Javier Santibáñez*, Leire Alcañiz* y Fernando GómezBezares*


 Violet Reed
 3 years ago
 Views:
Transcription
1 6 Javier Santibáñez*, Leire Alcañiz* y Fernando GómezBezares* Cost of funds on the basis of Modigliani and Miller and CAPM propositions: a revision Coste de los fondos bajo las hipótesis de Modiagliani y Miller ABSTRACT When facing with any process involving financial valuation it is of a crucial importance to find and use the accurate discount rate. CAPM provides us with an accurate and very commonly used solution to solve the problem, but it requires the estimation of the Beta, which is quite difficult, especially when talking about nonquoted companies. For many years, text books have suggested to look for a quoted company with a strong similarity with the one to be priced in order to use its Beta. Nevertheless, this may bring up an important problem, since both companies could show different leverage, which would also affect to Taxes and Betas. Both academics and practitioners usually use the wildly renowned formulation by Hamada, but we think that this proposal may introduce important biases, insofar as it only takes Corporation Tax into account, and not Personal Income Tax. In this paper we introduce the effect of Personal Income Tax in a simple and original way that can be useful for Financial practice. Keywords: Cost of funds, Levered Beta, Hamada equation, Tax effects. JEL Classification: G31, G32. RESUMEN En el proceso de valoración de empresas y, en general, en cualquier tipo de valoración financiera, es muy importante acertar con el tipo de descuento. El CAPM aporta una solución elegante y muy utilizada para resolver el problema, pero se encuentra con la dificultad del cálculo de la Beta, sobre todo en empresas no cotizadas. Desde hace años, los libros de texto recomiendan buscar empresas cotizadas similares y utilizar sus Betas. Sin embargo, existe una dificultad: las empresas tienen diferente grado de apalancamiento, lo que también afecta a los impuestos y a la Beta. Académicos y practitioners utilizan para resolver este problema la conocida fórmula de Hamada, pero creemos que su planteamiento tiene el problema de considerar el impuesto de sociedades, pero no el de la renta de las personas físicas. Nosotros introducimos el impuesto sobre la renta de una manera que creemos que es sencilla y original, lo que puede ser de gran utilidad en la práctica financiera. Palabras claves: Coste de los fondos, Beta apalancada, Fórmula de Hamada, Efecto de los impuestos. Clasificación JEL: G31, G32. Recibido: 31 de enero de 2014 Aceptado: 20 de febrero de 2014 * Departamento de Finanzas de la Universidad de Deusto. Autor de contacto: Javier Santibáñez Grúber
2 COST OF FUNDS ON THE BASIS OF MODIGLIANI AND MILLER AND CAPM PROPOSITIONS: INTRODUCTION When trying to value a company on a cashflow discount basis, it is of a crucial importance to estimate, among other variables, the appropriate discount rate. Assuming the conclusions of the Capital Asset Pricing Model (CAPM; Sharpe, 1970), the required return for any investment should depend on its systematic risk, which requires the estimation of the beta of the company, usually on the basis of a regression process between historical profitability of the studied company and the one provided by the market as a whole. However, an additional problem that we usually have to cope with is that not many companies are quoted in the market, so the process becomes a tough one when trying to calculate the beta of a nonquoted company. In those cases, professionals usually try to estimate the beta of the company to be priced on the basis of a similar one (this is known as levered Beta calculation); and it is very common to use the Hamada (1969) formulation, which implicitly assumes that we have to take the effect of Corporation Tax into account. Nevertheless, Miller (1977) made it clear that it is not only the Corporation Tax the one to be taken into account, but the Personal Income Tax as well, insofar as if the Tax System as a whole was properly designed (which means that the advantage for leverage in Corporation Tax should be eliminated in the Personal Income Tax, by treating better income coming from dividends than those coming from interest), no advantage would be reached by levering a company (which would take us back to Modigliani and Miller, 1958). While it is a very complex problem, as it is difficult to estimate accurately the Tax burden for dividends or interest in the Personal Income Tax 1, and even the real Corporation Tax rate that the companies are bearing (because of the effect of partial exemptions, etc.), we have to be aware of the distortion that we are introducing in the process when taking only Corporation Tax (Modigliani and Miller, 1963) into account. In this paper we will propose an alternative formulation to Hamada (1969) for the estimation of levered betas, in which Personal Income Tax is also taken into account (based on both Modigliani and Miller and CAPM propositions), which can be seen as a generalization of the Hamada one (that would remain as a particular case of the one that we pose) GENERAL FORMULATION Weighted Average Cost of Capital (WACC) is commonly calculated as follows: where: i k i k e WACC t D E Required rate of return for Debt Net cost of Debt Cost of Equity Weighted Average Cost of Capital Tax rate (Corporation Tax) Debt (Market value) Equity (Market value) (1) Let us assume stable conditions, no growth and that the company invests only the necessary amount to maintain the current value of assets (replacement investment, equal to depreciation, so as to keep constant its cashflow generation capability); if we do so, the Market value of the firm (understood as Market value of assets) should be calculated as follows (present value of a perpetuity): (2) whereas in addition to the previously defined nomenclature, EBIAT is Earnings Before Interest and After Taxes, that is to say, generated profits by assets to pay the whole providers of funds; under the described conditions, it should be equal to total payments for financing. In addition: (3)
