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Risk-adjusted discount rates-extensions from the average-risk case
Abstract
This paper provides an approach for developing risk-adjusted discount rates that follows naturally from the standard presentation of the weighted average cost of capital. In addition to examining the implied assumptions about the valuation of corporate debt, the paper shows the pedagogic advantages of the proposed approach.
... Discussion: In all cases of testing of beta coefficient of leveraged company, equation (1.9) formulated by the author of this paper gives identical results as equation (1.15) (which is a special case of equation (1.9)) formulated by (Harris & Pringle, 1985). However, for the use of equation (1.15) in the analysis, the data for the interest rate of debt and the rate of total capitalization must be adjusted so that they have values after tax. ...
... β levered =14,2156*; P m =6,18%; R riskfree =1,76%; T=33.3%; k e =89,61%(after tax); k d =3,51%(before tax); k d =2,34%(after tax); k u =10,64%(before tax); k u =7,10%(after tax); D/E=1734,48%; (2013) β levered =1,9334*; P m =5,60%; R riskfree =3,04%; T=21%; k e =13,87%(after tax); k d =5,44%(before tax); k d =4,30%(after tax); k u =9,50%(before tax); k u =7,51%(after tax); D/E=197,73%; (2012) β levered =2,2719*; P m =6,18%; R riskfree =1,76%; T=33.3%; k e =15,80%(after tax); k d =3,51%(before tax); k d =2,34%(after tax); k u =8,83%(before tax); k u =5,89%(after tax); D/E=279,72%; Harris&Pringle β l =1,7646* β l =1,7750* β l =1,5722* β l =1,5131* β l =0,8881* β l =0,7741* Source: Author; * relevant data for β levered were calculated by equation (1.10), formulated by (Harris & Pringle, 1985) (Harris & Pringle, 1985) EJAE 2023 20(2) 150 -167 ...
... β levered =14,2156*; P m =6,18%; R riskfree =1,76%; T=33.3%; k e =89,61%(after tax); k d =3,51%(before tax); k d =2,34%(after tax); k u =10,64%(before tax); k u =7,10%(after tax); D/E=1734,48%; (2013) β levered =1,9334*; P m =5,60%; R riskfree =3,04%; T=21%; k e =13,87%(after tax); k d =5,44%(before tax); k d =4,30%(after tax); k u =9,50%(before tax); k u =7,51%(after tax); D/E=197,73%; (2012) β levered =2,2719*; P m =6,18%; R riskfree =1,76%; T=33.3%; k e =15,80%(after tax); k d =3,51%(before tax); k d =2,34%(after tax); k u =8,83%(before tax); k u =5,89%(after tax); D/E=279,72%; Harris&Pringle β l =1,7646* β l =1,7750* β l =1,5722* β l =1,5131* β l =0,8881* β l =0,7741* Source: Author; * relevant data for β levered were calculated by equation (1.10), formulated by (Harris & Pringle, 1985) (Harris & Pringle, 1985) EJAE 2023 20(2) 150 -167 ...
The increase in the share of debt in the capital structure is accompanied by an increase in the required return on equity because companies are exposed to higher financial risk. The beta coefficient of debt-financed companies differs from the beta coefficient of companies that are financed exclusively with equity. Namely, the beta coefficient, under the influence of financial leverage, tends to increase with the growth of indebtedness, that is the systematic risk measured by the coefficient beta of debt-financed companies is higher than the systematic risk of non-leveraged companies, due to financial risk. Because interest payments on the debt of leveraged companies are excluded as an expense from the tax base, corporate income tax reduces the beta coefficient of a company with debt, compared to the beta coefficient of the same company when income tax is abstracted. The higher the corporate income tax, that will be the lower the beta coefficient of companies that have debt in the capital structure. There are several algebraic equations, by different authors, for the beta coefficient of leveraged companies. The algebraic equation for the beta coefficient of leveraged companies, which is derived in this paper, was obtained using the net operating income approach.
... We do not discuss the legitimacy of using WACC in the investment process or which of the rules adopted for calculating the WACC are more or less reasonable. We assume that investors can use either the Miles and Ezzell [36], Harris and Pringle [37], or Modigliani and Miller [8] approaches. We also do not discuss the relationship between WACC and risk, noting that such a reliance exists [38]. ...
... The second rule identified by Miles and Ezzel [36] and Harris and Pringle [37] supposes that "all tax shields have the same risk as to the firm's asset and should be discounted at the opportunity cost of capital" [23]. The hypothesis is that: D is proportional to VU, so rts = ra. ...
... The hypothesis is that: D is proportional to VU, so rts = ra. Taking into account the results of Harris and Pringle [37], these may be summarized in the following way for WACC [37] and the expected return on equity (re): ...
Recent economic anomalies, including the unprecedented lockdown generated by the COVID-19 crisis, have demonstrated that the weighted average cost of capital (WACC) remains an actual topic in the financial literature and in practice. Companies operate in an increasingly volatile environment, due to twin transitions and interlinked crises, and so they must have specific tools for measuring risk and profitability, in order to enable them to have a sound financial policy. Based on the earlier results obtained by Modigliani and Miller (1963), Harris and Pringle (1985), and Farber, Gillet, and Szafarz (2006), this study shows the relationship between WACC and interest rate. It offers a modified WACC formula that considers unstable market circumstances. The new redefined WACC can be a valuable tool in business planning for companies from different fields. The companies in the energy sector are very interested in the topic of WACC, considering not only the complex nature of the investments made and the long-term nature of investment recovery but also the multiple risks that have an impact on their activity and that can be found in different economic, social, and geopolitical spheres.
... where T S is the profit tax rate for an individual investor for their ownership of corporation stock, T C is the tax rate for corporate profit and T D is the profit tax interest rate for the provision of credit to other investors or companies. In [7][8][9][10], a more general expression for WACC than the Modigliani-Miller (MM) version was obtained [7]: ...
... When the WACC value is constant over time, the leveraged company value can be found by discounting the WACC from the unleveraged company cash flows. For this specific case, the formulae can be found in textbooks [9,10]. ...
... Mathematics 2022,10, 2479 ...
In practice, profit tax payments are (1) made more frequently than annually and (2) can be made in advance. To study the influence of these two factors on the financial indicators of a company, we generalized the Brusov–Filatova–Orekhova (BFO) theory for the case of advance profit tax payments with an arbitrary frequency for the first time. Using modified BFO formulae, we showed that all financial indicators of a company, such as company value, the weighted average cost of capital (WACC) and equity cost (ke), depend on the frequency of the profit tax payments. We found that the WACC increased with the payments and the company value decreased with the payments. This meant that more infrequent payments could be beneficial for the company. The tilt angle of the equity cost (ke(L)) also increased with the payments. Depending on the age of the company, the equity cost either decreased with L for all payment frequencies or increased for some frequencies. We compared the obtained results to those that we described recently for profit tax payments at the end of the financial period and found them to be totally different. We found that in spite the fact that the WACC decreased with the payments and the company value increased with the payments, the WACC value in this case turned out to be bigger and the company value turned out to be smaller than in the case of advance profit tax payments of any frequency. This underlined the importance of advance profit tax payments. Regulator recommendations were also developed to encourage the practice of advance profit tax payments due to the understanding of the benefits of this for both parties: the companies and the state. A new effect was discovered: the decrease in equity cost with an increase in the level of leverage (L).
... here bU is the CAPM βeta of the unleveraged company with the same asset risk as the leveraged company under consideration. Formula (13) represents the cost of equity (ke) for a leveraged firm as a sum of three components: risk-free rate (kF), risk premium for business/asset risk ( ) ...
... A more general formula for WACC, the famous Modigliani-Miller theory (MM) has been derived and discussed by a few authors in 2006-2007 [11][12][13][14]. It takes the following form (Equation (18) in [11]). ...
... This formula is derived from the definition of the weighted average cost of capital and the balance sheet identity (for a similar presentation, see [13]). At any point in time, it should therefore be verified, regardless of whether returns are annually or continuously compounded. ...
For the first time we have generalized the world-famous theory by Nobel Prize winners Modigliani and Miller for the case of variable profit, which significantly extends the application of the theory in practice, specifically in business valuation, ratings, corporate finance, etc. We demonstrate that all the theorems, statements and formulae of Modigliani and Miller are changed significantly. We combine theoretical and numerical (by MS Excel) considerations. The following results are obtained: (1) Discount rate for leverage company changes from the weighted average cost of capital, WACC, to WACC–g (where g is growing rate), for a financially independent company from k0 to k0–g. This means that WACC and k0 are no longer the discount rates as it takes place in case of classical Modigliani–Miller theory with constant profit. WACC grows with g, while real discount rates WACC–g and k0–g decrease with g. This leads to an increase of company capitalization with g. (2) The tilt angle of the equity cost ke(L) grows with g. This should change the dividend policy of the company, because the economically justified value of dividends is equal to equity cost. (3) A qualitatively new effect in corporate finance has been discovered: at rate g < g* the slope of the curve ke(L) turns out to be negative, which could significantly alter the principles of the company’s dividend policy.
