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VOLU ME 18 | NUMBER 2 | WINTER 2006

APPLIED CORPORATE FINANCEJournal of

A M O R G A N S T A N L E Y P U B L I C A T I O N

London Business School Roundtable on Shareholder Activism in the U.K. 8 Panelists: Victor Blank, GUS Plc and Trinity Mirror Plc; AlastairRoss Goobey, Morgan Stanley International; Julian Franks,

London Business School; Marco Becht, Université Libre

de Bruxelles; David Pitt-Watson, Hermes Focus Asset Man-

agement; Anita Skipper, Morley Fund Management; and

Brian Magnus, Morgan Stanley. Moderated by Laura Tyson,

London Business School, and Colin Mayer, Oxford University

The Role of Real Options in Capital Budgeting: Theory and Practice 28 Robert L. McDonald, Northwestern University

How Kimberly-Clark Uses Real Options 40 Martha Amram, Growth Option Insights, and Fanfu Li andCheryl A. Perkins, Kimberly-Clark Corporation

Handling Valuation Models 48 Stephen H. Penman, Columbia University

FMA Roundtable on Stock Market Pricing and Value-Based Management 56 Panelists: Tom Copeland, MIT; Bennett Stewart, Stern Stewart;Trevor Harris, Morgan Stanley; Stephen O’Byrne,

Shareholder Value Advisors; Justin Pettit, UBS; David Wessels,

University of Pennsylvania; and Don Chew, Morgan Stanley.

Moderated by John Martin, Baylor University, and Sheridan

Titman, University of Texas at Austin

Expectations-Based Management 82 Tom Copeland, MIT, and Aaron Dolgoff, CRAI

Incentives and Investor Expectations 98 Stephen O’Byrne, Shareholder Value Advisors,and S. David Young, INSEAD

The Effect of “Private” and “Public” Risks on Oileld Asset Pricing: EmpiricalInsights into the Georgetown Real Option Debate

106 Gavin L. Kretzschmar and Peter Moles,

University of Edinburgh

The Real Reasons Enron Failed 116 Bennett Stewart, Stern Stewart & Co.

Multinationals in the Middle Kingdom: Performance,Opportunity, and Risk

120 David Glassman, Prince Management Consulting

In This Issue: Valuation, Capital Budgeting, and Value-Based Management


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he value of a business is based on its futureprospects so it is understandable that valuationmodels that involve forecasts have consider-able currency. Benjamin Graham was skeptical,

however. He and his fellow fundamentalists warned that themathematical formulas underlying these models convey afalse sense of precision; worse, they provide cover for “play-ing with mirrors.”

A valuation model is usually expressed as a formula,but really is a directive about how to go about the task ofvaluation. A valuation model has two features: rst, it speci-es what is to be forecast to capture the future prospects;second, it dictates how to convert those forecasts to a valua-tion. For example, the dividend discount model instructs usto forecast future dividends, d, and convert those expecteddividends to a value by discounting them at a rate, r. Stated

in the form of a “formula out of higher mathematics” (!), thevalue of equity (now, at time 0) is

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This model, like most valuation models, views goingconcerns as continuing indenitely. But forecasting for very

long (innite) horizons is impractical, so long-term expecta-tions are summarized by a growth rate, g, which is appliedafter a period of years, T, over which dividends are explicitlyforecast. It is this “continued growth” that draws Graham’s

objection. Indeed, due diligence teams in IPOs, acquisi-tions, and other corporate transactions, as well as expert witnesses in valuation cases, all understand how a formulacan be used to justify any desired value through the choiceof a growth rate.

In expressing his cynicism about valuation formulas,Graham was adhering to the fundamentalist dictum: under-stand what you know and distinguish it from speculation;put your weight on what you know and avoid buildingspeculation into your valuation. He saw long-term growthrates as particularly speculative. That discipline would haveserved an investor well in speculative times like the late

1990s. However, under such discipline, one would havefailed to invest in many of the successful growth compa-nies of the last half of the 20th century.1 The mathematicalformulas are correct to say that growth is a part of value,and to ignore it is to omit a component of value. How cangrowth be handled in a disciplined way? This paper exploresschemes for handling growth that honor the fundamentalistdictum of putting our weight on what we know and avoid-

by Stephen H. Penman, Columbia University*

T

* This paper draws on themes in the author’s book, Financial Statement Analysis andSecurity Analysis, 3rd ed. (New York: The McGraw-Hill Companies, 2006). Commentsfrom Jim Ohlson and Carl Vieregger have been helpful.

1. Later value investing books persist with warnings about growth, though more accom-modating. See S. Cottle, R. Murray and F. Block,Graham and Dodd’s Security Analysis ,

5th ed. (New York: McGraw-Hill Book Company, 1988), pp. 542-546 and B. Greenwald, J.Kahn, P. Sonkin, and M. van Biema,Value Investing : From Graham to Buffett and Beyond .(New York: John Wiley & Sons, Inc.), pp. 31-43.