3 8 where S is net sales, C is disbursement operating costs, AM is depreciation and amortization (of tangible and intangible fixed assets), and EBIT is Earnings Before Interest and Taxes. 3. MODIGLIANI AND MILLER PROPOSITIONS (1958 and 1963) In their wildly renowned paper of 1958, Modigliani and Miller proposed that the Financial Structure does not have any impact on the Weighted Average Cost of Capital (and therefore, neither on the value of the firm). The line of reasoning is quite simple: the capital funds providers of the company as a whole would ask for a return depending on the risk of the assets; so if we assume the assets remain the same, no change should be expected on the required rate of return for financing them, even if we use different proportions of Debt and Equity. In other words, in competitive and efficient Markets two identical assets could not be priced differently (that is what would happen if different Financial Structures for the same assets had different costs). Modigliani and Miller proposal can be summed up in figure 1. Nevertheless, Corporation Tax changes it all, since it brings about a distortion due to the different treatment of interests and dividends. In fact, interests are deductible (provoking tax savings) from the Tax base, while dividends are not; therefore, all the rest remaining the same, if it is true that under perfect Market conditions the Financial Structure would be irrelevant, the imperfection mentioned above would cause an interest for leverage. The effect of the Corporation Tax advantage can be easily shown. If we assume a non leveraged company (fully Equity financed), the free cashflow (that under the formerly proposed conditions could be used for paying dividends) can be expressed as follows: (4) whose present value should be calculated using a discount rate considering the Assets risk (R). This way, the Enterprise value (that in a nonleveraged company would be both Assets value and Equity value) should be estimated as follows:
4 COST OF FUNDS ON THE BASIS OF MODIGLIANI AND MILLER AND CAPM PROPOSITIONS:... 9 (5) So if we now equalize expressions (8) and (9) we reach (10): If we now consider the possibility for the company to borrow money, the free cashflow to be distributed among the funds providers after Corporation Tax would be: (6) where I refers to the Interests to be paid on the Debt (so it is calculated by multiplying the interest rate by the total amount of Debt), and as can be seen, we face a new situation insofar as there is an additional item in the formula which is related to the savings that the interest payment causes in the Corporation Tax; if we assume both that this Tax shield can always be accomplished and that lenders do not assume any risk, this part of the income should be discounted at the Riskfree rate, and so: (7) It can be seen that the Enterprise value can be obtained by adding to the nonleveraged one a term that grows with Debt (the formerly mentioned Tax shield), so there is an interest for the company to increase leverage to its maximum. An important consequence of the former is that now the Weighted Average Cost of Capital is no longer independent from the leverage, but decreases as Debt rises. In fact, on the basis of expression (2) we can reach equation (8): (8) And if we now take equation (7) into account it is easy to see that: (9) (10) where the cost reduction effect related to leverage appears very clearly. In addition, a different formula for estimating the cost of Equity can be raised on the basis of the former; so, if we make equal expressions (1) and (10) we have equation (11): 4. CAPM (11) CAPM (Capital Asset Pricing Model) is built on the basis of Markowitz Model hypothesis, and sets out a fundamental relationship between a given asset and the required rate of return to finance it. The model highlights the fact that the total risk of any asset can be split up into Systematic risk and Diversifiable (Nonsystematic) risk. Systematic risk is due to the Market, that is to say, it is given by the fact that any asset is in some way related to the general economic course, and because of that, it has a certain amount of non Diversifiable risk; Nonsystematic is the specific risk of the investment (the portion of risk that the Market is unable to explain), so it can be avoided with a proper diversification. If this is the case and we assume riskaverse individuals, nobody would take avoidable risks, so we all would eliminate Diversifiable risks and only Systematic risk would remain. The classical measure for Systematic risk is Beta, which can be calculated as follows:
5 10 (12) where COV (R j, R m ) is the Covariance between the studied asset and Market returns; and VAR (R m ) is the Variance of the Market returns. The model poses a positive linear relationship between the required return on any investment and its relevant risk (measured with Beta), that can be summarized in the following expression (Security Market Line, SML; the model requires adjustment to the purposed line to any asset correctly valued): (13) where E (R j ) is the expected return on the asset, R f is the Riskfree rate and the Premium is the difference between the expected return for the Market and the Riskfree rate. Under CAPM conditions, all Assets, Equity and Debt should perfectly adjust to equation (13), so: for estimating a company Beta on the basis of observed Betas in the Market. Again, the idea is quite simple: it would be very difficult to estimate Equity Beta in a nonquoted company, since we have no historical data about its returns, so Covariance with the Market would remain unknown 3 ; but in some cases, it could be derived from the Beta of a quoted company. This proposal poses one important problem: even if the activity of both companies were the same, leverage could be totally different, so we have to face an adjusting process in which first of all, Beta of the observed company assets must be inferred from its Equity one (taking both leverage and Beta of Debt into account); and in a second step, Equity Beta of the studied company would be estimated (again, taking its leverage and the Beta of Debt into account). This process is commonly known as levered Beta calculation. Formulation to be used is quite simple to derive. Let us remember that when equaling expressions (1) and (10) (that is to say we accept Modigliani and Miller 1963 propositions) we have: (14) (15) (16) where β a, β i and β e are the Systematic risk measures for the Assets (assuming nonleveraged company), for Debt and for Equity. 5. INTRODUCING CAPM INTO THE MODIGLIANI AND MILLER PROPOSALS (1958 and 1963) Clearing R we reach expression (17): (17) Combining CAPM and Modigliani and Miller propositions takes us to the classical formulas commonly used If we now take into account CAPM (expressions 15 and 16), equation (17) becomes the following:
