50 1 year vs. 2 year CAPM Equity Beta 1.1 Betas - Equity Beta 1.1 MDAX50-1y Equity Beta MDAX50-2y Equity Beta 1 year vs. 2 year CAPM R² Betas - R² MDAX50-1y R² MDAX50-2y R² 22

26 Development of CAPM Beta Factors - Automobiles 1 year vs. 2 year CAPM Equity Beta 1.40 Betas - Equity Beta Automobiles - 1y Equity Beta Automobiles - 2y Equity Beta 1 year vs. 2 year CAPM R² Betas - R² Automobiles - 1y R² Automobiles - 2y R² 23

27 Development of CAPM Beta Factors - TecDAX 30 1 year vs. 2 year CAPM Equity Beta 1.1 Betas - Equity Beta 1.1 TecDAX30-1y Equity Beta TecDAX30-2y Equity Beta 1 year vs. 2 year CAPM R² 0 Betas - R² TecDAX30-1y R² TecDAX30-2y R² 24

28 Development of CAPM Beta Factors - Banks 1 year vs. 2 year CAPM Equity Beta Betas - Equity Beta Banks - 1y Equity Beta Banks - 2y Equity Beta 1 year vs. 2 year CAPM R² Betas - R² Banks - 1y R² Banks - 2y R² 25

29 Development of CAPM Beta Factors - Basic Resources 1 year vs. 2 year CAPM Equity Beta 1.4 Betas - Equity Beta Basic Resources - 1y Equity Beta Basic Resources - 2y Equity Beta 1 year vs. 2 year CAPM R² Betas - R² Basic Resources - 1y R² Basic Resources - 2y R² 26

30 Development of CAPM Beta Factors - Chemicals 1 year vs. 2 year CAPM Equity Beta 1.3 Betas - Equity Beta Chemicals - 1y Equity Beta Chemicals - 2y Equity Beta 1 year vs. 2 year CAPM R² Betas - R² Chemicals - 1y R² Chemicals - 2y R² 27

31 Development of CAPM Beta Factors - Construction 1 year vs. 2 year CAPM Equity Beta 1.5 Betas - Equity Beta Construction - 1y Equity Beta Construction - 2y Equity Beta 1 year vs. 2 year CAPM R² Betas - R² Construction - 1y R² Construction - 2y R² 28

32 Development of CAPM Beta Factors - Consumer 1 year vs. 2 year CAPM Equity Beta Betas - Equity Beta Consumer - 1y Equity Beta Consumer - 2y Equity Beta 1 year vs. 2 year CAPM R² Betas - R² Consumer - 1y R² Consumer - 2y R² 29

33 Development of CAPM Beta Factors - Financial Services 1 year vs. 2 year CAPM Equity Beta Betas - Equity Beta Financial Services - 1y Equity Beta Financial Services - 2y Equity Beta 1 year vs. 2 year CAPM R² Betas - R² Financial Services - 1y R² Financial Services - 2y R² 30

34 Development of CAPM Beta Factors - Food & Beverages 1 year vs. 2 year CAPM Equity Beta Betas - Equity Beta Food & Beverages - 1y Equity Beta Food & Beverages - 2y Equity Beta 1 year vs. 2 year CAPM R² 0 Betas - R² Food & Beverages - 1y R² Food & Beverages - 2y R² 31

35 Development of CAPM Beta Factors - Industrial 1 year vs. 2 year CAPM Equity Beta 1.20 Betas - Equity Beta Industrial - 1y Equity Beta Industrial - 2y Equity Beta 1 year vs. 2 year CAPM R² 0 Betas - R² Industrial - 1y R² Industrial - 2y R² 32

36 Development of CAPM Beta Factors - Insurance 1 year vs. 2 year CAPM Equity Beta 1.3 Betas - Equity Beta Insurance - 1y Equity Beta Insurance - 2y Equity Beta 1 year vs. 2 year CAPM R² Betas - R² Insurance - 1y R² Insurance - 2y R² 33

