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Abstract:
This paper is a summarized compendium of all the methods and theories on company valuation using discounted cash flows. It shows ten discounted cash flow valuation methods: 1) free cash flow discounted at the WACC; 2) equity cash flows discounted at the required return to equity; 3) capital cash flows discounted at the WACC before tax; 4) APV (Adjusted Present Value); 5) the business's risk-adjusted free cash flows discounted at the required return to assets; 6) the business's risk-adjusted equity cash flows discounted at the required return to assets; 7) economic profit discounted at the required return to equity; 8) EVA discounted at the WACC; 9) the risk-free rate-adjusted free cash flows discounted at the risk-free rate; and 10) the risk-free rate-adjusted equity cash flows discounted at the required return to assets. All ten methods always give the same value. This result is logical, as all the methods analyze the same reality under the same hypotheses; they differ only in the cash flows taken as the starting point for the valuation. The disagreements among the various theories of firm valuation arise from the calculation of the value of the tax shields (VTS). The paper shows and analyses 9 different theories on the calculation of the VTS: No-cost-of-leverage, Modigliani and Miller (1963), Myers (1974), Miller (1977), Miles and Ezzell (1980), Harris and Pringle (1985), Damodaran (1994), With-cost-of-leverage, and Practitioners method. The paper lists the most important valuation equations according to each of these theories, and also shows how the valuation equations change when the debt's market value is not equal to its book value.

discounted cash flows, APV, WACC, Equity Cash Flow, beta

Abstract:
In this paper, I describe the four main groups comprising the most widely used company valuation methods: balance sheet-based methods, income statement-based methods, mixed methods, and cash flow discounting-based methods. The methods that are conceptually correct are those based on cash flow discounting. I briefly comment on other methods since - even though they are conceptually incorrect - they continue to be used frequently.

I also present a real-life example to illustrate the valuation of a company as the sum of the value of different businesses, which is usually called the break-up value.

I finish the paper showing the most common errors in valuations: a list that contains the most common errors that the author has detected in the more than one thousand valuations he has had access to in his capacity as business consultant or teacher.

Value, Price, Free cash flow, Equity cash flow, Capital cash flow, Book value, Market value, PER, Goodwill, Required return to equity, Working capital requirements

Abstract:
We analyze 582 American companies using EVA, MVA, NOPAT and WACC data provided by Stern Stewart. For each of the 582 companies, we have calculated the 10-year correlation between the increase in the MVA (Market Value Added) each year and each year's EVA, NOPAT and WACC. For 296 (of the 582) companies, the correlation between the increase in the MVA each year and the NOPAT was greater than the correlation between the increase in the MVA ach year and the EVA. There are 210 companies for which the correlation with the EVA has been negative! The average correlation between the increase in the MVA and EVA, NOPAT and WACC was 16%, 21% and -21.4%. The average correlation between the increase in the MVA and the increases of EVA, NOPAT and WACC was 18%, 22.5% and -4.1%.

We also find that the correlation between the shareholder return in 1994-1998 and the increase in the CVA (according to the Boston Consulting Group) of the world's 100 most profitable companies was 1.7%.

Shareholder value creation, Shareholder return, Value creation, EVA, Cash value added, Economic profit, Management performance indicator, Valuation

Abstract:
I show that the three residual Income models for equity valuation always yield the same value as the Discounted Cash Flow Valuation models.

I use three residual income measures: Economic Profit (EP), Economic Value Added (EVA) and Cash Value Added (CVA). I first show that the present value of the EP discounted at the required return to equity plus the equity book value equals the value of equity (the present value of the Equity cash flow discounted at the required return to equity).

Then, I show that the present value of the EVA discounted at the WACC plus the enterprise book value (equity plus debt) equals is the enterprise market value ( the present value of the Free cash flow discounted at the WACC).

Then, I show that the present value of the CVA discounted at the WACC plus the enterprise book value (equity plus debt) is also equal to the enterprise market value.

Cash value added, EVA, Economic profit, Residual income valuation, Discounted cash flow valuation, Valuation

Abstract:
This paper addresses the valuation of firms by cash flow discounting.

The first part shows that the four most commonly used discounted cash flow valuation methods (free cash flow discounted at the WACC; cash flow for equityholders discounted at the required return to equity; capital cash flow discounted at the WACC before taxes; and Adjusted Present Value) always give the same value. This result is logical because all the methods analyse the same reality under the same hypotheses; they only differ in the flows used as the starting point for the valuation.

The disagreements in the various theories on the valuation of the firm arise from the calculation of the value of tax shields (VTS). The paper shows and analyses 7 different theories on the calculation of the VTS: Modigliani and Miller (1963), Myers (1974), Miller (1977), Miles and Ezzell (1980), Harris and Pringle (1985), Ruback (1995), Damodaran (1994), and Practitioners method.

When analysing the results given by the different theories, it should be remembered that the DVTS is not actually the present value of the tax saving due to the payment of interested discounted at a certain rate but the difference between two present values: the present value of the taxes paid by the firm with no debt minus the present value of the taxes paid by the company with debt. The risk of the taxes paid by the company with no debt is less than the risk of the taxes paid by the company with debt.

The paper also shows the changes that take place in the valuation formulas when the debt's market value does not match its book value.

valuation methods, WACC, cash flow discounting, Adjusted Present Value

Abstract:
I revise several methods used for valuing brands. Among them, those of Interbrand, Damodaran, Financial World, Houlihan Valuation Advisors, Market Facts, Young & Rubicam and CDB Research & Consulting.

In particular, I analyze in depth the valuations of Kellogg's and Coca-Cola performed by Damodaran and the method proposed by Interbrand. Damodaran valued the brand Coca-Cola in 24,6 billion dollars in 1993 and in 102,6 billion dollars in 1998. In recent years, a lot has been spoken about the value of companies' intellectual capital. However, almost all of the studies on the subject are highly descriptive and a long way from obtaining a quantitative valuation. It is by no means clear what the company's intellectual capital is, and even less so if we intend to value the company's brand and intellectual capital separately.

My goal is to show the limitations of a number of the methods proposed for valuing brands and intellectual capital and, within the limits imposed by the brand's intrinsic reality, establish guidelines for value creation through the study of brands and intellectual capital. We also propose a scheme for identifying brand value drivers, that is, the parameters influencing the brand's value.

brand, brand value, brand value drivers, brand equity, intellectual capital, brand valuation, brand valuation process

Abstract:
This document has 100 questions from students, alumnae and other persons (judges, clients,...). They are useful to clarify some useful concepts in finance. Most of the questions have a clear answer. The document also has short answers to all questions.

Value creation, shareholder value creation, EVA, book value, return

Abstract:
This paper contains a collection and classification of 120 errors seen in company valuations performed by financial analysts, investment banks and financial consultants. The author had access to most of the valuations referred to in this paper in his capacity as a consultant in company acquisitions, sales, mergers, and arbitrage processes.

We classify the errors in seven main categories: 1) Errors in the discount rate calculation and concerning the riskiness of the company; 2) Errors when calculating or forecasting the expected cash flows; 3) Errors in the calculation of the residual value; 4) Inconsistencies and conceptual errors; 5) Errors when interpreting the valuation; 6) Errors when interpreting financial reports; and 7) Organizational errors.

company valuation, equity premium, valuation errors, valoracion de empresas

Abstract:
This paper focuses on equity valuation using multiples. Our basic conclusion is that multiples nearly always have broad dispersion, which is why valuations performed using multiples may be highly debatable. We revise the 14 most popular multiples and deal with the problem of using multiples for valuation: their dispersion. 1,200 multiples from 175 companies illustrate the dispersion of multiples of European utilities, English utilities, European constructors, hotel companies, telecommunications, banks and Internet companies.

We also show that PER, EBITDA and Profit after Tax (the most commonly used parameters for multiples) were more volatile than equity value during the period 1991-99.

We also provide additional evidence of the analysts' recommendations for Spanish companies: less than 15% of the recommendations are to sell.

However, multiples are useful in a second stage of the valuation: after performing the valuation using another method, a comparison with the multiples of comparable firms enables us to gauge the valuation performed and identify differences between the firm valued and the firms it is compared with.

Multiples, Dispersion of multiples, PER, Relative multiples, Analysts' recommendations

Abstract:
In this paper, we will define and analyze shareholder value creation. To help us understand this concept better, we will use the example of a listed company, General Electric, between 1991 and 1999.

To obtain the created shareholder value, we must first define the increase of equity market value, the shareholder value added, the shareholder return, and the required return to equity.

A company creates value for the shareholders when the shareholder return exceeds the required return to equity. In other words, a company creates value in one year when it outperforms expectations.

The created shareholder value is quantified as follows:
Created shareholder value = Equity market value x (Shareholder return - Ke)

The created shareholder value can also be calculated as follows:
Created shareholder value = Shareholder value added - (Equity market value x Ke)

We also calculate the created shareholder value of 142 American companies during the three-year period 1997-99 and during the eight-year period 1992-99.

Shareholder value creation; Created shareholder value; Increase of equity market value; Shareholder value added; Shareholder return; Required return to equity

Abstract:
In this paper we will present an analysis of the optimal capital structure using two examples: one proposed by the Harvard Business School and the other proposed by Damodaran.

First, we highlight certain inconsistencies in the debt and equity costs assumed by the Harvard Business School note from a number of viewpoints. We calculate the incremental cost of debt implied in Harvard's note and we find also inconsistencies: surprisingly, the last two debt increments have a cost of 14.75% and 18.5%, while the required return to equity in the unlevered company is 12%. With respect to the cost of debt, the inconsistency is not the cost of debt (the bank can charge whatever interest it likes) but in assuming that the debt's cost is the same as its required return (or that debt's value equals its nominal value). We also calculate the required return to incremental equity cash flow implied in Harvard's note and we find that the required return first falls, then increases, and then falls again. The required incremental return should fall as the leverage decreases. The probability of bankruptcy almost doubles beyond the optimal capital structure. The difference between the required return to equity and the required return to debt decreases for debt levels above the optimal capital structure. It is also shown that assuming no leverage costs there is no optimal structure (the company's value increases with the debt ratio) and the difference between required return to equity and the required return to debt is constant.

