Inflation Adjusted Economic Value Added (EVA )

Transcription

1 Inflation Adjusted Economic Value Added (EVA ) George W. Blazenko Simon Fraser University Faculty of Business Administration Burnaby, British Columbia January 22 Tel Facs blazenko@sfu.ca Download:

2 Inflation Adjusted Economic Value Added (EVA ) Abstract In this paper, we measure economic profit in an inflationary environment. Inflation adjusted EVA requires two principal alterations. First, we obtain the replacement cost of assets by adjusting the book value of non-current assets for past inflation. This adjustment reduces EVA because replacement cost tends to exceed book value. Second, we add a term to EVA to represent a manager s ability to increase product price as costs increase. This adjustment is positive because this ability adds value to the business. When assets are largely current, the second adjustment dominates because the first is not necessary. In this case, EVA underestimates economic profit. Economic profit remains positive when the rate of return on invested capital, after tax and after depreciation, is less than the weighted average cost of capital by as much as the rate of inflation. Even when inflation is modest, unadjusted EVA has the potential to seriously misrepresent the operating performance of business investments. Keywords: Economic Value Added, inflation. JEL classification code: G3 ii

3 INTRODUCTION The measurement of economic profit, that is, the dollar excess above that which keeps capital over the long-term in its current employment, originates in the classic works of Smith [15], Ricardo [14] and Marshall [11]. More recently, a number of financial authors and business consultants have rejuvenated the study of economic profit for the purpose of evaluating corporate operating performance, capital allocation, strategic planning, and for portfolio decisions. 1 The most prominent of the metrics and measures from this rejuvenation is Stern Stewart & Co. s EVA. To calculate EVA, an opportunity cost for capital is subtracted from net operating income after tax (NOI). The opportunity cost is the weighted average cost of capital (WACC) times invested capital (IC). 2 In practice, Weaver [16] finds that firms measure these three component terms of EVA in a variety of different ways. IC depends on the rearrangement of accounts from a firm s GAAP-based balance sheet to represented operating and financial assets. See COMPUSTAT [2] for a common definition of invested capital. Young [17] summarizes a number of accounting adjustments to NOI and IC that help better represent economic profit. Weaver finds that all of the respondents in his survey of corporate EVA adopters use the capital asset pricing model for the opportunity cost of equity within the WACC, but divergence arises in the market risk premium and market versus book versus target value weights. While these accounting adjustments are important, in this paper, we investigate economic adjustments to EVA required to correctly measure economic profit. We measure economic profit in an inflationary environment. Inflation adjusted EVA requires two 1

4 principal alterations. First, we obtain the replacement cost of assets by adjusting the book value of non-current assets for past inflation. This adjustment reduces EVA because replacement cost tends to exceed book value. Second, we add a term to EVA to represent a manager s ability to increase product price as costs increase. This adjustment is positive because this ability adds value to the business. When assets are largely current, the first adjustment is not necessary, and therefore, the second dominates. In this case, EVA underestimates economic profit. Because inflation and inflation predictions are relatively easy to establish, inflation adjusted EVA (IEVA) is only modestly more difficult to implement than is EVA. EVA is often interpreted as the annualized increment to wealth created by managers for the owners of the business. Thus, the discounted value of predicted future EVA should equal total wealth creation. Total wealth creation is the value of assets less capital employed. Hartman [8] and Shrieves and Wachowicz [13] demonstrate this relation between EVA and total wealth creation. We use this principle to show that in an inflationary environment, the opportunity cost that is applied against the replacement cost of assets should be the real weighted average cost of capital rather than the nominal weighted average cost of capital (WACC). In other words, the nominal WACC is an unduly harsh charge on capital in EVA. When this charge is changed to the real WACC, which is lesser, and if there is little difference between book and replacement cost of assets because assets are mainly current, then EVA underestimates economic profit measured by IEVA. 2

