Economic Value Added

Free Cash Flow (FCF), Economic Value Added (EVA ), and Net Present Value(NPV): A Reconciliation of Variations of Discounted-Cash-Flow (DCF) Valuation Ronald E. Shrieves, Ph.D. SunTrust Bank Professor of Finance John M. Wachowicz, Jr., Ph.D., CPA Professor of Finance Department of Finance College of Business Administration The University of Tennessee Stokely Management Center Knoxville, TN 37996 865.974.3216 Department 865.974.1716 Fax [email protected] [email protected] June, 2000

Abstract: The paper assists the user of DCF methods by clearly setting forth the relationship of free-cashflow (FCF) and economic value added (EVA ) concepts to each other and to the more traditional applications of DCF thinking. We follow others in demonstrating the equivalence between EVA and NPV, but our approach is more general in that it links the problems of security valuation, enterprise valuation, and investment project selection, and additionally, our approach relates more directly to use of standard financial accounting information. Beginning with the cash budget identity, we show that the discounting of appropriately defined cash flows under the free-cash-flow valuation approach (FCF) is mathematically equivalent to the discounting of appropriately defined economic profits under the EVA approach. The concept of net operating profit after-tax (NOPAT), found by adding after-tax interest payments to net profit after taxes, is central to both approaches, but there the computational similarities end. The FCF approach focuses on the periodic total cash flows obtained by deducting total net investment and adding net debt issuance to net operating cash flow, whereas the EVA approach requires defining the periodic total investment in the firm. In a project valuation context, both FCF and EVA are conceptually equivalent to NPV. Each approach necessitates a myriad of adjustments to the accounting information available for most corporations.

Free Cash Flow (FCF), Economic Value Added (EVA ), and Net Present Value (NPV): A Reconciliation of Variations of Discounted-Cash-Flow (DCF) Valuation Introduction The use of discounted-cash-flow (DCF) methods for investment decision making and valuation is well entrenched in finance theory and practice. This rigorous treatment dates back at least to the Old Babylonian period of 1800-1600 B.C. [11]. Relative newcomers with profound conceptual insights are Irving Fisher [6] and Jack Hirshleifer [9, 10], who provided concise, rigorous utility-theoretic foundations. While originally conceived primarily in response to compound interest problems, the modern literature has broadened application of DCF techniques, most notably to capital budgeting and security valuation problems. More recent extensions of the DCF concepts to security valuation using so-called “free-cash-flow” techniques [3, 4] and to managerial performance evaluation using an “economic value added” concept [13], have stirred interest in the application of DCF methods to a broader range of practical business problems. Financial performance assessment using the concept of residual income known as economic value added, has received much attention in the recent academic literature [1, 2]. These extensions, however, have also raised a number of concerns related to putting DCF theory into practice. The last few years have witnessed a tremendous growth in writing on EVA , in the financial press, practitioner publications, and numerous unpublished working papers. Printed and web-published lecture notes on the subject abound. The primary purpose of this paper is to assist users of DCF methods by clearly setting forth the relationship of free-cash-flow (FCF) and economic value added (EVA ) concepts to each other and to the more traditional applications of DCF thinking such as net present value (NPV). Although we follow others [7, 8] in demonstrating the equivalence between EVA and NPV, we feel that our approach is more general in that it links the problems of security valuation, enterprise valuation, and investment project selection. Additionally, our approach relates more directly to use of standard financial accounting information. Though the FCF approach discounts cash flow, whereas the EVA

approach discounts profits, we demonstrate in the familiar terminology of cash flow

analyses that the two approaches are conceptually equivalent. We do not claim that any of the conclusions presented herein are new, but we do hope that the presentation of ideas in the manner we have chosen will provide a useful synthesis in a theoretically rigorous format. The paper also briefly summarizes some implications of the analysis for problems encountered in translating the theoretical concepts into practice. These are primarily related to issues of adjustments to accounting information that are required to implement the FCF and EVA

1

methods.

1.

Cash Flow

1.a.