48 Journal of Applied Corporate Finance• Volume 18 Number 2 A Morgan Stanley Publication• Spring 2006

The concept of future prospects and particularly of continued growth in the future

invites the application of formulas out of higher mathematics to establish the present

value of the favored issue. But the combination of precise formulas with highly

imprecise assumptions can be used to establish, or rather justify, practically any valueone wishes, however high, for a really outstanding issue.—Benjamin Graham,The Intelligent Investor , 4th rev.ed. (New York: Harper and Row, 1973), pp. 315-316.

Handling Valuation Models


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ing speculation. Indeed, the paper will show how valuationmodels can be applied to use what we know to challengespeculation about growth.

Growth rates are not the only component of a valuationmodel that is suspect. All valuation models incorporate adiscount rate—the r in the dividend discount model above—and a desired valuation can also be justied by the choiceof discount rates. Despite considerable effort to develop so-called “asset pricing models,” we really do not know howto quantify discount rates. The premier model, the Capital Asset Pricing Model (CAPM), is another formula, amongmany, that encourages playing with mirrors; the due-diligence team and valuation expert know well that changesin beta estimates or in the market risk premium (which isessentially a guess) have a signicant effect on the discountrate and the value calculated. If we are honest, the discountrate is a matter of considerable speculation and, again, soundfundamental analysis warns about building speculationinto a valuation. Valuation formulas are correct to includediscount rates, for expected payoffs must be discounted fortheir risk and the time value of money. Can we developschemes that acknowledge this principle but honestly recog-nize that we don’t know how to measure the discount rate?

Minimalist Valuation SchemesSince anticipating payoffs is inherently speculative, onemight throw up one’s hands and avoid any forecasting atall. The widespread use of comparables does this by simply

pricing a target rm on the basis of price multiples—price-to-earnings, price-to-book, and so on—of comparablerms. Such methods are useful for identifying the price at which a private rm might trade were it listed, but hardlyprovide the discipline of avoiding speculation. If the compa-rable rm is trading at a speculative price, one will overpricethe target. Indeed prices bubbles are perpetuated if pricesare set on the basis of speculative prices of other stocks inthe mode of a chain letter. The method delivers price butnot value. It dees another fundamentalist dictum that saysthat, when valuing stocks (to challenge prices), be carefulnot to build price into the valuation. The method assumes

that markets are efcient in capturing future prospects, butif all stocks were priced on the basis of each other’s price,how would future prospects ever show up in price?

Valuation via comparables cuts against another invest-ing strategy: distinguish price from value by observingdifferences between price multiples within a set of compa-rable rms. These are so-called screening technologies: buylow P/E stocks and sell high P/E stocks, or buy low price-to-book (P/B) stocks and sell high P/B stocks, for example.But this raises another issue. With such simple schemes toidentify mispriced stocks, why would one embrace a valua-tion model? Well, the short answer is that such schemes are

too simple. Using a single screen (like P/E) uses only one

piece of information (earnings) and one ignores informa-tion at one’s peril. Screeners typically add information byusing multiple screens (both P/E and P/B, say), but arestill in danger of trading with someone who has done theirhomework, someone with an anticipation of the futurebased on wider information. Further, the screener could beloading up on risk, and both P/E and P/B surface as riskattributes in the asset pricing literature. Thus both methods,pricing from comparables and screening analysis, are toosimple. The diligent investor requires a model that builds inanticipations and incorporates risk. A valuation model doesboth. But, given Graham’s objections to valuation modelsand uncertainty about the discount rate, there clearly is atension. How can this tension be resolved?

Accounting for Value: Anchoring on What We KnowConsider how the fundamentalist dictum—understand whatyou know, anchor to it, and separate it from speculation—might be operationalized in a valuation model. A valuationmodel can be broken down into three components:

V 0 = Value based on the present (1) + Value based on information about

near-term prospects (2) + Value based on long-term prospects (3)

The rst component is based on what we know now

(from the present and the past) and includes the earnings,book values, cash ows, and so on that are used in activescreens. If we are to anchor on what we know, this part ofthe valuation gets signicant weight. The second compo-nent is based on forecasts of earnings, book values and cashows for the near term (two years, say) about which we areless sure but feel we can get a reasonable grip on. The thirdcomponent is the speculative component. We have separated what we know (and are reasonably sure about), components(1) and (2), from speculation, component (3). What is nowneeded is a model that shows how to convert the informa-tion we rely on into a valuation.