Damodaran (1994) offers a similar approach to that of the Harvard Business School note, but applies it to a real company (Boeing in 1990) and assumes a constant cash flow growth. One problem with Damodaran results is that the value of the firm (D+E) for debt ratios above 70% is less than the value of debt, which implies a negative value for equity. We calculate the incremental cost of debt implied in Damodaran's example. It can be seen that increasing debt to take the debt ratio from 30% to 40% implies contracting that debt at 21.5%, which is an enormous figure. Stranger still is the finding that the next debt increment (which has a higher risk) is cheaper: it costs 19%. An additional error in Damodaran's calculations is that he calculates the WACC using book values in the weighting, instead of market values.

It is also shown that if it is assumed that the debt's market value is the same as its book value, then the capital structure that minimizes the WACC also maximizes the share price. However, without this assumption, the minimum value of the WACC may not occur at the same point as the maximum share price.

Optimal capital structure; Required return to incremental equity cash flow; Incremental cost of debt; Required return on debt; Required return to equity; Adjusted present value; Return on assets; Return on equity; Weighted average cost of capital; Free cash flow

Abstract:
This paper contains a collection and a classification of 75 errors seen in company valuations performed by financial analysts, investment banks and financial consultants. The author had access to most of the valuations that are referred to in this paper when consulting in purchases, sales and mergers of companies, and in arbitrage processes. Some valuations are public reports of financial analysts.

We classify the errors in six main categories:
1. Errors on the discount rate calculation and about the riskiness of the company
2. Errors when calculating or forecasting the expected cash flows
3. Errors in the calculation of the residual value
4. Inconsistencies and conceptual errors
5. Errors when interpreting the valuation
6. Organizational errors

valuation, company valuation, valuation errors

Abstract:
We claim that in a world without leverage cost the relationship between the levered beta (BL) and the unlevered beta (Bu) of a company depends upon the financing strategy. For a company that maintains a fixed book-value leverage ratio, the relationship is Fernandez (2004): BL = Bu + (Bu - Bd) D (1 - T) / E. For a company that maintains a fixed market-value leverage ratio, the relationship is Miles and Ezzell (1980):BL = Bu + (D / E) (Bu - Bd) [1 - T Kd / (1 + Kd)]. For a company with a preset debt in every period, the relationship is Modigliani and Miller (1963):BL = Bu + [Bu - Bd] (D-VTS) / E, being the Value of Tax Shields (VTS) the present value of the future tax shields discounted at the cost of debt.

We also analyze alternative valuation theories proposed in the literature to estimate the relationship between the levered beta and the unlevered beta (Harris and Pringle (1985), Damodaran (1994), Myers (1974), and practitioners) and prove that all provide inconsistent results.

unlevered beta, levered beta, asset beta, value of tax shields, required return to equity, leverage cost

Abstract:
We analyze frequently made errors when valuing real options. The best way of doing it is through examples. We analyze Damodaran's proposal to value the option to expand the business of Home Depot. Some of the errors and problems of this and other approaches are: 1) Assuming that the option is replicable and using Black and Scholes' formula; 2) The estimation of the option's volatility is arbitrary and has a decisive effect on the option's value; 3) As there is no riskless arbitrage, the value of the option to expand basically depends on expectations about future cash flows. However, Damodaran assumes that this parameter does not influence the option's value - he does not use it - because he assumes that the option is replicable; 4) It is not appropriate to discount the expected value of the cash flows at the risk-free rate (as is done implicitly when Black and Scholes' formula is used) because the uncertainty of costs and sales on the exercise date may be greater or less than that estimated today; 5) Damodaran's valuation assumes that we know exactly the exercise price; and 6) Assuming that the option's value increases when interest rates increase.

real options, riskless arbitrage, expectations

Abstract:
In this paper, we analyze frequently made errors when valuing real options. The best way of doing it is through examples. We start by analyzing Damodaran proposal to value the option to expand the business of Home Depot. Some of the errors and problems of this and other approaches are:

- Assuming that the option is replicable and using Black and Scholes' formula.

- The estimation of the option's volatility is arbitrary and has a decisive effect on the option's value.

- As there is no riskless arbitrage, the value of the option to expand basically depends on expectations about future cash flows. However, Damodaran assumes that this parameter does not influence the option's value (he does not use it) because he assumes that the option is replicable.

- It is not appropriate to discount the expected value of the cash flows at the risk-free rate (as is done implicitly when Black and Scholes' formula is used) because the uncertainty of costs and sales in the exercise date may be greater or less than that estimated today.

- Damodaran's valuation assumes that we know exactly the exercise price.

- Belief that options' value increases when interest rates increase.

- "Play" with volatility.

- Valuing contracts as real options when they are not.

real options, volatility, Black and Scholes, option replication

Abstract:
We use three different definitions of cash flow: equity cash flow (ECF), free cash flow (FCF) and capital cash flow (CCF). We also answer to the question: When net income is equal to the equity cash flow? When making projections, dividends and other payments to shareholders forecasted must be exactly equal to expected equity cash flows.

May a company have positive net income and negative cash flows? Of course: one has only to think of the many companies that file for voluntary reorganization after having a positive net income. This is precisely what happens to the company AlphaCommerce that we show as an example.

A company's net income is a quite arbitrary figure obtained after assuming certain accounting hypotheses regarding expenses and revenues (.one of several that can be obtained, depending on the criteria applied). However, the ex-post cash flow is an objective measure, a single figure that is not subject to any personal criterion.

equity cash flow, free cash flow, capital cash flow, net income

Abstract:
This document has 160 questions from students, alumnae and other persons (judges, lawyers, clients,...). They are useful to clarify some useful concepts in finance. Most of the questions have a clear answer. The document also has short answers to all questions.

questions, shareholder value creation, EVA, book value, return

Abstract:
The average Market Risk Premium (MRP) used in 2008 by professors in the USA (6.3%) was higher than the one used by their colleagues in Europe (5.3%). We also report statistics for 18 countries: the average MRP used in 2008 ranges from 4.1% (Belgium) to 10.5% (India).

The dispersion of the MRP used was high: the average MRP used by professors of the same institution range was 3.5% and the one of the same country was 6.9%.

The average MRP used in 2007 was 1.5% lower than the one used in 2000. 15% of the professors decreased their MRP in 2008 (1.5% on average) and 24% increased it (2% on average). 66% of the professors used a lower MRP in 2007 than in 2000 (22% used a higher one).

Most surveys have been interested in the Expected MRP, but this survey asks about the Required MRP. The paper also contains the references that professors use to justify their MRP, and comments from 180 professors that illustrate the various interpretations of what is the required MRP and explain the confusion of students and practitioners about its concept and magnitude.

We also report 416 answers from the field: the average MRP used by European Companies in 2008 was 6.4%.

equity premium puzzle, equity premium, market risk premium, survey

Abstract:
This paper will analyze the evolution of a number of companies (Terra, Amazon, America Online, Microsoft, B2B companies, online brokers, . . .), although our focus will be the valuation of Amazon. We compare Damodaran's valuation by cash flow discounting ($35/share), Copeland's valuation by scenarios and cash flow discounting ($66/share) and our valuation by simulation and cash flow discounting: $21/share

We claim that in a company such as Amazon, it is necessary to introduce uncertainties in the expectations. We deal with uncertainty (volatility) in the hypotheses doing simulations. In our valuation, the likelihood of bankruptcy or voluntary reorganization is 43.43%.

It is very interesting to compare and try to differentiate what Internet may signify in the first years of the 21st century with the revolutionary effect on society that the railways, freeways, airlines, radio, television and the telephone had when they first appeared. We also urge the reader to analyze the history of companies such as Levitz, Home Shopping Network, MCI, LTCM and Boston Chicken.

Internet is no King Midas. Business ideas related with Internet must be analyzed with the same rigor as any other business initiative. On the other hand, it is fairly obvious that Internet will reduce (it is already reducing them) the margins of banks as a whole. Some banks may succeed in benefiting partially from Internet if it manages to increase its customers by taking them from other banks. However, for the industry as a whole, Internet will bring about a decrease in their margins that will not be matched by a parallel decrease in their costs.

A website is not necessarily a business. Selling below cost gets you lots of customers, but not much money.

Internet; Valuation; Value creation

Abstract:
Valuation Methods and shareholder value creation is a complete book about business valuation and value creation. The book explains the nuances of different valuation methods and provides the reader with the tools for analyzing and valuing any business, no matter how complex. With 631 pages divided into four parts, Valuation and shareholder value creation uses 140 diagrams, 211 tables, and more than 100 examples to help the reader absorb these concepts.

This book contains materials of the MBA and executive courses that I teach in IESE Business School. It also includes some material presented in courses and congresses in Spain, US, Austria, Mexico, Argentina, Peru, Colombia, UK, Italy, France and Germany. The chapters have been modified many times as a consequence of the suggestions of my students since 1988, my work in class, and my work as a consultant specialized in valuation and acquisitions. I want to thank all my students their comments on previous manuscripts and their questions. The book also has results of the research conducted in the International Center for Financial Research at IESE.

Part I - Basics of Valuation Methods and Shareholder Value Creation
Part II - Shareholder Value Creation
Part III - Rigorous Approaches to Discounted Cash Flow Valuation
Part IV - Real options and brands

Free cash flow, WACC, equity cash flow, required return to equity, capital cash flows, APV, economic profit, EVA, value creation, VTS

Abstract:
We calculate betas of 3,813 companies using 60 monthly returns each day of December 2001 and January 2002.

The median of [maximum beta / minimum beta] was 3.07.

Industry betas are also very unstable. The median (average) of the percentage daily change (in absolute value) of the industry betas was 7% (16%). On average, the maximum beta was 2.7 times its minimum beta in December 2001 and January 2002.