6 COST OF FUNDS ON THE BASIS OF MODIGLIANI AND MILLER AND CAPM PROPOSITIONS: (18) Let us compare expression (18) with equation (14), that indicates the required rate of return on assets in a nonleveraged company under CAPM conditions; it is easy to derive equation (19) in order to estimate Beta of assets (assumed that both Beta of Equity and Debt and the leverage of the observed company are all known): (19) We then only have to clear Beta of Equity in expression (19), as can be seen in equation (20): (20) A particular case of the former happens if we assume fully guaranteed Debt (no risk taken by Debt providers; which means to assume Beta of Debt equal to zero): it is the formula of Hamada (1969) for estimating Beta of Equity: (21) NOTE: the whole formulation is applicable for the original proposal by Modigliani and Miller (1958; we only have to assume Tax Corporate rate equal to zero). 6. THE EFFECT OF PERSONAL INCOME TAX (MILLER, 1977) In the work of 1963, Modigliani and Miller assume that there is only Corporation Tax, which introduces a distortion, insofar as Debt and Equity are not treated the same. However in 1977, Miller points out that if the Tax System as a whole was properly designed, it should not interfere with the financial decisions of the companies; to put it another way, the function of the Tax System is not to provide companies with the proper Financial Structure, but to drain money from the Economic System in order to redistribute wealth, accomplish public investments, etc. If so, and if we assume no other Market imperfections, we would go back to the original proposal: Financial Structure is not relevant in order to put value on the company (the Financial Objective of the firm), since the advantage of Debt in Corporation Tax disappears when considering the Tax System as a whole. Let us revise the previous formulation, taking now into account that the Personal Income Tax treats differently Debt income and Equity income (interests and dividends) 4. Be m the Tax rate for dividends in Personal Income Tax, and n the one for interests (assuming that, obviously, m < n). Let us now first consider a nonleveraged company. The generated income to be distributed among funds providers can be seen in equation (22):
7 12 (22) R being the required rate of return for the nonlevered company before taking Personal Income Tax into account; the Enterprise value would be calculated as follows: (23) In a leveraged company the income generated and distributed among funds providers after taxes is shown in expression (24): (24) If we again assume that tax shields can always be reached, both items in expression (24) should be discounted at different discount rates: first element is identical to the one corresponding to a nonlevered company, so we have to use R (1 m); and the second one should be discounted using i (1 n) (since all taxes have been deducted in equation (24); so discount rates must be defined after taxes in order to avoid duplicities). Then: (25) On the basis of (25) it is easy to reach equation (26): (26) where tax advantage related to leverage disappears when (1 t) (1 m) = (1 n); and obviously, if m=n we go back to expression (7). Let us call T to the tax distortion in the whole system: equation (26) can be expressed therefore as follows: (27) (28) T is always lower or equal than t (if we assume that m < n): at worst, Personal Income Tax would not discriminate interests and dividends, which means T=t (Modigliani and Miller 1963). Let us remember equation (8): (8) If we clear EBIAT in equation (28) it is easy to reach expression (29): (29) If we now put it together with equation (8) we reach expression (30): (30) where now again can be seen clearly the cheapen effect related to leverage (assuming that the Tax System is not neutral T 0 ; however, the advantage is lower now, since T < t, so the Weighted Average Cost of Capital decreases less when taking Personal Income Tax into account; see expression (10) in comparison with (30)). On the other hand, if we make equal expressions (1) and (30) we can derive the formulation for estimating the required rate of return for a nonleveraged company:
8 COST OF FUNDS ON THE BASIS OF MODIGLIANI AND MILLER AND CAPM PROPOSITIONS: Let us deepen on what the former means. Remember that T was defined as the measure of the imperfection related to the Tax System as a whole (considering both Corporation and Personal Income Taxes): (31) Nevertheless, expression (31) is not a logical one, since the weights for both cost of Debt and Equity should add up to one (as happens under Modigliani and Miller propositions when taking only Corporation Tax into account; see expression (17)). This leads us to bring about a correction in expression (1) that seems to be reasonable. Let us remember equation (1) that has been used both in a world without taxes, and in a single Corporation Tax context: (1) where t is the Corporation Tax rate (that would be zero in a world without taxes). Under Miller (1977) conditions it must be said that if the Tax System as a whole was properly designed, dividend collectors should have an advantage over interest ones in Personal Income Tax (that is to say, m<n); and this different treatment would lead lenders to ask for a higher profitability than what they would expect if the aforementioned difference did not happen. To make it clearer, let us think about a nonleveraged company fully owned by a sole investor. Only by shifting Equity for Debt he or she could collect part of the profitability in the form of interests, which are deductible from the Corporation Tax Base; so the higher the leverage, the lower the Corporation Tax to be paid, and the higher the money collected by that sole owner. But if Debt incomes are treated worse in Personal Income Tax, the advantage reached in Corporation Tax would decrease, and it could disappear if the system as a whole was properly designed (that is to say, T=0). This way, the tax correction should be given by a tax shield considering the system as a whole (so we might use (1 T) instead of (1 t)). Expression (1) can be then rewritten as follows: (32) 5 so: (27) The former implies that requirement of Debt Providers changes: (33) In other words, the proposed formulation might be seen as a correction to the one we use when only Corporation Tax exists, insofar as the tax shield achieved in Corporation Tax could be minored by the Personal Income Tax effect (since the item (1 m)/(1 n) should logically be higher than 1 and the decrease of Debt cost is lower; and if we assume m=n we would go back to 1963 Modigliani and Miller case). Under the proposed conditions, we can equal expressions (32) and (30): (34) Equation (34) seems to be more reasonable; and we can also clear the cost of Equity in this proposal, coherent with Miller (1977): (35)
9 14 7. INTRODUCTION OF THE CAPM INTO THE MILLER (1977) PROPOSAL Introducing CAPM into the Miller proposal is again quite simple. As we said earlier, CAPM poses the following formulation in order to estimate the required rate of return on Assets, Debt and Equity: (14) (15) (16) Let us remember as well equation (34): (34) If we now substitute expressions (15) and (16) in equation (34), the required rate of return on the assets in a nonleveraged company would be as follows: (36) If we now compare expressions (36) and (14) we can derive equation (37), under the assumption that both Beta of Equity and Beta of Debt, as well as leverage (all data referred to the observed company) are known: (37) where the Beta of Equity for the studied company can be cleared: adapted to Miller (1977) propositions, which we call SGHAMM formula (2014). (39) (38) If we assume that Debt is fully guaranteed (Beta of Debt equal to zero), then we have the Hamada formulation NOTE: Observe that all formulation proposed is valid for 1958 Modigliani and Miller propositions (T=0) and also for 1963 proposal (by substituting T for t).