The cash budget identity. Consider the single-period cash budget identity. The components are operating revenues and costs, net

security issuance, interest payments, dividend payments, taxes paid, and net investments. Investments may be divided into working capital (i.e., current assets net of “spontaneous” changes in current liabilities such as payables and accrued wages) and so-called long-term investments such as plant and equipment. For now, our discussion assumes that the listed components of the cash budget correspond to items found in the firm's financial statements. In practice, use of accounting information for economic analysis requires a number of adjustments to bring the accounting numbers into conformity with economic reality. In Section 3, we briefly comment on measurement issues that arise due to "distortions" introduced by use of generally accepting accounting principles. The single-period cash budget identity may be expressed as follows: Sources = Uses Rt + ∆Bt = Ot + Int t + Divt + Taxest + ∆I t + ∆WCt ,

(1)

where subscript (t) is used to index these components of cash flow according to date, and Rt = operating revenue ∆Bt = net debt issuance (i.e., new borrowing net of repayment) Ot = out - of - pocket operating costs Intt = int erest payments on debt, less any interest income Divt = dividendson common stock (defined here as net of equity issuance and repurchase) Taxest = total taxes paid ∆It = net investment in non-current assets (i.e., net of asset sales) ∆WCt = net investment in working capital, inclusiveof cash and marketable sec urities. 1.b.

Dividends. Solving Eq. (1) for dividends paid in period t gives: Divt = [Rt − Ot − Intt − Taxest ] − [∆It + ∆WCt ] + ∆Bt .

(2)

After simultaneously subtracting, then adding, tax depreciation (Deprt ) from the right-hand side of Eq. (2), dividends paid can now be expressed as follows: Divt = {[Rt − Ot − Deprt − Intt − Taxes t ] + Deprt } − [∆It + ∆WCt ] + =

{NPATt + depreciationt }

∆Bt

− total net investmentt + net debt issuancet ,

where NPAT t is net profit after tax.

2

(3)

1.c.

Division of cash flow among investors. Let CFE t be the cash flow to equity (also known as free cash flow to equity, FCFE) in period t. A s

defined in (Copeland, et al., p.480), cash flow to equity is equivalent to our expression for dividends in Eq. (3): CFEt = {[ Rt − Ot − Deprt − Intt − Taxest ] + Deprt } − [∆It + ∆WCt ] + =

N [ PATt + depreciationt ]

∆Bt

− total net investmentt +

net debt issuancet

(4)

Proponents of the FCFE method emphasize that free-cash-flow to equity is “ . . . dividends that could be paid to shareholders. This is usually not the same as actual dividends in a given year because management deliberately smoothes dividend payments across time” [3, p. 481]. In fact, by separating the investment in working capital into discretionary and nondiscretionary components (a.k.a. “excess marketable securities”), and including the latter in the WC term in Eq. (3), but excluding it from the

WC term in Eq. (4), then dividends and CFE will differ by the

amount of such discretionary investment. The difference between FCFE and dividends paid in a given year may be characterized as investment in “excess marketable securities,” and its omission from consideration is moot so long as such investments have zero NPV [4]. Cash flow to debtholders in period t, CFDt , would then be: CFDt = Intt − ∆ Bt = int erest paymentst − net debt issuancet .

1.d.

(5)

Taxes. Consider the total-taxes-paid component of cash flow to equity. We can view it as being equal to the tax

on operating income before interest (which is equivalent to the tax that would be paid if the firm had no debt financing) minus the tax-shield benefits provided by interest payments. Letting Taxest =

denote the tax rate, we have:

( Rt − Ot − Deprt − Int t )

= (Rt − Ot − Deprt ) − Int t = tax with no debt financingt − interest − tax − shield benefitst

(6)

Also, remember that the above assumes depreciation (Deprt ) is that which is claimed for tax purposes, and that there are no other tax accounting distortions. If such distortions are present, then an additional "tax adjustment" term must be included in the right-hand side of Eq. (6). Also, note that net investment can be defined broadly to include research and development (R&D), advertising, investment in human capital, and so forth. However, reclassification of these items from "operating costs" to "investments" will require a "tax adjustment."

3

1.e.

