Business Valuation DCF-Methods Consistency of Valuation Results WP/StB MMag. Alexander Enzinger, CVA www.rabelpartner.at January 2018
Contents Overview of DCF-Methods Consistency of valuation results Example Debt Beta Case Study Summary 2 MMag. Alexander Enzinger Rabel & Partner GmbH
Overview of DCF methods (1) 3 MMag. Alexander Enzinger Rabel & Partner GmbH
Overview of DCF methods (2) Adjusted-Present-Value (APV) method 4 MMag. Alexander Enzinger Rabel & Partner GmbH
Overview of DCF methods (3) Entity (WACC) Approach 5 MMag. Alexander Enzinger Rabel & Partner GmbH
Overview of DCF methods (4) Entity (WACC) Approach 6 MMag. Alexander Enzinger Rabel & Partner GmbH
Overview of DCF methods (5) Equity Approach 7 MMag. Alexander Enzinger Rabel & Partner GmbH
Overview of DCF methods (6) Equity Approach 8 MMag. Alexander Enzinger Rabel & Partner GmbH
Overview of DCF methods (7) Roll-back method Roll-back method: Calculation of SHV beginning from the end The previous period s SHV can be derived free of the circularity problem Roll-back method (based on the assumptions of Harris/Pringle): Detailed forecast period: SHV t1 EC * t1 FTE t EC * t CoE u 1 CoE CoD u DC * t1 Perpetuity: SHV t1 EC * T FTE T 1 CoE CoE u u CoD g DC * T 9 MMag. Alexander Enzinger Rabel & Partner GmbH
Overview of DCF methods (8) DCF methods and financing policy Autonomous financing policy ( D-Policy ) An absolute amount of debt capital is pre-determined, regardless of the results of the business (e.g. fixed repayment schedule) Value-based financing policy ( L-Policy ) Budgeted leverage ratios (target gearing based on market value) instead of a fixed amount of debt capital The amount of debt capital is geared to the current value of the business Future amounts of debt capital and therefore future interest expense and hence resulting tax savings uncertain 10 MMag. Alexander Enzinger Rabel & Partner GmbH
Overview of DCF methods (9) DCF methods and financing policy Comparison of the DCF approaches and financing assumptions: Retrograde calculation / iteration necessary Progressive calculation /no iteration necessary 11 MMag. Alexander Enzinger Rabel & Partner GmbH
Consistency of valuation results (1) Requirements of Professional Standard ( Fachgutachten ) KFS/BW 1: In applying discounting methods, appropriate assumptions must be made concerning the financing policy of the valuation object (e.g. value-based or autonomous, c.f. Rz (41) f) and the risk content of tax savings from the deductibility of the cost of debt (i.e. tax shields). These assumptions must be stated and justified in the valuation report. (Rz 116) If identical assumptions are made for the valuation parameters, in particular as regards financing and the risk content of the tax shields, and the appropriate formulas for adapting the beta factor to the capital structure are applied, the choice of discounting method should not affect the valuation result. (Rz 117) 12 MMag. Alexander Enzinger Rabel & Partner GmbH
Consistency of valuation results (2) Requirements to obtain consistent valuation results: Identical expected values for free cash flows Identical assumptions regarding financing Appropriate assumptions concerning the financing policy of the valuation object (e.g. value-based or autonomous) Future amount and development of debt Future amount and risk content of cost of debt (debt beta) Identical assumptions for the risk content of tax savings from the tax deductibility of the cost of debt (tax shields) The application of appropriate formulas for adapting the beta factor to the capital structure 13 MMag. Alexander Enzinger Rabel & Partner GmbH