... In the CAPM framework under credit risk, the equity beta is reduced and the debt beta is introduced. The debt beta approach has been developed since the 1970s (Haugen and Pappas, 1971;Conine, 1980;Harris and Pringle, 1985;Kaplan and Stein, 1990). While Haugen and Pappas (1971) and Harris and Pringle (1985) at least mention that a combined stock-corporate bond index is needed to compute the debt beta, more recent literature omits this fact and mainly focuses on tax shield analyses under credit risk (Ruback, 2002;Fernandez, 2004;Arzac and Glosten, 2005). ...
... The debt beta approach has been developed since the 1970s (Haugen and Pappas, 1971;Conine, 1980;Harris and Pringle, 1985;Kaplan and Stein, 1990). While Haugen and Pappas (1971) and Harris and Pringle (1985) at least mention that a combined stock-corporate bond index is needed to compute the debt beta, more recent literature omits this fact and mainly focuses on tax shield analyses under credit risk (Ruback, 2002;Fernandez, 2004;Arzac and Glosten, 2005). Other authors suggest to employ the implied debt beta (Cohen, 2008) consistent with the company's debt interest rate. ...
... As we assume that neither equity nor debt of the company to be valued is publicly traded, formula (9) is used for the unlevering-relevering peer group procedure. To estimate the peer group debt beta, Haugen and Pappas (1971), Bierman and Oldfield (1979), and Harris and Pringle (1985) suggest to measure the sensitivity of debt returns to a generalized market portfolio that consists of both stocks and corporate bonds. This approach requires that the equity beta also has to be calculated with respect to this stock-bond market portfolio to obtain the assets beta. ...
Credit risk analysis represents a growing field in financial research since decades. However, in cost of capital computations, credit risk is merely taken into consideration at the level of the debt beta approach. Our paper proves that applications of the debt beta approach suffer from unrealistic assumptions. As an advantageous approach, we develop an alternative framework to determine costs of capital based on Merton’s model. We present (quasi-) analytic formulas for costs of equity and debt which are consistent with Modigliani-Miller theory in continuous-time and discrete-time settings without taxes. Our framework is superior to the debt beta approach regarding the quantity and quality of required data in peer group analysis. Since equity and debt are represented by options in Merton’s model, we compute expected option rates of return. Thereby, our paper is also related to the recently growing literature on expected option returns.
... The Modigliani-Miller theory had numerous limitations, the main of which were its perpetual nature and the absence of taxes: corporate and individual. Many scientists have tried to modify the Modigliani-Miller theory in different aspects [4][5][6][7][8][9][10][11][12][13][14][15]. ...
... Alternative Expression for WACC From the WACC definition and the balance identity (see [6]) an alternative formula for the WACC, different from Modigliani-Miller one has been derived in [6][7][8][9]: ...
Taking into account the conditions of the real functioning of companies, one of the most striking effects in financial management is investigated: the “golden age” of the company (when the cost of capital raised is below the perpetuity limit, and the company’s value is higher). With this aim the dependence of cost of raising capital, WACC, on the age of company, n, is studied at various leverage levels, at various values of equity and debt costs, at different frequencies of tax on income payments, p, with advance payments of tax on income and payments at the end of periods, at variable income of the companies. The existence of the weighted average cost of capital, WACC, minimum and its behavior at wide range of above parameters is investigated. All calculations are made within modern theory of capital cost and capital structure by Brusov-Filatova-Orekhova (BFO theory), generalized to the conditions of the real functioning of the company. Practical recommendations for using and maintaining the “golden age” effect are given. It is shown, that “the golden age” depends on the financial indicators of the company. It can change and be controlled by changing parameters such as the cost of capital (equity and debt), frequency and method of tax on income payments, growth income rate etc. The study of the dependence of WACC on the age of the company n, WACC(n) , which can only be carried out within the framework of the BFO theory, turns out to be very important in the income approach to business valuation. This allows you to link a retrospective analysis of a company’s financial condition with a representative analysis as part of a business valuation.
... The authors, under a variety of assumptions, including the absence of corporate and individual taxes, the perpetuity of all companies and all cash flows, etc., obtained results that are completely different from the results of the traditional approach that existed before: the capital structure does not affect the financial performance of companies. Over the decades, many attempts have been made to modify the Modigliani-Miller theory [4][5][6][7][8][9][10][11][12][13][14]. ...
... The equity cost, ke, as it is seen from Fig. 4, 5,8,9,12,13 linearly grows with level of leverage L at all falling rate g and all company age 'n'. The tilt angle of the curve ke (L) grows with g, but decrease with company age 'n'. ...
The recent rise in inflation in Europe, caused by the pandemic, the increase in prices for energy resources and the violation of the logistics of energy supplies, has led to a decrease in company income. This makes it relevant to study the financial condition of companies with falling revenues. The purpose of this study is the development of tools for quantifying the impact of falling company incomes is becoming essential for making adequate management decisions. Until recently, such tools in capital structure theory did not exist. Two main theories of the capital cost and capital structure — Brusov — Filatova — Orekhova (BFO) theory and Modigliani — Miller (MM) theory — described companies with constant revenue: the first — for arbitrary age company, the second — for perpetuity companies. Within last couple years both these theories have been generalized for the case of variable revenue. In this paper the peculiar properties of the financial state of companies with falling income are studied within the modern capital cost and capital structure theory — Brusov–Filatova– Orekhova (BFO) theory, generalized for the case of variable revenue. As part of the goal, the tasks are solved to study the behavior of the main financial indicators (the cost of raising capital, the discount rate, the company’s capitalization, the cost of equity, and others), their dependence on debt financing, the age of the company in the face of declining income, which will make it possible to make adequate management decisions and reduce risks for companies.
... The authors of (Farber et al. 2006;Fernandez 2006;Berk and De Marzo 2017;Harris and Pringle 1985) have formed a more general expression for WACC compared to the one found in the Modigliani-Miller (MM) theory: ...
... The levered company value can be found by discounting the WACC for the unlevered company cash flows in cases when the WACC value is constant over time. For this special case, the formulas could be found in textbooks (Berk and De Marzo 2017;Harris and Pringle 1985). ...
Two modifications of a modern theory of capital structure—the Brusov–Filatova–Orekhova (BFO) theory—with variable income are considered: (1) with the income tax payments at the end of periods and (2) with advance income tax payments. BFO formulas for the WACC, and for company capitalization, V, were derived for these two cases. Using the obtained formulas, the dependence of the weighted average cost of capital, WACC; the discount rate; WACC–g (here, g, is the growth rate); company value, V; and the equity cost, ke, on the leverage level, L, at different values of g, at different values of the debt capital cost, kd, and at different values of company age, n, were studied. Comparing the results for cases (1) and (2) shows that case (2) is always preferable for both the company and the regulator. Recommendations have been developed for both parties to expand the practice of advance income tax payments. The managerial implications are as follows. Companies may choose to pay income tax either in advance or at the end of the reporting period in accordance with current results and tax laws. The developed methodology makes it possible to study companies with growing profits and companies with falling profits, which is very important in practice. It also allows the study of companies for which profits could rise and fall in different periods.
... Alternative formula for the WACC, different from Modigliani -Miller one has been derived in (Farber et al. 2006;Fernandez P, 2006;Berk and DeMarzo 2007;Harris and Pringle 1985) from the WACC definition and the balance identity (see Farber et al. 2006): ...
... In textbooks (Berk and DeMarzo 2007;Harris and Pringle 1985) formulas for the special cases, where the WACC is constant, could be found. ...
The Brusov–Filatova–Orekhova (BFO) theory is generalized for the simultaneous account of variable company profit and advance tax on income payments. The generalized BFO formula for the WACC, has been derived. The dependence of WACC, discount rate, WACC–g (here g is growth rate), company capitalization, V, the equity cost, ke, on leverage L at various values of g, on debt cost, kd, and on age of the company, n, is studied. It is shown, that WACC, is no longer a discount rate. This role passes to WACC–g, which decreases with g, while the company's value increases with g. The tilt of curve k(L) growths with g. It is found that at the growth rate g < g* the tilt of the curve ke(L) is negative. This changes significantly the company's dividend policy principles. WACC(L) as well as the discount rate, WACC–g, decrease with the increase of debt cost kd. V (L) at all values of kd increases with leverage L, as well V(L) increases with kd. This means that tax shield advantages the decrease of the cost of raising capital. Examining the main financial parameters of the company at the positive (g=0.2) and negative (g=–0.2) growth rates, we found a huge difference in their behavior. This allows you to explore companies with growing profits and companies with decreasing profits, as well investigate the financial state of the companies whose profits rise and fall in different periods.