10 COST OF FUNDS ON THE BASIS OF MODIGLIANI AND MILLER AND CAPM PROPOSITIONS: CONCLUSIONS Formulation most frequently used by practitioners to estimate the appropriate rate of return to be used in the assessment of assets or stocks is based on CAPM and Modigliani and Miller (1963) propositions, taking only the effect of Corporation Tax into account (Hamada, 1969). Insofar as it is also very usual that dividends and interests are not equally treated in the Personal Income Tax (in order to eliminate the advantage that Debt has in Corporation Tax; Miller, 1977), the aforementioned formulation introduces a distortion in the results to be reached. In this paper we have developed, on the basis of both CAPM (Sharpe, 1970) and Modigliani and Miller propositions (Modigliani and Miller, 1958 and 1963; and Miller, 1977), an alternative formulation which takes the effect of both Taxes (Corporation and Personal Income Tax) into account, and allows to overcome the distortion mentioned before. 9. BIBLIOGRAPHY BREALEY, R.A., S.C. MYERS and F. ALLEN (2007): Principles or corporate finance, McGraw Hill, New York, 9 th ed. GÓMEZBEZARES, F. (2014): Dirección financiera, Desclée de Brouwer, Bilbao, 5 th ed. GÓMEZBEZARES, F. (2012): Elementos de finanzas corporativas, Desclée de Brouwer, Bilbao. HAMADA, R.S. (1969): Portfolio analysis, market equilibrium and corporation finance, Journal of Finance, March, pp MILLER, M.H. (1977): Debt and Taxes, Journal of finance, 32, May, pp MODIGLIANI, F. and M.H. MILLER (1958): The cost of capital, corporation finance and the theory of investment, American economic review, 48, June, pp MODIGLIANI, F. and M.H. MILLER (1963): Corporate income taxes and the cost of capital: Acorrection, American economic review, 53, June, pp SHARPE, W.F. (1970): Portfolio theory and capital markets, McGraw Hill, New York. APPENDIX Let us deepen in an alternative way to reach the logic of expression (39). Be q the required return (before Personal Income Tax) for a stock with identical risk (after Taxes) than Debt. It should happen that: so: Let us remember that: so: If we now make equal (1) and (30) we have: Taking (A.4) into account: which takes us directly to the logic of (34). (A.1) (A.2) (A.3) (A.4) (A.5) (A.6) (A.7) (A.8) Taking now the CAPM into account, and following the same process than before (from (14) to (39)): Substituting (A.10) and (A.11) in (A.8): (A.9) (A.10) (A.11)
11 16 (A.12) Taking now (A.9) into account: (A.13) (A.14) where the Beta of Equity for the studied company can be cleared: (A.15) (A.16) If we assume that Debt (or the proposed stock for which return q is required) is fully guaranteed (Beta of Debt equal to zero), we reach again (39): Notes (A.17) 1. And even more in the Corporation Tax, when it is a company the owner of stock or debt (with different rates depending on the kind of company). Not to talk about the additional problems that arise when facing with international ownership. 2. Deeper explanations and formulation of both Modigliani and Miller propositions and Capital Asset Pricing Model (CAPM) can be found in GómezBezares (2014), chapters 5 and 7. GómezBezares (2012) and Brealey, Myers and Allen (2007) may be consulted as well for some particular issues. Formulation related to the inclusion of CAPM in Miller s proposal (1977) can be seen as original. 3. Accounting data could be used, but this approach shows important theoretical problems. 4. This was the way the Tax System worked in Spain since 1995 to The changes introduced in Personal Income Tax in 2007 took us back to a more coherent situation with Modigliani and Miller (1963), insofar as interests and dividends are since then equally treated (Tax rate of 21% nowadays). Anyway, when trying to measure the impact of the distortion, we face a more complicated problem, if we also take into account that there is an exemption in Personal Income Tax for the first euros collected as dividends, and that taxation for dividends collected by companies or Mutual Funds has a different treatment. 5. In this context, i should be understood as the required return for Debt assuming m=n=0; or, in general, if no discrimination was made in the Personal Income Tax (that is to say, (1 m) = (1 n)). This will be treated in more depth in the Appendix.
The value of tax shields is NOT equal to the present value of tax shields
The value of tax shields is NOT equal to the present value of tax shields Pablo Fernández * IESE Business School. University of Navarra. Madrid, Spain ABSTRACT We show that the value of tax shields is
More informationLeverage. FINANCE 350 Global Financial Management. Professor Alon Brav Fuqua School of Business Duke University. Overview
Leverage FINANCE 35 Global Financial Management Professor Alon Brav Fuqua School of Business Duke University Overview Capital Structure does not matter! Modigliani & Miller propositions Implications for
More informationChapter 17 Corporate Capital Structure Foundations (Sections 17.1 and 17.2. Skim section 17.3.)
Chapter 17 Corporate Capital Structure Foundations (Sections 17.1 and 17.2. Skim section 17.3.) The primary focus of the next two chapters will be to examine the debt/equity choice by firms. In particular,
More informationSource of Finance and their Relative Costs F. COST OF CAPITAL
F. COST OF CAPITAL 1. Source of Finance and their Relative Costs 2. Estimating the Cost of Equity 3. Estimating the Cost of Debt and Other Capital Instruments 4. Estimating the Overall Cost of Capital
More information1. CFI Holdings is a conglomerate listed on the Zimbabwe Stock Exchange (ZSE) and has three operating divisions as follows:
NATIONAL UNIVERSITY OF SCIENCE AND TECHNOLOGY FACULTY OF COMMERCE DEPARTMENT OF FINANCE BACHELOR OF COMMERCE HONOURS DEGREE IN FINANCE PART II 2 ND SEMESTER FINAL EXAMINATION MAY 2005 CORPORATE FINANCE
More informationROSS, S.; WESTERFIELD, R. y JAFFE, J. (2005), Corporate Finance, McGrawHill Irwin, Chicago.
Degree: Licenciatura en Administración y Dirección de Empresas Department: Economía Financiera y Contabilidad III Academic Year: 2008/2009 Plan: 2000 Subject: Corporate Finance (Economía Financiera de
More informationUse the table for the questions 18 and 19 below.
Use the table for the questions 18 and 19 below. The following table summarizes prices of various defaultfree zerocoupon bonds (expressed as a percentage of face value): Maturity (years) 1 3 4 5 Price
More informationTaxadjusted discount rates with investor taxes and risky debt
Taxadjusted discount rates with investor taxes and risky debt Ian A Cooper and Kjell G Nyborg October 2004 Abstract This paper derives taxadjusted discount rate formulas with MilesEzzell leverage policy,
More informationWACC and a Generalized Tax Code
WACC and a Generalized Tax Code Sven Husmann, Lutz Kruschwitz and Andreas Löffler version from 10/06/2001 ISSN 0949 9962 Abstract We extend the WACC approach to a tax system having a firm income tax and
More informationTest3. Pessimistic Most Likely Optimistic Total Revenues 30 50 65 Total Costs 2520 15
Test3 1. The market value of Charcoal Corporation's common stock is $20 million, and the market value of its riskfree debt is $5 million. The beta of the company's common stock is 1.25, and the market
More informationNORTHWESTERN UNIVERSITY J.L. KELLOGG GRADUATE SCHOOL OF MANAGEMENT
NORTHWESTERN UNIVERSITY J.L. KELLOGG GRADUATE SCHOOL OF MANAGEMENT Tim Thompson Finance D42 Fall, 1997 Teaching Note: Valuation Using the Adjusted Present Value (APV) Method vs. Adjusted Discount Rate
More informationDividend Policy. Vinod Kothari
Dividend Policy Vinod Kothari Corporations earn profits they do not distribute all of it. Part of profit is ploughed back or held back as retained earnings. Part of the profit gets distributed to the shareholders.