Consistency of valuation results (3) Risk content of the tax shields The amount by which market value increases as a result of debt capital (the value added by the tax shields) is determined by discounting the tax savings from the deductibility for tax purposes of the interest expense (tax shields). A risk-adequate interest rate must be applied in discounting the tax shields. The assumptions made in this connection must be stated and justified in the valuation report. (Rz 44) Possible discount rates for the tax shield: Risk-free interest Debt-capital interest rate/cost of debt Cost of equity for the unlevered business [CoE u ] Discounting at the risk-free rate is generally not justifiable in practice. The reason for this is the uncertainty of the individual parameters affecting the tax shields. The approach using the cost of equity for an unlevered business [CoE u ] is increasingly seen in valuation practice. 14 MMag. Alexander Enzinger Rabel & Partner GmbH
Consistency of valuation results (4) Formulas for adjusting the beta factor The basic formula for adapting beta factors to the capital structure (Enzinger/Kofler, RWZ 2011/16, 52): This adjusting formula is of general application. Taking into account the respective restrictive premises, it is possible to derive the beta-adjusting formulas described further below. 15 MMag. Alexander Enzinger Rabel & Partner GmbH
Consistency of valuation results (5) Formulas for adjusting the beta factor The Hamada formula based on the Modigliani-Miller arbitrage model ( standard textbook formula) (Relevering) (Unlevering) with β l for the levered business and β u for the unlevered business Model premises: Autonomous financing policy, constant amount of debt capital Assumption of risk-free debt capital, hence no debt beta Assumption of risk-free tax shields Zero growth in perpetuity 16 MMag. Alexander Enzinger Rabel & Partner GmbH
Consistency of valuation results (6) Formulas for adjusting the beta factor Harris-Pringle Model premises: The risk of the tax shields corresponds to the risk of the unlevered business The cost of debt need not correspond to the risk-free interest rate May also be applied where debt capital is not risk-free Growth in pepetuity can be taken into account 17 MMag. Alexander Enzinger Rabel & Partner GmbH
Example (1) The following parameters are assumed for the valuation of a company: Free cash flow for the first year of perpetuity 150 Growth of free cash flows in perpetuity 1% pa Risk free interest rate 1,5% Market risk premium 5,5% Unlevered beta factor 1,0 Cost of debt = interest rate of debt 1,5% Corporate tax rate 25% Debt Capital at the beginning of perpetuity 800 Apply the following formula (Harris/Pringle) for adjusting the beta factor: 18 MMag. Alexander Enzinger Rabel & Partner GmbH
Example (2) Tasks: 1. What financing policy is applied in this example? 2. Calculate the Shareholder Value of the company applying the following DCF methods: a) APV method b) WACC approach c) Equity approach d) Roll back approach 3. Assume that the amount of debt at the beginning of perpetuity is not given as an absolute amount, but that a target debt-equity ratio on a market-value basis (DC*/EC*) of 50% is assumed. How does this change the approach and the result of the valuation? 4. What are the limiting assumptions in this example that are not realistic in real world? 5. What is the circularity problem and how can it be solved? 19 MMag. Alexander Enzinger Rabel & Partner GmbH