Free cash flow to the firm. Free cash flow to the firm (CFFt ) is the sum of cash flow to equity (CFEt ) and cash flow to debtholders

(CFDt ), reduced by the interest-tax-shield benefits from the cash flow to debtholders. Subtracting the interest-taxshield benefits from the cash flow to debtholders produces an after-tax cash flow to debtholders). Since the discount rate to be used later is the after-tax weighted average cost of capital, the appropriate cash flows are before the tax advantage of debt (i.e., we account for the tax advantage of debt financing by reducing the discount rate, rather than by including the interest tax shield in the cash flow to investors). In effect, cash flow to a levered firm is defined as that which would be realized by an otherwise equivalent unlevered firm. Free cash flow to the firm may now be written: CFFt =

+

CFEt

CFDt −

Intt

= {[( Rt − Ot − Deprt − Intt − Taxes t ) + Deprt ] − [∆It + ∆WCt ] + ∆Bt } + [Intt − ∆Bt ] − Intt

= [(Rt − Ot − Deprt − Intt − Taxest ) + {Int t − (Intt )}] + =

NPAT [ t +(1- )Intt ]

Deprt

− [∆I t + ∆WCt ]

(7)

+ depreciationt - total net investmentt

In Eq. (7), the deduction of interest and the inclusion of net debt issuance in CFEt allowed us to offset the payment of interest and the subtraction of net debt issuance in CFDt . Also, adding the after-tax interest costs ((1- ) Int t ) back to NPAT in Eq. (7) in effect adjusts after-tax profit to what it would be for an otherwise equivalent unlevered firm [13, p. 87; 3, p. 155; 4, p. 237]. We use Stewart’s [13] terminology by referring to this restatement of income as net operating profit after taxes (NOPAT): CFFt = [ NPATt + (1- )Intt ] + depreciationt - total net investmentt = NOPATt + depreciationt - total net investmentt .

(8)

Thus, CFFt can be expressed as after-tax operating profit from an otherwise equivalent unlevered firm, plus depreciation, minus total net investment. 2. Valuation The three most basic business contexts in which valuation issues arise are: project valuation (i.e., capital budgeting), security valuation, and firm valuation. Unfortunately, students of finance are exposed to a variety of DCF techniques, depending upon the context in which they are being instructed (e.g., NPV for project valuation; free-cash-flow for firm valuation; discounted dividend models for equity valuation). Our purpose is to demonstrate the conceptual consistency in valuation methodology among the various computational techniques employed in the three valuation contexts.

4

Let k se be the required rate of return on equity, and k sb , the pre-tax required rate of return on debt, respectively, during period s. Then the compound discount factors used in obtaining the present value of cash flows to equity and debt in period t are: −1

e t

2.a.

 t  = ∏ (1 + k se )  and  s=1 

−1

b t

 t  = ∏ (1 + k bs )  . s =1 

(9)

Equity valuation by the dividend discount approach. Assuming that the life of the firm is T periods, the value of the firm’s equity by the dividend discount

approach, using Eq. (3), is: V0e = = =

T

∑

t=0

e t Div t

T

∑ te {{[Rt − Ot − Deprt − Intt − Taxest ] + Deprt } − [It + ∆WCt ]

t=0 T

∑ te {{NPATt + depreciationt }

t=0

2.b.

+ ∆Bt

}

(10)

}

− total net investmentt + net debt issuancet .

Equity valuation by the free-cash-flow-to-equity approach. The value of the firm’s equity by the free-cash-flow-to-equity approach, using Eq. (4), is: V0e = = =

T

∑

t=0

e t CFEt

T

∑ te {{[Rt − Ot − Deprt − Intt − Taxest ] + Deprt } − [∆I t + ∆WCt ] + ∆Bt }

(11)

t=0 T

∑ te {[NPATt + depreciationt ] − total net

t=0

investmentt + net debt issuancet } .

Given our assumptions, this is identical to the valuation under the dividend discount approach. 2.c.

Debt valuation. The value of the firm’s debt is: T

V0b = ∑

t =0 T

=∑

t =0

b t

CFDt (12)

b t (Int t

5

− ∆Bt ) .

2.d.