... The relationships between the cost of capital and differing financing policies have been examined in numerous studies. They are linked to the seminal contributions of Modigliani and Miller (1963) (MM), as well as of Miles and Ezzell (1980) (ME) and Harris and Pringle (1985). 1 MM assume the interest-bearing debt to be planned deterministically. Future tax shields are treated as certain, leading to a comparatively low cost of capital. ...
... Future tax shields are treated as certain, leading to a comparatively low cost of capital. ME and Harris and Pringle (1985) consider the case where debt is periodically resp. continuously adapted to a target capital structure (Appleyard and Strong 1989;Clubb and Doran 1991;Taggart 1991). ...
The insights of Modigliani and Miller (Am Econ Rev 53:433–443, 1963) and Miles and Ezzell (15:719–730, https://doi.org/10.2307/2330405, 1980) on the cost of capital of firms rank among the most important results in financial theory. The underlying assumptions regarding the financial policy, however, can hardly be reconciled with empirical findings. We investigate the implications of an alternative approach that is characterized by a fixed payout ratio. By introducing additional assumptions about investment opportunities, we find relationships between the cost of equity of levered and unlevered firms. The results contribute to explaining empirical findings and open the possibility to base valuation techniques on realistic and yet practicable assumptions.
... (4) In [6][7][8][9], the following formula for the WACC has been derived [6]: ...
... If, as it is stated in [6], the WACC is constant over time, the financially dependent company capitalization can be found by discounting with the WACC for the financially independent company cash flows. The formulas for this special cases, where the WACC is constant, could be found in textbooks [8,9]. ...
The modern capital cost and capital structure theory—the Brusov–Filatova–Orekhova (BFO) theory and its perpetuity limit, the Modigliani–Miller theory—describe the case of the payments of income tax at the end of the year. However, in practice, companies could make these payments in advance. Recently, the Modigliani–Miller theory has been modified for the case of advanced payments of income tax and has shown that the obtained results are quite different from ones in the “classical” Modigliani–Miller theory. In the current paper, for the first time, we modify the Brusov–Filatova–Orekhova (BFO) theory for the case of advanced payments of income tax and show that the impact of the transition to advance payments is much more significant than in the case of a perpetuity limit (the MM theory) and even leads to a qualitatively new effect in the dependence of equity cost on leverage. An important conclusion drawn in this paper is that the tax shield is very important, and the way it is formed (payments at the end of the year or in advance) leads to very important consequences, changing all the financial indicators of the company, such as the cost of raising capital and company value and radically changing the company’s dividend policy.
... In [13][14][15][16] more general than Modigliani-Miller (MM) formula for the WACC has been derived: it is described by the following formula [13] ...
... If the WACC is constant over time, as it is stated in [13], the levered company value can be found by discounting with the WACC for the unlevered free cash-flows. The resulting formulas, which describe the special cases, where the WACC is constant, can be found in textbooks [15,16]. ...
Both main theories of capital cost and capital structure—the Brusov–Filatova–Orekhova (BFO) theory and its perpetuity limit, the Modigliani–Miller theory—consider the payments of tax on profit once per year, while in real economy these payments are made more frequently (semi-annual, quarterly, monthly etc.). Recently the Modigliani–Miller theory has been generalized by us for the case of tax on profit payments with an arbitrary frequency. Here for the first time, we generalized the Brusov–Filatova–Orekhova (BFO) theory for this case. The main purpose of the paper is bringing the BFO theory closer to economic practice, taking into account one of the features of the real functioning of companies, the frequent payments of tax on profit. We derive modified BFO formulas and show that: (1) All BFO formulas change; (2) all main financial parameters of the company, such as company value, V, equity cost, ke, and the weighted average cost of capital, WACC, depend on the tax on profit payments frequency. The increase of the frequency of payments of income tax leads to a decrease in the cost of attracting capital, WACC, and increase in the capitalization of the company, V. At a certain age n of the company and at certain frequency of tax on profit payments p, a qualitatively new anomalous effect takes place: the equity cost, ke(L), decreases with an increase in the level of leverage L. This radically changes the company′s dividend policy, since the economically justified amount of the dividends is equal to the cost of equity. For both parties–for the company and for the tax regulator more frequent payments of tax on profit are beneficial: for the company, because this increases the company capitalization, and for the tax regulator, because earlier payments are beneficial for it due to the time value of money.
... Zur Harris/Pringle (1985); Enzinger/Kofler (2011); IDW (2018a) Kap. A Tz. 413. ...
... 15 Vgl. Harris /Pringle (1985), S. 238. 16 Vgl. ...
German Abstract: Auch wenn dem Debt Beta Konzept in Theorie und Bewertungspraxis mittlerweile viel Raum eingeräumt wird, bleiben die Interdependenzen mit dem APV-Ansatz oft unbeachtet. Der vorliegende Beitrag versucht diese Lücke zu schließen. Aufbauend auf den Grundlagen zur Ermittlung des Debt Beta wird zum einen gezeigt, welche impliziten Annahmen zum Debt Beta das APV-Verfahren in der Regel unterstellt, die zur Herstellung der Konsistenz bei Anwendung anderer DCF-Verfahren zu berücksichtigen sind. Zum anderen wird dargestellt, wie die bei Anwendung anderer DCF-Verfahren getroffenen Annahmen zum Debt Beta den nach dem APV-Verfahren ermittelten Unternehmenswert beeinflussen.
English Abstract: Even though the debt beta concept is meanwhile comprehensively covered in theory and practical valuation, the interdependence with the APV-approach is barely considered. This paper aims to close this gap. Based on the principles of debt beta calculation first the implicit assumptions regarding the debt beta that are regularly supposed by applying the APV-approach, relevant for achieving consistent valuation results with other DCF methods, are examined. Second it is analyzed, how assumptions regarding debt beta when applying other DCF-methods influence the company value calculated by the APV-approach.
... Alternative approaches are provided as answer options, such as formal risk analysis, a modified CAPM including additional risk factors, average historical returns on common stock, current market return adjusted for risk, discount rates set by regulatory decisions, dividend discount model, earnings/price ratio, cost of debt plus a risk premium, benchmarking approaches with comparable companies or comparable investments, and whatever our investors tell us they require. Furthermore, respondents have the choice to rate concepts discussed within finance theory, including that discount rates are at least as high as defined hurdle rates (Weston, 1973;Harris and Pringle, 1985;Ehrhardt, 2001) and the more flexible and robust CE method 6 (Sick, 1986;Ryan and Gallagher, 2006;Brealey et al., 2011;Espinoza and Morris, 2013). The latter method addresses the critics of coupling time value of money and risk within a single factor, the discount rate, in valuation Myers, 1966, 1968;Hamada, 1977) by analysing them separately (Zeckhauser and Viscusi, 2008) while adjusting cash flows and discount rates for uncertainty and hence focusing on downside risk consideration and value protection (Espinoza, 2014(Espinoza, , 2015. ...
... There are, however, still a certain amount of organisations which use a single discount rate for the whole company. This is only feasible if project risks are similar to the investment firm's risk and both have similar capital structures (Harris and Pringle, 1985;Brigham and Ehrhardt, 2008). Discount rates based on past experiences are applied by 31.5% of participants, mainly by small and low leveraged companies and not as the sole approach, but as a complementary method to some of the other more frequently applied methods (Appendix Table A1.10). ...
... This beta transformation is not shown in detail in the reports. When we reconstructed the valuations manually, we saw that the predominant way to link unlevered and levered beta values was to follow Harris and Pringle (1985) in recent years in that they link unlevered and levered cost of equity, since Harris and Pringle do not apply the CAPM. ...
The objective of our paper is to analyze, how valuation practice deals with inflation especially for the terminal value, and how company value is influenced by assumptions set by practitioners. For that reason, we examine how vulnerable companies could be regarding struggles to pass on inflationary effects to their customers. We analyze the inflation rates assumed for the steady-state (terminal value) by comparing them to different estimators for the inflation rate expected at the valuation date (Survey of Professional Forecasters, inflation rates derived by comparing real and nominal rate of returns, inflation swaps). We quantify the implications of using different inflation rates for future cash flow development, terminal value and the company value at the valuation date, and compare nominal reported values with company values in a (hypothetical) world without inflation. Our sample consists of 263 valuation reports written by German auditors with valuation dates between 2000 to 2021. Most of the reports aim at determining the price per share to compensate minority shareholders during a squeeze-out. Our results question inter alia the preference for a constant company specific inflation rate of around 1% on average, and we quantify a number of value effects.