Example (3) Solutions 2a) APV method EC T 150 7.0% 1.0% 8001.5% 25% 7.0% 1.0% 800 EC T 2.500 50 800 1.750 20 MMag. Alexander Enzinger Rabel & Partner GmbH
Example (4) Solutions 2b) WACC approach DC EC l T T CoE l 800 1,750 45.71% DC TC 800 1.0 1,750 1.0 0,0 1. 4571 1.5% 1.45715.5% T T 9.514% 800 2,550 31.37% WACC 1,750 800 9.514% 1.5% 2,550 2,550 1 25% 6.88% EC T 150 6.88% 1.0% 800 1,750 21 MMag. Alexander Enzinger Rabel & Partner GmbH
Example (5) Solutions 2c) Equity approach EC T 149 9.51% 1.0% 1,750 FCF 150,00 -interest on debt -12,00 +Tax Shield 3,00 +/- Change in debt capital (perpetuity) 8,00 FTE 149,00 2d) Roll back approach EC T 149 7.00% 1.50% 7.00% 1.00% 800 1,750 22 MMag. Alexander Enzinger Rabel & Partner GmbH
Example (6) Solutions 3) DC EC l T T 1 2 DC TC T T 1 3 1 1.0 2 1.0 0,0 1. 50 CoE l 1.5% 1.505.5% 9.75% 2 1 WACC 9.75% 1.5% 1 25% 6.875% 3 3 150 TC 2,553.19 2 T EC 2,553.19 1,702. 13 6.875% 1.0% T 3 23 MMag. Alexander Enzinger Rabel & Partner GmbH
Debt Beta (1) Requirements of Professional Standard KFS/BW 1: (...) Taking the debt beta into consideration is necessary where the company s cost of debt equivalent in maturity to the base interest rate differs significantly from the base interest rate. (Rz 107) The cost of debt may include a risk premium, which should be taken into account where necessary by considering a debt beta when determining the cost of equity (see Rz (107)). (Rz 114) KFS/BW1 makes precise distinctions between the cost of debt ( Fremdkapitalkosten ) and interest on debt ( Fremdkapitalzinsen ) Cost of debt relevant for calculation of discount rates Rate of interest on debt relevant for calculation of cash flows Empfehlung der AG Unternehmensbewertung zur Berücksichtigung eines Debt Beta vom 21.5.2015 (Recommendation Debt Beta) 24 MMag. Alexander Enzinger Rabel & Partner GmbH
Debt Beta (2) Definitions Debt Beta (β DC ) Difference between the risk-free base interest rate and the cost of debt Shows to what extent parts of the systematic risk within the meaning of the CAPM are transferred to the debt-holders Calculation analogous to the equity beta applying the CAPM CoD i r DC MRP Cost of debt according to CAPM (CoD, r DC ): CoD i r MRP DC Interest on debt capital (i DC ) Yield to maturity, including all interest costs CoD or r DC (cost of debt according to CAPM) i DC (interest on debt capital) 25 MMag. Alexander Enzinger Rabel & Partner GmbH
Debt Beta (3) The contractually agreed interest on debt capital generally comprises a premium for unsystematic risk, other costs and profit margin of the bank the cost of debt according to the CAPM takes only systematic risk into account. 26 MMag. Alexander Enzinger Rabel & Partner GmbH
Debt Beta (4) Consequences of considering a Debt Beta Dependent on the form and specification of debt capital it is to analyse, if the assumption is justifiable that systematic risk is transferred to the debt holder. Only it debt holders actually assume parts of the systematic risk, the application of debt beta is justifiable. (Rz 10 Recommendation Debt Beta) Consequences of considering a debt beta: Reduction of financial risk of equity holders Reduction of costs of equity Increasing of shareholder value Risk of over-valuation if debt beta is applied undifferentiated 27 MMag. Alexander Enzinger Rabel & Partner GmbH
