Cost Of Unlevered Equity Research Articles

Innate Measurement Bias in EVA and How to Fix It: The Story of TRI and ORI

Economic value added (EVA) is the performance metric bound to be biased by design. The measurement bias comes from contrasting NOPAT, which is a purely operating profit, with the capital charge on the money investors have put into the firm, which is calculated by applying the after tax WACC made-up to incorporate the financing side effects. Such a synthetic construct can be uninformative or even misleading, and therefore is doubtfully eligible to be the period measure of either operating or total performance.To eliminate distortions in measuring performance we have to (A) recognize the two sources of income attributable to the providers of funds, primary is the NOPAT generated by the firm’s core assets, and another is the financial side effects, generally the interest tax shield subsidy from the government; and (B) use the cost of unlevered equity (i.e. the risk of assets) as a hurdle rate to calculate the charge on the book invested capital. Splitting the aggregate financial result into the operating and side effect financing components enables an undistorted concurrent assessment of the operating and the overall performance by means of the Operating EVA (OEVA) and the Total EVA (TEVA) metrics respectively. TEVA is a better choice than the EVA for the purpose of measuring corporate performance, and OEVA is the index giving an informative snapshot of the ongoing operations. The TEVA and OEVA analysis is consistent with the free cash flow valuation and provides additional managerially relevant information for the performance evaluation.

Value Added to Invested Capital (VAIC): New Financial Performance Metric and Valuation Tool

This article introduces a new financial metric for managerial performance evaluation, Value Added to Invested Capital (VAIC), with the cost of unlevered equity as a hurdle rate to calculate the capital charge rather than the widely accepted WACC. VAIC preserves all positive features of the conventional residual operating income and EVA® and has the distinct advantage of computational simplicity and straightforward interpretation. Associated valuation model is equivalent to the standard discounted cash flow approach; this equivalence is formally proved under certain assumptions regarding the risk of tax shields and confirms consistency of the new metric proposed. VAIC can serve as an aggregate financial indicator on the business performance dashboards, and might as well be considered a valid substitute for the established EVA© and ReOI metrics in evaluating managerial performance. Equivalence of the VAIC valuation model to the fundamental approach of valuing a business by cash flow discounting makes this metric not only a robust measure of financial performance but also a full-fledged investment valuation tool.

Análisis De Portafolio, Diapositivas (Portfolio Analysis Slides)

This is a course material (slides) for the book Managerial Decision Making Under Risk and Uncertainty. The book is originally in Spanish and is untitled as Decisiones empresariales bajo riesgo e incertidumbre. The level of the book is basic. It handles very few mathematics and it is expected to be used by managers. This chapter presents the relationship between risk and return using the Markowitz portfolio analysis model and the Capital Asset Pricing Model CAPM. The chapter (and the slides) also presents a procedure to derive the efficient frontier and the optimum portfolio. Finally, it studies how to derive unlevered betas associated to Ku, the cost of unlevered equity, from levered betas.

Risky Tax Shields and Risky Debt: A Monte Carlo Approach

I identify three sources of risk for the tax shields: two of them associated to the risk of debt and one associated to the operating risk. I present a set of conditions for defining risky debt associated to cash flow and not to accounting earnings. I explain why realization of tax shields for finite cash flows in any period of time t are correlated to Earnings before Interest and Taxes and are not correlated to interest expenses at time t. I question the validity of Miles and Ezzell proposal.Using Monte Carlo Simulation I explore the behavior of the four basic cash flows, Earnings before Interest and Taxes plus Other income OI, and interest charges, with eight scenarios applied to a financial planning model. I conclude that the risk of tax shields is Ku, the unlevered cost of equity.

Constructing Consistent Financial Planning Models for Valuation

In this work we show a simplified financial planning model. In reality, financial planning models are huge and cumbersome. This is a very simplified model compared with what is found in practice. We present some basic principles for constructing the financial statements needed for valuation. We show in detail all the items of the financial model and show the formulae to be used for constructing the financial planning model. The relevant financial statements are: the Balance Sheet (BS), the Income statement (IS) and the Cash Budget (CB). The construction of the financial statements starts from input data and policies and/or targets (i.e. accounts receivable policy or target). With these targets or policies we can construct the financial statements. The contribution of this work is twofold: one is to show that we can construct financial statements without the use of plugs and circularity and the second is that we can use a very simple approach to construct cash flows and to value them. Keeping track of value creation is a major duty of management and this can be done with the proposed model. The model exhibits two parts. One is the proper financial statements forecast. The second one is a simple cash flow calculation and valuation exercise using the Capital Cash Flow and assuming the risk of the tax savings equal to Ku, the cost of unlevered equity

Valuing Enterprise Cash Flows

This paper presents a valuation method, which determines the enterprise value and cost of unlevered equity simultaneously through a numerical search using the enterprise cash flow forecast. The capital cash flow method is derived from the return expectations on the enterprise as a whole (i.e. the return on the asset), meaning that enterprise valuations may be performed without reference to the concept of tax-shield risk. This should come as a relief, as tax-shield risk is not measurable and hence hardly of any practical utility. Source code is provided with which the numerical search can be implemented.