... This beta transformation is not shown in detail in the reports. When we reconstructed the valuations manually, we saw that the predominant way to link unlevered and levered beta values was to follow Harris and Pringle (1985) in recent years in that they link unlevered and levered cost of equity, since Harris and Pringle do not apply the CAPM. ...
Schmalenbach Journal of Business Research, published online (see DOI above):
The objective of our paper is to analyze, how valuation practice deals with inflation especially for the terminal value, and how company value is influenced by assumptions set by practitioners. For that reason, we examine how vulnerable companies could be regarding struggles to pass on inflationary effects to their customers. We analyze the inflation rates assumed for the steady-state (terminal value) by comparing them to different estimators for the inflation rate expected at the valuation date (Survey of Professional Forecasters, inflation rates derived by comparing real and nominal rate of returns, inflation swaps). We quantify the implications of using different inflation rates for future cash flow development, terminal value and the company value at the valuation date, and compare nominal reported values with company values in a (hypothetical) world without inflation. Our sample consists of 263 valuation reports written by German auditors with valuation dates between 2000 to 2021. Most of the reports aim at determining the price per share to compensate minority shareholders during a squeeze-out. Our results question inter alia the preference for a constant company specific inflation rate of around 1% on average, and we quantify a number of value effects.
... Extensive and probably the most detailed analysis of existing methods covering the estimated capital structure is introduced in the recently published work of P. Fernandez (Fernandez, 2015), who presents not only his own evaluation of Tax Shield (Fernandez, 2004), unlevered beta and unlevered company, but also the evaluation methods of Damodaran (Damodaran, 1994), Miles-Ezzel (Miles & Ezzel, 1980, Myers (Myers, 1974) and Harris-Pringle (Harris & Pringle, 1985). An interesting work of P. ...
em>The article contains a theoretical analysis of the impact of additional issue of shares on the value of the invested and stock capital. The present analysis encompasses aspects of redistribution of capital between the old and new shareholders, as well as valuation procedures in different situations, both in terms of the volume of additional issue of shares and of payment methods. The income approach is used in the value appraisal. The principal place under the income approach is given to the shareholder value added model (model SVA). This article may be useful in solving a number of practical problems related to the issues of restructuring of the company's capital. Investment analysts will find in this article a tool of benefit-sharing analysis of the capital structure changes between “old” and “new” company’s shareholders and will be able to make a calculation of the parameters of the additional issue of shares.</em
... An alternate formula for the WACC has been suggested [9][10][11][12]. It has the form below (Equation (18) ...
To expand the applicability in practice of the modern theory of cost and capital structure, the theory of Brusov–Filatova–Orekhova (BFO), which is valid for companies of arbitrary age, is generalized for the case of variable income. The generalized theory of capital structure can be successfully applied in corporate finance, business valuation, banking, investments, ratings, etc. income. A generalized Brusov–Filatova–Orekhova formula for the weighted average cost of capital, WACC, is derived using a formula in MS Excel, where the role of the discount rate shifts from WACC to WACC–g (here g is the growth rate) for financially dependent companies and k0–g for financially independent companies is shown. A decrease in the real discount rates of WACC–g and k0–g with g ensures an increase in the company’s capitalization with g. The tilt of the equity cost curve, ke(L), increases with g. Since the cost of equity justifies the amount of dividends, this should change the dividend policy of the company. It turns out that for the growth rate g < g*, the tilt of the curve ke(L) becomes negative. This qualitatively new effect, discovered here for the first time, can significantly change the principles of the dividend policy of the company. The obtained results are compared with the results of the MM theory with variable income.
... As a more general formula for the WACC, the famous Modigliani-Miller (MM) has been derived and discussed by a few authors (Farber, A., R. Gillet, and A. Szafarz, 2006, Fernandez, P., 2007, Harris, R., and J. Pringle, Miles, J.A., and J.R. Ezzel, Peter MDeMarzo et al.) [6][7][8]. It takes the following form (Equation (18) in FGS, 2006 [6]) ...
The main purpose of the current study is the generalization and further development of the Modigliani–Miller theory taking into account one of the conditions of the real functioning of companies for the case of paying income tax with an arbitrary frequency (monthly, quarterly, semi-annual or annual payments). While a return is not required more than once a year, businesses may be responsible for filing estimated taxes based on profits earned. This requirement is dependent on showing a profit. For example, sole proprietors must file estimated taxes on profits quarterly, on the 15th day of April, June, September and January. In Russia, tax on profit payments could be made annually, quarterly, or monthly. We suppose, that more frequent payment of income tax impacts on all main financial indicators of the company and leads to some important consequences. We use analytical and numerical methods: we derive all main formulas of the modified Modigliani–Miller theory theoretically and then use them to obtain all main financial indicators of company and their dependences on different parameters by MS Excel. We show that: (1) all Modigliani–Miller theorems, statements and formulas change; (2) all main financial indicators, such as the weighted average cost of capital (WACC), company value, V, and equity cost, ke, depend on the frequency of tax on profit payments; (3) in the case of income tax payments more than once per year (at p ≠ 1), as takes place in practice, the WACC, company value, V and equity cost, and ke start depend on debt cost, kd, while in ordinary (classical) Modigliani–Miller theory all these values do not depend on kd; (4) obtained results allow a company to choose the number of payments of tax on profit per year (of course, within actual tax legislation): more frequent payments of income tax are beneficial for both parties, for the company and for the tax regulator.
... Warum sich erhebliche Ausfallrisiken ohne weiteres mit einer wertorientierten Finanzierungspolitik vereinbaren lassen sollten, lassen die Autoren offen. Sie befinden sich dabei in prominenter Gesellschaft, da auchHarris/Pringle (1985),Miles/Ezzell (1980) oder andere Autoren und Autorengespanne zu diesem Problem schweigen. ...
Der Beitrag beschäftigt sich mit dem Vorschlag im IDW Praxishinweis 2/2018 „Berücksichtigung des Verschuldungsgrads bei der Bewertung von Unternehmen“, der im Beitrag von Haesner/Jonas (2020) in der Zeitschrift Die Wirtschaftsprüfung ausführlicher dargestellt worden ist, den WACC einer Gruppe vergleichbarer Unternehmen (Peer Group) zur Bewertung eines hoch verschuldeten Unternehmens einzusetzen. Dazu wird ausgehend von dem vorliegenden Zahlenbeispiel gezeigt, welche Implikationen dieser Vorschlag hat. Es besteht Raum für Verbesserung, nicht zuletzt weil man das nachvollziehbare Ziel einer Vermeidung überbordender Steuervorteile der Fremdfinanzierung (Tax Shields) nicht durch eine Entkoppelung der Tax Shields des zu bewertenden hoch verschuldeten Unternehmens von dessen Verschuldungsumfang und -konditionen erreicht. Der Aufsatz soll ein konstruktiver Beitrag zur laufenden Diskussion des Praxishinweises sein. Er ist nicht nur aufgrund des „zarten Alters“ des Praxishinweises, sondern (leider) auch aufgrund der wirtschaftlichen Folgen der Pandemie, wie steigende Verschuldungsgrade und Ausfallrisiken, von Relevanz.
... 1 L-hybrid financing: the leverage of the steady-state phase is determined at the valuation date 2 In the case of active debt management according to HP, all tax shields are uncertain which yields the adjustment formula for the levered cost of equity q ' ¼ q u þ ðq u À rÞ Á L (Harris and Pringle 1985). Under active debt management of ME, the tax shields are certain in the period of their emergence and uncertain in all other periods, which yields q ' ¼ q u þ ðq u À rÞ Á 1þrÁð1ÀsÞ 1þr Á L (Miles and Ezzell 1985). ...
In corporate valuation, it is common to assume either passive or active debt management. However, it is questionable whether these pure financing policies reflect the real financing policies of firms with a sufficient degree of accuracy. This shortcoming has led to the development of mixed financing strategies as combinations of pure financing strategies. Whereas hybrid financing is directly linked to the two-phase model, it is unclear how to apply discontinuous financing in such a setting. In this study, according to the two versions of hybrid financing, we analyze the implementation of discontinuous financing in a two-phase model. Thereby, we present a simpler and more intuitive derivation of the valuation equation for discontinuous financing to increase its acceptance and its use for corporate valuation practice. Moreover, we compare the different mixed financing strategies with each other theoretically, and we conduct simulations to elucidate the impact on market values and the sensitivities of input parameters. The study concludes that the presented mixed financing strategies can help in the attempt to reflect the real financing behavior of firms more accurately and, therefore, constitute a valuable alternative to pure financing strategies for valuation.