Beta, calculated betas

Abstract:
This paper shows that ten methods of company valuation using discounted cash flows (WACC; equity cash flow; capital cash flow; adjusted present value; residual income; EVA; business's risk-adjusted equity cash flow; business's risk-adjusted free cash flow; risk-free-adjusted equity cash flow; and risk-free-adjusted free cash flow) always give the same value when identical assumptions are used. This result is logical, since all the methods analyze the same reality using the same assumptions; they differ only in the cash flows taken as the starting point for the valuation. We present all ten methods, allowing the required return to debt to be different from the cost of debt. Seven methods require an iterative process. Only the APV and business risk-adjusted cash flows methods do not require iteration.

Company valuation, equity cash flow, adjusted present value, residual income, EVA

Abstract:
This paper shows that ten methods on company valuation using cash flow discounting (WACC; equity cash flow; capital cash flow; adjusted present value; residual income; EVA; business's risk-adjusted equity cash flow; business's risk-adjusted free cash flow; risk-free-adjusted equity cash flow; and risk-free-adjusted free cash flow) always give the same value when identical assumptions are used. This result is logical, since all the methods analyze the same reality based upon the same assumptions; they only differ in the cash flows taken as the starting point for the valuation. We present all ten methods allowing the required return to debt being different from the cost of debt. Seven methods require an iterative process. Only APV and the business risk-adjusted cash flows methods do not require iteration.

Abstract:
In this paper, we quantify shareholder value creation for 276 American companies. We provide the created shareholder value for each and every company for years 1998, 1999, 2000 and 2001. The market value of the 276 companies was 8,716 billion dollars in 2001 and 9,729 billion dollars in 2000. We define created shareholder value and provide the ranking of created shareholder value for the 276 companies. In 2001 Microsoft was the leading shareholder value creator and, on the other end of the spectrum, Cisco was the top shareholder value destroyer. We also calculate the cumulative created shareholder value of selected American companies during the four-year period 1998-2001. Wal-Mart Stores was the first company in created shareholder value companies during the four-year period 1998-2001.

We also claim that EVA does not properly measure Wealth Creation. We have compared EVA calculated by Stern Stewart and Co with created shareholder value of 269 companies. The correlation of EVA with created shareholder value was only 17.66%. 60 companies had negative EVA and positive created shareholder value. 64 companies had positive EVA and negative created shareholder value. On average, the difference of shareholder value creation minus EVA was -434% of EVA. The absolute value of the difference of shareholder value creation minus EVA was 8972% of EVA. With this evidence, we conclude that EVA does not properly measure Wealth Creation.

Shareholder value creation; Created shareholder value; Equity market value; Shareholder value added; Shareholder return; Required return to equity; EVA

Abstract:
I review 100 finance and valuation textbooks published between 1979 and 2008 (Brealey, Myers, Copeland, Damodaran, Merton, Ross, Bruner, Bodie, Penman, Weston, Arzac...) and find that their recommendations regarding the equity premium range from 3% to 10%, and that several books use different equity premia in different pages.

Some confusion arises from not distinguishing among the four concepts that the word equity premium designates: Historical equity premium, Expected equity premium, Required equity premium and Implied equity premium.

Finance professors should clarify the different concepts of equity premium and convey a clearer message about their sensible magnitudes.

equity premium, required market risk premium, historical market risk premium

Abstract:
In this paper, we review twelve valuations of Terra performed by Spanish and non-Spanish bank analysts and brokers.

Of the twelve valuations, only one used cash flow discounting. Another valuation was based on multiples, but also used cash flow discounting to perform a reverse valuation. All others used several multiples. Only one valuation report recommended to sell.

Terra started trading on the stock market in November 1999. The placement price was 13 euros per share (11.81 for retailers). In February 2000, its price stood at 139.75 euros. Between November 1999 and February 2000, Terra provided a return of 975% for its shareholders. However, by December 2000, the share price had plummeted to 11.6 euros, 8.3% of its February high. The average annual volatility of the Terra share was almost 100%.

If you can't find a rational explanation for a share to continue rising, you can be sure that it will fall. To become a millionaire, you must sell your shares at the right time. A website is not necessarily a business. Selling below cost gets you lots of customers, but not much money.

Internet, Valuation, Internet valuation

Abstract:
Although Copeland et al. (2000) claim that "the finance literature does not provide a clear answer about which discount rate for the tax benefit of interest is theoretically correct," we show that we can provide some clear answers on that topic.

This paper provides clear, theoretically sound, guidelines to evaluate the appropriateness of different valuation methods to estimate the present value of tax shields.

We first show that the discounted value of tax shields is the difference between the present values of two different cash flows with their own risk: the present value of taxes for the unlevered company and the present value of taxes for the levered company. This implies as a first guideline that, for the particular case of a perpetuity and a world without costs of leverage, the discounted value of tax shields is equal to the tax rate times the value of debt (i.e. Modigliani-Miller). The discounted value of tax shields can be lower, when costs of leverage exist. In that case, we show that, since the existence of leverage costs is independent of taxes, a second guideline for the appropriateness of the valuation method should be that the discounted value of tax shields when there are no taxes is negative. We then look at the case of constant growth and derive similar implications.

Second, we identify 23 valuation theories proposed in the literature to estimate the present discounted value of tax shields and show their performance relative to the proposed guidelines. Eight of these theories do not satisfy the two proposed guidelines for the case of perpetuities. Only one of the valuation methods is consistent with these restrictions when we look at the case of constant growth and no leverage costs. Three theories provide consistent valuations when we allow for leverage costs and growth.

Finally, we use the 23 theories to value a hypothetical firm and show remarkable differences in the obtained values suggesting the importance of using a method consistent with the proposed guidelines.

Value of the tax shield; Tax shield valuation; APV; Present value of taxes; Required return to taxes; Taxes; Debt value; Creation

Abstract:
In this paper, we revise several methods used for valuing brands. Among them, those of Interbrand, Damodaran, Financial World, Houlihan Valuation Advisors, Market Facts, Young & Rubicam and CDB Research & Consulting.

Our goal is to show the limitations of a number of the methods proposed for valuing brands and intellectual capital and, within the limits imposed by the brand's intrinsic reality, establish guidelines for value creation through the study of brands and intellectual capital. We also propose a scheme for identifying brand value drivers, that is, the parameters influencing the brand's value.

brand, brand value, brand value drivers, brand equity, intellectual capital, brand valuation, brand valuation process

Abstract:
This paper contains a collection and classification of 96 errors seen in company valuations performed by financial analysts, investment banks and financial consultants. The author had access to most of the valuations referred to in this paper in his capacity as a consultant in company acquisitions, sales, mergers, and arbitrage processes.

We classify the errors in six main categories: 1) Errors in the discount rate calculation and concerning the riskiness of the company; 2) Errors when calculating or forecasting the expected cash flows; 3) Errors in the calculation of the residual value; 4) Inconsistencies and conceptual errors; 5) Errors when interpreting the valuation; and 6) Organizational errors.

Abstract:
This paper contains a collection and classification of 80 errors seen in company valuations performed by financial analysts, investment banks and financial consultants. The author had access to most of the valuations referred to in this paper in his capacity as a consultant in company acquisitions, sales and mergers, and arbitrage processes. Some of the errors are taken from published reports by financial analysts.

We classify the errors in six main categories: 1) Errors in the discount rate calculation and concerning the riskiness of the company; 2) Errors when calculating or forecasting the expected cash flows; 3) Errors in the calculation of the residual value; 4) Inconsistencies and conceptual errors; 5) Errors when interpreting the valuation; and 6) Organizational errors.

Company valuation, valuation errors, valuation

Abstract:
There is a wealth of literature about discounted cash flow valuation. In this paper, we will discuss the most important papers, highlighting those that propose different expressions for the value of the tax shield (VTS). The discrepancies between the various theories on the valuation of a company's equity using discounted cash flows originate in the calculation of the value of the tax shield (VTS). This paper illustrates and analyzes 7 different theories and presents a new interpretation of the theories.

Discounted cash flow valuation, cash flow valuation, value of tax shields, present value of the net increases of debt, required return to equity

Abstract:
We show that the three valuation methods (if used correctly) always yield the same result. The most striking result of this paper is that for a firm growing at a rate g, the Net Present Value of the tax shield due to interest payments (in the APV approach) must be calculated as follows: NPV OF INTEREST TAX SHIELDS = D Ku T / (Ku - g) T = Corporate tax rate; Ku = Cost of unlevered equity; D = Value of debt in period 0. It seems that this formula considers that the debt has a cost of Ku, and discounts these flows also at Ku, but this is not the case. The Net Present Value of interest tax shields is not (and this is the main error in previous papers about this topic) the NPV of a unique flow, but the difference of two NPVs of two flows with different risk: the NPV of the taxes paid in the unlevered firm and the NPV of taxes paid in the levered firm. Our formula is the difference of the two NPV. Obviously, the flow of taxes paid in the levered firm is smaller, but riskier than the flow of taxes paid in the unlevered firm. We show the equivalence of the three approaches to firm valuation for perpetuities, then for growing companies (at a constant rate g) and, finally, for any company.

Abstract:
The market risk premium is one of the most important but elusive parameters in finance. It is also called equity premium, market premium and risk premium. The term market risk premium is difficult to understand because it is used to designate three different concepts:

1. Required market risk premium. It is the incremental return of a diversified portfolio (the market) over the risk-free rate (return of treasury bonds) required by an investor. It is needed for calculating the required return to equity (cost of equity).

2. Historical market risk premium. It is the historical differential return of the stock market over treasury bonds.

3. Expected market risk premium. It is the expected differential return of the stock market over treasury bonds.

Many authors and finance practitioners assume that expected market risk premium is equal to the historical market risk premium and to the required market risk premium. The CAPM assumes that the required market risk premium is equal to the expected market risk premium. The three concepts are different. The historical market risk premium is equal for all investors, but the required and the expected market risk premium are different for different investors. We also claim that there is no required market risk premium for the market as a whole: different investors use different required market risk premiums.