A Step by Step Guide to Construct a Financial Model Without Plugs and Without Circularity for Valuation Purposes (Guia Paso a Paso Para Construir Estados Financieros Sin Cuentas De Cuadre 'Plugs' Y Sin Circularidad Para Efectos De Valoracion De La Empresa)

In this teaching note the reader finds a simplified financial model. In reality, financial models are huge and cumbersome. This is a very simplified model compared with what is found in practice. We present some basic principles for constructing the financial statements needed for valuation. The reader is encouraged to construct the financial statements for herself on a spreadsheet. The relevant financial statements are: the Balance Sheet (BS), the Income statement (IS) and the Cash Budget (CB). The construction of the financial statements starts from policies and/or targets (i.e. accounts receivable policy or target). With these targets or policies we can construct the financial statements. The first table to be constructed is the table of parameters. This table organizes all of the relevant information. The subsequent tables are linked to the table of parameters via formulas. We construct other supplementary tables that will be used in the construction of the main financial statements. We indicate the formulas that have to be utilized in the construction of the financial model. In the first line and in the first column the reader finds the letters and numbers corresponding to the Excel? spreadsheet in order to make it easier the localization and the construction of the formulas. In the last two columns we have written those formulas. Usually they correspond to the year 0 and/or year 1. When necessary, we show the formulas for other years and we indicate it. Shaded cells are for the input data. If the reader wishes to construct the model exactly as we did, she will be able to do that step by step.The contribution of this work is double: one is to show that we can construct financial statements without the use of plugs and circularity and the second is that we can use a very simple approach to construct cash flows and to value them.The model shown has two parts. One is the proper financial statements forecast. The second one is a simple cash flow calculation and valuation exercise using the Capital Cash Flow and assuming the risk of the tax savings equal to Ku, the cost of unlevered equity.

A Step by Step Guide to Construct a Financial Model Without Plugs and Without Circularity for Valuation Purposes

In this teaching note the reader finds a simplified financial model. In reality, financial models are huge and cumbersome. This is a very simplified model compared with what is found in practice. We present some basic principles for constructing the financial statements needed for valuation. The reader is encouraged to construct the financial statements for herself on a spreadsheet. The relevant financial statements are: the Balance Sheet (BS), the Income statement (IS) and the Cash Budget (CB). The construction of the financial statements starts from policies and/or targets (i.e. accounts receivable policy or target). With these targets or policies we can construct the financial statements. The first table to be constructed is the table of parameters. This table organizes all of the relevant information. The subsequent tables are linked to the table of parameters via formulas. We construct other supplementary tables that will be used in the construction of the main financial statements. We indicate the formulas that have to be utilized in the construction of the financial model. In the first line and in the first column the reader finds the letters and numbers corresponding to the Excel spreadsheet in order to make it easier the localization and the construction of the formulas. In the last two columns we have written those formulas. Usually they correspond to the year 0 and/or year 1. When necessary, we show the formulas for other years and we indicate it. Shaded cells are for the input data. If the reader wishes to construct the model exactly as we did, she will be able to do that step by step.The contribution of this work is double: one is to show that we can construct financial statements without the use of plugs and circularity and the second is that we can use a very simple approach to construct cash flows and to value them.The model shown has two parts. One is the proper financial statements forecast. The second one is a simple cash flow calculation and valuation exercise using the Capital Cash Flow and assuming the risk of the tax savings equal to Ku, the cost of unlevered equity.

Deriving the Capital Cash Flow Method as a Rational Return Expectation

This note shows that a rational investor (as defined here) will use the capital cash flow (CCF) method to perform enterprise valuations, which implies that the most appropriate discount rate for the tax benefits of debt is the cost of unlevered equity. This result is useful as the CCF method allows derivation of a stable expression for the cost of unlevered equity in terms of the cost of levered equity and the cost of debt—irrespective of the shape of the cash-flow forecast.

Cash Flow Valuation

This paper aims (a) to show that the expression for the weighted average cost of capital generally used in the finance literature is only valid if the firm's debt is short-term in nature, and to provide an alternative expression that is valid irrespective of the maturity of the firm's debt; (b) to develop a new method for forecasting the cost of levered equity; (c) to show that it is possible to determine the enterprise value and the cost of unlevered equity simultaneously through a numerical search using the enterprise cash flow forecast; and (d) to demonstrate that enterprise valuations may be performed without reference to Modigliani and Miller's concept of tax-shield risk. This paper collects and improves the results of Schmidle (2006a, b, c), while at the same time correcting the inappropriate definition of the cost of levered equity used there.