... In particular, if the risk of the tax shield is equal to the risk of debt, then r TS t = r D t ; if the risk of the tax shield is equal to the risk of the unlevered operating assets, then r TS t = k uo t . Other assumptions are possible and the determination of r TS t will depend on the financing policy and on the level of the prospective operating income as opposed to net interest (if the latter is greater than the former, no tax saving arises) (see Myers 1974;Ezzell 1980, 1985;Inselbag and Kaufold 1997;Harris and Pringle 1985;Lewellen and APV (see Kaplan and Ruback 1995;Ruback 2002;Fernández 2002;Tham and Vélez-Pareja 2004;Booth 2007;Cooper and Nyborg 2007;Jagannathan et al. 2017) and is mainly presented under the additional assumption of constant rates: ...
We present the well-known Internal Rate of Return, and show that it suffers from many pitfalls and bears no direct relationship to the business transactions underlying the project’s activities (and, therefore, no relationship to the capital actually employed). Therefore, we advise practitioners to dispense with. We present two related approaches, the Modified-Internal-Rate-of-Return approach and Teichroew-Robichek-Montalbano model, discussing pros and cons, and concluding that all these metrics have serious drawbacks which are overcome by the AIRR approach presented in Chapter 8.
... Even though it is not explicitly stated, their analysis only treats the case of risk-free debt. Harris and Pringle (1985) go on to develop risk-adjusted discount 1.3. Description and integration of the different articles (2011). ...
In this dissertation I treat questions of asset pricing under the presence of taxes. I present four published articles. The first three articles are concerned with topics of company valuation when debt is risky. The first article analyzes the applicable discount rate for the valuation of tax savings in a simple setting without taxes on cancelled debt. The article concludes that the discount rate of tax savings is the same as the one for interest payments. Other than frequently assumed, this discount rate is not necessarily the same as the discount rate for debt as a whole. With the prioritization of interest or principal payments in case of losses on debt payments, the discount rates on interest payments and of tax savings are regularly different from the one for the overall debt issue. Only a pro rata distribution of losses on principal and interest payments generally leads to equal discount rates for interest payments, principal payments, and, therefore, also for debt payments as a whole. The second article continues to look at the valuation of tax savings. It differentiates the case with and the one without the taxation of cancelled debt. For both cases, the article derives equations for the value of tax savings as well as for risk-adjusted discount rates and WACC-like equations. A major finding is that the previous corporate finance literature on this topic usually makes the implicit assumption that cancelled debt is taxed. In this case valuation equations have a simple form since they are independent from the distribution of losses between interest and principal payments. Without the taxation of cancelled debt, the distribution of losses on interest and principal payments becomes important for the valuation procedures and a differentiation between cases such as interest prioritization, principal prioritization and pro rata loss distribution is necessary. The third article uses the findings of the first two articles and constructs equations for a de- and re-levering procedure using the expected return equations from the mean-variance CAPM. It extends the regularly used procedure that uses the assumption of risk-free debt to simple settings with risky debt. The forth article looks at two economies, which differ only with respect to taxation - one features taxes on capital gains and one does not. The analysis leads to several extensions on prior findings on the question of the conditions under which asset prices are the same in both economies. The article provides sufficient conditions for unchanged prices for the case of a zero risk-free rate, which entails that all agents consume exactly the same in each state. Without a zero risk-free rate, prices are the same in both economies with exponential utility and normal returns and with linear marginal utility.
In this paper, we develop two complete discounted-cash flow (DCF) frameworks for the valuation of constant-growth annuities and perpetuities. By ‘complete’ we mean that these frameworks allow the valuation of a firm or project by means of different DCF methods, particularly, the equity method, the free-cash-flow (FCF) method, the adjusted-present-value-method, and the capital-cash-flow method. This also requires the derivation of formulas that allow the translation between different required returns, like the required return on unlevered and levered equity, the discount rate in the FCF method, and the required return on the tax-shield. Our paper departs from the two most advocated and mutually exclusive frameworks when dealing with DCF. The first is based on Modigliani and Miller (M&M), where the FCF at different points in time are independently distributed. The second framework rests on the analysis of Miles and Ezzell (M&E) who presume a first-order autoregressive cash-flow process. Some elements of a ‘complete’ framework exist in the literature, but in our opinion, a complete picture has not been developed yet. The contributions of this paper are the following: (1) We develop (or expand) the set of formulas that are required for the valuation of constant-growth annuities and perpetuities; (2) The formulas we develop in this paper are based on a backward-iteration process, which in itself represents a suitable tool for firm valuation; (3) Using a numerical example, we show that the two mutually exclusive frameworks of M&M or M&E achieve very different valuation results; (4) It turns out that the expected returns and the growth rate of the FCF are partly linked, but this relationship is different in the two frameworks; (5) In our numerical examples, we show how the constant-growth annuity or perpetuity, can be integrated with an explicitly planned FCF.
This paper presents a novel approach to calculate the weighted average cost of capital (WACC) but considering additional relevant variables to be applied to a specific cash flow, free cash flow to firm (FCFF), or capital cash flow (CCF), in order to value an asset. The analytical expressions deduced for this approach, one for each case, are based not only on the ratio debt to the value of the asset and the cost of debt and equity, as in the usual expression, but also includes the debt and firm's cash flow durations. The proposed novel approach to cost of capital has key advantages in comparison to the usual expression for WACC: It is an analytical expression that could be applied to whatever kind of debt or capital structure, not only perpetual debt or permanent capital structure.
It is a single discount rate, and for its calculation, it is not necessary to recalculate financial factors involved, which makes easier its application.
The additional financial variables involved, debt and firm's cash flow duration, allow to obtain better results for the right discount rate and for the value of an asset in the sense that the discount rate for the asset effectively will permit to reach the required level for the profitability for the investor and to cover the cost of debt.