Required market risk,premium, historical market risk premium, expected market risk premium, risk premium, equity premium, market premium

Abstract:
The value of tax shields is the difference between the present values of two different cash flows, each with their own risk: the present value of taxes for the unlevered company and the present value of taxes for the levered company. For constant growth companies, the value of tax shields in a world with no leverage cost is the present value of the debt, times the tax rate, times the unlevered cost of equity, discounted at the unlevered cost of equity. This result arises as the difference of two present values and does not mean that the appropriate discount for tax shields is the unlevered cost of equity.

Value of tax shields, required return to equity, leverage cost, unlevered beta, levered beta

Abstract:
The value of tax shields is the difference between the present values of two different cash flows, each with their own risk: the present value of taxes for the unlevered company and the present value of taxes for the levered company. For constant growth companies, the value of tax shields in a world with no leverage cost is the present value of the debt, times the tax rate, times the unlevered cost of equity, discounted at the unlevered cost of equity. This result arises as the difference of two present values and does not mean that the appropriate discount for tax shields is the unlevered cost of equity.

value of tax shields, required return to equity, leverage cost, unlevered beta, levered beta

Abstract:
In this paper, we quantify shareholder value creation for 274 American companies. We provide the created shareholder value for each and every company for years 1998, 1999, 2000 as well as for 1993-2000. The market value of the 274 companies was 9,680 billion dollars.

We define created shareholder value and provide the ranking of created shareholder value for the 274 companies. In 2000 Phillip Morris was the leading shareholder value creator and, on the other end of the spectrum, Microsoft was the top shareholder value destroyer.

We also calculate the cumulative created shareholder value of selected American companies during the three-year period 1998-2000 and during the eight-year period 1993-2000. General Electric was the first company in both, created shareholder value and equity market value in 2000.

We claim that EVA does not properly measure Wealth Creation. We have compared EVA calculated by Stern Stewart and Co with created shareholder value of 269 companies. The correlation of EVA with created shareholder value was only 17.66%. 60 companies had negative EVA and positive created shareholder value. 64 companies had positive EVA and negative created shareholder value. On average, the difference of shareholder value creation minus EVA was -434% of EVA. The absolute value of the difference of shareholder value creation minus EVA was 8972% of EVA. With this evidence, we conclude that EVA does not properly measure Wealth Creation.

Shareholder value creation; Created shareholder value; Equity market value; Shareholder value added; Shareholder return; Required return to equity; EVA

Abstract:
This paper explores the discounted cash flow valuation methods. We start the paper with the simplest case: no-growth, perpetual-life companies. Then we will study the continuous growth case and, finally, the general case.

The different concepts of cash flow used in company valuation are defined: equity cash flow (ECF), free cash flow (FCF), and capital cash flow (CCF). Then the appropriate discount rate is determined for each cash flow depending on the valuation method used.

Our starting point will be the principle by which the value of a company's equity is the same, whichever of the four traditional discounted cash flow formulae is used. This is logical: given the same expected cash flows, it would not be reasonable for the equity's value to depend on the valuation method.

Discounted cash flow valuation, cash flow valuation, value of tax shields, required return to equity

Abstract:
The concept market risk premium is difficult to understand because it is used to designate three different concepts:

1. Required market risk premium. It is the incremental return of the market over the return of treasury bonds required by an investor. It is needed for calculating the required return to equity (cost of equity).

2. Historical market risk premium. It is the historical differential return of the stock market over treasury bonds.

3. Expected market risk premium. It is the expected differential return of the stock market over treasury bonds.

Many authors and finance practitioners assume that expected market risk premium is equal to the historical market risk premium and to the required market risk premium. The CAPM assumes that the required market risk premium is equal to the expected market risk premium.

The three concepts are different. The historical market risk premium is equal for all investors, but the required and the expected market risk premium are different for different investors. We also claim that there is no required market risk premium for the market as a whole: different investors use different required market risk premiums.

required market risk premium, historical market risk premium, expected market risk premium, risk premium, equity premium, market premium, prima de riesgo

Abstract:
We analyze the movement of the IBEX 35 between December 1990 and October 2008, the movement of the IGBM between December 1940 and October 2008 and movement of the S&P 500 between January 1926 and October 2008.

Share price, Maximum, Minimum, IBEX 35

Abstract:
118 companies out of 121 had negative return in 2008. In 2008, the 121 companies destroyed 366 billion euros (15 billion euros in 2007). The average return of the 125 companies was -39.6%.

Shareholder Value Creation, Spain, Shareholder return

Abstract:
On July 2008, a judge considered that the book value of the shares of a profitable and consolidated company was a good proxy for their market value in 2005. An expert in the trial wrote: "We consider that the best and most trustworthy criteria in order to value the shares of the company is based on the value of its shareholder's equity given by its consolidated balance sheet". Later on, another expert called this valuation: "a sound diagnosis" and backed his colleague's valuation by stating: "Actually, the previous report, which follows accurately the Technical Auditing Normative, chose one of the methods approved by the normative (the one based on net assets) and based its calculations on the annual accounts of the company, as they are a set of public and verified data, backed by a favourable auditing report, and he therefore proceeded to a valuation on these grounds".

WACC, Free Cash Flow, Value of growth, Value of growing opportunities, book value

Abstract:
The correct way of valuing seasonal companies by cash flow discounting is to use monthly data. We may use annual data, but it requires some adjustments. We show that when using annual data in the context of the adjusted present value (APV), the value of the unlevered equity (Vu) and the value of the tax shields (VTS) calculations must be adjusted. However, the debt that we have to substract to calculate the equity value does not need to be adjusted. We derive the adjustments to be made. Errors due to using annual data without doing the adjustments are big. To adjust only by using average debt and average working capital requirements does not provide a good approximation.

When the inventories are a liquid commodity such as grain or seeds, it is not correct to consider all of them as working capital requirements. The excess inventories financed with debt are equivalent to a set of futures contracts. We show that not considering it undervalues the company.

This paper values a company in which the seasonality is due to the purchases of raw materials: the company buys and pays all raw materials in the moth of December. We show that the equity value calculated using annual data without doing the adjustments understates the true value in a 45% if the valuation is done at the end of December, and overstates the true value in a 38% if the valuation is done at the end of November. The error of adjusting only by using average debt and average working capital requirements ranges from -17.9% to 8.5%.

valuation of seasonal companies, seasonality, cash flow discounting

Abstract:
It is a big mistake to use betas calculated from historical data to compute the required return to equity. It is a mistake for seven reasons: because betas calculated from historical data change considerably from one day to the next; because calculated betas depend very much on which stock index is used as the market reference; because calculated betas depend very much on which historical period is used to calculate them; because calculated betas depend on what returns (monthly, daily, ...) are used to calculate them; because very often we do not know if the beta of one company is lower or higher than the beta of another; because calculated betas have little correlation with stock returns; and because the correlation coefficients of the regressions used to calculate the betas are very small.

We illustrate these seven reasons with data from the USA and from Spain.

For these seven reasons we can say that the beta calculated from historical data is not a good approximation to the company's beta, or the CAPM does not work (the required return is affected by other factors, besides the covariance of the company's return with the market return, the risk-free rate and the market risk premium), or both things at once.

G12, G31, M21

Abstract:
We report 2,510 answers from professors from 65 countries and 934 institutions. 1,791 respondents use betas, but 107 of them do not justify the betas they use.

97.3% of the professors that justify the betas use regressions, webs, databases, textbooks or papers (the paper specifies which ones), although many of them admit that calculated betas “are poorly measured and have many problems”.

Only 0.9% of the professors justify the beta using exclusively personal judgement (named qualitative, common sense, intuitive, and logical magnitude betas by different professors).

The paper includes interesting comments from 160 professors.

We all admit that different investors may have different expected cash flows, but many of us affirm that the required return should be equal for everybody: That is a kind of schizophrenic approach to valuation.

beta, historical beta, calculated beta, common sense

Abstract:
I review 150 textbooks on corporate finance and valuation published between 1979 and 2009 by authors such as Brealey, Myers, Copeland, Damodaran, Merton, Ross, Bruner, Bodie, Penman, Arzac…and find that their recommendations regarding the equity premium range from 3% to 10%, and that 51 books use different equity premia in various pages. The 5-year moving average has declined from 8.4% in 1990 to 5.7% in 2008 and 2009.

Some confusion arises from not distinguishing among the four concepts that the phrase equity premium designates: the Historical, the Expected, the Required and the Implied equity premium. 129 of the books identify Expected and Required equity premium and 82 identify Expected and Historical equity premium.

Finance textbooks should clarify the equity premium by incorporating distinguishing definitions of the four different concepts and conveying a clearer message about their sensible magnitudes.

equity premium, equity premium puzzle, required equity premium, expected equity premium

Abstract:
During the last 10 years (1997-2006), the average return of the mutual funds in Spain (2.7%) was smaller than the average inflation (2.9%). Nevertheless, on December 31, 2006, 8,819,809 investors in the 2,779 existing mutual funds had 254 billion euros. 246 new mutual funds were launched during 2006. Only 23 of the 649 mutual funds with 10-year history outperformed the benchmark.

mutual funds, Spain, benchmark, mutual fund performance

Abstract:
We value a company that targets its capital structure in book - value terms. This capital structure definition provides us with a valuation that lies between those of Modigliani - Miller (fixed debt) and Miles - Ezzell (fixed market - value leverage ratio).

We show that if a company targets its leverage in market - value terms, it has less value than if it targets the leverage in book - value terms. We also present empirical evidence that permits us to conclude that debt is more related to the book - value of the assets than to their market - value.

value of tax shields, required return to equity, WACC, company valuation, APV, cost of equity

Abstract:
The equity premium designates four different concepts: Historical Equity Premium (HEP); Expected Equity Premium (EEP); Required Equity Premium (REP); and Implied Equity Premium (IEP).