5 De Villiers [5] also studies EVA and inflation, he presumes that inflation distorts the measurement of EVA only because financial statements do not inflation-adjust the book values and depreciation charges of non-current assets. In this paper, we show that inflation distorts EVA even for businesses that have only current assets. For these businesses, EVA under-represents economic profit by approximately the rate of inflation times invested capital. PRELIMINARIES A manager operates a business for which real operating earnings before interest, before tax, and before depreciation (EBITDA) are random and non-growing. 3 If EBITDA follows a non-growing random walk, then predicted future EBITDA for every future period equals the current value of EBITDA. 4 Thus, in the following, we do not distinguish between predicted future EBITDA and its current value. Of course, while predicted future real EBITDA does not grow, nominal EBITDA grows at the expected rate of inflation. Denote the replacement cost of invested capital as RIC. If the opportunity cost of operating a business to owners is the piece-by-piece sale of assets so that these owners can invest elsewhere (at the cost of capital), then RIC represents the net receipt from this liquidation. We presume no difference between liquidation value and replacement cost. BIC is the book value of invested capital as obtained from a rearrangement of the GAAPbased balance sheet. See COMPUTSTAT [2] for a standard definition of invested capital in terms of its component pieces. We denote this measure with the notation BIC. The 3

6 replacement cost of assets (RIC) typically exceeds the book value (BIC) because inflation dilutes the reporting of past non-current asset expenditures. Denote current assets, when measured as a fraction of the replacement cost of all assets, with the symbol γ. The replacement cost of current and non-current assets is γ RIC and (1 γ )RIC respectively. Define economic depreciation as the reduced ability of an asset to generate future cash flows. From a set of predicted future cash flows, Bierman and Smidt [1] illustrate a methodology to determine a per-period depreciation charge to reflect this economic depreciation. 5 When real cash flows decline geometrically, a constant per-period real investment in non-current assets offsets the adverse effect of economic depreciation. We describe this per-period investment as maintenance capital expenditure. 6 In the absence of maintenance capital expenditures, if the decline in real cash flows is δ 1% per period, then in our case, the real maintenance capital expenditure must be (1 γ ) δ RIC per period. We presume that the managers of the business make these per-period real maintenance capital expenditures to offset economic depreciation. 7 This presumption is consistent with non-declining real EBITDA. In other words, our presumption requires that maintenance capital expenditures be positive NPV investments. Otherwise, managers do not make these investments, in which case, we must redo our analysis for a declining rather than a non-growing business. At least as an approximation, in the absence of maintenance capital expenditures, the 4

7 inverse of δ measures the economic life of an asset that faces economic depreciation at the rate δ 1% per period. Other than possible tax effects, 8 the economic life of an asset is independent of inflation. Thus, we presume that δ is also the rate that management uses in the declining balance method for financial reporting to represent economic depreciation. BOOK VERSUS REPLACEMENT COST OF NON-CURRENT ASSETS If π is the rate of inflation, 9 if δ is the rate of depreciation for reporting, if the manager has made t-1 yearly maintenance capital expenditures of (1 γ ) δ RIC dollars each in real terms, and if (1 γ )RIC is the initial investment in non-current assets (also measured in real terms), then, today (that is, time ), the reported value of non-current assets net of accumulated depreciation, that is, net fixed assets (NFA), is NFA ( ) = t 1 δ 1 δ 1 δ 1 γ ) δric + (1 γ ) δric (1 γ ) δric + (1 γ ) RIC (1) 1+ π 1+ π 1+ π ( t 1 t The first term on the right hand side of Eq. (1) is the maintenance capital expenditure made in the last instant. The penultimate term is the depreciated book value of the nominal maintenance capital expenditure made t-1 years ago. The last term is the depreciated book value of the initial non-current asset investment made t years ago. In real terms, the initial investment is (1 γ )RIC, in nominal terms, it is (1 γ ) RIC. (1 + π ) t Eq. (1) simplifies as, 5