Total firm valuation. Let ks be the overall capitalization rate for the free cash flow to the firm (CFF) during period s. Then ks is

the weighted average (after-tax) discount rate, with the property that when the CFFs are discounted at ks, the resulting value equals the sum of the values of debt and equity:     Ve Vb k s =  e s −1 b  k se +  e s −1 b  ksb (1 − ).  Vs −1 + Vs−1   Vs−1 + Vs −1  Then the compound discount factor associated with the CFFt is: −1

t

 t  = ∏ (1 + k s ) , s =1 

(13)

and total firm value is V0 = V0e + V0b = T

=∑

t =0

t =0

t=0

e t CFEt

t

[CFFt ]

t

[CFEt + CFDt −

T

=∑

T

∑

+

T

∑

t=0

b t CFDt

(14) Intt ] .

Equivalently, using Eq. (8) to express the free cash flow to the firm, firm value can be described in terms of NOPAT, depreciation, and total net investment: T

V0 = ∑

t =0

t CFFt =

T

=∑

t =0

t

T

∑ t {[( Rt − Ot − Deprt )(1 −

t=0

{NOPATt + depreciationt − total net

) + Deprt ] − [∆I t + ∆WCt ]} investmentt } .

(15)

The value of the firm’s equity is then obtained by deducting the market value of the firm’s debt (V0b ). 2.e.

Project valuation. Assume that we are evaluating a potential investment project, call it project j, with initial cash flow in

period m and final incremental cash flow in period m+M. The incremental cash flow effects of the project are: ∆ j CFFt = ∆ j {[(Rt − Ot − Deprt )(1 − ) + Deprt ] − [∆I t + ∆WCt ]} , t = m, ...,m + M . The

j

(16)

operator represents the incremental impact of project j acceptance on the components of cash flow.

Assuming average risk and financial leverage per period for the incremental project flows, then the additional market value (or net present value, NPVj ) resulting from the project is:

6

 1 m + M j NPVj =   ∑ t (∆ CFFt ) .  m  t=m

(17)

Using Eq. (7) to separate the overall effect of the project on free cash flow to the firm into equityholder, debtholder, and interest tax shield components, and applying Eq. (14), gives:  1 m + M j NPVj =   ∑ t (∆ CFFt )  m  t=m  1 m + M j j j =  ∑ t [∆ CFEt + ∆ CFDt − (∆ Intt )]  m  t=m  1 m + M = e ∑  m  t=m

e j t (∆ CFEt )

 1 m + M + b  ∑  m  t=m

(18)

b j t (∆ CFDt ).

Since the last term on the right-hand-side of Eq. (18) is zero if debt is always issued at fair market value, then the NPV of the project is also seen to be the present value of the incremental free-cash-flow-to-equity:  1 m + M NPVj =  e  ∑  m  t=m 2.f.

e j t (∆ CFEt ).

(19)

Economic profit (EP) and economic value added (EVA™). The concept of economic profit (EP) boils down to a simple restatement of total firm valuation that

“reallocates” investment expenditures from the periods in which they are made to periods over which their resulting benefits occur. In the EVA™ approach to EP, the reallocation assigns to each period an “EVA™ depreciation” component representing the “usage” of a portion of the cost of the firm’s assets, plus a “capital charge” representing the opportunity cost of the remaining net investment in the firm. The present values of these two charges, when discounted at the cost of capital, equals the capital investment in the firm. The Appendix formalizes the reallocations that enable the restatement of the free cash flow valuation relationship in Eq. (15) in terms of the economic profit concept. The first relationship relates the reallocation for investments in capital goods ( ∆It ), while the second applies to investments in working capital ( ∆WCt ). These relationships are restated here for convenience. For investments: T

∑

t=0

t ∆It

T

=∑

t =1

t [Pt

+ kt Ut −1 ] ,

(A.4)

where Pt is EVA™ depreciation in period t and Ut-1 is the “EVA™ book value” of the capital stock at the beginning of period t. For working capital: T

∑

s=0

s ∆WCs

T

=∑

s =1

s ks WCs −1 .

7

(A.8)

First restate the total firm valuation in Eq. (15) as follows: T

V0 = ∑

t =0

t CFFt

=

T

T

t=0

t=0

∑ t {NOPATt + Deprt } − ∑

t[∆I t

+ ∆WCt ] .

(20)

Using Eqs. (A.4) and (A.8), Eq. (19) becomes: T

V0 = ∑

t =0

t CFFt

T

=∑

t =0

t

=

T

T

t=0

t=0

∑ t {NOPATt + Deprt } − ∑ t {Pt + k tUt −1 + kt WCt −1}

{[NOPATt + Deprt ] − [Pt + ktU t−1 + k tWCt −1 ]}

(21) .