Debt Beta (5) Calculation of Debt Beta Starting point for the indirect calculation is the credit spread (i DC i r ) Unsystematic risks, other costs and the profit margin of the bank are to be eliminated from the credit spread Remaining part of the credit spread consists only of systematic risk and equals (CoD i r ) or (r DC i r ) Estimation of proportion of systematic risk in credit spread (a sys ) DC ( i DC i r MRP ) a sys rdc i MRP r Empirical studies imply that the proportion of systematic risk in the total credit spread amounts to 20% to 40%, whereas the proportion can also be below or above this range in the individual case. (Rz 12 Recommendation Debt Beta) 28 MMag. Alexander Enzinger Rabel & Partner GmbH
Debt Beta (6) Consequences if r DC (cost of debt) i DC (interest on debt) When determining the discount rate, it is always r DC and not i DC that is applied When determining debt beta, a credit spread that only accounts for systematic risk (r DC i r ) is applied The valuation formulas have to be adjusted for the difference between r DC and i DC under consideration of tax deductibility of this difference. See further reading 29 MMag. Alexander Enzinger Rabel & Partner GmbH
Case Study DCF-Valuation (1) Tasks Using a company s business plan the following cash flows can be derived: t 0 t 1 t 2 t 3 t 4 on Free Cash Flows (FCF) 1,152.25 1,716.25 2,515.70 2,895.95 Flows to Equity (FTE) 187.25 1,266.25 1,565.70 2,750.95 Debt capital (DC) 15,500.00 15,000.00 15,000.00 14,500.00 Additionally, the valuation is to be based on the following premises: Risk-free interest rate (ir) 1,58% Growth reduction in perpetuity 2,00% Unlevered beta factor 1,00 Interest rate of debt 4,00% Corporate tax rate 25% Market risk premium (MRP) 7,00% 30 MMag. Alexander Enzinger Rabel & Partner GmbH
Case Study DCF-Valuation (2) Debt Beta Assume that there is no systematic risk (a sys ) transferred to the debt holders. Therefore cost of debt corresponds to the risk-free interest rate: CoD i r i i a 1.58% 4.0% 1.58% 0.0% 1.58% DC r sys Due to the fact that debt holders do not participate on company s systematic risk debt beta is supposed to be zero: DC CoD i MRP r 1.58% 1.58% 7.00% 0 The valuation formulas have to be adjusted in the APV method for the difference between r DC and i DC see further reading. 31 MMag. Alexander Enzinger Rabel & Partner GmbH
Case Study DCF-Valuation (3) Roll-Back-Method Return of equity for the unlevered business (CoE u ): CoE u i r u MRP 1.58% 1.0 7.0% 8.58% Perpetuity EC FTE Detailed planning period CoE CoD DC 2,750.95 8.58% 1.58% 14,500 T 1 u T t 3 T CoEu g 8.58% 2.00% 26,382.22 EC EC EC t2 t1 t0 FTE FTE FTE t2 t1 t3 EC EC EC t1 t3 t2 CoEu CoD DCt 1,565.70 26,382.22 8.58% 1.58% 1 CoE CoEu CoD DCt 1,266.25 24,772.44 8.58% 1.58% 1 CoE CoEu CoD DCt 187.25 23,014.08 8.58% 1.58% 1 CoE u u u 0 2 1 1 8.58% 1 8.58% 1 8.58% 15,000 24,772.44 15,000 23,014.08 15,500 20,368.70 32 MMag. Alexander Enzinger Rabel & Partner GmbH
Case Study DCF-Valuation (4) Discount Rates From the results of the Roll-Back-Method the discount rates shown below can be derived (Harris/Pringle): t 1 t 2 t 3 t 4 on Gearing 76,10% 65,18% 60,55% 54,96% DC proportion 43,21% 39,46% 37,71% 35,47% EC proportion 56,79% 60,54% 62,29% 64,53% i r 1,58% 1,58% 1,58% 1,58% ß u 1,00 1,00 1,00 1,00 i DC 4,00% 4,00% 4,00% 4,00% r DC 1,58% 1,58% 1,58% 1,58% ß DC 0,00 0,00 0,00 0,00 ß l 1,76 1,65 1,61 1,55 MRP 7,00% 7,00% 7,00% 7,00% CoE l 13,91% 13,14% 12,82% 12,43% CoE u 8,58% 8,58% 8,58% 8,58% Tax rate (τ u ) 25,00% 25,00% 25,00% 25,00% CoD 4,00% 4,00% 4,00% 4,00% WACC 9,19% 9,14% 9,12% 9,08% 33 MMag. Alexander Enzinger Rabel & Partner GmbH
