Valuing companies by cash flow discounting: Ten methods and nine theories

This paper is a summarized compendium of all the methods and theories on company valuation using cash flow discounting. The paper shows the ten most commonly used methods for valuing companies by cash flow discounting: 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, since all the methods analyze the same reality under the same hypotheses; they only differ in the cash flows taken as 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 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 contains the most important valuation equations according to these theories, and also shows the changes that take place in the valuation equations when the debt's market value does not match its book value.Financial management; Company valuation

Company valuation methods. The most common errors in valuations

In this paper, we 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 will briefly comment on other methods since -even though they are conceptually "incorrect"- they continue to be used frequently. We 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. We finish the paper with a list of 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 and teacher.Value; price; free cash flow; equity cash flow; market value;

Convertible bonds in Spain: A different security

Spanish convertible bonds are different from 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 at only 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. In the period 1984 to 1990, 248 issues of convertibles accounted for 1.9 trillion pesetas. In this period, companies issued more convertibles than new shares (1.4 trillion pesetas). Several formulas for valuing 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 1990 amounts to 125 billion pesetas.Convertible bonds;

Equivalence of the APV, WACC and flows to equity approaches to firm valuation

This paper shows that the three valuation methods (if used correctly) always yield the same result. The most striking result of this paper is that the Net Present Value of the tax shield due to interest payments (in the APV approach) should be calculated as follows in order to derive an accurate result: NPV OF INTEREST TAX SHIELDS = ƒ Dt-1 Kut T Â ------ t=1 t ' (1+Kut) t=1 T = Corporate tax rate / Kut = Cost of unlevered equity in period t / Dt­1 = Value of debt in period t­1 At first, it would appear that this formula implies that debt has a cost of Ku, and that the interest tax shields are discounted 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 single flow, but the difference of two NPVs of two flows with different risks: 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 these two NPVs. 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 that, if used correctly, these three approaches to firm valuation will yield the same result. We apply these valuation procedures to perpetuities, to growing companies (at a constant rate g) and, finally, to any company. The main objective of this paper is to show that the three valuation methods always yield the same result. The paper also helps to think more about the meaning of the formulas and their relationships.Valuation methods; interest payments;

A definition of shareholder value creation

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 its 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 1997-1999 and during the eight-year period 1992-1999.Financial management; Stockholders; Value creation

Valuation of brands and intellectual capital

In this paper we review 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, we analyze in depth the valuations of Kellogg's and Coca-Cola performed by Damodaran and the method proposed by Interbrand. Damodaran valued the Coca-Cola brand at 24.6 billion dollars in 1993 and at 102.6 billion dollars in 1998. In recent years, a lot has been said 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. 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 value; brand value drivers; intellectual capital; brand valuation process

The value of tax shields is not equal to the present value of tax shields

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. Since the existence of leverage costs is independent of taxes, the value of tax shields when there are no taxes should be negative. We later on look at the case of constant growth and derive similar implications. We then identify 9 valuation theories proposed in the literature to estimate the present value of tax shields and show that only one valuation method is consistent when we look at the case of constant growth and no leverage costs. Three theories provide consistent valuations once leverage costs and growth are allowed for. For constant growth companies, 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 this does not mean that the appropriate discount for the tax shields is the unlevered cost of equity. We discount D T Ku, which is higher than the shield. This expression arises as the difference of two present values, each with different riskFinancial management;

Equivalence of the different discounted cash flow valuation methods. Different alternatives for determining the discounted value of tax shields and their implications for the valuation

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 available for equity holders discounted at the required return on the equity flows; 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 differ only 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 discounted value of tax shields (DVTS). The paper shows and analyses 7 different theories on the calculation of the DVTS: Modigliani and Miller (1963), Myers (1974), Miller (1977), Miles and Ezzell (1980), Harris and Pringle (1985), Ruback (1995), Damodaran (1994), and Practitioners method. It is shown that Myers' method (1974) gives inconsistent results. 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 firms; cash flow valuation methods;