Eva© Made Simple: Is it Possible? (Una Forma Sencilla De Calcular El Eva© )

Velez-Pareja and Tham, 2003a, Velez-Pareja and Tham, 2003b and Tham and Velez-Pareja, 2004 showed the matching between discounted cash flow (DCF) methods and value added methods. They departed from the net operating profit less adjusted taxes NOPLAT and net income when using market values to calculate the weighted average cost of capital (WACC) and the cost of levered equity, Ke. In those previous works they assumed that the proper discount rate for the tax savings is the unlevered cost of equity, Ku. We assume the same discount rate in this paper. The previous procedures implied circularity between the cost of capital and the levered values. In this paper we show that the same firm values can be obtained using the cost of unlevered equity, Ku and the net income and the interest charges. No circularity is found using this procedure. This article is based upon Velez-Pareja and Tham 2004.

EVA(c) Made Simple: Is it Possible?

Velez-Pareja and Tham, 2003a, Velez-Pareja and Tham, 2003b and Tham and Velez-Pareja, 2004 showed the matching between discounted cash flow (DCF) methods and value added methods. They departed from the net operating profit less adjusted taxes NOPLAT and net income when using market values to calculate the weighted average cost of capital (WACC) and the cost of levered equity, Ke. In those previous works they assumed that the proper discount rate for the tax savings is the unlevered cost of equity, Ku. We assume the same discount rate in this paper. The previous procedures implied circularity between the cost of capital and the levered values. In this paper we show that the same firm values can be obtained using the cost of unlevered equity, Ku and the net income and the interest charges. No circularity is found using this procedure.

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

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.

The Use of Capital Cash Flow and an Alternate Formulation for 
 WACC with Foreign Currency Debt

In this note we show with a simple example the proper way to use the adjusted WACC , the Cash Flow to Equity and the Capital Cash Flow, CCF to calculate the levered value of a firm when it has debt in foreign currency (FC). In this note we assume we are valuating the firm in the context of the domestic currency. We calculate the levered value of a firm using four approaches: the WACC for the Free Cash Flow, FCF, the adjusted WACC (that takes into account the tax savings, TS in absolute terms), the Capital Cash Flow discounted with the unlevered cost of equity and the independent calculation of the levered equity. Except for the calculation with CCF, all of them have to solve the circularity that arises between the cost of capital and the levered value. All the approaches match. However, the WACC for FCF takes into account the effect of tax savings through the factor (1-T) and the other approaches need to consider not only the tax savings related to the interest charges, but the tax savings associated with the losses in exchange for the debt.

The Value of Tax Shields is NOT Equal to the Present Value of Tax Shields

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.

The Correct Value of Tax Shields

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.

Equivalence of the APV, WACC and Flows to Equity Approaches to Firm Valuation

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.

On The Relevance And The Irrelevance Of Personal Income Taxes For The Valuation Of Equity Investments

This paper presents a comprehensive and consistent valuation approach including investor taxes (personal taxes) in addition to corporate taxes. It is shown that personal taxes do not influence the valuation result as long as the expected rate of return of an alternative investment opportunity is used as a discount rate, which is comparable in all relevant dimensions. These dimensions are the growth rates of expected cash flows, the risk associated with this growth profile, and the taxation of these cash flows relative to the taxation of potential capital gains. If, however, the alternative investment opportunity is taxed differently, e.g., by means of different tax rates to be applied or different treatment of capital gains, personal taxes become relevant. The valuation approach then has to account for the relative difference in taxation. It is shown how to modify unlevered cost of equity, cost of debt, and the weighted average cost of capital.

The Value of Tax Shields is the Difference of Two Present Values with Different Risk

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.

Equilibrium in the Pricing of Capital Assets, Risk-Bearing Debt Instruments, and the Question of Optimal Capital Structure

After integrating risky debt instruments into the generalized asset pricing model developed by Sharpe and Lintner, we have demonstrated that the required return-to-equity capital in this model is a linear function of the debt-to-equity ratio with a slope equal to the difference between the unlevered cost of equity and the direct cost of debt. Consequently, we take the average cost of capital to be invariant with respect to leverage. The particular nature of the debt instrument issued by the firm does not affect this result.Our analysis supporting the net operating income valuation construct is of interest in that it takes into account not only the variance of the probability distribution of equity returns but also the covariance relationships between these returns and all other returns in the system. Further, we need not rely on assumptions of “equivalent return” classes or arbitrage possibilities to arrive at our solution. More important, our conclusion is quite general in that we demonstrate indifference toward finance with any instrument regardless of its inherent risk characteristics.