37 Development of CAPM Beta Factors - Media 1 year vs. 2 year CAPM Equity Beta Betas - Equity Beta Media - 1y Equity Beta Media - 2y Equity Beta 1 year vs. 2 year CAPM R² 0.2 Betas - R² Media - 1y R² Media - 2y R² 34

38 Development of CAPM Beta Factors - Pharma & Healthcare 1 year vs. 2 year CAPM Equity Beta 1.1 Betas - Equity Beta 1.1 Pharma - 1y Equity Beta Pharma - 2y Equity Beta 1 year vs. 2 year CAPM R² 0.2 Betas - R² Pharma - 1y R² Pharma - 2y R² 35

39 Development of CAPM Beta Factors - Retail 1 year vs. 2 year CAPM Equity Beta Betas - Equity Beta Retail - 1y Equity Beta Retail - 2y Equity Beta 1 year vs. 2 year CAPM R² 0.2 Betas - R² Retail - 1y R² Retail - 2y R² 36

40 Development of CAPM Beta Factors - Software 1 year vs. 2 year CAPM Equity Beta Betas - Equity Beta Software - 1y Equity Beta Software - 2y Equity Beta 1 year vs. 2 year CAPM R² 0.2 Betas - R² Software - 1y R² Software - 2y R² 37

41 Development of CAPM Beta Factors - Technology 1 year vs. 2 year CAPM Equity Beta 1.4 Betas - Equity Beta Technology - 1y Equity Beta Technology- 2y Equity Beta 1 year vs. 2 year CAPM R² 0.2 Betas - R² Technology - 1y R² Technology - 2y R² 38

42 Development of CAPM Beta Factors - Telecommunication 1 year vs. 2 year CAPM Equity Beta 1.2 Betas - Equity Beta Telecommunication - 1y Equity Beta Telecommunication- 2y Equity Beta 1 year vs. 2 year CAPM R² 0.2 Betas - R² Telecommunication - 1y R² Telecommunication - 2y R² 39

43 Development of CAPM Beta Factors - Transport & Logistics 1 year vs. 2 year CAPM Equity Beta 1.3 Betas - Equity Beta Transportation - 1y Equity Beta Transportation- 2y Equity Beta 1 year vs. 2 year CAPM R² Betas - R² Transportation - 1y R² Transportation - 2y R² 40

44 Development of CAPM Beta Factors - Utilities 1 year vs. 2 year CAPM Equity Beta 1.4 Betas - Equity Beta Utilities - 1y Equity Beta Utilities- 2y Equity Beta 1 year vs. 2 year CAPM R² 0.2 Betas - R² Utilities - 1y R² Utilities - 2y R² 41

45 Yield Curve: Svensson 42

46 Yield Curve: Svensson (1994) In this section, we provide a detailed overview on the estimation of a single risk -free rate for corporate valuation out of a non-flat yield curve. The yield curve depicts the relation between the time to maturity and the yield of a bond without any default risk. Due to the lack of zero bonds for each maturity, the continuous yield curve has to be estimated out of observed bond yields either using the Nelson and Siegel (1987) or the parametric approach by Svensson (1994). To determine the yield curve according to the Svensson procedure, the following standard formula is applied: All necessary parameters are provided by the German Central Bank (Deutsche Bundesbank). To illustrate the results, Figure 2 displays the overall minimum (December 2016) and maximum (July 2017) yield curves for the year As a reference, the estimated yield curve for November 2017 is also displayed. Note that, as last year, for all three cases short term rates are negative, but the maturities at which the rates become positive decreased. For the minimum yield curve of December 2016 the rates are negative untill a maturity of 8 years while they were negative until a maturity of 13 years for the minimum yield curve of September The maturity-specific average reached positive values for more than 8 years of time to maturity in 2016 while it becomes positive now after 7 years of time to maturity. In comparison to our last report the average starting point has decreased from a -0,58 in 2016 to -0,78 in 2017 while the average rate for 30 years of time to maturity increased from 0,87 last year to 1,27 this year. For all maturities the difference between the highest and the lowest yields is less than 0,5 percentage points, variance of the monthly estimations is between 10% of the variance 2016 for higher maturities and 40% for shorter maturities. Summarized we observe a tendency of decreasing rates for short term maturities and increasing long term maturities with reduced variance. 43