More informationAsymmetry and the Cost of Capital
Asymmetry and the Cost of Capital Javier García Sánchez, IAE Business School Lorenzo Preve, IAE Business School Virginia Sarria Allende, IAE Business School Abstract The expected cost of capital is a crucial
More informationThe Tangent or Efficient Portfolio
The Tangent or Efficient Portfolio 1 2 Identifying the Tangent Portfolio Sharpe Ratio: Measures the ratio of rewardtovolatility provided by a portfolio Sharpe Ratio Portfolio Excess Return E[ RP ] r
More informationCost of Capital, Valuation and Strategic Financial Decision Making
Cost of Capital, Valuation and Strategic Financial Decision Making By Dr. Valerio Poti,  Examiner in Professional 2 Stage Strategic Corporate Finance The financial crisis that hit financial markets in
More informationChapter 14: Capital Structure in a Perfect Market
Chapter 14: Capital Structure in a Perfect Market1 Chapter 14: Capital Structure in a Perfect Market I. Overview 1. Capital structure: mix of debt and equity issued by the firm to fund its assets Leverage:
More informationMASTER FINANZAS DE EMPRESA
MASTER FINANZAS DE EMPRESA Subject Corporate Finance Code 607627 Mode Credits 4 Compulsory Attending 4 Nonattending Course First Year Semester 1 Language English LECTURERS 0 Department Professor Alejandro
More informationt = 1 2 3 1. Calculate the implied interest rates and graph the term structure of interest rates. t = 1 2 3 X t = 100 100 100 t = 1 2 3
MØA 155 PROBLEM SET: Summarizing Exercise 1. Present Value [3] You are given the following prices P t today for receiving risk free payments t periods from now. t = 1 2 3 P t = 0.95 0.9 0.85 1. Calculate
More informationA Test Of The M&M Capital Structure Theories Richard H. Fosberg, William Paterson University, USA
A Test Of The M&M Capital Structure Theories Richard H. Fosberg, William Paterson University, USA ABSTRACT Modigliani and Miller (1958, 1963) predict two very specific relationships between firm value
More informationRevisiting WACC) By S. K. Mitra Institute of Management Technology, Nagpur, India.
Global Journal of Management and Business Research Volume Issue Version.0 November 20 Type: Double Blind Peer Reviewed International Research Journal Publisher: Global Journals Inc. (USA) Online ISSN:
More informationMM1  The value of the firm is independent of its capital structure (the proportion of debt and equity used to finance the firm s operations).
Teaching Note Miller Modigliani Consider an economy for which the Efficient Market Hypothesis holds and in which all financial assets are possibly traded (abusing words we call this The Complete Markets
More informationPractice Bulletin No. 2
Practice Bulletin No. 2 INTERNATIONAL GLOSSARY OF BUSINESS VALUATION TERMS To enhance and sustain the quality of business valuations for the benefit of the profession and its clientele, the below identified
More informationCalculating the weighted average cost of capital for the telephone industry in Russia
Calculating the weighted average cost of capital for the telephone industry in Russia Abstract: John Gardner University of New Orleans Carl McGowan, Jr. Norfolk State University Susan Moeller Eastern Michigan
More informationChapter 17 Does Debt Policy Matter?
Chapter 17 Does Debt Policy Matter? Multiple Choice Questions 1. When a firm has no debt, then such a firm is known as: (I) an unlevered firm (II) a levered firm (III) an allequity firm D) I and III only
More informationJeffrey F. Jaffe Spring Semester 2016 Corporate Finance FNCE 100 Syllabus, page 1. Spring 2016 Corporate Finance FNCE 100 Wharton School of Business
Corporate Finance FNCE 100 Syllabus, page 1 Spring 2016 Corporate Finance FNCE 100 Wharton School of Business Syllabus Course Description: This course provides an introduction to the theory, the methods,
More information15 Solution 1.4: The dividend growth model says that! DIV1 = $6.00! k = 12.0%! g = 4.0% The expected stock price = P0 = $6 / (12% 4%) = $75.
1 The present value of the exercise price does not change in one hour if the riskfree rate does not change, so the change in call put is the change in the stock price. The change in call put is $4, so
More informationInternational Glossary of Business Valuation Terms*
40 Statement on Standards for Valuation Services No. 1 APPENDIX B International Glossary of Business Valuation Terms* To enhance and sustain the quality of business valuations for the benefit of the profession
More informationCHAPTER 9: THE CAPITAL ASSET PRICING MODEL
CHAPTER 9: THE CAPITAL ASSET PRICING MODEL PROBLEM SETS 1. E(r P ) = r f + β P [E(r M ) r f ] 18 = 6 + β P(14 6) β P = 12/8 = 1.5 2. If the security s correlation coefficient with the market portfolio
More informationISSUES ON USING THE DISCOUNTED CASH FLOWS METHODS FOR ASSET VALUATION
ISSUES ON USING THE DISCOUNTED CASH FLOWS METHODS FOR ASSET VALUATION CRISTINA AURORA BUNEABONTAŞ 1, MIHAELA COSMINA PETRE 2 CONSTANTIN BRANCOVEANU UNIVERSITY OF PITESTI, FACULTY OF MANAGEMENTMARKETING
More information1) Firm value and stock value We demonstrate that maximizing the value of the rm s equity is equivalent tomaximizing the value
Financial Leverage and Capital Structure Policy A) Introduction The objective of the capital structure decision, like any corporate objective, should be to maximize the value of the rm s equity. In this
More informationThe Assumptions and Math Behind WACC and APV Calculations
The Assumptions and Math Behind WACC and APV Calculations Richard Stanton U.C. Berkeley Mark S. Seasholes U.C. Berkeley This Version October 27, 2005 Abstract We outline the math and assumptions behind
More informationIndustrial and investment analysis as a tool for regulation
Industrial and investment analysis as a tool for regulation Marina Di Giacomo, Università di Torino Turin School of Local Regulation International Summer School on Regulation of Local Public Services 1
More informationCHAPTER 10 RISK AND RETURN: THE CAPITAL ASSET PRICING MODEL (CAPM)
CHAPTER 10 RISK AND RETURN: THE CAPITAL ASSET PRICING MODEL (CAPM) Answers to Concepts Review and Critical Thinking Questions 1. Some of the risk in holding any asset is unique to the asset in question.
