### Valuing Companies By Cash Flow Discounting: Ten Methods And Nine Theories

University of Navarra – IESE Business School

November 17, 2015

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**Abstract: **

This paper shows 10 valuation methods based on equity cash flow; free cash flow; capital cash flow; APV (Adjusted Present Value); business’s risk-adjusted free cash flow and equity cash flow; risk-free rate-adjusted free cash flow and equity cash flow; economic profit; and EVA.

All 10 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 or parameters 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, lists the most important assumptions and valuation equations according to each of these theories, and provides an example in which the VTS of a company with debt of 1,500 goes from zero to 745.

Note: Previoulsy Titled: Valuing Companies by Cash Flow Discounting: Eight Methods and Six Theories

### Valuing Companies By Cash Flow Discounting: Ten Methods And Nine Theories – Introduction

**An example. Valuation of the company Toro Inc.**

The company Toro Inc. has the balance sheet and income statement forecasts for the next few years shown in Table 1. After year 3, the balance sheet and the income statement are expected to grow at an annual rate of 2%. Using the balance sheet and income statement forecasts in Table 1, we can readily obtain the cash flows given in Table 2. Obviously, the cash flows grow at a rate of 2% after year 4.

The unlevered beta is 1. The risk-free rate is 6%. The cost of debt is 8%. The corporate tax rate is 35%. The required market risk premium1 is 4%. With these parameters, the valuation of this company’s equity, using the above equations, is given in Table 3.

The required return to equity (Ke) appears in the second line of the table. The required return to equity (Ke) has been calculated according to Fernandez (2007) (see Appendix 1). Equation [1] enables the value of the equity to be obtained by discounting the equity cash flows at the required return to equity (Ke). Likewise, equation [2] enables the value of the debt to be obtained by discounting the debt cash flows at the required return to debt (Kd). The value of the debt is equal to the nominal value (book value) given in Table 1 because we have considered that the required return to debt is equal to its cost (8%). Another way to calculate the value of the equity is using equation [4]. The present value of the free cash flows discounted at the WACC (equation [5]) gives us the value of the company, which is the value of the debt plus that of the equity. By subtracting the value of the debt from this quantity, we obtain the value of the equity. Another way of calculating the value of the equity is using equation [6]. The present value of the capital cash flows discounted at the WACCBT (equation [7]) gives us the value of the company, which is the value of the debt plus that of the equity. By subtracting the value of the debt from this quantity, we obtain the value of the equity. The fourth method for calculating the value of the equity is using the Adjusted Present Value, equation [9]. The value of the company is the sum of the value of the unlevered company (equation [10]) plus the present value of the value of the tax shield (VTS). As the required return to equity (Ke) has been calculated according to Fernandez (2007), we must also calculate the VTS accordingly: VTS = PV (Ku; D T Ku).

The business risk-adjusted equity cash flow and free cash flow (ECF\Ku and FCF\Ku) are also calculated using equations [14] and [12]. Equation [13] enables us to obtain the value of the equity by discounting the business risk-adjusted equity cash flows at the required return to assets (Ku). Another way to calculate the value of the equity is using equation [11]. The present value of the business risk-adjusted free cash flows discounted at the required return to assets (Ku) gives us the value of the company, which is the value of the debt plus that of the equity. By subtracting the value of the debt from this quantity, we obtain the value of the equity.

The economic profit (EP) is calculated using equation [16]. Equation [15] indicates that the value of the equity (E) is the equity’s book value plus the present value of the expected economic profit (EP) discounted at the required return to equity (Ke).

The EVA (economic value added) is calculated using equation [18]. Equation [17] indicates that the equity value (E) is the present value of the expected EVA discounted at the weighted average cost of capital (WACC), plus the book value of the equity and the debt (Ebv0+ N0) minus the value of the debt (D).

The risk-free-adjusted equity cash flow and free cash flow (ECF\RF and FCF\RF) are also calculated using equations [22] and [20]. Equation [21] enables us to obtain the value of the equity by discounting the risk-free-adjusted equity cash flows at the risk-free rate (RF). Another way to calculate the value of the equity is using equation [19]. The present value of the risk-free-adjusted free cash flows discounted at the required return to assets (RF) gives us the value of the company, which is the value of the debt plus that of the equity. By subtracting the value of the debt from this quantity, we obtain the value of the equity.

Table 3 shows that the result obtained with all ten valuation methods is the same. The value of the equity today is 3,958.96. As I have already mentioned, these valuations have been performed according to the Fernandez (2007) theory. The valuations performed using other theories are discussed further on.

Tables 4 to 11 contain the most salient results of the valuation performed on the company Toro Inc. according to Damodaran (1994), Practitioners method, Harris and Pringle (1985), Myers (1974), Miles and Ezzell (1980), Miller (1977), With-cost-of-leverage theory, and Modigliani and Miller (1963).

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