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Expected Inflation and the Constant-Growth Valuation Model* by Michael Bradley, Duke University, and Gregg A

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Expected Inflation and the Constant-Growth Valuation Model* by Michael Bradley, Duke University, and Gregg A VOLUME 20 | NUMBER 2 | SPRING 2008 Journal of APPLIED CORPORATE FINANCE A MORGAN STANLEY PUBLICATION In This Issue: Valuation and Corporate Portfolio Management Corporate Portfolio Management Roundtable 8 Panelists: Robert Bruner, University of Virginia; Robert Pozen, Presented by Ernst & Young MFS Investment Management; Anne Madden, Honeywell International; Aileen Stockburger, Johnson & Johnson; Forbes Alexander, Jabil Circuit; Steve Munger and Don Chew, Morgan Stanley. Moderated by Jeff Greene, Ernst & Young Liquidity, the Value of the Firm, and Corporate Finance 32 Yakov Amihud, New York University, and Haim Mendelson, Stanford University Real Asset Valuation: A Back-to-Basics Approach 46 David Laughton, University of Alberta; Raul Guerrero, Asymmetric Strategy LLC; and Donald Lessard, MIT Sloan School of Management Expected Inflation and the Constant-Growth Valuation Model 66 Michael Bradley, Duke University, and Gregg Jarrell, University of Rochester Single vs. Multiple Discount Rates: How to Limit “Influence Costs” 79 John Martin, Baylor University, and Sheridan Titman, in the Capital Allocation Process University of Texas at Austin The Era of Cross-Border M&A: How Current Market Dynamics are 84 Marc Zenner, Matt Matthews, Jeff Marks, and Changing the M&A Landscape Nishant Mago, J.P. Morgan Chase & Co. Transfer Pricing for Corporate Treasury in the Multinational Enterprise 97 Stephen L. Curtis, Ernst & Young The Equity Market Risk Premium and Valuation of Overseas Investments 113 Luc Soenen,Universidad Catolica del Peru, and Robert Johnson, University of San Diego Stock Option Expensing: The Role of Corporate Governance 122 Sanjay Deshmukh, Keith M. Howe, and Carl Luft, DePaul University Real Options Valuation: A Case Study of an E-commerce Company 129 Rocío Sáenz-Diez, Universidad Pontificia Comillas de Madrid, Ricardo Gimeno, Banco de España, and Carlos de Abajo, Morgan Stanley Expected Inflation and the Constant-Growth Valuation Model* by Michael Bradley, Duke University, and Gregg A. Jarrell, University of Rochester he Constant-Growth model is a discounted cash the incorrect transformations of this formula found throughout flow method of valuing companies and their the valuation literature for the value of a company that makes T projects that is taught in all top-tier business no new investments or invests only in zero NPV projects. schools and used widely throughout the finan- Perhaps the most common application of the Constant- cial community. It is found in virtually all graduate-level Growth model is its use in estimating what is referred to in corporate finance textbooks and valuation manuals. But, as the valuation literature as a company’s “continuation value” or, we found during an extensive review of this literature, there alternatively, its “terminal value.” When valuing a company, has no been careful, systematic analysis of the effects of infla- it is standard practice to estimate a company’s free cash flows tion on this model.1 As we show in the pages that follow, over a finite (say, five-year) forecast period, and then assume the failure to account properly for the effects of inflation that the firm will simply earn its cost of capital thereafter. The has led to what academics call a “misspecification,” and thus justification for this practice is the standard assumption of an incorrect use, of the model in a particular set of cases— financial economists that the arrival of competitors, along with those where a company is assumed either to make no net technological innovation and obsolescence, cause above-normal new investments or to invest only in zero net present value returns to become normal returns over time, and that, after the (NPV) projects. We show that the error produced by this forecast period, the firm will earn a normal rate of return on its misapplication of the model is significant even at moderate investments into perpetuity. The continuation value, as given levels of expected inflation. by Equation (1), is the present value of the expected free cash In addition to its reliance on operating cash flows rather flows beyond the forecast period into perpetuity.4 than earnings or P/E multiples, the main appeal of the The assumption that the company will earn only normal Constant-Growth valuation model is its simplicity. As shown rates of return during the post-forecast period is equiva- in Equation (1), lent to assuming that either the firm will make no new net investments—that is, capital expenditures will equal depreci- FCF (1)ation—or that any investments that are made will have zero V = 1 0 WG− NPVs. Using this “zero-rent” argument, financial economists often assert that the terminal value of the firm can be estimated the market value