In practice, profit tax payments are (1) made more frequently than annually and (2) can be made in advance. To study the influence of these two factors on the financial indicators of a company, we generalized the Brusov–Filatova–Orekhova (BFO) theory for the case of advance profit tax payments with an arbitrary frequency for the first time. Using modified BFO formulae, we showed that all financial indicators of a company, such as company value, the weighted average cost of capital (WACC) and equity cost (ke), depend on the frequency of the profit tax payments. We found that the WACC increased with the payments and the company value decreased with the payments. This meant that more infrequent payments could be beneficial for the company. The tilt angle of the equity cost (ke(L)) also increased with the payments. Depending on the age of the company, the equity cost either decreased with L for all payment frequencies or increased for some frequencies. We compared the obtained results to those that we described recently for profit tax payments at the end of the financial period and found them to be totally different. We found that in spite of the fact that the WACC decreased with the payments and the company value increased with the payments, the WACC value in this case turned out to be bigger and the company value turned out to be smaller than in the case of advance profit tax payments of any frequency. This underlined the importance of advance profit tax payments. Regulator recommendations were also developed to encourage the practice of advance profit tax payments due to the understanding of the benefits of this for both parties: the companies and the state. A new effect was discovered: the decrease in equity cost with an increase in the level of leverage (L).KeywordsGeneralized Brusov–Filatova–Orekhova (BFO) theoryFrequent advance profit tax paymentsAbnormal dependence effects of equity costs on leverage levelNew approach to company dividend policies
To expand the applicability in practice of the modern theory of cost and capital structure, the theory of Brusov–Filatova–Orekhova (BFO), which is valid for companies of arbitrary age, is generalized for the case of variable income. The generalized theory of capital structure can be successfully applied in corporate finance, business valuation, banking, investments, ratings, etc. income. A generalized Brusov–Filatova–Orekhova formula for the weighted average cost of capital, WACC, is derived using a formula in MS Excel, where the role of the discount rate shifts from WACC to WACC-g (here, g is the growth rate) for financially dependent companies and k0-g for financially independent companies is shown. A decrease in the real discount rates of WACC-g and k0-g with g ensures an increase in the company’s capitalization with g. The tilt of the equity cost curve, ke(L), increases with g. Since the cost of equity justifies the amount of dividends, this should change the dividend policy of the company. It turns out that for the growth rate g < g*, the tilt of the curve ke(L) becomes negative. This qualitatively new effect, discovered here for the first time, can significantly change the principles of the dividend policy of the company. The obtained results are compared with the results of the MM theory with variable income.KeywordsGeneralized Brusov–Filatova–Orekhova theoryGrowth rateVariable incomeCompany’s capitalizationThe weighted average cost of capitalWACCEquity cost
The Brusov–Filatova–Orekhova (BFO) theory is generalized for the simultaneous account of variable company profit and advance tax on income payments. The generalized BFO formula for the WACC has been derived. The dependence of WACC, discount rate, WACC-g (here g is growth rate), company capitalization, V, the equity cost, ke, on leverage L at various values of g, on debt cost, kd, and on age of the company, n, is studied. It is shown that WACC is no longer a discount rate. This role passes to WACC-g, which decreases with g, while the company’s value increases with g. The tilt of curve k(L) growths with g. It is found that at the growth rate g < g* the tilt of the curve ke(L) is negative. This changes significantly the company’s dividend policy principles. WACC(L) as well as the discount rate, WACC-g, decreases with the increase of debt cost kd. V (L) at all values of kd increases with leverage L, as well V(L) increases with kd. This means that tax shield advantages the decrease of the cost of raising capital. Examining the main financial parameters of the company at the positive (g = 0.2) and negative (g = −0.2) growth rates, we found a huge difference in their behavior. This allows you to explore companies with growing profits and companies with decreasing profits, as well as investigate the financial state of the companies whose profits rise and fall in different periods.KeywordsGeneralized BFO theoryVariable incomeAdvance tax on income paymentsCompany valueWACCCost of equity
In this chapter, we analyze all existing theories of capital structure (with their advantages and disadvantages) in order to understand all aspects of the problem and make correct management decisions in practice. The role of the capital structure is that the correct determination of the optimal capital structure allows the company’s management to maximize the capitalization of the company and the long-term goal of the function of any company. The review examines the state of the capital structure and capital cost theory from the middle of the last century, when the first quantitative theory was created, to the present. The two main theories, Modigliani–Miller (MM) and Brusov–Filatova–Orekhova (BFO), are discussed and analyzed, as well as their numerous modifications and generalizations. Additionally discussed is the latest stage in the development of the theory of capital structure, which began a couple of years ago and is associated with the adaptation of the two main theories of capital structure (Brusov–Filatova–Orekhova and Modigliani–Miller) to establish the practice of the function of companies. This generalization takes into account the real conditions of the work of the companies. It was noted that taking into account some effects that are present in economic practice (such as variable income, frequent payments of tax on income, advance payments of tax on income, etc.) brings both theories closer, and even the Modigliani–Miller theory, with all its many limitations, becomes more applicable in economic practice. However, it should be remembered that the Modigliani–Miller theory is only true for perpetual companies, while the BFO theory is valid for companies of any age, and from this point of view, they never coincide.KeywordsCapital structureModigliani–Miller (MM) theoryBrusov–Filatova–Orekhova (BFO) theoryTrade-off theory
Two modifications of the modern theory of the capital cost and capital structure—the theory of Brusov–Filatova–Orekhova (BFO) with variable income are considered: (1) with the payment of income tax at the end of periods and (2) with advance payments of income tax. BFO formulas for the weighted average cost of capital, WACC, for company value, V, were derived for these two cases and within these formulas, a comprehensive analysis of the dependence of WACC, of discount rate, WACC–g (here g is the growth rate), company capitalization, V, the equity cost, ke, on the leverage level L at different values of the growth rate, g, at different values of the cost of debt capital, kd, and at different values of company age, n was carried out.The results for cases (1) and (2) are compared, which allows us to conclude that case (2) is always preferable for both the company and the regulator. This allows for developing recommendations for both parties to expand the practice of advance payments of income tax.KeywordsGeneralized Brusov–Filatova–Orekhova theoryAdvance payments of tax on profitVariable profitCompany valueEquity costThe weighted average cost of capitalWACC
Both main theories of capital cost and capital structure—the Brusov–Filatova–Orekhova (BFO) theory and its perpetuity limit—the Modigliani–Miller theory—consider the payments of tax on profit once per year, while in real economy these payments are made more frequently (semi-annual, quarterly, monthly, etc.). Recently the Modigliani–Miller theory has been generalized by us for the case of tax on profit payments with an arbitrary frequency. Here for the first time we generalized the Brusov–Filatova–Orekhova (BFO) theory for this case. The main purpose of the chapter is to bring the BFO theory closer to economic practice, taking into account one of the features of the real functioning of companies—the frequent payments of tax on profit. We derive modified BFO formulas and show that: (1) all BFO formulas change; (2) all main financial parameters of the company, such as company value, V, the weighted average cost of capital, WACC, and equity cost, ke, depend on the frequency of tax on profit payments. It turns out that the increase in the number of payments of tax of profit per year leads to a decrease in the cost of attracting capital, WACC and increase in the company value, V. At a certain age n of the company and at certain frequency of tax on profit payments p, a qualitatively new anomalous effect takes place: the equity cost, ke(L), decreases with an increase of the level of leverage L. This radically changes the company’s dividend policy, since the economically justified amount of the dividends is equal to the cost of equity. More frequent payments of income tax are beneficial for both parties—for the company and for the tax regulator: for the company, this leads to an increase in the value of the company, and for the tax regulator, earlier payments are beneficial due to the time value of money.KeywordsGeneralized Brusov–Filatova–Orekhova (BFO) theoryThe Modigliani–Miller theoryFrequency of payment of income taxEquity costThe weighted average cost of capitalCompany capitalizationA qualitatively new anomalous effect
The purpose of this review is to analyze all existing theories of the capital structure (with their advantages and disadvantages) in order to understand all aspects of the problem and make correct management decisions in practice. The role of the capital structure is that the correct determination of the optimal capital structure allows the company’s management to maximize the capitalization of the company and the long-term goal of the function of any company. The review examines the state of the capital structure and capital cost theory from the middle of the last century, when the first quantitative theory was created, to the present. The two main theories, Modigliani–Miller (MM) and Brusov–Filatova–Orekhova (BFO), are discussed and analyzed, as well as their numerous modifications and generalizations. Additionally, discussed is the latest stage in the development of the theory of capital structure, which began a couple of years ago and is associated with the adaptation of the two main theories of capital structure (Brusov–Filatova–Orekhova and Modigliani–Miller) to establish the practice of the function of companies. This generalization takes into account the real conditions of the work of the companies. It was noted that taking into account some effects that are present in economic practice (such as variable income, frequent payments of tax on income, advance payments of tax on income, etc.) brings both theories closer, and even the Modigliani–Miller theory, with all its many limitations, becomes more applicable in economic practice. However, it should be remembered that the Modigliani–Miller theory is only true for perpetual companies, while the BFO theory is valid for companies of any age, and from this point of view, they never coincide.
We derive a consistent valuation approach that integrates the interdependent effects of cash dividends, share repurchases, and active debt management while considering personal taxes. The valuation approach is based on the assumption that a predetermined proportion of the flow to equity is used for share repurchases instead of cash dividends. Additionally, we examine the effects of share repurchases on the cost of equity by deriving appropriate adjustment formulae. Furthermore, we run simulations to investigate the valuation differences caused by the distribution of excess cash via cash dividends or share repurchases. The results show that share repurchases have a significant positive effect on equity market value. This article is protected by copyright. All rights reserved
Two main capital structure theories: Brusov–Filatova–Orekhova (BFO theory) and its perpetuity limit—Modigliani–Miller theory—describe the case of annual payments of tax of profit at the end of periods, but in practice, these payments (1) are made more frequent: semiannually, quarterly, monthly; (2) could be made in advance. To study the influence of these two effects on main financial indicators of the company, such as the weighted average cost of capital, WACC, company value, V, and equity cost, ke, we modify the Modigliani–Miller theory for the case of arbitrary frequency of payments of tax on profit: for payments at the end of periods as well as for advanced payments. Account of two these effects leads to very important consequences. We show that:
1.
All Modigliani–Miller theorems, statements, and all formulas change.
2.
All main financial indicators, WACC, V, and ke depend on the frequency of tax on profit payments and start depend on debt cost kd, while in ordinary (classical) Modigliani–Miller theory all these indicators DO NOT depend on kd.
3.
The tilt angle of the curve of equity cost, ke (L), changes with the frequency of payments of tax of profit p, this modifies the dividend policy of the company, because the economically justified value of dividends is equal to equity cost.
4.
For payments of tax of profit at the end of periods more frequent payments of income tax are beneficial for both parties: for the company and for the tax regulator: (1) for the company, this leads to decrease of the cost of attracting capital, WACC, and thus to an increase in the value of the company, V, and (2) for the tax regulator, more frequent payments are beneficial due to the time value of money.
5.