Case Study DCF-Valuation (5) DCF-Valuation Entity approach based on FCFs t 0 t 1 t 2 t 3 t 4 on Entity approach based on FCFs FCF t 0 t 1 1,152.25 t 2 1,716.25 t 3 2,515.70 t 4 on 2,895.95 Discount FCF rate 1,152.25 9.194% 1,716.25 9.140% 2,515.70 9.116% 2,895.95 9.084% Discount Diskontierungsatz rate 9.194% 1.09 9.140% 1.09 9.116% 1.09 9.084% 0.07 Diskontierungsatz Entity Value 35,868.70 38,014.08 1.09 39,772.44 1.09 40,882.22 1.09 0.07 Entity Value Net Debt 35,868.70-15,500 38,014.08-15,000 39,772.44-15,000 40,882.22-14,500 Net Debt Equity Value -15,500 20,368.70-15,000 23,014.08-15,000 24,772.44-14,500 26,382.22 Equity Value 20,368.70 23,014.08 24,772.44 26,382.22 Equity approach t 0 t 1 t 2 t 3 t 4 on Equity approach FTE t 0 t 187.25 1 t 1,266.25 2 t 1,565.70 3 t 4 on 2,750.95 Discount FTE rate 13.907% 187.25 1,266.25 13.142% 1,565.70 12.819% 2,750.95 12.427% Discount Diskontierungsatz rate 13.907% 1.14 13.142% 1.13 12.819% 1.13 12.427% 0.10 Diskontierungsatz Equity Value 20,368.70 23,014.08 1.14 24,772.44 1.13 26,382.22 1.13 0.10 Equity Value 20,368.70 23,014.08 24,772.44 26,382.22 34 MMag. Alexander Enzinger Rabel & Partner GmbH
Case Study DCF-Valuation (6) DCF-Valuation APV method t 0 t 1 t 2 t 3 t 4 on APV FCF method t 0 1,152.25t 1 1,716.25t 2 2,515.70t 3 2,895.95 t 4 on Discount APV FCF method rate t 0 1,152.25 8.580% t 1 1,716.25 8.580% t 2 2,515.70 8.580% t 3 2,895.95 8.580% t 4 on Discount Diskontierungsatz APV FCF method rate t 0 1,152.25 8.580% 1.09 t 1 1,716.25 8.580% 1.09 t 2 2,515.70 8.580% 1.09 t 3 2,895.95 8.580% 0.07 t 4 on Discount Diskontierungsatz FCF Market Value rate of the unlevered 38,862.92 41,045.10 1,152.25 8.580% 1.09 42,850.52 1,716.25 8.580% 1.09 44,011.40 2,515.70 8.580% 1.09 2,895.95 8.580% 0.07 Discount Diskontierungsatz Market Value rate of the unlevered 38,862.92 41,045.10 8.580% 1.09 42,850.52 8.580% 1.09 44,011.40 8.580% 1.09 8.580% 0.07 Diskontierungsatz Market Difference Value arising of the from unlevered interest expense and systematic cost of debt (incl. tax saving) 38,862.92 41,045.10-281.33 1.09 42,850.52-272.25 1.09 44,011.40-272.25 1.09-263.18 0.07 Discount Market Difference Value ratearising of the from unlevered interest expense and systematic cost of debt (incl. tax saving) 38,862.92 41,045.10-281.33 8.580% 42,850.52-272.25 8.580% 44,011.40-272.25 8.580% -263.18 8.580% Discount Diskontierungsatz Difference ratearising from interest expense and systematic cost of debt (incl. tax saving) -281.33 8.580% 1.09-272.25 8.580% 1.09-272.25 8.580% 1.09-263.18 8.580% 0.07 Discount Diskontierungsatz Difference Value discount ratearising credit from spread interest (VDCS) expense and systematic cost of debt (incl. tax saving) -3,827.11-3,874.15-281.33 8.580% 1.09-3,934.31-272.25 8.580% 1.09-3,999.62-272.25 8.580% 1.09-263.18 8.580% 0.07 Discount Diskontierungsatz Value discount rate credit spread (VDCS) -3,827.11-3,874.15 8.580% 1.09-3,934.31 8.580% 1.09-3,999.62 8.580% 1.09 8.580% 0.07 Diskontierungsatz Value Tax shields discount credit spread (VDCS) -3,827.11-3,874.15 61.23 1.09-3,934.31 59.25 1.09-3,999.62 59.25 1.09 57.28 0.07 Discount Value Tax shields discount rate credit spread (VDCS) -3,827.11-3,874.15 8.580% 61.23-3,934.31 8.580% 59.25-3,999.62 8.580% 59.25 8.580% 57.28 Discount Diskontierungsatz Tax shields rate 8.580% 61.23 1.09 8.580% 59.25 1.09 8.580% 59.25 1.09 8.580% 57.28 0.07 Discount Diskontierungsatz Tax Value shields added