We highlight the confusing message of the textbooks and academic articles regarding the equity premium and its evolution. The confusion arises from not distinguishing among the four concepts and from not recognizing that although the HEP is equal for all investors, the REP, the EEP and the IEP are different for different investors.

There is a kind of schizophrenic approach to valuation: while all authors admit different expectations of equity cash flows, most authors look for a unique discount rate. It seems as if the expectations of equity cash flows are formed in a democratic regime, while the discount rate is determined in a dictatorship.

A unique IEP requires assuming homogeneous expectations for the expected growth (g), but we show that there are several pairs (IEP, g) that satisfy current prices. We claim that different investors have different REPs and that it is impossible to determine the REP for the market as a whole, because it does not exist.

We also investigate the relationship between (IEP - g) and the risk free rate.

equity premium, equity premium puzzle, required market risk premium, historical market risk premium, expected market risk premium, risk premium, market risk premium, market premium

Abstract:
This paper analyzes the incredible mistakes written by a court in Spain in a case of insider trading.

insider trading, judges, Spain, indirect transactions

Abstract:
This paper contains a collection and a classification of the 12 most common errors seen in company valuations performed by financial analysts, investment banks and financial consultants. The author had access to most of the valuations that are referred to in this paper when consulting in purchases, sales and mergers of companies, and in arbitrage processes. Some of the errors belong to public reports of financial analysts.

Valuation, company valuation, valuation errors

Abstract:
This paper contains three articles published in the economic newspapers Expansion, La Gaceta de los Negocios and Cinco Dias about the value of the shares of Endesa.

On January 6 and on January 18, 2006, we published that the value of a share of Endesa was 28 euro. On February 21, E.ON offered 27,5 euro per share of Endesa.

The paper also contains the main hypothesis and inputs of our valuation.

Endesa, E.ON, Gas Natural, valuation, OPA

Abstract:
This paper contains a collection and classification of 110 errors seen in company valuations performed by financial analysts, investment banks and financial consultants. The author had access to most of the valuations referred to in this paper in his capacity as a consultant in company acquisitions, sales, mergers, and arbitrage processes.

We classify the errors in six main categories: 1) Errors in the discount rate calculation and concerning the riskiness of the company; 2) Errors when calculating or forecasting the expected cash flows; 3) Errors in the calculation of the residual value; 4) Inconsistencies and conceptual errors; 5) Errors when interpreting the valuation; and 6) Organizational errors.

company valuation, valuation errors, valuation, historical beta, CAPM

Abstract:
During the last 3, 5, 10 and 15 years, the average return of the equity mutual funds in Spain was 600 basis points smaller than the average return of the Spanish Index ITBM. Nevertheless, on December 31, 2006, 348,000 investors in the 120 existing equity mutual funds had 10.7 billion euros. Only one of the 43 equity mutual funds with 10-year history outperformed the benchmark.

Spain, equity mutual funds, fondos de inversión, CNMV, INVERCO, benchmark, apreciación de los fondos, TER

Abstract:
This paper contains a collection and classification of 96 errors seen in company valuations performed by financial analysts, investment banks and financial consultants. The author had access to most of the valuations referred to in this paper in his capacity as a consultant in company acquisitions, sales, mergers, and arbitrage processes.

We classify the errors in six main categories: 1) Errors in the discount rate calculation and concerning the riskiness of the company; 2) Errors when calculating or forecasting the expected cash flows; 3) Errors in the calculation of the residual value; 4) Inconsistencies and conceptual errors; 5) Errors when interpreting the valuation; and 6) Organizational errors.

company valuation, valuation errors, valuation

Abstract:
This paper is a revision of the recommendations about the risk premium found in the the main finance and valuation textbooks. We revise several editions of books written by authors such as Brealey and Myers; Copeland, Koller and Murrin (McKinsey); Ross, Westerfield and Jaffe; Bodie, Kane and Marcus; Damodaran; Copeland and Weston; Van Horne; Bodie and Merton; Stowe et al; Pratt; Penman; Bruner; Weston & Brigham; and Arzac.

We highlight the confusing message of the textbooks regarding the equity premium and its evolution.

The main confusion arises from not distinguishing among the four concepts that the word equity premium designates: Historical equity premium (HEP), Expected equity premium, Required equity premium (REP) and Implied equity premium (IEP).

Some confusion also arises from not recognizing that although the HEP is equal for all investors, the REP, the EEP and the IEP are different for different investors. A unique IEP requires assuming homogeneous expectations for the expected growth (g), but there are several pairs (IEP, g) that satisfy current prices.

equity premium, equity premium puzzle, required market risk premium, historical market risk premium, expected market risk premium, risk premium, market risk premium, market premium

Abstract:
We show that the value of tax shields is the difference between the present values of two different cash flows with their own risk: the present value of taxes for the unlevered company and the present value of taxes for the levered company. For perpetuities without costs of leverage, the value of tax shields is equal to the tax rate times the value of debt. For any company, we claim that the value of the tax shield in a world with no leverage cost is the present value of the debt (D) times the tax rate (T) times the required return to the unlevered equity (Ku), discounted at the unlevered cost of equity (Ku): VTS = PV[Ku; D T Ku]. Please note that it does not mean that the appropriate discount for the tax shields is the unlevered cost of equity. We discount D T Ku, which is not the tax shield. This expression arises as the difference of two present values each with different risk.

Value of tax shields; Tax shields, APV; Costs of leverage

Abstract:
We compute the shareholder value creation of the companies in the IBEX 35 for the 16-year period 1992-2007. The average return was 15.1%, but 4.4% was due to the decline in interest rates (from 12.5% to 4%). The shareholder value creation was 222 billion euros. As usual, smaller companies were more profitable.

IBEX 35, shareholder value creation, IGBM, ITBM, Spain

Abstract:
During the last 10 years (1998-2007), the average return of the mutual funds in Spain (2.2%) was smaller than the average inflation (3.0%). Nevertheless, on December 31, 2007, 8,264,240 investors in the 2,907 existing mutual funds had 239 billion euros. Only 30 of the 935 mutual funds with 10-year history outperformed the benchmark.

mutual funds, Spain, benchmark, mutual fund performance

Abstract:
Spanish convertible bonds are different from the American convertible bonds. First, the conversion price is not fixed in pesetas, but is defined as a percentage discount off the average share price over a number of days before conversion. Second, the conversion option can be exercised only at a few (usually two or three) different dates. Third, the first conversion opportunity is usually only two or three months after the subscription (issue) date.

These characteristics allow us to say that convertible bonds in Spain have been used for "Back Door" equity financing. In fact, more than 80% of the convertibles were converted. In the period 1984 to 1996, 290 issues of convertibles accounted for $20 billion.

In this period, companies issued more convertibles than new shares ($19 billion).

Several formulas to value Spanish convertible bonds are derived using option theory. Convertibles have been undervalued by an average of 21.6% on average. The expropriation effect in the period 1984 to 1995 accounts for $1.15 billion.

Convertible bonds; "Back Door" equity financing; Undervaluation; Expropriation

Abstract:
In this paper, we will define and analyze shareholder value creation. To help us understand this concept better, we will use the example of two listed companies, General Electric and Microsoft, between 1992 and 2003.

To obtain the created shareholder value, we must first define the increase of equity market value, the shareholder value added, the shareholder return, and the required return to equity.

A company creates value for the shareholders when the shareholder return exceeds the required return to equity (Ke). In other words, a company creates value when it outperforms expectations.

The created shareholder value can also be calculated as follows:

Created shareholder value = Shareholder value added - (Equity market value x Ke)

We also calculate the created shareholder value of 400 American companies during the eleven-year period 1992-2003.

Shareholder value added, shareholder value creation, created shareholder value

Abstract:
We analyze the movement of the share price between December 1990 and October 2008 of 154 Spanish companies that trade in the Mercado Continuo. 85 companies had a minimum price that was lower than 30% of their maximum price. The average loss was 73%.

Share price, Maximum, Minimum

Abstract:
CAF had the highest return in 2007. 74 companies had negative return in 2007 and 98 out of 125 had a return smaller than that of the IBEX 35. In 2007, the 125 companies destroyed 15 billions (and 89 billion in the first 17 days of 2008). In the years 1994, 1997-8, 2000-6 and, on average, in the period 1992-2007, the smaller companies had higher returns than the big ones.

Shareholder Value Creation, Spain, Shareholder return

Abstract:
We compute the Shareholder Value Creation of Endesa, Iberdrola and Union Fenosa between 1991 and 2006. The shareholder value creation during this period was: Endesa 29.9 billion euros; Iberdrola 23.9; and Union Fenosa 9.6.

The average shareholder return was: Endesa 18.5%; Iberdrola 19.1% and Union Fenosa 21.6%, all higher than that of the IBEX 35 (15.4%).

Endesa, Iberdrola, Union Fenosa, Shareholder Value Creation

Abstract:
2002 was a bad year: The shareholder value destruction of the companies in the S&P 500 was $3.3 trillion. In 2002 only 16% of the companies created value (80 companies created value and 420 companies destroyed value). The percentage of value creators was 35%, 54%, 47% and 53% for 2001, 2000, 1999 and 1998. The market value of the 500 companies was $8.1 trillion in 2002 and $10.4 trillion in 2001.

The top shareholder value creators in 2002 were Boston Scientific ($6.5 billion), Bank of America ($6.4 billion), Wachovia ($4.7 billion), and Procter ($3.3 billion). The top shareholder value destroyers in 2002 were General Electric (-$185 billion), Intel (-$125 billion), Microsoft (-$119 billion) and AOL Time Warner (-$101 billion). We define created shareholder value and provide the ranking of created shareholder value for the 500 companies. We also calculate the created shareholder value of the 500 companies during the five-year period 1998-2002. Wal-Mart Stores was the top shareholder value creator ad Coca Cola the top shareholder value destroyer during the five-year period.

We also provide the shareholder return of the 500 companies. Only 148 companies (out of the 500) had positive return on 2002, been the highest Providian Financial (82.8%). Dynegy had the lowest return (95.3%).