More informationModule 7 Asset pricing models
1. Overview Module 7 Asset pricing models Prepared by Pamela Peterson Drake, Ph.D., CFA Asset pricing models are different ways of interpreting how investors value investments. Most models are based on
More informationFinal Exam MØA 155 Financial Economics Fall 2009 Permitted Material: Calculator
University of Stavanger (UiS) Stavanger Masters Program Final Exam MØA 155 Financial Economics Fall 2009 Permitted Material: Calculator The number in brackets is the weight for each problem. The weights
More information6. Debt Valuation and the Cost of Capital
6. Debt Valuation and the Cost of Capital Introduction Firms rarely finance capital projects by equity alone. They utilise long and short term funds from a variety of sources at a variety of costs. No
More informationMGT201 Solved MCQs(500) By
MGT201 Solved MCQs(500) By http://www.vustudents.net Why companies invest in projects with negative NPV? Because there is hidden value in each project Because there may be chance of rapid growth Because
More informationCh. 18: Taxes + Bankruptcy cost
Ch. 18: Taxes + Bankruptcy cost If MM1 holds, then Financial Management has little (if any) impact on value of the firm: If markets are perfect, transaction cost (TAC) and bankruptcy cost are zero, no
More informationRisk (beta), Return & Capital Budgeting Chpt. 12: problems 2,6,9,13,15. I. Applications of CAPM. 1) risk premium
Risk (beta), Return & Capital Budgeting Chpt. 12: problems 2,6,9,13,15 I. Applications of CAPM 1) risk premium estimate from historical data (Ibbotson) 2) risk free rate Tbill vs. Tbond, consistent with
More informationCATÓLICALISBON. Equity Valuation. Apple Inc intrinsic value and market price adjustment towards equilibrium
CATÓLICALISBON Equity Valuation Apple Inc intrinsic value and market price adjustment towards equilibrium Marco António Lourenço Madeira 03062013 ABSTRATC The main objective in this dissertation is
More informationCORPORATE FINANCE (28C00100)
IMPORTANT The submitted exercise answers will be accepted only for those students that have successfully registered for the course lectures. (Please check the list on the course website to make sure your
More information( ) ( )( ) ( ) 2 ( ) 3. n n = 100 000 1+ 0.10 = 100 000 1.331 = 133100
Mariusz Próchniak Chair of Economics II Warsaw School of Economics CAPITAL BUDGETING Managerial Economics 1 2 1 Future value (FV) r annual interest rate B the amount of money held today Interest is compounded
More informationUniversity of Pennsylvania The Wharton School
University of Pennsylvania The Wharton School FNCE 100 PROBLEM SET #6 Fall Term 2005 A. Craig MacKinlay Capital Structure 1. The XYZ Co. is assessing its current capital structure and its implications
More informationWHY NOT VALUE EQUITY CFs DIRECTLY?
WHY NOT VALUE EQUITY CFs DIRECTLY? WHAT HAVE WE DONE SO FAR? Discount the firm s projected Free Cash Flows at their Weighted Average Cost of Capital to get the aggregate value of the firm s securities
More informationCHAPTER 18. Capital Budgeting and Valuation with Leverage. Chapter Synopsis
CHAPTER 18 Capital Budgeting and Valuation with everage Chapter Synopsis 18.1 Overview of Key Concepts There are three discounted cash flow valuation methods: the weighted average cost of capital (WACC)
More informationThe cost of capital. A reading prepared by Pamela Peterson Drake. 1. Introduction
The cost of capital A reading prepared by Pamela Peterson Drake O U T L I N E 1. Introduction... 1 2. Determining the proportions of each source of capital that will be raised... 3 3. Estimating the marginal
More informationCourse Title : Financial Management. Teaching Hours : 42 hours (3 hours per week)
Course Title : Financial Management Course Code : BUS201 / BUS2201 No of Credits/Term : 3 Mode of Tuition : Sectional Approach Teaching Hours : 42 hours (3 hours per week) Category in major Programme :
More informationTaxadjusted discount rates with investor taxes and risky debt
Taxadjusted discount rates with investor taxes and risky debt Ian A Cooper and Kjell G Nyborg October 2005, first version October 2004 Abstract This paper derives taxadjusted discount rate formulas with
More informationFigure 1.1: The capital market. From your previous accounting studies, identify the main functions of a capital market.
Financial managers do not operate in a vacuum; they depend on longterm funds from the capital market, which acts as an intermediary for the allocation of investors capital through debt and equity (see
More informationFinance 2 for IBA (30J201) F.Feriozzi Resit exam June 14 th, 2011. Part One: MultipleChoice Questions (45 points)
Question 1 Finance 2 for IBA (30J201) F.Feriozzi Resit exam June 14 th, 2011 Part One: MultipleChoice Questions (45 points) Assume that financial markets are perfect and that the market value of a levered
More informationCHAPTER 12 RISK, COST OF CAPITAL, AND CAPITAL BUDGETING
CHAPTER 12 RISK, COST OF CAPITAL, AND CAPITAL BUDGETING Answers to Concepts Review and Critical Thinking Questions 1. No. The cost of capital depends on the risk of the project, not the source of the money.
More informationChapter 15: Debt Policy
FIN 302 Class Notes Chapter 15: Debt Policy Two Cases: Case one: NO TAX All Equity Half Debt Number of shares 100,000 50,000 Price per share $10 $10 Equity Value $1,000,000 $500,000 Debt Value $0 $500,000
More informationWACC and a Generalized Tax Code
The European Journal of Finance Vol. 12, No. 1, 33 40, January 2006 WACC and a Generalized Tax Code SVEN HUSMANN, LUTZ KRUSCHWITZ & ANDREAS LÖFFLER EuropaUniversität Viadrina, Frankfurt, Germany, Freie
More informationCFA Examination PORTFOLIO MANAGEMENT Page 1 of 6
PORTFOLIO MANAGEMENT A. INTRODUCTION RETURN AS A RANDOM VARIABLE E(R) = the return around which the probability distribution is centered: the expected value or mean of the probability distribution of possible
More informationCHAPTER 11: ARBITRAGE PRICING THEORY
CHAPTER 11: ARBITRAGE PRICING THEORY 1. The revised estimate of the expected rate of return on the stock would be the old estimate plus the sum of the products of the unexpected change in each factor times
More informationWorking Paper. WP No 549 March, 2004. Pablo Fernández *
CIIF Working Paper WP No 549 March, 2004 EQUIVALENCE OF TEN DIFFERENT DISCOUNTED CASH FLOW VALUATION METHODS Pablo Fernández * * Professor of Financial Management, PricewaterhouseCoopers Chair of Finance,
More informationDiscount Rates and Tax
Discount Rates and Tax Ian A Cooper and Kjell G Nyborg London Business School First version: March 1998 This version: August 2004 Abstract This note summarises the relationships between values, rates of
More informationDUKE UNIVERSITY Fuqua School of Business. FINANCE 351  CORPORATE FINANCE Problem Set #7 Prof. Simon Gervais Fall 2011 Term 2.