8 t t (1 γ ) δric (1 + π ) 1 δ 1 δ NFA ( t) = 1 + (1 γ ) RIC (2) π + δ 1+ π 1+ π To reduce notation, presume a business for which t is large. Then, NFA = lim NFA ( ) = t t 1 γ ) δric (1 + π ) π + δ ( (3) As t increases, the book value of the initial investment (the last term in Eq. 2) approaches zero. Because the initial investment is in the distant past, inflation dilutes its book value to zero. A little algebra shows that the book value of non-current assets ( NFA ) is less than the replacement cost (( 1 γ ) RIC ) when inflation is positive ( π > ), NFA = 1 γ ) δric (1 + π ) π + δ ( ( 1 γ ) RIC, when π At the same time, when inflation is zero, the book value of non-current assets equals the replacement cost ( NFA = 1 γ ) RIC, when π ) ( =. Similarly, reported depreciation is less than economic depreciation, reflected in maintenance capital expenditures, when inflation is positive ( δ NFA δ(1 γ) RIC when π ) < >. If reported depreciation understates economic depreciation, then reported earnings overstate economic earnings. Lee, Press, and Choi [1] arrive at this conclusion from their empirical tests. They recognize historical cost depreciation as a primary distortion in financial statements. Note that a rearrangement of Eq. (3) gives a formula for the replacement cost of assets 6

9 ( RIC ) as a function of the book value of non-current assets (NFA), inflation (π), depreciation (δ), and the fraction of the replacement cost of assets that is current (γ). INFLATION ADJUSTED EVA (IEVA) In free cash flow (FCF) valuation, the value of assets, asset value, 1 is the discounted value of predicted future FCF. The discount rate is the weighted average cost of capital. Also, asset value is the discounted value of predicted future EVA plus capital employed. As a consequence, EVA is often interpreted as an annualized measure of net present value (NPV). In a non-inflationary environment, Hartman [8] and Shrieves and Wachowicz 13] demonstrate these relations between EVA, total wealth creation, and asset value. In this section, we show that with a number of inflation adjustments to EVA, discounted IEVA plus capital employed is asset value. This demonstration justifies IEVA as the appropriate measure of economic profit in an inflationary environment. Begin with FCF valuation. FCF in the current period is FCF = FFO Incremental Investment (4) Because the business does not grow in real terms, the expression for incremental investment is maintenance capital expenditures only and does not include growth investments. That is, incremental investment is (1 γ ) δ RIC. The term FFO is Funds From Operations, which represents the benefit of prior investment. One can calculate 7

10 FFO in a number of different ways; one of these ways is, FFO = (1 τ )( EBITDA TDEPREC ) + TDEPREC (5) The term τ is the corporate tax rate and TDEPREC is depreciation for tax purposes. At least in a general way, governments recognize economic depreciation when choosing depreciation rates and allowances for taxes. Whether or not they exactly recognize economic depreciation is a matter of debate. At least in the first instance, we make this presumption. Then, NFA is the book value of non-current assets and δ is the rate of depreciation for both reporting and tax. 11 Most importantly, deductions from taxable income for depreciation depend on book values and are not inflation adjusted. They under-represent actual maintenance capital expenditures that a business incurs to prevent deterioration of asset cash flows. Symbolically, TDEPREC = NFA δ = ( 2 1 γ ) δ RIC (1 + π ) ( π + δ ) δ ( 1 γ ) RIC Because depreciation for tax and reporting is the same, the first term in Eq. (5) is net operating income (NOI). Rewrite Eq. (5) as FFO = NOI + δ NFA Substitute Eq. (5) into Eq. (4) with, in addition, expressions for Incremental Investment and TDEPREC. Rearrange to find, 8

