CONSTANT LEVERAGE AND CONSTANT COST OF CAPITAL: A COMMON KNOWLEDGE HALF-TRUTH

A typical approach for valuing finite cash flows is to assume that leverage is constant (usually as target leverage) and the cost of equity, Ke and the Weighted Average Cost of Capital, WACC are also assumed to be constant. For cash flows in perpetuity, and with the cost of debt, Kd as the discount rate for the tax shield, it is indeed the case that the Ke and WACC applied to the FCF are constant if the leverage is constant. However this does not hold true for finite cash flows. In this document we show that for finite cash flows, Ke and hence WACC depend on the discount rate that is used to value the tax shield, TS and as expected, Ke and WACC are not constant with Kd as the discount rate for the tax shield, even if the leverage is constant. We illustrate this situation with a simple example. We analyze five methods: DCF using APV, FCF and traditional and general formulation for WACC, present value of CFE plus debt and Capital Cash Flow, CCF.WACC, constant cost of capital, constant leverage, cash flows

VAIC: Nueva métrica de evaluación de desempeño gerencial y herramienta de evaluación de inversiones

Artículo de reflexiónEste artículo introduce una nueva métrica financiera para la evaluación del desempeño gerencial, el Valor Añadido de la Inversión de Capital (VAIC), con el costo de capital no apalancado como una tasa de corte para el cálculo de los requerimientos de capital en lugar del CPPC (WACC) ampliamente aceptado. VAIC conserva todas las características positivas de la utilidad operativa residual convencional y VEA (EVA®) y tiene la ventaja de la sencillez en su cálculo y una interpretación directa y clara. El modelo de valoración asociado es equivalente al método de flujo de caja descontado estándar; esta equivalencia se demuestra formalmente bajo ciertas hipótesis sobre el riesgo de los escudos fiscales (ahorros en impuestos) y confirma la consistencia de la nueva medida propuesta. VAIC puede servir como un indicador económico global en los cuadros de mando de desempeño empresarial, y bien podría ser considerado como un sustituto válido para el VEA (EVA©) ya establecido y ROI en la evaluación de desempeño de la gerencia. La equivalencia del modelo de valoración VAIC con el enfoque fundamental de la valoración de una empresa con flujos de caja descontados hace que este indicador no sea sólo una medida de solidez financiera, sino también una herramienta de valoración de inversiones en el más completo sentido

Subsidized loan financing and its impact on the cost of capital and levered firm value. A non-technical reply to "Adjustment of the WACC with subsi...

Debt financing with subsidizes interest rate has a multidimensional impact on the firm. Value of the levered equity, value of the debt and overall firm value will be different of those values with debt financing at market rate. Subsidized interest rate on debt does not create any additional cash flow and all the changes in values and the cost of capital are the result of the redistribution of cash flows among debt, equity and government, and subsequent reduction in financial risk due to lower leverage. In this note we show that the levered firm value with the loan provided at a rate below market rate is lower (or equal, in a no tax world) compared to the same firm value with the loan at market rate. For the given nominal value of debt the cost of capital of the levered firm with the subsidized interest rate is higher than the cost of capital of the same firm with `the market cost of debt, and “intuitive” adjustment of the WACC by direct substitution of the contractual interest rate into the classic WACC formulation produces inconsistent cost of capital estimate and flawed valuation. Debt financing with subsidized interest rate converts into the gain for the levered equity. This value gain originates from the value transfer from debt to equity and to ensure correct and consistent cost of capital and value estimates we need properly incorporate the effect of the subsidy in the interest rate on the cost of the levered equity. Required return to the levered equity with subsidized debt financing does not depend on the contractual interest rate. “Extended APV valuation” performed by adding value of the loan subsidy to the sum of the unlevered firm value and the value of the tax shield is based on inconsistent value relationship and leads to false results. To illustrate our non-technical discussion we use perpetuity model and a simple numerical example.