DUKE UNIVERSITY Fuqua School of Business FINANCE 351  CORPORATE FINANCE Problem Set #7 Prof. Simon Gervais Fall 2011 Term 2 Questions 1. Suppose the corporate tax rate is 40%, and investors pay a tax
More informationBeta levered and beta unlevered
Pablo Fernández * PricewaterhouseCoopers Professor of Corporate Finance IESE Business School Camino del Cerro del Aguila 3. 28023 Madrid, Spain. Telephone 3491357 08 09 Fax 3491357 29 13 email: fernandezpa@iese.edu
More informationIESE UNIVERSITY OF NAVARRA OPTIMAL CAPITAL STRUCTURE: PROBLEMS WITH THE HARVARD AND DAMODARAN APPROACHES. Pablo Fernández*
IESE UNIVERSITY OF NAVARRA OPTIMAL CAPITAL STRUCTURE: PROBLEMS WITH THE HARVARD AND DAMODARAN APPROACHES Pablo Fernández* RESEARCH PAPER No 454 January, 2002 * Professor of Financial Management, IESE Research
More informationFinance 2 for IBA (30J201) F. Feriozzi Resit exam June 18 th, 2012. Part One: MultipleChoice Questions (45 points)
Finance 2 for IBA (30J201) F. Feriozzi Resit exam June 18 th, 2012 Part One: MultipleChoice Questions (45 points) Question 1 Assume that capital markets are perfect. Which of the following statements
More informationCHAPTER 15 Capital Structure: Basic Concepts
Multiple Choice Questions: CHAPTER 15 Capital Structure: Basic Concepts I. DEFINITIONS HOMEMADE LEVERAGE a 1. The use of personal borrowing to change the overall amount of financial leverage to which an
More informationCapital Structure II
Capital Structure II Introduction In the previous lecture we introduced the subject of capital gearing. Gearing occurs when a company is financed partly through fixed return finance (e.g. loans, loan stock
More informationValuation Free Cash Flows. Katharina Lewellen Finance Theory II April 2, 2003
Valuation Free Cash Flows Katharina Lewellen Finance Theory II April 2, 2003 Valuation Tools A key task of managers is to undertake valuation exercises in order to allocate capital between mutually exclusive
More informationQuestion 1. Marking scheme. F9 ACCA June 2013 Exam: BPP Answers
Question 1 Text references. NPV is covered in Chapter 8 and real or nominal terms in Chapter 9. Financial objectives are covered in Chapter 1. Top tips. Part (b) requires you to explain the different approaches.
More informationNIKE Case Study Solutions
NIKE Case Study Solutions Professor Corwin This case study includes several problems related to the valuation of Nike. We will work through these problems throughout the course to demonstrate some of the
More informationMonika Goel Online Classes FINANCIAL, TREASURY AND FOREX MANAGEMENT Module II (C.S Professional Course)
Monika Goel Online Classes FINANCIAL, TREASURY AND FOREX MANAGEMENT Module II (C.S Professional Course) Session Plan Day Date Time Topics to be covered 14 h July, Nature and Scope of Financial Management
More informationPortfolio Performance Measures
Portfolio Performance Measures Objective: Evaluation of active portfolio management. A performance measure is useful, for example, in ranking the performance of mutual funds. Active portfolio managers
More informationCAPITAL STRUCTURE [Chapter 15 and Chapter 16]
Capital Structure [CHAP. 15 & 16] 1 CAPITAL STRUCTURE [Chapter 15 and Chapter 16] CONTENTS I. Introduction II. Capital Structure & Firm Value WITHOUT Taxes III. Capital Structure & Firm Value WITH Corporate
More informationSOLUTIONS. Practice questions. Multiple Choice
Practice questions Multiple Choice 1. XYZ has $25,000 of debt outstanding and a book value of equity of $25,000. The company has 10,000 shares outstanding and a stock price of $10. If the unlevered beta
More informationAppendix B Weighted Average Cost of Capital
Appendix B Weighted Average Cost of Capital The inclusion of cost of money within cash flow analyses in engineering economics and lifecycle costing is a very important (and in many cases dominate) contributing
More informationFundamentals Level Skills Module, Paper F9
Answers Fundamentals Level Skills Module, Paper F9 Financial Management June 2008 Answers 1 (a) Calculation of weighted average cost of capital (WACC) Cost of equity Cost of equity using capital asset
More informationSusana SanduveteChaves, Salvador ChacónMoscoso, Milagrosa Sánchez Martín y José Antonio PérezGil ( )
ACCIÓN PSICOLÓGICA, junio 2014, vol. 10, n. o 2, 320. ISSN: 1578908X 19 THE REVISED OSTERLIND INDEX. A COMPARATIVE ANALYSIS IN CONTENT VALIDITY STUDIES 1 EL ÍNDICE DE OSTERLIND REVISADO. UN ANÁLISIS
More informationM.I.T. Spring 1999 Sloan School of Management 15.415. First Half Summary
M.I.T. Spring 1999 Sloan School of Management 15.415 First Half Summary Present Values Basic Idea: We should discount future cash flows. The appropriate discount rate is the opportunity cost of capital.