11 2 (1 γ ) δ RIC(1 + π) (1 γ ) δric(1 δ) π FCF = (1 τ ) EBITDA ( π + δ) ( π + δ) (6) The first term on the right hand side of this equation is net operating income (NOI). The second term measures the extent to which NOI over-represents FCF. When inflation is zero (π=), depreciation accurately represents maintenance capital expenditure and NOI equals FCF. Looking forward, we expect each term in Eq. (6) to increase at the rate of inflation (π). If FCF t is predicted free cash flow t years from today, then with FCF valuation, asset value (AV) is, FCF1 FCF (1 + π ) AV = = WACC π WACC π (7) Fisher s [6] relation for nominal and real financial rates of return when applied to the weighted average cost of capital is WACC = (1 + WACC*)(1 + π ) 1 (8) where, WACC and WACC* represent the nominal and real weighted average costs of capital respectively. Substitute Eq. (8) into Eq. (7) to find, AV FCF WACC * = (9) Eq. (7) says that asset value is the discounted value of predicted future nominal FCF at the nominal opportunity cost. At the same time, in Eq. (9), asset value is the discounted 9

12 value of predicted future real FCF at the real opportunity cost. Eq. (7) uses the formula for a growing perpetuity because investors expect nominal FCF to grow at the rate of inflation. On the other hand, Eq. (9) uses the formula for a level perpetuity because investors do not expect real FCF to increase. INFLATION ADJUSTED EVA (IEVA) Denote IEVA as real economic profit in the current period. Investors do not expect real economic profit to grow, but as we verify shortly, nominal economic profit grows at the rate of inflation (π). For the dollar opportunity cost of asset investment, we use replacement cost (RIC) to measure capital. Because discounted predicted future economic profit plus capital equals asset value, we have AV FCF IEVA WACC * WACC * = = + RIC (1) Rearrange to find IEVA, IEVA = FCF WACC * RIC (11) Economic profit is free cash flow (FCF) less an opportunity cost. 12 In an inflationary environment, this opportunity cost is the real WACC times the replacement cost of assets. In order to compare with EVA, use Eq. (6) to rewrite IEVA as 13 (1 γ ) δric(1 δ) π IEVA = NOI WACC * RIC ( π + δ) (12) 1

13 In addition, with the notation of the current paper, write EVA, as EVA = NOI WACC BIC (13) Generally, other than for very specific parameter combinations, inflation adjusted EVA equals EVA ( IEVA EVA ) = only when inflation is zero ( π = ). Further, it is clear that discounted predicted future EVA plus capital is not asset value regardless of whether one uses replacement, book, or any other measure of capital. Finally, rewrite IEVA in Eq. (12) as (1 γ ) δric (1 δ) π IEVA = NOI WACC RIC + π (1 + WACC*) RIC ( π + δ) (14) Compare Eq. (14) to Eq. (13) to highlight the fact that EVA correctly measures economic profit only after three distinct inflation adjustments. The three terms following NOI in Eq. (14) represent these adjustments. The first of these adjustments, ( 1 γ ) δric (1 δ ) π, is the extent to which NOI over- ( π + δ ) representations FCF. Note that when inflation is zero ( π = ), depreciation accurately represents maintenance capital expenditure, and therefore, NOI accurately represents FCF. In this case, this adjustment is not necessary. The second term ( WACC RIC ) is the nominal cost of capital applied against the replacement cost of capital. By comparison, EVA applies the nominal cost of capital 11

