Trắc nghiệm kiến thức chứng khoán Mỹ tại : www.net A Theory of the Firm’s Cost of Capital How Debt Affects the Firm’s Risk, Value, Tax Rate and the Government’s Tax Claim Trắc nghiệm kiến thức chứng khoán Mỹ tại : www.net This page intentionally left blank Trắc nghiệm kiến thức chứng khoán Mỹ tại : www.net A Theory of the Firm’s Cost of Capital How Debt Affects the Firm’s Risk, Value, Tax Rate and the Government’s Tax Claim Ramesh K S Rao University of Texas at Austin, USA Eric C Stevens USA World Scientific Trắc nghiệm kiến NEW JERSEY• thức LONDON • chứng khoán SINGAPORE•BEIJING• Mỹ tại : www.net SHANGHAI •HONG KONG TA I P E I • • CHENNAI Published by World Scientific Publishing Co. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE Library of Congress Cataloging-in-Publication Data Rao, Ramesh K. A theory of the firm’s cost of capital : how debt affects the firm’s risk, value, tax rate, and the government’s tax claim / by Ramesh K. Includes bibliographical references.
Capital assets pricing model.6'04101--dc22 2006052555 British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. Copyright © 2007 by World Scientific Publishing Co. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher.
For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. Typeset by Stallion Press Email: enquiries@stallionpress.com Printed in Singapore. Trắc nghiệm kiến thức chứng khoán Mỹ tại : www.net CheanChian - A theory of the filrm;s.pmd 1 4/17/2007, 5:13 PM December 12, 2006 15:11 spi-b456 A Theory of the Firm’s Cost of Capital 9in x 6in fm 3rd Reading Preface Modigliani and Miller’s (MM) seminal analyses spawned two broad research strands in corporate finance, the first relating to the effects of leverage on the firm risk and cost of capital, and the second to the firm’s optimal capital structure (mix of debt and equity).
This book is concerned with the first, and it is a slightly expanded version of our paper that was published by the Berkeley Electronic Journals in Economic Analysis and Policy.* Our original motivation for this research was the “pie-slicing” analogy that is the core intuition of modern corporate finance theory. In essence, the firm’s investment decision determines the size of the economic pie that the firm creates, and debt and equity are simply two different claims on this pie. Thus, as MM argued, it does not matter, in frictionless capital markets, how this pie is sliced; the firm’s capital structure is unimportant. When this intuition is extended to include corporate taxes, the size of the pie is determined by the firm’s after-tax cash flows and, in this case, thanks to the government’s ∗ Rao, RKS and EC Stevens (2006).
The firm’s cost of capital, its effective marginal tax rate, and the value of the government’s tax claim. Topics in Economic Anal- ysis & Policy, 6(1), Article 3, published by Berkeley Electronic Press, available at http://www.com/bejeap/topics/vol6/iss1/art3. This article is adapted here with permission. v Trắc nghiệm kiến thức chứng khoán Mỹ tại : www.net December 12, 2006 15:11 spi-b456 A Theory of the Firm’s Cost of Capital 9in x 6in fm 3rd Reading vi A Theory of the Firm’s Cost of Capital subsidy of the firm’s interest payments, maximizing debt becomes optimal.
With taxes, there are now three claimants to the economic pie— stockholders, bondholders and the tax authority. Thus, one should, in principle, be able to value the firm as the sum of the values of three claims. Although this intuition was well known, we did not see a satisfactory formal analysis of the “three claims view of the firm” with risky debt and corporate tax effects. The literature’s focus was on “two claims models” of the firm.
Our primary goal, thus, was to develop a theoretical framework that can identify how the value of the government’s tax claim varies with corporate borrowing. In the analysis that is presented here, the value of the firm is consistent with the standard perspective that the firm’s after-tax output is dis- tributed between the debt and the equity, and also with the view that the pre-tax output is apportioned among three risky claims, with the tax authority being the third claimant. As we worked on this research, it became clear that with risky debt and corporate taxes it is critical to understand how the risks of the firm’s depreciation and the debt tax shields change with leverage. To our knowledge, the risk of the tax shields had not been adequately formalized in the research, and authors have relied on various ad hoc assumptions about the tax shields’ risks.
A second research goal, therefore, was to model how the tax shields’ risks are affected by leverage. The outcome of this effort, which is presented here, is a frame- work for better measuring the firm’s cost of capital while, at the same time, identifying the marginal effects of debt policy on market val- ues, risks, and expected rates of return. The ability of our model to capture several important economic interdependencies (e., between the borrowing rate and the tax shields) within a simple analytical framework allows us to illustrate the model with numerical examples and graphical illustration. As we discuss, the model can be used to generate better estimates of the firm’s cost of capital and marginal Trắc nghiệm kiến thức chứng khoán Mỹ tại : www.net December 12, 2006 15:11 spi-b456 A Theory of the Firm’s Cost of Capital 9in x 6in fm 3rd Reading Preface vii corporate tax rates.