The terms in the summation represent economic profit, or EPt , for the respective periods. Each term can be rewritten as: EPt = [NOPATt + Deprt ] − [Pt + k tUt −1 + kt WCt −1 ] = NOPATt + (Deprt − Pt ) − k t[U t −1 + WCt −1 ]

(22)

Alternatively, we can summarize the computation of EPt as:

NOPATt + difference between tax depreciationt and EVA depreciationt − capital charges on EVA operating assetst =

economic profit t

It is important to recall that the NOPAT t term in Equations (20) through (22) is defined in terms of the tax depreciation (Deprt ) appropriate to calculation of cash flows used in computing NPV. Note that if EVA™ depreciation is set equal to tax depreciation (Pt =Deprt ), then the second term in the EVA™ economic profit expression vanishes. But when EVA™ depreciation is not equal to tax depreciation, adding the difference to the NOPAT calculated using tax depreciation gives NOPAT which would result from use of EVA™ depreciation (note that the depreciation tax shield is still based on tax depreciation). This condition that EVA™ depreciation equals tax depreciation is implicit in the definitions of NOPAT used by Hartman [8] to show that EVA™ and NPV measures are equivalent "for all methods of depreciation." As noted by Harris [7, Appendix 2], who also assumed equivalence between EVA™ depreciation and tax depreciation, using a different depreciation schedule will change the economic profits for any given year, but will not affect the present value of economic profits (also see the discussion in our Appendix). Making explicit the assumption that our NOPAT is based upon tax depreciation, the inclusion of the term for the difference between tax depreciation and EVA™ depreciation, coupled with the 8

observation that the method of EVA™ depreciation will not influence the present value of economic profits, resolves the concern noted in Dillon and Owers [5, p. 39] that the present value of economic profits equals NPV “only under very limiting conditions.” The value of the firm is seen to be the discounted present value of the stream of EPs that will be produced, and Eq. (21) can be written as: T

V0 = ∑

t =0

Proponents of EVA

t FCFt

=

T

∑

t=0

t EPt

.

(23)

define the notion of market value added (MVA) as the difference between market value of the

firm and the (EVA ) book value of investment in the firm’s assets: MVA0 =

T

∑

t EPt

t=0

− BV0

(24)

Now reconsider the notion of project value. From Eqs. (16) and (17), an investment decision made in period m has the following impact on firm value:  1 m + M j NPVm =   ∑ t (∆ {[(Rt − Ot − Deprt )(1 − ) + Deprt ] − [∆It + ∆WCt ]})  m  t=m  1  m+M =  ∑  m t = m+1

( ∆ {(R j

t

t

− Ot − Deprt )(1 − )] + ( Deprt − Pt ) − k t (Ut −1 + WCt −1)

})

(25)

 1  m+M j =  ∑ t (∆ EPt ).  m t = m+1 Note that, in the second line of Eq. (25), the summation begins at period m+1, since Eq. (A.4) indicates that the initial investment outlay, ∆Im , may be replaced by the present value of its associated stream of future EVA depreciation and investment opportunity costs, [Pm, t + ktU m,t −1 ] , for t=m+1,...,m+L. A subtle but important distinction between EVA™ in theory and as practiced should be noted. The results in Eqs. (23) and (24) represent the value of a project or policy change determined by discounting the difference between estimated EP with the change, and what it would be in the absence of the change. As practiced, EVA™ is measured as the year-to-year difference in EP, i.e., as (EPt -EPt-1 ). There appears to be an implicit assumption that year-to-year changes in EP reflect the results from management decisions regarding projects and policies. Economic value added is the stream of changes in economic profits that result from the project: EVAtj = ∆ j EPt , for t=m+1,...,m+L. Therefore, project value is simply the present value of the stream of economic value added resulting from the project:

9

 1  m+M NPVm =   ∑  m t = m+1

t

EVAtj .