14 against the book value of capital (BIC). Due to inflation, the replacement cost exceeds book value, and therefore, the dollar opportunity cost in IEVA is greater than the dollar opportunity cost in EVA. That is, WACC RIC WACC BIC. Last, add a term to EVA ( (1 WACC*) RIC ) π + that is independent of asset structure: it is unchanged regardless of whether assets are current or non-current, depreciable or nondepreciable. Further, it arises from the forward-looking anticipation of inflation by investors in FCF valuation; it is an economic adjustment rather than an accounting adjustment to correctly measure economic profit. One can interpret this term as a value added per-period measure of the manager s ability to increase product price as costs increase. 14 This adjustment is positive because this ability adds value to the business. Note that when inflation is zero ( π = ), this adjustment is zero. Other things equal, the first two inflation adjustments make EVA greater than IEVA (EVA IEVA). The last adjustment makes EVA less than IEVA (EVA < IEVA). Thus, EVA can either under or over-represent economic profit, depending upon the nature of the business. We consider this issue in the following section. IEVA VERSUS EVA The book value of capital is, BIC = γric + NFA = γric + 1 γ ) δric (1 + π ) π + δ ( 12

15 Substitute this expression ( for BIC ) into that for EVA in Eq. (13). Subtract Eqs. (12) and (13) to find, IEVA EVA (1 γ ) δric(1 + π) (1 γ ) δric(1 δ) π = WACC γ RIC + π + δ ( π + δ) -WACC * RIC (15) BUSINESSES THAT HAVE ONLY CURRENT ASSETS If assets are entirely current ( γ = 1) they turnover rapidly and adjust continuously to inflation. Then, the book value of assets equals the replacement cost ( BIC RIC ) =. In addition, because there are no depreciation charges for either tax or reporting, NOI correctly measures free cash flow (FCF). However, the nominal rather than the real cost of capital is an unduly harsh opportunity cost in EVA. Consequently, EVA underrepresents economic profit measured by IEVA. In this case, IEVA EVA = ( WACC WACC *) RIC. Further, EVA correctly measures economic profit only when inflation is zero ( π = ). The nominal and the real opportunity costs equal one another only in this case. BUSINESSES THAT HAVE ONLY NON-CURRENT ASSETS At the other extreme, when assets are entirely non-current ( γ = ), then EVA overrepresents economic profit ( IEVA EVA ) < when, 13

16 (1 ) (1 ) WACC δ + π δ δ π π δ < WACC * (16) + ( π + δ) This condition requires that depreciation be minor ( δ ). Further, these requirements, that assets be non-current and non-depreciable ( γ, δ ), are not at odds with one another. For example, they describe assets like land. Because these assets are nondepreciable ( δ ), NOI accurately represents FCF. In addition, because depreciation is zero ( δ ), the book value of non-current assets is zero ( BIC = ). Recall that in Eq. (3) we presume that the initial non-current asset investment is in the distant past, and therefore, inflation has completely diluted the book value ( BIC = ). 15 In this circumstance, the dollar opportunity cost of capital in EVA is zero ( WACC BIC ) =. However, the economic opportunity cost is not zero because the replacement cost of assets is not zero, ( WACC RIC > ). EVA under-represents opportunity cost and, consequently, it over-represents economic profit. If assets are entirely non-current ( γ = ), but depreciation is not minor ( δ > ) less likely that EVA over-represents economic profit. That is, it is less likely that, then it is IEVA < EVA. Because nominal maintenance capital expenditures increase over time with inflation, the book value of non-current assets is closer to the replacement cost. Then, the dollar opportunity cost in EVA is closer to the economic opportunity cost. 16 Formally, as depreciation approaches one from the left ( δ 1), the book value of assets approaches the replacement cost ( BIC RIC ). In addition, as ( δ 1), IEVA 14