For payments of tax of profit in advance more frequent payments of income tax are NOT beneficial for the company: this leads to increase of the cost of attracting capital, WACC, and thus to decrease in the value of the company, V, but for the tax regulator it remains beneficial: earlier payments are beneficial due to the time value of money.
All these allow company to choose the method of payments of tax of profit(at the end of period or in advance) and number of payments of tax of profit per year, as many, as it is profitable to it (of course, within actual tax legislation).KeywordsModified Modigliani–Miller theoryFrequency of payment of tax on profitAdvanced payments of tax on profitEquity costThe weighted average cost of capitalCompany value
One of the two main theories of capital cost and capital structure is the theory of Nobel Prize winners Modigliani and Miller (Am Econ Rev 48:261–297, 1958, Am Econ Rev 53:147–175, 1963, Am Econ Rev 56:333–391, 1966). In this chapter, we describe the main results of this theory.Under the capital structure, one understands the relationship between equity and debt capital of the company. Does capital structure affect the company’s main settings, such as the cost of capital, profit, value of the company, and the others, and, if it affects, how? Choice of an optimal capital structure, i.e., a capital structure, which minimizes the weighted average cost of capital, WACC, and maximizes the value of the company, V, is one of the most important tasks solved by a financial manager and by the management of a company. The first serious study (and first quantitative study) of the influence of capital structure of the company on its indicators of activities was the work by Modigliani and Miller (Am Econ Rev 48:261–297, 1958, Am Econ Rev 53:147–175, 1963, Am Econ Rev 56:333–391, 1966). Until this study, the approach existed (let us call it traditional), which was based on empirical data analysis.
For the first time, we have generalized the world-famous theory by Nobel Prize winners Modigliani and Miller for the case of variable profit, which significantly extends the application of the theory in practice, specifically in business valuation, ratings, corporate finance, etc. We demonstrate that all the theorems, statements and formulae of Modigliani and Miller are changed significantly. We combine theoretical and numerical (by MS Excel) considerations. The following results are obtained:
1.
Discount rate for leverage company changes from the weighted average cost of capital, WACC, to WACC − g (where g is growing rate), for a financially independent company from k0 to k0 − g. This means that WACC and k0 are no longer the discount rates as it takes place in case of classical Modigliani–Miller theory with constant profit. WACC grows with g, while real discount rates WACC − g and k0 − g decrease with g. This leads to an increase of company capitalization with g.
2.
The tilt angle of the equity cost ke(L) grows with g. This should change the dividend policy of the company, because the economically justified value of dividends is equal to equity cost.
3.
A qualitatively new effect in corporate finance has been discovered: at rate g < g* the slope of the curve ke(L) turns out to be negative, which could significantly alter the principles of the company’s dividend policy.
KeywordsGeneralization of Modigliani and Miller theoryVariable profitCompany capitalizationEquity costThe weighted average cost of capitalWACC
Purpose
The paper proposes using modified duration in calculating the proper risk-adjusted discount rate (RADR) to account for downside risk scenarios in capital budgeting.
Design/methodology/approach
The paper shows how to use modified duration to summarize in a single number the bidimensional information about the inflows and terms in which they are charged in the use of the RADR. If a short modified duration characterizes the project, that is, the most relevant inflows are charged in short times, then discounting at RADR has mild effects on net present value (NPV). Else, if a long modified duration characterizes the project, discounting at RADR may have severe effects on NPV. The study proves that RADR's effectiveness increases with the project's modified duration.
Findings
The study builds a bridge between the regular NPV method used in academia and the RADR method used in the managerial context by identifying the proper RADR that leads the same NPV risk-adjustments, whichever method is used by including modified duration into the analysis.
Practical implications
The results show how to select the proper RADR by reducing the subjectivity and increasing financial precision based on modified duration, thus providing an alternative to the norm. Simulations are used to make sensitivity analysis more effective and spotlight the main drivers in the risk-adjustments providing robust results.
Originality/value
This paper fulfils the gap between the RADR method and the expected net present value method by providing simple relations between the characteristic parameters.
Purpose
The purpose of this paper is to establish the flow-to-equity method, the free cash flow (FCF) method, the adjusted present value method and the relationships between these methods when the FCF appears as an annuity. More specifically, we depart from the two most widely used evaluation settings. The first setting is that of Modigliani and Miller who based their analysis on a stationary FCF. The second setting is that of Miles and Ezzell who worked with an FCF that represents an autoregressive possess of first order.
Design/methodology/approach
Inspired by recent observations in the literature concerning cash flows, discount rates and values in discounted cash flow (DCF) methods, we mathematically derive DCF valuation formulas for annuities.
Findings
The following relationships are established: (a) the correct discount rate of the tax shield when the free cash flow takes the form of a first-order autoregressive annuity, (b) the direct valuation of the tax shield from the free cash flow for a first-order autoregressive annuity, (c) the correct translation from the required return on unlevered equity to the levered equity, when the free cash flow is a stationary annuity and (d) direct calculation of the unlevered and levered firm values and the value of the tax shield for a stationary annuity.
Originality/value
Until now the complete set of formulas for the valuation of stochastic annuities by different DCF methods has not been established in the literature. These formulas are developed here. These formulas are important for practitioners and academics when it comes to the valuation of cash flows of finite lifetime.
8., vollständig überarbeitete und erweiterte Auflage 2021 Dieses Buch ist eine grundlegende und zugleich vertiefende Einführung in den Bereich der Unternehmensbewertung. Es ist konzipiert für Studierende der Betriebs- und Volkswirtschaftslehre und des Rechts, für Wirtschaftsprüfer, Unternehmensberater, Investmentbanker, Steuerberater und alle mit dem Erwerb, Verkauf bzw. der Restrukturierung von Unternehmen befassten Praktiker. Der gesamte Text der Vorauflage wurde überarbeitet, z. T. gestrafft und in einigen Teilen deutlich erweitert. Nach den einleitenden Kapiteln 1 bis 3, die Grundlagen der Bewer- Bewertung bei Unsicherheit unter Beachtung von Steuern präsentieren, startet die Behandlung tung des Kerns des Buches in Kapitel 4, das die Konzeptionen der DCF-Bewertung vorstellt. Kapitel 5, überschrieben mit „Bewertungsrelevante Überschüsse“, diskutiert neben deren Definition auch deren Planung einschließlich verschiedener Ausprägungen der Gestaltung der Lebensphasen eines Unternehmens und damit des Wachstums. Die Kapitel 6, 7 und 8 behandeln die Bewertungsansätze, die in Literatur und Praxis als herrschend anzusehen sind: APV-Ansatz, WACC-Ansatz und Flow-to-Equity-Ansatz bzw. Ertragswertmethode. Wir bemühen uns, die relativen Vor- bzw. Nachteile der Methoden detailliert und anschaulich zu erläutern. Anzufügen ist, dass diese relativen Vorteile oder Nachteile in späteren Kapiteln des Buches ebenfalls deutlich zutage treten werden. Dies gilt z. B.