rate of the tax shields (VAT 832.90 843.14 8.580% 61.23 1.09 856.23 8.580% 59.25 1.09 870.44 8.580% 59.25 1.09 8.580% 57.28 0.07 Discount Diskontierungsatz Value Entity added Value rate of the tax shields (VAT 35,868.70 832.90 38,014.08 843.14 8.580% 1.09 39,772.44 856.23 8.580% 1.09 40,882.22 870.44 8.580% 1.09 8.580% 0.07 Diskontierungsatz Net Value Entity Debt added Value of the tax shields (VAT 35,868.70 832.90-15,500 38,014.08 843.14-15,000 1.09 39,772.44 856.23-15,000 1.09 40,882.22 870.44-14,500 1.09 0.07 Net Value Entity Equity Debt added Value of the tax shields (VAT 35,868.70 20,368.70 832.90-15,500 38,014.08 23,014.08 843.14-15,000 39,772.44 24,772.44 856.23-15,000 40,882.22 26,382.22 870.44-14,500 Net Entity Equity Debt Value 35,868.70 20,368.70-15,500 38,014.08 23,014.08-15,000 39,772.44 24,772.44-15,000 40,882.22 26,382.22-14,500 Net Equity Debt Value 20,368.70-15,500 23,014.08-15,000 24,772.44-15,000 26,382.22-14,500 Equity Value 20,368.70 23,014.08 24,772.44 26,382.22 35 MMag. Alexander Enzinger Rabel & Partner GmbH
Summary In order to obtain consistent valuation results required under the Professional Standard (Fachgutachten) on Company Valuation (KFS/BW 1), appropriate formulas for adapting the beta factor must be applied. In most cases, the standard textbook formula is inappropriate due to its restrictive premises. The valuer must decide on the risk content of the tax shields and take this into account in choosing the beta-adjusting formulas a general application of Harris-Pringle is in my opinion justifiable. Where the cost of debt (r DC =CoD) exceeds the risk-free interest rate (i r ), a debt beta must be taken into account. A differentiation must be made between the cost of debt (r DC =CoD) and the interest on debt (i DC ). Unsystematic components in the credit spread are disregarded in defining CAPM discount rates and must therefore be adjusted for. It is mandatory to disclose and justify the assumptions made in the valuation report! 36 MMag. Alexander Enzinger Rabel & Partner GmbH
Further reading Professional Standard (Fachgutachten) KFS/BW 1, Sections 4.1, 4.2, 4.5 and 4.6 Empfehlung der AG Unternehmensbewertung zur Berücksichtigung eines Debt Beta vom 21.5.2015, RWZ 2015/47, p.175. Enzinger/Mandl, Das Debt Beta nach dem Fachgutachten KFS/BW1, RWZ 2015/46, p.168. Enzinger/Pellet/Leitner, Der Wertabschlag Credit Spread (WACS) beim APV-Verfahren, Bewertungspraktiker 4/2014, p.114 ff. Enzinger/Pellet/Leitner, Debt Beta und Konsistenz der Bewertungsergebnisse, RWZ 7-8/2014, p.211 ff. Enzinger/Kofler, Das Roll Back-Verfahren zur Unternehmensbewertung, Bewertungspraktiker 4/2011, p.2 ff. Enzinger/Kofler, DCF-Verfahren: Anpassung der Beta-Faktoren zur Erzielung konsistenter Bewertungsergebnisse, RWZ 2/2011, p.52 ff. Enzinger/Kofler, Das Adjusted-Present-Value Verfahren in der Praxis, in Königsmaier/Rabel, Unternehmensbewertung (FS Mandl), 2010, p. 185 ff. Download: www.rabelpartner.at (menu item: Service) 37 MMag. Alexander Enzinger Rabel & Partner GmbH
Nomenclature 38 MMag. Alexander Enzinger Rabel & Partner GmbH
MMag. Alexander Enzinger, CVA Wirtschaftsprüfer und Steuerberater, Unternehmensberater, Allgemein beeideter und gerichtlich zertifizierter Sachverständiger Geschäftsführender Gesellschafter Rabel & Partner GmbH Wirtschaftsprüfungs- und Steuerberatungsgesellschaft Hallerschloßstraße 1, A-8010 Graz +43 316 3171-400 alexander.enzinger@rabelpartner.at www.rabelpartner.at 39 MMag. Alexander Enzinger Rabel & Partner GmbH