17 increases above EVA (that is, the inequality in (16) is violated). PROFITABILITY AND THE DISTORTION OF EVA BY INFLATION A comparison of Eq. (11) to Eq. (13) illustrates that inflation distorts EVA to the greatest extent for less profitable businesses. Measure profitability with the rate of return on invested capital after tax and after depreciation (ROIC = NOI ). When NOI is RIC constant, ROIC increases as capital (RIC) decreases. In the extreme, when RIC is zero, ROIC is infinitely great and IEVA in Eq. (11) equals EVA in Eq. (13). On the other hand, if RIC increases by $1, IEVA falls by (1 γ ) δ (1 δ ) π + WACC * ( π + δ) and EVA falls by (1 γ ) δ (1 + π ) WACC γ +. Because these amounts are constant with respect to RIC, π + δ the dollar difference between IEVA and EVA ( IEVA EVA ) is greatest (in absolute value) when RIC is great and ROIC is modest. This dollar difference can be positive or negative. It is positive and increasing as RIC increases when the inequality in (16) is violated. It is negative and decreasing as RIC increases when the inequality in (16) holds. A NUMERICAL EXAMPLE Figure 1 depicts the difference between IEVA and EVA when the real WACC is 1% (WACC*=.1), and inflation is 3% ( π =.3 ) as economic depreciation (δ) varies between and 1% and the fraction of assets that is current (γ) varies between zero and 1. In this case, the greatest discrepancy between IEVA and EVA occurs when assets are non-current and non-depreciable ( δ, γ ) = =. Then, EVA over-represents 15

18 economic profit ( ) IEVA by 1% (that is, IEVA EVA= WACC * RIC =-1%). On the other hand, if assets are entirely current ( γ = 1), then EVA under-represents economic profit ( ) IEVA by 3.3% (that is, IEVA EVA= ( WACC WACC*) RIC =3.3%). It is clear that these discrepancies between EVA and economic profit can be significant percentages of capital and can cause distortions. For example, in the last illustration, the rate of return on invested capital after tax and after depreciation ( ROIC = NOI ) can be 3.3% less than the nominal WACC, so that EVA IC is negative, when actual economic profit is zero. This mis-measurement of economic profit occurs even though the business has no non-current assets and the book value of assets correctly represents replacement cost. π =.3, WACC*=.1, RIC = 1 16

19 A DECLINING BUSINESS Eq. (11) illustrates that the real WACC (WACC*) is the appropriate opportunity cost to apply against the replacement cost of capital when measuring economic profit in an inflationary environment. Are there businesses for which the nominal WACC is the appropriate cost of capital? We answer this question in this section. Suppose that investors expect the nominal free cash flow (FCF) of a business to be constant into the future. We describe this business as declining, because real FCF declines at the rate of inflation (π). An interpretation of this decline, that takes place at the rate of inflation (π), is that the manager is unable to increase product price as costs increase. Asset value (AV) is AV FCF = WACC Because nominal FCF does not grow, asset valuation requires the formula for a level perpetuity (rather than a growing perpetuity) and the nominal WACC is the discount rate. In addition, because nominal FCF does not growth, nominal economic profit (IEVA) also does not grow with inflation. Consequently, AV FCF WACC IEVA WACC = = + RIC Rearrange to find inflation adjusted economic profit (IEVA) IEVA = FCF WACC RIC (17) 17

20 The essential difference between IEVA in Eq. (17) and IEVA in Eq. (14) is the final term in Eq. (14). This term represents the ability of the manager of the business that we studied in the previous sections of this paper to increase product price as costs increase. This term is positive because this ability adds value. On the contrary, this term is absent from Eq. (17) because the manager of the declining business, in the current section of this paper, does not have this ability. This comparison illustrates that when measuring economic profit, the ability to maintain real free cash flow (FCF), or equivalently increase nominal FCF at the rate of inflation (π), effectively reduces the cost of capital from the nominal to the real WACC. This ability can be recognized either as this reduction in the cost of capital (by approximately the rate of inflation) or, other things equal, as a positive term in IEVA (Eq. 14) that is equal to (approximately) the rate of inflation times the replacement cost of assets. CONCLUSION We investigate the measurement of economic profit in an inflationary environment. EVA requires three inflation-adjustments to correctly measure economic profit. The first two adjustments correct financial reports, the income statement and the balance sheet, for inflation distortions. Depreciation for reporting under-represents economic depreciation and the maintenance capital expenditures required to prevent it. Consequently, net operating income over-represents free cash flow (FCF) for a nongrowing business. As a correction, economic profit requires a downward adjustment to NOI. In addition, the book value of non-current assets under-represents the replacement 18