Endeudamiento constante y costo de capital constante: conocimientos generalizados parcialmente ciertos

Un enfoque típico para valorar flujos de caja finitos es suponer que el endeudamiento es constante (generalmente como un endeudamiento objetivo o deseado) y que por tanto, el costo del patrimonio, Ke y el costo promedio ponderado de capital CPPC, también son constantes. Para los flujos de caja perpetuos, y con el costo de la deuda, Kd como la tasa de descuento para el ahorro en impuestos o escudo fiscal, Ke y el CPPC aplicado al flujo de caja libre FCL son constantes si el endeudamiento es constante. Sin embargo esto no es verdad para los flujos de caja finitos. En este documento mostramos que para flujos de caja finitos, Ke y por lo tanto el CPPC dependen de la tasa de descuento que se utiliza para valorar el ahorro en impuestos, AI y según lo esperado, Ke y el CPPC no son constantes con Kd como la tasa de descuento para el ahorro en impuestos, aunque el endeudamiento sea constante. Ilustramos esta situación con un ejemplo simple. Analizamos cinco métodos: el flujo de caja descontado, FCD, usando APV, el FCD y la formulación tradicional y general del CPPC, el valor presente del flujo de caja del accionista, FCA más deuda y el flujo de caja de capital, FCC

Constant leverage and constant cost of capital: a common knowledge half-truth

In this teaching note we show that using the findings of Tham and Velez-Pareja 2002, for finite cash flows, Ke and hence WACC depend on the discount rate that is used to value the tax shield, TS and as expected, Ke and WACC are not constant with Kd as the discount rate for the tax shield, even if the leverage is constant. We illustrate this situation with a simple example. We analyze five methods: DCF using APV, FCF and traditional and general formulation for WACC, present value of CFE plus debt and Capital Cash Flow, CCF. In Tham and Velez-Pareja 2002, they derive a general expression for Ke, the cost of levered equity and for the Weighted Average Cost of Capital (WACC) applied to the Free Cash Flow (FCF) and Capital Cash Flow (CCF). For finite cash flows and perpetuities, the derivation presents the analysis for different levels of risk with respect to discounting the tax shields (TS). Taggart 1991 presents a revision of the set of formulations for the cost of levered Ke and WACC. He introduces the formulation with and without personal taxes and for different level of risk for discounting the TS, including the proposal by Miles and Ezzel 1980. However, Taggart does not include the case of Kd, the cost of debt as the level of risk for the TS and finite cash flows. A typical approach for valuing finite cash flows is to assume that leverage is constant (usually as target leverage) and the Ke and WACC are also assumed to be constant. For cash flows in perpetuity, and with Kd as the discount rate for the tax shield, it is indeed the case that the Ke and WACC applied to the FCF are constant if the leverage is constant. However this does not hold true for finite cash flows. Though it might be convenient to perform calculations under such assumption, it is not in fact always true that Ke and WACC are constant under the constant leverage financing policy. As could be seen from the findings and example of Inselbag and Kaufold (1997), and as a general expression for Ke and WACC derived by Tham and Velez-Pareja (2002) shows, both the cost of levered equity and the Weighted Average Cost of Capital depend on the value of the interest tax shield (VTS), and in the case of finite cash flows valuation they could be changing from period to period if certain choice is made for the rate to discount for the expected tax shields.

How the regulator overpays investor? A simple exposition of the principles of tariff setting

In this teaching note, we discuss the basic principles for tariff setting. Tariff setting is very important for regulated industries, such as water and power. The tariff should provide an appropriate risk-adjusted return to the investor. If the tariff were too low, then the investors would not be willing to invest. On the other hand, if the tariff were too high, then it would reduce the consumers’ welfare. We examine the Rate of Return method for calculating the tariff in a regulated firm. In the rate of return method, the tariff compensates the investor for all the costs that the investor incurs, including a fair return. We use the discounted cash flow approach to value the return that the investor receives. The results of both calculations must be consistent. In particular, using simple examples, we show that in the presence of a positive expected inflation rate, the typical tariff calculation, Rate of return method, is an overestimation of the required payment to the equity holder.