of the firm (V0) is a function of just three vari- by a simple perpetuity of next period’s free cash flows, with the ables: the expected free cash flows in the next (or first future) capitalization rate being the firm’s nominal cost of capital. This period (FCF1); the firm’s cost of capital (W); and the projected formulation is equivalent to setting G, the nominal growth growth rate of the firm’s future free cash flows (G).2 This model, rate in Equation (1), equal to zero: which can be found in virtually all finance textbooks, is always written in nominal terms as in Equation (1).3 FCF1 (2) V0 We have no quarrel with this equation. It is simply the W formula for a growing perpetuity. Rather, our quarrel is with * We thank Michael Barclay, John Coleman, Magnus Dahlquist, Doug Foster, Jennifer 2. According to Brealey, Myers and Allen, p. 65, this formula was first developed in Francis, John Graham, Campbell Harvey, David Hsieh, Albert “Pete” Kyle, Richmond 1938 by J.B. Williams and rediscovered in 1956 by M.J. Gordon and E. Shapiro. It is Mathews, Michael Moore, Stephen Penman, Michael Roberts, Frank Torchio, S. “Vish” often called the Gordon Growth Model. Viswanathan and Ross Watts for helpful comments. We have benefited from many dis- 3. Throughout this paper we adopt the convention of stating nominal variables in up- cussions over the years regarding these and related issues with Robert Dammon, Tim per-case letters and real variables in lower-case letters. Also, since the models developed Eynon, and, especially, Al Rappaport. herein are forward-looking, all rates should be thought of as expectations. 1. The popular valuation texts, Rappaport (1998), Copeland, Koller and Murin (1994) 4. Rappaport (1998) refers to the continuing value as the firm’s residual value, pp. and Cornell (1993) all discuss various aspects of the effects of inflation on the valuation 40-47. Also see Copeland et al. (1994), Chapter 9, “Estimating Continuing Value,” and process. However, none develops the effects of inflation on the Constant-Growth model Cornell (1993), Chapter 6, “Estimating the Continuing Value at the Terminal Date.” It from first principles, as we do in this paper. This is also the case for the leading textbook should be noted that the continuing value as given by Equation (1) is the value of the in the field, Brealey, Myers and Allen (2006). Our analysis most closely resembles that firm at the end of the forecast period. Thus, in order to find the present value as of to- of Rappaport. On page 47 he presents a formula for a “perpetuity with inflation” that is day, the terminal value has to be discounted by (1+W)T, where T is the end of the last equivalent to an important relation that we develop in this paper. forecast period. 66 Journal of Applied Corporate Finance • Volume 20 Number 2 A Morgan Stanley Publication • Spring 2008 We accordingly refer to this version of Equation (1) as the overvaluation of the firm. We develop a correction factor that, Zero-Nominal-Growth (“ZNG”) model. when added to the (nominal) M&M WACC formula, yields Use of the ZNG model, or the simple perpetuity formula, a company’s true nominal WACC in the face of inflation.6 is typically justified by the following reasoning: (1) with zero Finally, to complete our analysis, we show that the nominal net new investments, there will be no growth; and (2) growth WACC model developed by two finance academics—James through the acceptance of zero NPV projects does not affect Miles and John Ezzell—is compatible with any level of growth, the (present) value of the firm. Therefore, under either condi- whether attributable to inflation or real investments.7 tion, it is appropriate to set G = 0 in Equation (1) and rely on Equation (2). Although this logic might appear to be The Constant-Growth Model with Inflation sound, we show that this ZNG model is based on a mistaken Our analysis of the effects of inflation on the Constant- specification of the nominal growth in free cash flows—G in Growth model begins with a derivation of an expression for Equation (1)—in the presence of inflation. the firm’s nominal free cash flows (FCFt). We then derive Specifically, the generally accepted expression for the value an expression for the growth in nominal cash flows (G). We of a “zero-investment” or a “zero-NPV” firm—as presented defer our discussion of the appropriate discount rate (W) throughout the finance literature and typically applied in until our later discussion of the firm’s WACC. For present practice—ignores the effect of inflation on the company’s total purposes, suffice it to say that in the subsequent analysis, we (accumulated) invested capital. In the traditional Constant- assume that the firm’s nominal cost of capital (W) is consis- Growth model without inflation, if there is no new investment, tent with the Fisher Equation: there is no growth. However, in the presence of inflation, the value of the initial invested capital will grow at the rate of infla- W w0 + w=+ 0 (3) tion.
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