21 cost. The dollar opportunity cost of capital requires replacement cost rather than book value. The third and final inflation adjustment arises from the forward-looking anticipation of inflation by investors in FCF valuation. It is an economic rather than an accounting adjustment that is independent of asset structure. That is, it is unchanged regardless of whether assets are current or non-current, depreciable or non-depreciable. We interpret this adjustment as a value added per-period measure of the manager s ability to increase product price as costs increase. This adjustment is positive because this ability adds value to the business. For presentation purposes, we make a number of simplifying assumptions in this paper. Managers and analysts that implement IEVA will want to relax these assumptions. First, we presume a non-growing business. For a growing business, an inflation adjusted growth term is added to IEVA. Second, we presume a regular periodic interval, that is, yearly, for capital expenditures (in particular, maintenance capital expenditures). In practice, the adjustment of book values to replacement cost for non-current assets requires actual inflation rates between possibly irregularly timed capital expenditures and the present. Third, expected future inflation may differ from past inflation. One calculates the real WACC (WACC*) from the nominal WACC with predicted future inflation. On the other hand, the adjustment of book values to replacement cost requires actual inflation rates between the time of past non-current asset investments and the present. Last, other than inflation factors, we presume that financial reports and tax deductions accurately reflect economic depreciation. Discrepancies require adjustment to the financial accounts before measuring economic profit. 19

22 REFERENCES [1] Bierman, J. and S. Smidt. The Capital Budgeting Decision: Economic Analysis of Investment Projects, Sixth Edition, New York: Macmillan Publishing Company, [2] COMPUSTAT. Compustat (North America): Data Guide, Englewood, CO: Standard and Poor s, McGraw-Hill, [3] Copeland, T., T. Koller and J. Murrin. Valuation: Measuring and Managing the Value of Companies, second edition, New York: John Wiley and Sons Inc, [4] Ehrbar, A. EVA: The Real Key to Creating Wealth, New York: John Wiley and Sons Inc, [5] De Villiers, J. The Distortions in Economic Value Added (EVA) Caused by Inflation, Journal of Economics and Business 49, (1997), pp [6] Fisher, I. The Theory of Interest, (193), Reprints of Economic Classics, New York: Augustus M Kelley, Bookseller, [7] Grant, J.L. and J.A. Abate. Focus on Value: A Corporate and Investor Guide to Wealth Creation, New York: John Wiley and Sons Inc, 21. [8] Hartman, J.C. On the Equivalence of Net Present Value and Market Value Added as Measures of a Project s Economic Worth, The Engineering Economist 45, (2), pp [9] Howe, K.M. and H. Lapan. Inflation and Asset Life: The Darby Versus the Fisher Effect, Journal of Financial and Quantitative Analysis, Vol 22, 1987, pp [1] Lee, B.B., E. Press, and B. Choi. Capital Assets and Financial Statement Distortions, Competitiveness Review 11, (21), pp [11] Marshall, A. Principles of Economics, Vol 1, New York: MacMillan & Co, 189. [12] Modigliani, F. and M.H. Miller. The Cost of Capital, Corporation Finance, and the Theory of Investment, American Economic Review 48, (1958), pp [13] Shrieves, R.E. and J.M. Wachowicz. Free Cash Flow (FCF), Economic Value Added (EVATM), and Net Present Value (NPV): A Reconcilition of Variations of Discounted-Cash-Flow (DCF) Valuation, The Engineering Economist 46, (21), pp [14] Richardo, D. (1817), The Principles of Political Economy and Taxation, London: Dent and Sons Ltd, 196. [15] Smith, A. (1776), An Inquiry into the Nature and Causes of the Wealth of Nations, 2