(26)

3. Measurement Issues The previous section confirmed the conceptual equivalence of various DCF procedures, given the necessary information regarding cash flows. In practice, most valuation tasks are carried out using information from a firm’s financial and tax accounting records. This is especially true for valuations of an entire firm by “outsiders,” who have access only to publicly available financial statements. Even for internal project valuation analyses, elements of revenue and costs are often estimated using historical experience as reflected in the firm’s accounting records, hence even the valuation of new projects is dependent on knowledge of a firm’s accounting procedures. Another important use of valuation concepts requiring use of accounting information is determination of managerial compensation. Since the spirit of managerial compensation arrangements is to reward managers for improving shareholder wealth, the measurement of periodic changes in firm value is critical. Benchmarks may be based on a firm’s own historical performance or on performance of a peer group, or both. In either case, the metrics utilized for performance evaluation are developed largely from historical financial reports. Proper utilization of this information involves adjusting the reported data for known deficiencies with respect to the metric of performance evaluation. For example, the use of reported earnings or earnings per share as a metric for performance evaluation has been heavily criticized for distortions induced by generally accepted accounting principles [12]. Since application of each of the techniques of valuation relies in practice upon accounting numbers, each incorporates a number of “corrections” to accounting income and/or assets. With the free cash flow models, income must be adjusted for the fact that Generally Accepted Accounting Principles (GAAP) involve reliance on both the realization and matching principles. In short, revenue and most costs should be recognized when a good or service is provided to the customer, rather than when the cash is received. Other subjective accounting choices, such as LIFO vs. FIFO inventory accounting, will also affect accounting income. The critical role of capital charges in the EVA

framework raises issues about accounting for investment.

R&D is the classic example of inadequacy of accounting practices in describing the level of investment in a firm. Unfortunately, R&D is but one of many such problems (another is investment in firm-specific human capital through employee training programs). 3.a.

Derivation of operating cash flow from accounting profit. As a result of application of the realization and matching principles and tax rules, accounting statement

reporting of periodic revenues and costs may deviate considerably from actual cash flows relating to the same 10

revenue and cost items. The dividend discount and free cash flow to equity models adjust accounting profits by starting with NPAT, then adding depreciation and net debt issuance, and subtracting total net investment (see Eqs. (3) and (4)): Divt = CFEt

= {[Rt − Ot − Deprt − Intt − Taxes t ] + Deprt } − [∆It + ∆WCt ] + =

{NPATt + depreciationt }

∆Bt

− total net investmentt + net debt issuancet .

The free cash flow to the firm approach is similar, but because it accounts for the tax advantage of debt by using an after-tax discount rate, it uses operating income after tax, which excludes the tax shield due to interest expense (NOPAT): CFFt = [ NPATt +(1- )Intt ] + depreciationt - total net investmentt = NOPATt + depreciationt - total net investmentt

(8)

The myriad of adjustments to accounting earnings found in firms’ statements of cash flow are appropriate when deriving the CFE or CFF measures of cash flow from accounting data. Examples, to name a few, include: adjustments for deferred taxes; equity income from subsidiaries, net of dividends; changes in LIFO reserves; goodwill amortization; and foreign currency adjustments. 3.b.

Derivation of economic profit from accounting profit As evidenced by the expression for economic profit in Eq. (22), the economic profit/EVA

approach

discounts economic profit, rather than cash flow, and is therefore not only concerned with reconciliation of accounting profit and cash flow, but also focuses on issues defining the capital investment in the firm. EPt = [NOPATt + Deprt ] − [Pt + k tUt −1 + kt WCt −1 ] = NOPATt + (Deprt − Pt ) − k t[U t −1 + WCt −1 ]

(22)

Since reflection of investment expenditures and depreciation in a firm’s financial statements may deviate considerably from the treatment appropriate for deriving economic profits, application of EVA

requires

adjustments to the accounting value of the firm’s assets. Examples of adjustments to the firm’s invested capital (Ut-1 in Eq. (22)) include: capitalization of R&D and other expenditures that contribute to future income (with depreciation of R&D included in future NOPATs); investment in goodwill of acquired companies (with depreciation of goodwill included in future NOPATs); capitalization of non-capital leases; and LIFO inventory valuation reserves.

11

4.

Conclusions Conceptually, free cash flow, economic value added, and net present value approaches to valuation and

decision-making are equivalent. While this fact appears well-known, this paper partially fills a void in the literature by rigorously demonstrating the linkage among the problems of security valuation, enterprise valuation, and investment project selection, and by doing so in a manner that relates directly to the use of standard financial accounting information.