Abstract:
For constant growth companies, we prove that the value of tax shields in a world with no leverage cost is the present value of the debt, times the tax rate, times the required return to the unlevered equity, discounted at the unlevered cost of equity. Please note that this does not mean that the appropriate discount for tax shields is the unlevered cost of equity, since the amount being discounted is higher than the tax shield (it is multiplied by the unlevered cost of equity and not the cost of debt). Rather, this result arises as the difference of two present values.

We also show that the value of tax shields is the difference between the present values of two different cash flows with their own risk: the present value of taxes for the unlevered company and the present value of taxes for the levered company. This is the difference between the present values of two separate cash flows each with its own risk.

value of tax shields, required return to equity, leverage cost, unlevered beta, levered beta

Abstract:
This paper corrects some equations of Farber, Gillet and Szafarz (2006). The WACC is a discount rate widely used in corporate finance. However, the correct calculation of the WACC rests on a correct valuation of the tax shields. The value of tax shields depends on the debt policy of the company. Many authors, (e.g. Inselbag and Kaufold (1997), Booth (2002), Cooper and Nyborg (2006), Farber, Gillet and Szafarz (2006)) consider that debt policy may only be framed in terms of maintaining a fixed market value debt ratio (Miles-Ezzell assumption) or a fixed dollar amount of debt (Modigliani-Miller assumption).

WACC, required return to equity, value of tax shields, company valuation, APV, cost of equity

Abstract:
Between December 1996 and October 1998, the value destroyed by Boston Chicken for its shareholders amounted to 3,293 million euros (a return of -100%). During the same period, the stock market yield (S&P500) was 54%.

Between June 1998 and October 1999, the value destroyed by TelePizza for its shareholders amounted to 1,543 million euros (a return of -55%). During the same period, the stock market yield (IBEX 35) was -7%.

It is very interesting to compare and try to differentiate what happened to these two companies. We also urge the reader to analyze the history of companies such as Levitz, Home Shopping Network, OM Scott, MCI, and LTCM.

Value creation, company valuation, value destruction, analysts

Abstract:
It is a big mistake to use betas calculated from historical data to compute the required return to equity. It is a mistake for seven reasons: because betas calculated from historical data change considerably from one day to the next; because calculated betas depend very much on which stock index is used as the market reference; because calculated betas depend very much on which historical period is used to calculate them; because calculated betas depend on what returns (monthly, daily, . . .) are used to calculate them; because very often we do not know if the beta of one company is lower or higher than the beta of another; because calculated betas have little correlation with stock returns; and because the correlation coefficients of the regressions used to calculate the betas are very small.

Beta, CAPM, beta-ranked portfolios, historical beta, expected beta

Abstract:
During the last 10 and 17 years, the average return of the pension funds in Spain was lower than the return of Government Bonds. Nevertheless, on December 31, 2007, 10.4 million investors in the 3,185 existing pension funds had 86,6 billion euros.

pension funds, fondos de pensiones, fondos de inversion, INVERCO, Spain, benchmark

Abstract:
This paper contains 100 questions that students, alumni and other persons (judges, arbitrageurs, clients') have posed to me over the past years. They were recompiled so as to help the reader remember, clarify and, in some cases, discuss some useful concepts in finance. Most of the questions have a clear answer but others can receive several emphasis. A short answer to all of the questions is provided at the end of the paper.

cash flow; net income, intangibles, required return, simple return, weighted return, market premium, beta, value, book value, value creation, EVA, FCF, WACC

Abstract:
We report 1,466 answers from European managers and professors. 1,143 respondents use required return and 824 use betas to calculate it.

44.4% of the managers and 8% of the professors do not use beta to justify the required return. Only 2% of the professors and 15% of the managers justify the beta using exclusively personal judgement (named qualitative, common sense, intuitive, and logical magnitude betas by different persons).

The paper includes interesting comments from 235 respondents.

beta, historical beta, calculated beta, common sense

Abstract:
This book of 273 pages contains a collection and classification of 201 errors seen in company valuations performed by financial analysts, investment banks and financial consultants. The author had access to most of the valuations referred to in this paper in his capacity as a consultant in company acquisitions, sales, mergers, and arbitrage processes.

The errors are classified in six main categories: 1) Errors in the discount rate calculation and concerning the riskiness of the company; 2) Errors when calculating or forecasting the expected cash flows; 3) Errors in the calculation of the residual value; 4) Inconsistencies and conceptual errors; 5) Errors when interpreting the valuation; and 6) Organizational errors.

company valuation, valuation errors, valuation, historical beta, CAPM

Abstract:
During the last 5 years (2001-2006), the average return of the pension funds in Spain (2.9%) was lower than the average inflation (3.2%). Nevertheless, on December 31, 2006, 9.9 million investors in the 2,759 existing pension funds had 81 billion euros. Only 6 of the 115 equity pension funds with 5-year history outperformed the benchmark.

pension funds, fondos de pensiones, fondos de inversion, INVERCO, rentabilidad para los partícipes, benchmark

Abstract:
Pablo and his wife have five children. As they like traveling by road with the whole family, often including the grandparents, they decided to buy a German van with nine seats.

On October 24, 2005, Pablo took the van to the a dealer to have the spare key repaired. But the spare key was not ready until 5 weeks later.
Pablo sent this case to the CEO in Spain of the carmaker and he got the following reply:

"Having read very carefully what you grandly describe as case, I have the following comments to make:

I recommend that in future... you use the official complaints form or get in touch with customer service.

The action of posting your "case" ... seems to obey demagogic or exhibitionistic instincts rather than the ethical precepts to be expected of a professor.

Certainly, at Northwestern University, where I did my postgraduate work, the Ethics Committee would never have allowed faculty to give students a personal case.

What action plan would you recommend to Pablo?

spare key, customer service, ethical precepts, Ethics Committee, action plan

Abstract:
During the last 10 years (1998-2008), the average return of the mutual funds in Spain (0.91%) was smaller than the average inflation. Nevertheless, on December 31, 2008, 6.1 million investors in the 2,936 existing mutual funds had 168 billion euros. Only 18 of the 1,025 mutual funds with 10-year history outperformed the benchmark.

mutual funds, Spain, benchmark, mutual fund performance

Abstract:
The value of tax shields depends upon the nature of the stochastic process of the net increase of debt, and does not depend upon the nature of the stochastic process of the free cash flow. The value of tax shields in a world with no leverage cost is the tax rate times the debt plus the tax rate times the present value of the net increases of debt. This expression is the difference between the present values of two different cash flows, each with their own risk: the present value of taxes for the unlevered company and the present value of taxes for the levered company. For perpetual debt, the value of tax shields is the debt times the tax rate. When the company forecast to repay the actual debt without issuing new debt, the value of tax shields is the present value of the interest times the tax rate, discounted at the required return to debt.

Value of tax shields, present value of the net increases of debt

Abstract:
We compute the Shareholder Value Creation of Santander, BBVA, Popular and Bankinter between 1991 and 2006. The shareholder value creation during this period was: Santander 20.7 billion euros; BBVA 25.4; Popular 13.4 and Bankinter 3.9.

The average shareholder return was: Santander 18.7%; BBVA 20.1%; Popular 19.3% and Bankinter 18.1%, all higher than that of the IBEX 35 (15.4%). However, the weighted shareholder return (taking into consideration the number of shares outstanding at different dates) was quite different: Santander 14%; BBVA 17%; Popular 20.7% and Bankinter 19.5%.

Value creation, shareholder value creation, Santander, BBVA, Popular, Bankinter, weighted shareholder return

Abstract:
We compute the shareholder value creation of the companies in the IBEX 35 for the 15-year period 1992-2006. The average return was 15.4%, but 5.2% was due to the decline in interest rates (from 12.5% to 4%). The shareholder value creation was 196 billion euros. As usual, smaller companies were more profitable.

IBEX 35, Shareholder value creation, IGBM, ITBM

Abstract:
The market cap of Telefonica increased between December 1991 and December 2007 in 99.2 billion euros. The shareholder value creation during this period was 57.2 billion euros. The average shareholder return of Telefonica in this 16 years was 19.1%, higher than that of the IBEX 35 (15.1%). We also compare the shareholder return of Telefonica with that of other Telecoms.

Telefonica, IBEX, shareholder return, shareholder value creation

Abstract:
This paper is a summarized compendium of all the methods and theories on company valuation using discounted cash flows. It shows ten discounted cash flow valuation methods:

1) equity cash flows discounted at the required return to equity;
2) free cash flow discounted at the WACC;
3) capital cash flows discounted at the WACC before tax;
4) APV (Adjusted Present Value);
5) the business's risk-adjusted free cash flows discounted at the required return to assets;
6) the business's risk-adjusted equity cash flows discounted at the required return to assets;
7) economic profit discounted at the required return to equity;
8) EVA discounted at the WACC;
9) the risk-free rate-adjusted free cash flows discounted at the risk-free rate; and
10) the risk-free rate-adjusted equity cash flows discounted at the required return to assets.

All ten methods always provide the same value. This result is logical, as all the methods analyze the same reality under the same hypotheses; they differ only in the cash flows taken as the starting point for the valuation.

The disagreements among the various theories of firm valuation arise from the calculation of the value of the tax shields (VTS). The paper shows and analyses 7 different theories on the calculation of the VTS: No-cost-of-leverage, Modigliani and Miller (1963), Myers (1974), 7 Miles and Ezzell (1980), Harris and Pringle (1985), Damodaran (1994), 7 and Practitioners method.

The paper lists the most important valuation equations according to each of these theories, and also shows how the valuation equations change when the debt's market value is not equal to its book value.

discounted cash flows, APV, WACC, equity cash flow

Abstract:
We analyze the results of a recent survey of executives and finance professors. We present the required equity premium used in 2008 by 216 companies and 39 professors and their comments. The range of the 216 companies goes from 2% to 30% (average 6.3%) and the range of the 39 academics goes from 3.5% to 10% (average 5.5%). We also present comments from140 companies and 3 professors that do not use any required equity premium.

equity premium, required market risk premium, historical market risk premium, expected market risk premium, market risk premium

Abstract:
133 companies out of 136 had negative return in 2008. The 136 companies destroyed 420 billion euros (17 billion euros in 2007). The average return of the 136 companies was -40%.