47 To highlight these differences Table 5 displays the maturity-specific-minimum (min), maximum (max), average (avg), median and variance of the monthly estimations from December 2016 to November Figure 2: Highest and lowest yield curve for the year 2017 Table 5: Minimum, maximum, arithmetic average, median and variance of maturity specific Term min -0,9218-0,9193-0,8580-0,7396-0,5858-0,4174-0,2494-0,0907 0,0542 0,1840 max -0,6620-0,5957-0,5068-0,3815-0,2288-0,0530 0,1166 0,2751 0,4201 0,5507 avg -0,7720-0,7390-0,6518-0,5195-0,3621-0,1966-0,0349 0,1165 0,2544 0,3780 median -0,7672-0,7386-0,6514-0,5162-0,3598-0,1966-0,0349 0,1170 0,2565 0,3824 var 0,0041 0,0054 0,0075 0,0093 0,0102 0,0104 0,0104 0,0103 0,0103 0,0103 Term min 0,2990 0,4001 0,4891 0,5608 0,6204 0,6729 0,7194 0,7608 0,7979 0,8314 max 0,6670 0,7700 0,8607 0,9401 1,0097 1,0706 1,1239 1,1706 1,2116 1,2477 avg 0,4877 0,5845 0,6698 0,7449 0,8111 0,8697 0,9216 0,9678 1,0091 1,0461 median 0,4940 0,5888 0,6726 0,7469 0,8142 0,8735 0,9260 0,9725 1,0138 1,0507 var 0,0105 0,0107 0,0109 0,0111 0,0113 0,0115 0,0116 0,0117 0,0117 0,0117 Term min 0,8616 0,8892 0,9143 0,9374 0,9586 0,9781 0,9962 1,0131 1,0287 1,0434 max 1,2796 1,3078 1,3329 1,3553 1,3754 1,3935 1,4098 1,4247 1,4382 1,4506 avg 1,0794 1,1095 1,1368 1,1617 1,1844 1,2053 1,2245 1,2422 1,2587 1,2739 median 1,0836 1,1132 1,1399 1,1640 1,1859 1,2059 1,2241 1,2408 1,2563 1,2726 var 0,0117 0,0116 0,0115 0,0114 0,0113 0,0112 0,0111 0,0109 0,0108 0,

48 The IDW recommends to use the average of the daily calculated spot rates over the last three months for each term to reduce the impact of high interest rate volatility on the calculation of firm values (see "WP-Handbuch" (IDW), Band II, 14. Aufl. 2014, S. 119ff.). Figure 3 shows the respective curve as of November 30th, Figure 3: Svensson Yield curve using the IDW 3-month-average technique Based on this 3-month-average yield curve, we calculate a single interest rate over all maturities that results in the same present value as the term specific rates (For a detailed explanation refer to Dörschel / Franken / Schulte, "Der Kapitalisierungszinssatz in der Unternehmensbewertung" (IDW), 1. Aufl. 2009, S. 52 ff.). If this requirement shall be met, the following equality has to hold: Rearranging yields where i 0,t is the term specific rate, i e the single interest rate that results in an equivalent present value, z the risk premium (MRP * β) and g the growth rate of the firms future cash flows. We assume the parameters g=1%, MRP=6% and β=1, and round the resulting single rate to quarter percentage points. This results in a final rate of i e =0%. Following the IDW recommendations this rate represents the risk-free rate for the estimation of the firms cost of equity. 45

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