Beginning with the cash budget identity, we demonstrate how the discounting of

appropriately defined cash flows under the free-cash-flow (FCF) valuation approach is logically equivalent to the discounting of economic profits under the EVA

approach. The concept of net operating profit after-tax (NOPAT),

found by adding after-tax interest payments to net profit after taxes, is central to both approaches, but there the computational similarities end. The FCF approach focuses on the periodic total cash flows obtained by deducting total net investment and adding net debt issuance to net operating cash flow, whereas the EVA

approach requires

defining the periodic total investment in the firm. Each approach necessitates a myriad of adjustments to the accounting information available for most corporations. While the debate as to which valuation techniques are best suited for various purposes rages (and is fed by the intense competition among major consulting firms), practitioners and teachers of finance principles can at least take comfort in the secure knowledge that the debate is not about theoretical issues. We sincerely hope that the paper leaves the reader better equipped to evaluate the claims by assorted purveyors of valuation expertise.

12

References: [1] Bacidore, Jeffrey, John Boquist, Todd Milbourn, and Anjan Thakor, 1997, “The Search for the Best Financial Performance Measure." Financial Analysts Journal 53, 11-20 (May/June). [2] Biddle, Gary C., Robert M. Bowen, and James S. Wallace, 1998, "Does Eva® Beat Earnings? Evidence on Associations with Stock Returns and Firm Values." Journal of Accounting and Economics 24, 301-336 (December). [3] Copeland, Tom, Tim Koller, and Jack Murrin, 1994, Valuation: Measuring and Managing the Value of Companies, John Wiley (New York). [4] Damodaran, Answath, 1996, Investment Valuation, John Wiley (New York). [5] Dillon, Ray D., and James E. Owers, 1997, “EVA as a Financial Metric: Attributes, Utilization, and Relationship to NPV,” Financial Practice and Education, v. 7, no. 1, 32-40 (Spring/Summer). [6] Fisher, Irving, 1930, The Theory of Interest, MacMillan & Co. (New York). [7] Harris, Robert, 1997, “Value Creation, Net Present Value and Economic Profit,” working paper UVA-F-1164, Darden School, University of Virginia. [8] Hartman, Joseph C., "On the Equivalence of Net Present Value and Economic Value Added as Measures of a Project's Economic Worth," forthcoming, The Engineering Economist. [9] Hirshleifer, J., 1958, “On the Theory of Optimal Investment Decision,” Journal of Political Economy, v. 66, no. 4, 329-352 (August). [10] Hirshleifer, J., 1970, Investment, Interest and Capital, Prentice-Hall (Englewood Cliffs). [11] Parker, R. H., 1968, “Discounted Cash Flow in Historical Perspective,” Journal of Accounting Research, 5871 (Spring). [12] Sloan, Richard G., 1996, “Using Earnings and Free Cash Flow to Evaluate Corporate Performance,” Journal of Applied Corporate Finance, v. 9, no. 1, 70-78 (Spring). [13] Stewart, G. Bennett, III, 1991, The Quest for Value, Harper Business. [14] Stewart, G. Bennett, III, 1994, “EVA: Fact and Fantasy,” Journal of Applied Corporate Finance, v. 7, no. 2, 71-84 (Summer ).

13

Appendix: Amortization of Investment Expenditures This appendix demonstrates two principles that are essential to formally linking EVA

with FCF and

NPV approaches to valuation. The first principle states that for an arbitrary depreciation schedule, any investment expenditure can be represented as the present value of the associated depreciation and capital charges. The second principle is based upon the assumption that investments in working capital will be recovered, from which it is shown that the present value of the series of investments in working capital equals the present value of capital charges on beginning-of-period working capital balances. First consider the firm’s investment in long-term assets. Let At,s , s=t+1,...,t+L be a set of L annual cash flows over the life (L periods) of investment It such that when discounted at the firm’s cost of capital, the present value of the annual flows equals the investment outlay: (A.1)

 1  t+L ∆It =   ∑ s At ,s .  t s =t +1

The annual flows, As,t may be separated into “depreciation” and investment opportunity cost components: (A.2)

