Getting the valuation formulas right when it comes to annuities

PurposeThe purpose of this paper is to establish the flow-to-equity method, the free cash flow (FCF) method, the adjusted present value method and the relationships between these methods when the FCF appears as an annuity. More specifically, we depart from the two most widely used evaluation settings. The first setting is that of Modigliani and Miller who based their analysis on a stationary FCF. The second setting is that of Miles and Ezzell who worked with an FCF that represents an autoregressive possess of first order.Design/methodology/approachInspired by recent observations in the literature concerning cash flows, discount rates and values in discounted cash flow (DCF) methods, we mathematically derive DCF valuation formulas for annuities.FindingsThe following relationships are established: (a) the correct discount rate of the tax shield when the free cash flow takes the form of a first-order autoregressive annuity, (b) the direct valuation of the tax shield from the free cash flow for a first-order autoregressive annuity, (c) the correct translation from the required return on unlevered equity to the levered equity, when the free cash flow is a stationary annuity and (d) direct calculation of the unlevered and levered firm values and the value of the tax shield for a stationary annuity.Originality/valueUntil now the complete set of formulas for the valuation of stochastic annuities by different DCF methods has not been established in the literature. These formulas are developed here. These formulas are important for practitioners and academics when it comes to the valuation of cash flows of finite lifetime.

Zur kapitalwertorientierten Bewertung (nicht nur) von immateriellen Vermögenswerten in der internationalen Rechnungslegung

Zusammenfassung Der Beitrag ist der Bewertung (nicht nur) immaterieller Vermögenswerte mit kapitalwertorientierten Verfahren in der internationalen Rechnungslegung gewidmet. Unter der Annahme, dass das Problem der Zuordnung von Zahlungsüberschüssen zu einzelnen Vermögenswerten bzw. Gruppen von Vermögenswerten (Assets) gelöst ist, wird insbesondere die Wahl des kapitalwertorientierten Bewertungsverfahrens und die Ermittlung der zugehörigen Diskontierungssätze diskutiert. Es werden Empfehlungen zur Abbildung des Investitionsrisikos und der Finanzierung bei der Bewertung von Vermögenswerten unter Berücksichtigung der Marktwertadditivität erarbeitet. Es wird gezeigt, dass der in der Praxis beliebte WACC-Ansatz dafür häufig weniger geeignet ist als der Adjusted-Present-Value (APV) -Ansatz. Dieser sollte soweit es die Datenlage zulässt, Bottom-up ausgefüllt werden. Sofern auf die Daten als vergleichbar eingestufter Unternehmen (Peer Group) zurückgegriffen wird, muss die Vergleichbarkeit im ersten Schritt hinsichtlich des Investitionsrisikos gegeben sein, um so die Eigenkapitalkosten bei Eigenfinanzierung vermögenswertspezifisch zu schätzen. Weitere pragmatische Lösungsansätze, wie Top-down erfolgende Zu- oder Abschläge zum bzw. vom unternehmensweiten WACC oder der sog. WARA (Weighted Average Return on Assets) -Ansatz, werden hinsichtlich der implizierten Fremdkapital- und Wertzuordnungen sowie hinsichtlich der Einhaltung des Marktwertadditivitätsprinzips kritisch gewürdigt.

Adjustment of the WACC with Subsidized Debt in the Presence of Corporate Taxes: The Finite-Horizon Case

When discounting free-cash flows (FCF) at the Weighted Average Cost of Capital (WACC), we assume that the cost of debt is the market, unsubsidized rate. With debt at the market rate and perfect capital markets, debt only creates value in the presence of taxes through the tax shield. In some cases, the firm may be able to obtain a loan at a rate that is below the market rate. With subsidized debt and taxes, there would be a benefit to debt financing, and the unleveraged and leveraged values of the cash flows would differ. The benefit of lower tax savings are offset by the benefit of the subsidy. These two benefits have to be introduced explicitly. In this article, we present the necessary adjustments to the WACC and the cost of leveraged equity under the existence of subsidized debt and taxes in a multiple-period setting. We analyze the cases of the WACC applied to the FCF and the WACC applied to the capital-cash flows (CCF). We also utilize the Adjusted Present Value (APV) to consider both the tax savings and the subsidy. We show that all these different approaches give the same answer.

Valuation Of Fmcg Company Using Adjusted Present Value Model

Valuation is the process of finding the current net worth of the company or finding the fair & market rate of particular company by consider the market rate of the asset of the company, capital structure of the company. For calculating the current net-worth of the company researcher used APV model for the study. Objective of the paper is to find out the current net-worth of the company, the researcher adopted analytical research method. FCFF, WACC, ROIC and growth rate are data analysis tools used for the study are. From this research it is found that company has to focus on increasing its profit by reducing its expenses. Company has to improve their operations in order to increase in the return on invested capital.

Capital Allocation in Decentralized Businesses

This paper described a theory of capital allocation for decentralized businesses, taking into account the costs associated with risk capital. We derive an adjusted present value expression for making investment decisions, that incorporates the time varying profile of risk capital. We discuss the implications for business performance measurement.

DuPont Corporation: Sale of Performance Coatings

In January 2012, Ellen Kullman, CEO and chairman of DuPont, must decide whether to retain or sell the company's Performance Coatings (DPC) division. This is an introductory case on valuing a leveraged buyout. The case focuses on a publicly listed corporation's decision to divest a large division and asks students to compare the division's value if it remains under DuPont's control or is sold to an outside party. The transaction size of approximately $4 billion is too large for potential strategic buyers in the industry, making private equity (PE) firms the most likely bidders. The case provides a base-case adjusted present value (APV) model of DPC as a stand-alone company and gives students specific assignments to adjust it to reflect the division's potential value under PE ownership (e.g., EBITDA growth, multiple arbitrage, and increased leverage).The case is designed to illustrate and discuss the differences between a public company's valuation based on unlevered free cash flows and a PE sponsor's valuation based on residual (levered) cash flows.This case has been successfully taught in a second-year elective course covering entrepreneurial finance and private equity and in an advanced undergraduate course on corporate finance. It is appropriate for use in classes on private equity, advanced corporate finance, or deal valuation.