– aber nicht nur– für das Kapitel10, das über Rückstellungen und Unternehmenswert referiert. Kapitel 9 behandelt den Diskontierungssatz, dessen Bestandteile und die Möglichkeiten der Messung. Erweiterungen des Problemgefüges finden sich in den folgenden Kapiteln. Kapitel10 greift das in der Literatur nur stiefmütterlich behandelte Problem des Zusammenhangs zwischen Rückstellungen und Unternehmenswert auf. Kapitel 11 untersucht den Kontext zwischen Finanzierungsleasing und Unternehmensbewertung. Dabei bilden wir auch die Auswirkungen des IFRS 16 auf die Unternehmensbewertung ab. Kapitel 12 und 13 bringen die ökonomische Schieflage von Unternehmen und damit die Bewertung von Eigentümer- und Gläubigerpositionen bei Ertrags- und Liquiditätsdefiziten ins Spiel. Kapitel 12 erläutert zunächst, welche Kriterien in Form sog. „Eröffnungsgründe“ die deutsche Insolvenzordnung kennt, um eine ökonomische Situation, die Gläubigerpositionen mit Ausfallrisiko belastet, zu markieren und welche Schwachstellen diese Kriterien aufweisen. Dies hat Konsequenzen für die anstehenden Restrukturierungsentscheidungen, die innerhalb oder außerhalb eines Insolvenzverfahrens zu treffen sind. Bei Restrukturierungen im Schatten einer ökonomischer Schieflage kommt der Bewertung der Position der Alteigentümer eine besondere Bedeutung zu. Wir erläutern den ökonomischen Kontext des Problems, der sich auftut zwischen dem Anreiz zu einer zeitigen Eigentümer-gesteuerten Initiierung eines Restrukturierungsprozesses und dem hinter der Prioritätenrangfolge der Ansprüche stehenden Sanktionscharakter der Insolvenzordnung. Wir zeigen auch, wie brauchbar sich der APV-Ansatz erweist, wenn es um eine transparente Aufbereitung der ökonomischen Folgen einer Sanierungsstrategie, z. B. in Form eines Debt-Equity-Swaps, geht. Kapitel 13 analysiert die Kalküle derjenigen, die bei temporären Ertrags- und Liquiditätsdefiziten, in der Vorinsolvenzphase oder im Rahmen eines Insolvenzverfahrens über Kreditverlängerung, Besicherung, Liquidation oder Fortführung mit oder ohne Insolvenzplan und die Neuzuordnung der Anteilsrechte entscheiden. Es stellt einen allgemein einsetzbaren Formelapparat bereit, der relevant wird, sobald Gläubiger Ausfallrisiko übernehmen. Wir haben das Kapitel um eine Würdigung des IDW Praxishinweises 2/2018 „Zur Berücksichtigung der Verschuldungsgrads bei der Bewertung von Unternehmen“ erweitert. Kapitel 14 behandelt Fragen und Ansätze der periodischen Performancemessung, die präzise Methoden der Bewertung voraussetzen, wenn man mindestens Barwertkompatibilität oder – anspruchsvoller – Barwertidentität verlangen will. Dabei stellen wir auch die aus Literatur und Praxis bekannten Konzepte wie EVA™ oder CVA vor und ordnen sie konzeptionell ein. Kapitel 15 wirft einen Blick auf die Bewertung von Unternehmen mittels Multiplika- Multiplikatoren, wobei auch den Querverbindungen unter den verschiedenen, in der Praxis zum Einsatz kommenden Multiplikatoren Aufmerksamkeit gewidmet wird. Nicht verändert hat sich unsere kritische Einstellung gegenüber diesem Bewertungsansatz. Kapitel 16 haben wir überschrieben mit „Gutachtenpraxis und Rechtsprechung“. Wir haben es erweitert um eine kritische Auswertung von fast 300 Bewertungsgutachten und einigen Dutzend Gerichtsentscheidungen, die sich mit einer Reihe dieser Gutachten auseinandersetzen. So können wir nach einer zusammenfassenden Darstellung der Rechtsprechung weiter untersuchen, wie diese Gutachten von den Gerichten gewürdigt werden und welche Änderungen vorgenommen werden. Zudem berechnen wir auch die Werteffekte, die durch die richterliche Korrektur der gutachterlichen Bewertung ausgelöst werden. Kapitel 17 ist neu. Es ist der Bewertung von Überschüssen in Fremdwährung gewidmet. Wir zeigen mögliche Bewertungsansätze auf, würdigen die Relevanz von Terminwechselkursen und weisen auf Besonderheiten bei der Abbildung von Fremdfinanzierungen in fremder Währung und Steuereffekten hin. Kapitel 18 bietet zahlreiche Übungsaufgaben an. Kurze Lösungshinweise sind beigefügt. Zudem haben wir die Übungsaufgaben durch Excel-Tabellen so aufbereitet, dass die eigene Entwicklung von Finanzplänen, Zufallsbäumen etc. nicht mehr erforderlich ist. Die Nutzung der Übungsaufgaben, die wir empfehlen, ist somit erheblich erleichtert. Wer an anspruchsvolleren und realitätsnahen „Aufgaben“ zur Bewertung von Unternehmen interessiert ist, sei auf unser Buch „Akquisitionen, Börsengänge und Restrukturierungen: Fallstudien zur Unternehmensbewertung“ verwiesen, das im gleichen Verlag erschienen ist. Zu den lebensnahen Fällen, die von der Bewertung mittelständischer GmbHs bis zu Großunternehmen (Fraport, Philipp Holzmann) bzw. Großprojekten (Airbus A380, Eurotunnel) reichen, bietet das Buch neben Sachverhaltsbeschreibungen und Daten auch ausführliche Lösungsvorschläge. Alle Berechnungen einschließlich der Lösungen der Übungsaufgaben stehen auf der Website zu diesem Buch unter http://www.vahlen.de/31026831 zum Download bereit. Wir haben in die einzelnen Kapitel eine Reihe von Wissensbausteinen eingearbeitet. Diese fassen die Kernbotschaften eines Abschnitts zusammen und repräsentieren aneinandergereiht die Essenz unseres Buches.
We derive stock returns for firms producing nonrenewable commodities employing the investment-based asset pricing approach. By identifying the appropriate time-varying discount rate the investment-based approach allows an alternative test of the Hotelling Valuation Principle. The empirical results support the principle and enable predicting returns from sorting firms into quintiles by expected return, producing a 16–20% realized difference between top and bottom quintile. The return differences cannot be explained by standard risk factors or a commodity-specific factor, suggesting that an important risk factor is still missing from standard models. The approach permits cost-of-capital estimation that circumvents identifying systematic risk factors.
This chapter discusses analyses and models related to equities. We show how to analyze projections. Then, we look at two components of the cost of equity: equity risk premium and betas. We then show how to perform relative valuation using regression analysis. We end the chapter by showing techniques that can help identify shifts in stocks returns.
It has been a long-established thought and rumor of the industry that aircraft asset investment returns are moderate with lower volatility compared with other asset-backed classes. No systemic, rigorous comprehensive empirical study with real historical data has been done to substantiate this mere hypothesis and this research intends to fill that gap through the hand-collected data set. Previous thoughts have been incomplete based on sample sets too small, short, biased, or based on non-publically available proprietary data sets that have not been conducted with the scientific rigor to make convincing augments and conclusions. There are gaps in the academic literature that can be filled by examining empirical analysis especially in regards to aviation through analysis of 21-year historical representation of the aircraft asset class and construction of various indexes to test the current theories on shocks and examine the effects and characteristics before and after the 2008 global financial crisis.
The paper seeks to develop a comprehensive framework to cross-border DCF valuation. Although the literature on company valuation and on international financial management is vast, such a framework has not yet been proposed. We build upon well-known fundamentals and relevant contributions, e.g. on the derivation of the risk-adjusted rate of return. Relevant risks are exchange rate risk, business risk, financial risk, the risk of the tax effects induced by debt financing, and the risk of default. Additional tax effects beyond the well-known tax shield on interest expenses must be considered. Risk discounts from cash flows and risk premia to be added to risk-free interest rates are derived according to the global CAPM. A conceptual choice occurs not only between the foreign currency and the home currency approach, but also regarding the estimation of future exchange rates. The paper shows how a valuation can be implemented with or without consideration of covariances between cash flows and rate of returns with exchange rates. It also derives the discount rates if forward exchange rates are applied. We discuss the consequences of assuming the uncovered interest parity to hold. We assume deterministic debt and apply the APV approach. In addition, we derive the RADR to be used in the FTE- and WACC approach. The paper addresses not only the valuation of a foreign company, but also the valuation of a domestic company that generates cash flows in foreign currency and/or uses debt in foreign currency. Forthcoming: Journal of Business Economics
There is a variety of problems in the valuation of firms. That is why the evaluator has to make some simplifications in order to come up with a result. That also goes for the theory of valuation. We will take the first step in assuming that the firm has no debt. In simplifying with this assumption, we shall see that a number of economic problems can be discussed. In the next step we will turn to indebted firms.
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Valuation of levered companies (IDW-Praxishinweis 2/2018)
Sumario: Part one: value -- Part two: Risk -- Part three: Practical problems in capital budgeting -- Part four: Financing decisions and market efficiency -- Part five: Dividend policy and capital structure -- Part six: Options -- Part seven: debt financing -- Part eight: Financial planning -- Part nine: Shhort- term financial decisions -- Part ten: Mergers and international finance -- Part eleven: Conclusions
This paper suggests that the pure‐play technique can be used in conjunction with the capital asset pricing model to determine the cost of equity capital for the divisions of a multidivision firm. Since the beta for a division is unobservable in the marketplace, a proxy beta derived from a publicly traded firm whose operations are as similar as possible to the division in question is used as the measure of the division's systematic risk. To provide empirical support for using the pure‐play technique, a sample of multidivision firms and pure‐plays associated with each division is examined. It is shown that an appropriately weighted average of the betas of the pure‐play firms closely approximates the beta of the multidivision firm.
Associate Professor of Finance, Sloan School of Management, Massachusetts Institute of Technology. This paper was greatly improved by comments of G. A. Pogue. I also thank Mr. Swaminathan Iyer for programming assistance. Any deficiencies in the paper are my own.