At ,s = Pt,s + kt Ut, s−1 , where

t+ L

∑ Pt, s = ∆I t

, and ,

s= t +1

where kt is the firm’s weighted average cost of capital during period t, and Ut,s-1 is the portion of initial cost of investment remaining as of period s-1, i.e., (A.3)

Ut, s−1 = ∆I t −

s−1

∑ Pt ,r .

r= t +1

It is important to note that Pt,s is an arbitrary measure of the depreciation for period s on the assets invested in period t, with the only constraint on the P-vector being that on the sum of its elements. For example, Damodaran (undated) assumes no depreciation for the first L-1 periods, so that all of the depreciation occurs in the last period of a project’s life. Harris [7, Appendix 2] uses straight-line depreciation in his examples, but notes that any depreciation schedule works in the sense of satisfying Eq. (A.1). Hartman [8], does not specify the method of depreciation. Although the use of true economic depreciation (the periodic rate of decline in the present value of future cash flow of the asset) has some appeal as the metric for P, any depreciation works in the sense that Eq. (A.1) will hold. One variant of calculating depreciation has been referred to as the “sinking-fund” method [14]. Though it does not necessarily represent true economic depreciation, which captures the decline in economic value of the producing assets, it has the advantage of expressing the value of the asset in such a way that the investment opportunity cost represents a stable percentage of the undepreciated asset base. 14

Assuming without loss of generality that all investments have the same economic life of L periods, Eq. (A.1) becomes:  1 s =t + L ∆It =   ∑ s[Pt,s + k sU t,s −1 ] .  t  s =t +1

(A.2)

Thus the present value of all investments over the life of the firm is: T

∑

t=0

t ∆It

T s= t + L

=∑

∑

t =1 s= t +1

s [Pt, s

+ k tUt ,s −1 ] ,

which may be rewritten as: T

∑

(A.3)

t=0

Noting that Pt =

t ∆It

L

∑ Pt −r, t

r =1

T

=∑

t+L

∑

t =1 r= t +1

r [Pt − r,t

+ k sUt −r, t −1 ] .

L

and Ut −1 = ∑ U t −r,t −1 , are, respectively, the sinking-fund depreciation and investment r =1

opportunity costs resulting from all investment up to and including period t-1, then we can express the present value of all present and future investment as the sum of the present values of all future depreciation and investment opportunity costs. Eq. (A.3) may be rewritten (assuming no further investment after period t=T-L) as: T

(A.4)

∑

t=0

t ∆It

T

=∑

t =1

t [Pt

+ kt Ut −1 ] .

Now consider the investment in net working capital. Since working capital investment equals working capital recoveries over the life of the firm (and, for that matter, over the life of any given investment project involving changes in working capital), then T

(A.5)

∑ ∆WCt = 0,

t=0

and for any period t, WCt = −

T

∑ ∆WCs .

s= t +1

(Note that ∆WCt > 0 for an increase in net working capital in period t, and ∆WCt < 0 for a decrease. Thus, in any period, if the current stock of working capital is thought of as a loan balance, then the remaining changes in working capital are the “principal” payments on the loan. It follows that for any given investment in working capital, WCt , a stream of future cash flows equal to the period change in working capital plus the interest on the previous period’s working capital “balance” will amortize the original investment: (A.6)

 1  T WCt =   ∑ s [k sWCs−1 − ∆WCs ].  t s =t +1

15

Rearranging terms gives:

(A.7)

 1  T 1  T WCt =   ∑ sk sWCs −1 −   ∑ s∆WCs , or  t s =t +1  t  s= t+1 1  T 1  T   ∑ s ∆WCs =   ∑ sk sWCs−1 − WCt .  t s =t +1  t  s= t +1

Since the working capital balance at inception of the firm is zero, then it follows that: T

(A.8)

∑

s=0

s ∆WCs

T

=∑

s =1

s ks WCs −1 .

Furthermore, since the same relationships among changes in working capital apply on a project basis, then letting ∆ j (⋅) represent the incremental effects of project j, we have: (A.9)

 1  m+ L  ∑  m  s =m

s∆

j

 1  m+L j (∆WCs ) =   ∑ s ks ∆ (WCs−1 ).  m s= m +1

16