23 with an Introduction by E. Cannan; reprinted by New York: Modern Library, [16] Weaver, S. Measuring Economic Value Added : A Survey of the Practices of EVA Proponents, Journal of Applied Finance, Fall/Winter, 21, pp [17] Young, S.D. Some Reflections on Accounting Adjustments and Economic Value Added, The Journal of Financial Statement Analysis, Winter, 1999, pp

24 ENDNOTES 1 See for example, Copeland, Koller, and Murrin [3], Ehbar [4], and Grant and Abate [7]. 2 The pioneering work on WACC and investment is Modigliani and Miller [12]. 3 The investigation of economic profit for a growing business in an inflationary environment proceeds in a similar fashion. See endnote 12 for details. 4 Rather than a random walk, if EBITDA follows a reverting process, then predicted future EBITDA differs from its current value. In this case, one must incorporate this divergence in the measurement of economic profit. 5 If one uses this schedule of depreciation when measuring the accounting rate of return (ARR) for investment, then the ARR is exactly the same as the internal rate of return (IRR). Consequently, one of the attractions of Bierman and Smidt s methodology is that from it one learns about the nature of economic depreciation. 6 Firms use a variety of phrases for maintenance capital expenditures. For example, the term sustaining capital expenditures is sometimes used. 7 If a firm replaces assets only periodically, once every few years, for example, then (1 γ ) δ RIC represents the equivalent annualized capital expenditure for replacement. See, for example, chapter 7 of Bierman and Smidt [1] for a discussion of equivalent annual costs. 8 See, for example, Howe and Lapan [9]. 9 The symbol π represents both the average of past inflation and expected future inflation. Of course, one can generalize, but for the sake of simplicity, we do not. 1 Asset value is sometimes called the enterprise value of a firm. 22

25 11 For the business that we study, in the absence of maintenance capital expenditures, cash flows decline geometrically. Thus, the declining balance method, for either tax or reporting, represents economic depreciation. If tax authorities use other methods, they impose tax penalties or confer tax subsidies on firms. In this paper, we do no consider the public policy implications of these penalties and subsidies. If depreciation methods for reporting and tax differ, then adjust net operating income (NOI) with deferred income tax (DIT). 12 A similar argument, but ignoring inflation, illustrates that a more general representation of economic profit than EVA for a growing firm is FCF WACC IC + g IC, where FCF is free cash flow and g is a factor for growth. Growth investments, subtracted in incremental investment for free cash flow, equal the term g IC added for growth in this more general representation. Because these two terms equal one another, they cancel. Further, if depreciation for tax equals maintenance capital expenditures, then this more general representation reduces to EVA. In this case, for either a growing or a nongrowing firm, one measures EVA in the same fashion. Consequently, we need not redo our analysis for a growing firm. The fundamental difference between real growth in FCF (g) and nominal growth in FCF due to inflation (π) is that the latter requires no incremental investment. Thus, to measure economic profit, one adds a term for the ability of the manager to increase prices as costs increases, but no term is subtracted for incremental investment. This discrepancy leaves the final term in Eq. (14) and inflation adjusted EVA (IEVA) does not reduce to EVA. 23

26 13 We expect all of the terms in (12) to grow at the expected rate of inflation (π). Consequently, one can verify that asset value (AV) is discounted predicted future nominal IEVA at the nominal WACC plus the replacement cost of capital (RIC). 14 If one allows firm specific inflation to differ from economy wide inflation (π), then this term is adjusted accordingly. 15 In Eq. (2), the non-current asset investment is made t years in the past. For finite, rather than infinite values of t, the smaller is t, the closer is book capital to replacement cost. In this instance, the opportunity cost on book capital in EVA is positive, rather than zero and EVA is less likely to over-represent economic profit ( IEVA EVA ) <. 16 While we have not done the analysis in this paper, by logical extension of the argument in this paragraph, EVA is also less likely to over-represent economic profit for growth oriented businesses for the same reason. 24