Shareholder Value Creation, Spain, Shareholder return

Abstract:
We value a company that targets its capital structure in book-value terms. This capital structure definition provides us with a Value of Tax Shields that lies between those of Modigliani-Miller (fixed debt) and Miles-Ezzell (fixed market-value leverage ratio).

If a company targets its leverage in market value terms, has less value than if it targets the leverage in book value terms. How could some manager target leverage in market value terms? We also present empirical evidence that permits to conclude that debt is more related to the book value of the assets than to their market value.

value of tax shields, required return to equity, WACC, company valuation, APV, cost of equity

Abstract:
I revise 100 finance and valuation textbooks published between 1979 and 2008 and find that their recommendations regarding the equity premium range from 3% to 10%. Several books use different equity premia in different pages.

Some confusion arises from not distinguishing among the four concepts that the word equity premium designates: Historical equity premium, Expected equity premium, Required equity premium and Implied equity premium.

Finance professors should clarify the different concepts of equity premium and convey a clearer message about their sensible magnitudes.

equity premium, required market risk premium, historical market risk premium

Abstract:
We develop valuation formulae for a company that maintains a fixed book-value leverage ratio and claim that it is more realistic than to assume, as Miles-Ezzell (1980), a fixed market-value leverage ratio. The value of tax shields depends only on the present value of the net increases of debt. The value of tax shields in a world with no leverage cost is the tax rate times the current debt plus the present value of the net increases of debt. We also show that the appropriate discount rates for the equity cash flows and for the expected value of the equity are different. It is more realistic to assume that a company maintains a fixed book-value leverage ratio than to assume, as Miles-Ezzell (1980) do, that the company maintains a fixed market-value leverage ratio because the amount of debt does not depend on the movements of the stock market, it is easier to follow for non quoted companies, and managers should prefer so because the value of tax shields is more valuable.

valuation, company valuation, valuation errors, value of tax shields, present value of the net increases of debt, required return to equity

Abstract:
We compute the Shareholder Value Creation of Banco Santander (SAN). The market cap of BS increased between December 1991 and December 2005 in 85.7 billion euros. The shareholder value creation during this period was 20.7 billion euros. The average shareholder return of BS in this 15-year period was 18.7%, higher than that of the IBEX 35 (15.4%). Average inflation was 3.3%. We also compare the shareholder return with that of other banks. In December 2006 BS was the biggest company in the IBEX 35 and the 4th biggest of the EuroStoxx 50.

Santander, IBEX, EuroStoxx, shareholder value creation

Abstract:
During the last 3, 5 and 10 years, the average return of the pension funds in Spain was lower than the inflation and than the return of Government Bonds. Nevertheless, on December 31, 2008, 10.6 million investors had 78,5 billion euros in the 3,293 existing pension funds .

pension funds, mutual funds, INVERCO, Spain, benchmark

Abstract:
We compute the shareholder value creation of the 123 companies that traded in the Spanish market during 2006. Santander was the top shareholder value creator, followed by Endesa, Telefonica, Arcelor, BBVA and Iberdrola. EADS was the top shareholder value destroyer. We also compute the shareholder value creation of the 72 companies that traded in the Spanish market during 1993-2006. As usual, small companies were more profitable.

Value creation, shareholder value creation, IBEX, Spain

Abstract:
I correct some expressions of Fernandez (2004) and provide a more general expression for the value of tax shields. This expression is the difference between the present values of two different cash flows, each with its own risk: The present value of taxes for the unlevered company and the present value of taxes for the levered company. The value of tax shields in a world with no leverage cost is the tax rate times the current debt, plus the tax rate times the present value of the net increases of debt. The value of tax shields depends only on the nature of the stochastic process of the net increase of debt; it does not depend on the nature of the stochastic process of the free cash flow.

Value of tax shields, present value of the net increases of debt, required return to equity

Abstract:
This document has 17 basic problems on finance, the right answers and 307 wrong answers from different exams.

Este documento contiene 17 preguntas sencillas de exámenes de finanzas básicas. También contiene sus respuestas y 307 respuestas erróneas

Cash flow, exam, NPV

Abstract:
During 2003, 87% of the companies included in the S&P 500 created value, while in 2002 just 17% of these companies did it. The market value of the 500 companies was $10.1 trillion in 2003 and $7.9 trillion in 2002. The top shareholder value creators in 2003 were Intel, Cisco, Citigroup, General Electric and Exxon. We define created shareholder value and provide the ranking of created shareholder value for the 500 companies. We also calculate the created shareholder value of the 500 companies during the eleven-year period 1993-2003. General Electric was the top shareholder value creator and AT&T was the top shareholder value destroyer during the eleven-year period. On average, the small market capitalization companies of the S&P were more profitable. The volatility of the S&P fell since 1998 to 2003, but the volatility of his components increased on average.

Shareholder value creation

Abstract:
The market cap of Telefonica increased between December 1991 and December 2005 in 55,695 million euros. The shareholder value creation during this period was 12.442 million euros. The average shareholder return of Telefonica in this 14 years was 16.8%, higher than that of the IBEX 35 (13.7%). We also compare the shareholder return of Telefonica with that of other Telecoms.

Telefonica, IBEX, shareholder return

Abstract:
We compute the Shareholder Value Creation of Banco Santander (BS). The market cap of BS increased between December 1991 and December 2007 in 89.8 billion euros. The shareholder value creation during this period was 22.6 billion euros. The average shareholder return of BS in this 15-year period was 18.0%, higher than that of the IBEX 35 (15.1%). Average inflation was 3.4%. We also compare the shareholder return with that of other banks. In December 2007 BS was the second biggest company in the IBEX 35 and the 6th biggest of the EuroStoxx 50.

Santander, IBEX, EuroStoxx, shareholder value creation

Abstract:
2003 was a good year for the shareholders of the companies in the Euro Stoxx 50: the shareholder value creation of these 50 companies was 150,016 million euros (E). The companies that created more value for their shareholder were Siemens (E18,778 million), Telefonica (15,382) and BSCH (12,443). The companies that destroyed more shareholder value were Nokia (-E12,051 million), L'Oreal (-8,089) and Ahold (-5,427). In 2003, the Euro Stoxx 50 was much more volatile than the S&P 500 or the Dow Jones. Shareholder value destruction in the three-year period 2001-2003 was E-1.75 trillion. The market value of the 50 companies was E1.65 trillion in 2003, and E1.4 trillion in 2002. We also calculate the created shareholder value of the 50 companies during the seven-year period 1997-2003. Siemens was the top shareholder value creator and Nokia the top shareholder value destroyer during the seven-year period. A portfolio long in the companies that entered the index and short in the companies that abandoned the index had on average a 6% return in the 20 days prior to the index recomposition and a 7% return in the 20 days after the index recomposition.

Shareholder value creation, created shareholder value, shareholder value added, shareholder return

Abstract:
2002 was a bad year for the shareholders of the companies in the Euro Stoxx 50: the shareholder value destruction of the companies in the Euro Stoxx 50 was Euro 958,968 million. In 2002 only Eni created value (Euro 3,374 million). The remaining 49 companies destroyed value and had negative returns. Alcatel had the lowest shareholder return in 2002 (-77.9%). Shareholder value destruction in the 3-year period 2000-2002 Euro was 1.9 trillion. The market value of the 50 companies was Euro 1.42 trillion in 2002, and Euro 2.24 trillion in 2001, and Euro 2.75 trillion in 2001. We also calculate the created shareholder value of the 50 companies during the six-year period 1997-2002. Nokia was the top shareholder value creator and Allianz the top shareholder value destroyer during the six-year period. We find a very weak relationship between return and size. A portfolio long in the companies that entered the index and short in the companies that abandoned the index had on average a 10% return in the 16 days prior to the index recomposition and a -6% return in the 12 days after the index recomposition. In 2002, the Euro Stoxx 50 was much more volatile than the S&P 500 or the Dow Jones.

shareholder value creation, created shareholder value, equity market value, shareholder value added, shareholder return, required return to equity

Abstract:
We compute the Shareholder Value Creation of Santander, BBVA, Popular and Bankinter between 1991 and 2007. The shareholder value creation during this period was: Santander 22.5 billion euros; BBVA 18.7; Popular 11.1 and Bankinter 4.0.

The average shareholder return was: Santander 18.0%; BBVA 18.3%; Popular 17.0% and Bankinter 17.4%, all higher than the return of the IBEX 35 (15.1%). However, the weighted shareholder return (taking into consideration the number of shares outstanding at different dates) was quite different: Santander 13.4%; BBVA 14.9%; Popular 18.9% and Bankinter 18.9%.

Value creation, shareholder value creation, Santander, BBVA, Popular, Bankinter, weighted shareholder return

Abstract:
Only 25 companies out of 136 had negative return in January-September 2009 (133 in 2008). The 136 companies created value in January-September 2009 (64 billion euros), but destroyed value in 2008 (420 billion euros) and in 2007 (17 billion euros). The average return of the 136 companies was 24% in January-September 2009 and -45% in 2008.

shareholder value creation, Spain, shareholder return, shareholder value destruction

Abstract:
MBA Finance students are in possession of mathematical skills that permit to present them the Black Scholes model. I show how Monte Carlo simulation may be employed to value plain options and other financial instruments.

Simulation, teaching, Black and Scholes

Abstract:
We compute the Shareholder Value Creation of BBVA. The market cap of BBVA increased between December 1991 and December 2007 in 59.1 billion euros. The shareholder value creation during this period was 18.7 billion euros. The average shareholder return of BBVA in this 16 years was 18.3%, higher than that of the IBEX 35 (15.1%). Average inflation was 3.4%. We also compare the shareholder return of BBVA with that of other banks.