In addition, it provides a conceptual framework for evaluating the implications of exogenous market forces (e., inter- est rates, tax laws, the market price of risk) on the firm’s economic balance sheet and on the value of the government’s claim on output, and thus may be useful for studies of tax and public policies. We are grateful to the Berkeley Electronic Press for permission to reproduce our earlier paper in modified form. We also thank our spouses for their support, and the colleagues that have provided feed- back on various drafts of the manuscript. Finally, we thank the staff of World Scientific, namely Juliet Lee, Venkatesh Sandhya, Chean Chian Cheong and Hooi-Yean Lee for their efforts at bringing this book into the present form.
Rao Austin, Texas, USA Eric C. Stevens Salt Lake City, Utah, USA September 2006 Trắc nghiệm kiến thức chứng khoán Mỹ tại : www.net December 12, 2006 15:11 spi-b456 A Theory of the Firm’s Cost of Capital 9in x 6in fm 3rd Reading This page intentionally left blank Trắc nghiệm kiến thức chứng khoán Mỹ tại : www.net December 12, 2006 15:11 spi-b456 A Theory of the Firm’s Cost of Capital 9in x 6in fm 3rd Reading Contents Preface v List of Figures xi List of Tables xiii I. Model Setting 5 III. Distributional Assumptions 19 IV.
Model Solution Procedure 23 V. Discussion of Results 33 VI. Extension to s × s states 45 VII. Numerical Illustration 47 VIII.
Conclusion 57 Appendix A 63 Appendix B 77 References 85 Index 89 ix Trắc nghiệm kiến thức chứng khoán Mỹ tại : www.net December 12, 2006 15:11 spi-b456 A Theory of the Firm’s Cost of Capital 9in x 6in fm 3rd Reading This page intentionally left blank Trắc nghiệm kiến thức chứng khoán Mỹ tại : www.net December 12, 2006 15:11 spi-b456 A Theory of the Firm’s Cost of Capital 9in x 6in fm 3rd Reading List of Figures 1. Output apportionment diagrams for the tax shields and claims. Impact of an incremental debt dollar on levered firm risk and value. Par yield (r) and the cost of debt (kD ) for the numerical examples.
Risk of the tax shields for the numerical examples. Cost of equity, kE , cost of debt, kD , and the WACC for the numerical examples. WACC from the numerical examples, and WACC computed using r(1 − T ), r(1 − M T R) as proxies for kD. Expected post-financing MTR for the numerical examples.
55 xi Trắc nghiệm kiến thức chứng khoán Mỹ tại : www.net December 12, 2006 15:11 spi-b456 A Theory of the Firm’s Cost of Capital 9in x 6in fm 3rd Reading This page intentionally left blank Trắc nghiệm kiến thức chứng khoán Mỹ tại : www.net December 12, 2006 15:11 spi-b456 A Theory of the Firm’s Cost of Capital 9in x 6in fm 3rd Reading List of Tables 1. Tax shield use, tax status, and financial solvency for different levels of output X̃ and of debt D in relation to assets A. Output apportionment for tax shields and claims. Pricing cases for the 2 × 2 model.
Illustration of valuation of the depreciation tax shield. Debt pricing for the 2 × 2 model. Relative magnitude of risks of the debt tax shield, the unlevered firm and the debt, for the 2 × 2 model with θx > 0. Value of the levered firm and the marginal value impact of debt.
Numerical illustration: parameters assumed. Risk of the tax shields and claims for each pricing case (Table 3), computed using Equation (12) and the output apportionment formulas (Table 2). Post-financing expected MTR computed as the expected value of the applicable tax rate. 76 xiii Trắc nghiệm kiến thức chứng khoán Mỹ tại : www.net December 12, 2006 15:11 spi-b456 A Theory of the Firm’s Cost of Capital 9in x 6in fm 3rd Reading xiv A Theory of the Firm’s Cost of Capital B.
Results for the 2 × 2 example, for seven debt levels. Results for the 5 × 5 example, for seven debt levels. 81 Trắc nghiệm kiến thức chứng khoán Mỹ tại : www.net December 12, 2006 11:29 spi-b456 A Theory of the Firm’s Cost of Capital 9in x 6in ch01 3rd Reading Chapter I Introduction The cost of capital is perhaps the most fundamental and widely used concept in financial economics. Business managers and regulators routinely employ estimates of the firm’s weighted average cost of capital (WACC ) and the marginal tax rate (MTR) for investment decisions, rate regulation, restructuring activities, and bankruptcy valuation.1 In economics, the cost of capital and the MTR are cen- tral to the research on tax policy, regulation, and welfare analysis.2 1 The MTR is the expected effective tax rate on an incremental dollar of taxable income arising from debt financing, holding investment fixed, and is the sum of the products of the tax rates (tax payment divided by taxable income) in each state of nature multiplied by the relevant state probability.
Fullerton (1984) provides a taxonomy of various definitions of the effective tax rate in economics. Also see Graham (1996b) and Graham and Lemmon (1998). 3) notes that the cost of capital “is now a standard variable in the analysis of macroeconomics and of investment behavior at the firm, industry and economy-wide levels. It has also become a standard tool for the assessment of economic impacts of changes in tax policy.
The concepts of the ‘cost of capital’ and its associated measure of a ‘marginal tax rate’ have generated a voluminous literature in the economics of taxation. The ‘cost of capital’ has been incorpo- rated into both conventional macroeconomic models and intertemporal general equilibrium models of the impacts of tax policy.” 1 Trắc nghiệm kiến thức chứng khoán Mỹ tại : www.