More informationLEVERED AND UNLEVERED BETA. Pablo Fernández
CIIF Working Paper WP no 488 January, 2003 (Rev. May 2006) LEVERED AND UNLEVERED BETA Pablo Fernández IESE Business School Universidad de Navarra Avda. Pearson, 21 08034 Barcelona, España. Tel.: (+34)
More informationValuing the Debt Tax Shield
INSTITUTT FOR FORETAKSØKONOMI DEPARTMENT OF FINANCE AND MANAGEMENT SCIENCE FOR 15 2007 ISSN: 15004066 MARCH 2007 Discussion paper Valuing the Debt Tax Shield BY IAN COOPER AND KJELL G. NYBORG This paper
More informationThe value of tax shields IS equal to the present value of tax shields
The value of tax shields IS equal to the present value of tax shields Ian A. Cooper London Business School Kjell G. Nyborg UCLA Anderson and CEPR October 2004 Abstract In a recent paper, Fernandez (2004)
More informationStock Valuation: Gordon Growth Model. Week 2
Stock Valuation: Gordon Growth Model Week 2 Approaches to Valuation 1. Discounted Cash Flow Valuation The value of an asset is the sum of the discounted cash flows. 2. Contingent Claim Valuation A contingent
More informationE. V. Bulyatkin CAPITAL STRUCTURE
E. V. Bulyatkin Graduate Student Edinburgh University Business School CAPITAL STRUCTURE Abstract. This paper aims to analyze the current capital structure of Lufthansa in order to increase market value
More informationValuation. The Big Picture: Part II  Valuation
Valuation The Big Picture: Part II  Valuation A. Valuation: Free Cash Flow and Risk Apr 1 Apr 3 Lecture: Valuation of Free Cash Flows Case: Ameritrade B. Valuation: WACC and APV Apr 8 Apr 10 Apr 15 Lecture:
More informationReturn on Equity has three ratio components. The three ratios that make up Return on Equity are:
Evaluating Financial Performance Chapter 1 Return on Equity Why Use Ratios? It has been said that you must measure what you expect to manage and accomplish. Without measurement, you have no reference to
More informationReview for Exam 2. Instructions: Please read carefully
Review for Exam 2 Instructions: Please read carefully The exam will have 25 multiple choice questions and 5 work problems You are not responsible for any topics that are not covered in the lecture note
More informationChapter 14 Assessing LongTerm Debt, Equity, and Capital Structure
I. Capital Structure (definitions) II. MM without Taxes (1958) III. MM with Taxes (1963) Chapter 14 Assessing LongTerm Debt, Equity, and Capital Structure IV. Financial Distress V. Business Risk VI. Financial
More informationINTERVIEWS  FINANCIAL MODELING
420 W. 118th Street, Room 420 New York, NY 10027 P: 2128544613 F: 2128546190 www.sipa.columbia.edu/ocs INTERVIEWS  FINANCIAL MODELING Basic valuation concepts are among the most popular technical
More informationLecture 1: Asset Allocation
Lecture 1: Asset Allocation Investments FIN460Papanikolaou Asset Allocation I 1/ 62 Overview 1. Introduction 2. Investor s Risk Tolerance 3. Allocating Capital Between a Risky and riskless asset 4. Allocating
More informationENTREPRENEURIAL FINANCE: Strategy Valuation and Deal Structure
ENTREPRENEURIAL FINANCE: Strategy Valuation and Deal Structure Chapter 9 Valuation Questions and Problems 1. You are considering purchasing shares of DeltaCad Inc. for $40/share. Your analysis of the company
More information15.433 Investments. Assignment 1: Securities, Markets & Capital Market Theory. Each question is worth 0.2 points, the max points is 3 points
Assignment 1: Securities, Markets & Capital Market Theory Each question is worth 0.2 points, the max points is 3 points 1. The interest rate charged by banks with excess reserves at a Federal Reserve Bank
More informationNIKE Case Study. Professor Corwin. An overview of the individual questions and their relation to the lecture topics is provided below.
NIKE Case Study Professor Corwin This case study includes several problems related to the valuation of Nike. We will work through these problems throughout the course to demonstrate some of the most important
More informationChapter 11. Topics Covered. Chapter 11 Objectives. Risk, Return, and Capital Budgeting
Chapter 11 Risk, Return, and Capital Budgeting Topics Covered Measuring Market Risk Portfolio Betas Risk and Return CAPM and Expected Return Security Market Line CAPM and Stock Valuation Chapter 11 Objectives
More informationCAPITALIZATION/DISCOUNT
Fundamentals, Techniques & Theory CAPITALIZATION/DISCOUNT RATES CHAPTER FIVE CAPITALIZATION/DISCOUNT RATES I. OVERVIEW Money doesn t always bring happiness People with ten million dollars are no happier
More information1 (a) Net present value of investment in new machinery Year 1 2 3 4 5 $000 $000 $000 $000 $000 Sales income 6,084 6,327 6,580 6,844
Answers Fundamentals Level Skills Module, Paper F9 Financial Management June 2013 Answers 1 (a) Net present value of investment in new machinery Year 1 2 3 4 5 $000 $000 $000 $000 $000 Sales income 6,084
More informationChapter 7. . 1. component of the convertible can be estimated as 1100796.15 = 303.85.
Chapter 7 71 Income bonds do share some characteristics with preferred stock. The primary difference is that interest paid on income bonds is tax deductible while preferred dividends are not. Income bondholders
More informationThe CAPM (Capital Asset Pricing Model) NPV Dependent on Discount Rate Schedule
The CAPM (Capital Asset Pricing Model) Massachusetts Institute of Technology CAPM Slide 1 of NPV Dependent on Discount Rate Schedule Discussed NPV and time value of money Choice of discount rate influences
More informationActuarial Society of India
Actuarial Society of India EXAMINATIONS November 2004 SUBJECT  108: Finance and Financial Reporting Indicative Solution S108 Page 1 of 7 1 D 2 C 3 B 4 D 5 D 6 A 7 B 8 C 9 B 10 D 11 Trade credit is shortterm
More informationMore Tutorial at Corporate Finance
Corporate Finance Question 1. The cost of capital (8 points) St. Claire Enterprises is a levered firm. The equity cost of capital for St. Claire is 7%. The debt cost of capital for St. Claire is 2%. Assume
More informationNet revenue 785 25 1,721 05 5,038 54 3,340 65 Tax payable (235 58) (516 32) (1,511 56) (1,002 20)
Answers Fundamentals Level Skills Module, Paper F9 Financial Management December 2013 Answers 1 (a) Calculating the net present value of the investment project using a nominal terms approach requires the
More informationDiscussion of Valuation Methods and Model Templates. May 6, 2013
Discussion of Valuation Methods and Model Templates May 6, 2013 Introduction The following presentation discusses the SPT Business Development valuation template and the key considerations related to each
More informationA General Formula for the WACC: A Comment
INTRNATIONAL JOURNAL OF BUSINSS, 12(3, 2007 ISSN: 1083 4346 A General Formula for the WACC: A Comment Pablo Fernandez a a IS Business School, University of Navarra Camino del Cerro del Aguila 3, 28023
More informationEquity Valuation. Lecture Notes # 8. 3 Choice of the Appropriate Discount Rate 2. 4 Future Cash Flows: the Dividend Discount Model (DDM) 3
Equity Valuation Lecture Notes # 8 Contents About Valuation 2 2 PresentValues 2 3 Choice of the Appropriate Discount Rate 2 4 Future Cash Flows: the Dividend Discount Model (DDM) 3 5 The TwoStage DividendGrowth
More information