Value creation, shareholder value creation, BBVA, Banco Bilbao Vizcaya Argentaria

Abstract:
We compute the Shareholder Value Creation of Banco Santander (BS). The market cap of BS increased between December 1991 and December 2005 in 67,070 million euros. The shareholder value creation during this period was 4,158 million euros. The average shareholder return of BS in this 14 years was 17.9%, higher than that of the IBEX 35 (14.0%). Average inflation was 3.4%. We also compare the shareholder return of BS with that of other banks.

In December 2005 BS was the biggest company in the IBEX 35.

BSCH, BS, Banco Santander, Shareholder Value Creation, Shareholder Value Added, creacion de valor para los accionistas, aumento del valor para los accionistas, rentabilidad para los accionistas

Abstract:
We compute the Shareholder Value Creation of Iberdrola. The market cap of Iberdrola increased between December 1991 and December 2007 in 48.4 billion euros. The shareholder value creation during this period was 32.0 billion euros. The average shareholder return of Iberdrola in this 16 years was 19.7%, higher than that of the IBEX 35 (15.1%). Average inflation was 3.4%. We also compare the shareholder return of Iberdrola with that of other utilities.

Value creation, shareholder return, shareholder value creation, IBEX, Iberdrola

Abstract:
I value several issues of 'bonos bolsa' issued in Spain. These instruments are the combination of a bond (usually a zero coupon bond) and one or more options.

bonos bolsa, teaching, Black and Scholes, simulation

Abstract:
Sniace had the highest return in 2005. Only 11 companies had negative return in 2005 and 45 out of 119 had a return smaller than that of the IBEX 35. The return of 100 companies was higher than the yield of the Government Bonds.

The market capitalization of 10 biggest companies accounted for 60% of the total. The market capitalization of 38 smallest companies accounted for 1% of the total.

In the period 1987-1992, the IBEX 35 destroyed €176 billions (in € of 2005). In the period 1993-2005, the IBEX 35 created €146 billions for the shareholders.

In the years 1994, 1997-8, 2000-5 and, on average, in the period 1992-2005, the smaller companies had higher returns than the big ones.

A portfolio long in the companies that entered the index and short in the companies that abandoned the index had on average a 16% return in the 40 days prior to the index recomposition.

Abstract:
I describe the four main groups comprising the most widely used company valuation methods: balance sheet-based methods, income statement-based methods, mixed methods, and cash flow discounting-based methods. The methods that are conceptually correct are those based on cash flow discounting. We briefly comment on other methods since - even though they are conceptually incorrect - they continue to be used frequently.

I also present a real-life example to illustrate the valuation of a company as the sum of the value of different businesses, which is usually called the break-up value.

I finish the paper showing the most common errors in valuations: a list that contains the most common errors that the author has detected in the more than one thousand valuations he has had access to in his capacity as business consultant or teacher.

Value, Price, Free cash flow, Equity cash flow, Capital cash flow, Book value, Market value

Abstract:
This note builds on the paper of Farber, Gillet and Szafarz (2006). The WACC is a discount rate widely used in corporate finance. However, the correct calculation of the WACC rests on a correct valuation of the tax shields. The value of tax shields depends on the debt policy of the company. Many authors, (e.g. Inselbag and Kaufold (1997), Booth (2002), Cooper and Nyborg (2006), Farber, Gillet and Szafarz (2006)) consider that debt policy may only be framed in terms of maintaining a fixed market value debt ratio (Miles-Ezzell assumption) or a fixed dollar amount of debt (Modigliani-Miller assumption).

WACC, required return to equity, value of tax shields, company valuation, APV, cost of equity

Abstract:
We compute the Shareholder Value Creation of Endesa. The market cap of Endesa increased between December 1991 and December 2006 in 33,403 million euros. The shareholder value creation during this period was 29,892 million euros. The average shareholder return of Endesa in this 15 years was 18.5%, higher than that of the IBEX 35 (15.4%). We also compare the shareholder return of Endesa with that of other utilities.

Endesa, shareholder value creation

Abstract:
We compute the Shareholder Value Creation of Repsol. The market cap of Repsol increased between December 1991 and December 2005 in 27.5 billion euros. The shareholder value creation during this period was 7.4 billion euros. The average shareholder return of Repsol in this 15 years was 14.1%, lower than that of the IBEX 35 (15.4%). Average inflation was 3.3%.

Repsol, Shareholder Value Creation, Shareholder Value Added

Abstract:
98 companies out of 136 had negative return in IT 2009 (133 in 2008). The 136 companies destroyed 94 billion euros in IT 2009, 420 billion euros in 2008 and 17 billion euros in 2007. The average return of the 136 companies was - 16% in IT 2009 and - 40% in 2008.

Shareholder Value Creation, Spain, Shareholder return

Abstract:
In a recent paper, Cooper and Nyborg (2004) argue that the results of Fernandez (2004) are wrong because value-additivity is violated and because "Fernandez paper comes from mixing the Miles-Ezzell leverage policy with the Miller-Modigliani leverage adjustment."

Cooper and Nyborg paper is thought provoking and helps a lot in rethinking the value of tax shields. However, their conclusions are not correct because, as will be proven below, the main result of Fernandez (2004) is correct for several situations.

An evident error of Cooper and Nyborg (2004) is that their formulae (4), (6), (8) and (11), that they attribute to Miles and Ezzell (1980), correspond to Harris and Pringle (1985) and Ruback (2002). In addition, their formulae (3) and (5) are not general: they are valid only for perpetuities without growth.

In this paper I also show that the value of tax shields depends only upon the nature of the stochastic process of the net increase of debt.

Value of tax shields, present value of the net increases of debt, required return to equity

Abstract:
I show: a) how to use the Black and Scholes formula to value options; b) what is the arbitrage portfolio; c) how to calculate the volatility; d) how the early exercise affects the value of the option; and e) how the dividends affect the value of the option; and f) what is the implicit volatility.

Black and Scholes, volatility, arbitrage, early exercise, put, call

Abstract:
During 2004, 64% of the companies included in the S&P 500 created value, while in 2003 87% of these companies did it. The market value of the 500 companies was $11.2 trillion in 2004 and $10.1 trillion in 2003. The top shareholder value creators in 2004 were Exxon, General Electric, Ebay, Johnson & Johnson and Qualcomm. We define created shareholder value and provide the ranking of created shareholder value for the 500 companies.

We also calculate the created shareholder value of the 500 companies during the twelve-year period 1993-2004. General Electric was the top shareholder value creator and AT&T was the top shareholder value destroyer during the twelve-year period.

On average, the small market capitalization companies of the S&P were more profitable. The volatility of the S&P fell since 1998 to 2004, but the volatility of his components increased on average.

Shareholder value creation, created shareholder value, equity market value, shareholder value added, shareholder return, required return to equity, EVA

Abstract:
The market cap of Telefonica increased between December 1991 and December 2006 in 72.5 billion euros. The shareholder value creation during this period was 28.2 billion euros. The average shareholder return of Telefonica in this 15 years was 17.7%, higher than that of the IBEX 35 (15.4%). We also compare the shareholder return of Telefonica with that of other Telecoms.

Telefonica, IBEX, shareholder return, shareholder value creation

Abstract:
Although Arzac and Glosten (2005) affirm that the value of tax shields depends upon the nature of the equity stochastic process, which, in turn depends upon the free cash flow process, I prove that the value of tax shields depends only upon the nature of the stochastic process of the net increase of debt. Arzac and Glosten (2005) formulate the constant leverage ratio assumption as Dt = L Et. The assumption of Fernandez (2004) is E{Dt}= L E{Et}, being E{bullet} the expected value operator, D the value of debt, E the equity value, and L a constant. Arzac and Glosten (2005) assumption requires continuous debt rebalancing, while mine does not. Under both financial policies, the expected leverage ratio is constant, but the Arzac and Glosten (2005) assumption is too extreme.

Value of tax shields, APV, required return to equity, cost of capital, net increase of debt

Abstract:
The value of tax shields depends only on the nature of the stochastic process of the net increases of debt. The value of tax shields in a world with no leverage cost is the tax rate times the current debt plus the present value of the net increases of debt. By applying this formula to specific situations, we show that Modigliani-Miller (1963) should be used when the company has a preset amount of debt, Fernández (2004) when the company maintains a fixed book-value leverage ratio, and Miles-Ezzell (1980) when the company maintains a fixed market-value leverage ratio.

Value of tax shields, present value of the net increases of debt, required return to equity, valuation

Abstract:
The Comment is thought provoking and helps a lot in rethinking the value of tax shields. However, the conclusion of Fieten, Kruschwitz, Laitenberger, Loffler, Tham, Velez-Pareja and Wonder (2005) is not correct because, as will be proven below, the main result of Fernandez (2004) is correct for several situations.

Equation (16a) shows that the value of tax shields depends only upon the nature of the stochastic process of the net increase of debt.

Value of tax shields, Required return to equity, leverage cost, unlevered beta, levered beta

Abstract:
We compute the Shareholder Value Creation of BBVA. The market cap of BBVA increased between December 1991 and December 2005 in 47,386 million euros. The shareholder value creation during this period was 15,617 million euros. The average shareholder return of BBVA in this 14 years was 19.8%, higher than that of the IBEX 35 (14.0%). We also compare the shareholder return of BBVA with that of other banks.

BBVA, Shareholder Value Creation, Shareholder Value Added, creacion de valor para los accionistas, aumento del valor para los accionistas, rentabilidad para los accionistas

Abstract:
We compute the shareholder value creation of the companies in the IBEX 35 for the 17-year period 1991-2008. The average return was 11.1%, but 4.7% was due to the decline in interest rates (from 12.5% to 4%). The shareholder value creation in the whole period was 4 billion euros, despite a value destruction of 238 billion euros in 2008.

IBEX 35, shareholder value creation, IGBM, ITBM, Spain