The dividend discount model introduced earlier involvescomponents (2) and (3): one forecasts dividends over thenear term up to a horizon, T, then adds a growth rate for thelong term. This model is intuitively appealing, for the valueof equity is surely based on the dividends it is expected to pay.But does it anchor on what we know about value? Well, no. We may be fairly sure about near-term dividends—they aretypically predictable—but that knowledge does not get usfar. A basic (Miller and Modigliani) proposition in nancesays that value should not be affected by the dividends arm is expected to pay over the near term. Value is basedon dividends that the rm will pay eventually, in the specu-

lative long term, but forecasting dividends over the nearJournal of Applied Corporate Finance• Volume 18 Number 2 A Morgan Stanley Publication• Spring 2006 49


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future has no bearing on value. This is easily appreciatedin the case of a (valuable) rm like Cisco Systems that paysno dividends: we might forecast that dividends will be zeroover the next few years, and be reasonably condent in thisprediction, but that tells us nothing about value; we havenot anchored on what we know about value.

Dividends pertain to the distribution of value, not thegeneration of value, and the timing of distributions mayhave nothing to do with value generation. Value is gener-ated by trading with customers, not by paying dividends outof that value. We need to articulate what is going on insidethe rm to quantify the generation of value. We need to dosome accounting on the rm. Refer to this as “accountingfor value.” A valuation model is really just a prescriptionfor accounting for value. Just as there can be good and bad

accounting, so we can have good and bad accounting forvalue, and good and bad valuation models.

Anchoring on Cash Flows: Cash Accounting andDiscounted Cash Flow ValuationThe popular discounted cash ow (DCF) model accountsfor value using cash accounting:

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The value of the equity is enterprise value (the value of the

rm) minus the net debt, and the enterprise value is given bythe present value of forecast free cash ows, FCF.2 Account-ing for value is accomplished by accounting for (future) cashows from the business (as in the cash ow statement):

Free cash ow (FCF) = Cash ow from operations– Cash investment

In terms of our three components of value, the modelrelies on component (2)— forecasts for the near term up to

a horizon, T—and component (3), the so-called “terminalvalue” or “continuing value,” which is based on a speculativeforecast about the long-term growth rate of free cash ow.Does this anchor on what we know? Well, component (1) isnot present. And we may also run into problems if we put our weight on the near term, component (2). Are free cash owsforecast over the next few years a good indicator of value?They can be, but often are not. Free cash ow is reduced bycash investment, but investment (generally) adds value ratherthan reducing it. Firms like General Electric, Wal-Mart, andHome Depot have consistently reported negative cash ows,not because they are troubled rms but because they arevaluable rms with a lot of investment opportunities.

To understand how DCF analysis can frustrate a valua-tion, consider the free cash ows that GE reported for

2000-2004 shown in Table 1.3 Pretend that you are standingat the end of 1999 and have been given advance knowledge

of the cash ows that will be reported over the next veyears. Go ahead and value the rm. With such privilegedinformation, one might be condent in the exercise, butstudents given this task balk (of course). The free cash owsare negative in all years except 2003, and the 2003 ow ispositive only because of a drop in investment. The terminalvalue, the speculative component, is over 100% of the value(for a positive price), but there is no indication how we mightcalculate it. Applying a growth rate to a negative 2004 cashow is problematic, to say the least. As a practical matter, we

have model failure. The extensive investments that result inthe negative cash ows will probably generate positive cashows after 2004, so one can extend the forecasting horizon.But that requires speculation about the long run.

Free cash ow is an unreliable indicator of value, notsomething to anchor on. In a sense, it is a liquidationconcept: companies can increase free cash ow by reduc-ing investment (as GE did in 2003) and reduce free cashows by making investments that add value (as in the otheryears). The DCF model gives the correct value because it

2. To be technically correct, the discount rate now is the enterprise discount rate, theso-called weighted-average cost of capital.

3. These cash ows are slightly different from those reported in GE’s cash ow state-ment because they have been unlevered by removing the interest and other nancing cashows that GAAP includes in operating ows.


Table 1 Free Cash Flows and Earnings for General Electric Co. for 2000-2004.(In millions of dollars, except EPS amounts)

2000 2001 2002 2003 2004

Cash from operations 30,009 39,398 34,848 36,102 36,484

Cash investments 37,699 40,308 61,227 21,843 38,414

Free cash ow (7,690) (910) (26,379) 14,259 (1,930)

Earnings 12,735 13,684 14,118 15,002 16,593

EPS 1.29 1.38 1.42 1.50 1.60


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compensates for the near-term forecast with a correctivelong-term forecast, but the effect is to shift the weight in thevaluation from component (2) to component (3). BenjaminGraham would not approve. Is there an alternative account-ing that introduces a valuation component (1) and providesa component (2) on which we can place some weight?

Anchoring on Book Value and Earnings: Accrual Accounting Valuation Accrual accounting, which focuses on the balance sheet(book value) and the income statement (earnings) ratherthan the cash ow statement, differs from cash accountingin two ways: First, investments are placed on the balancesheet rather than subtracted from earnings; second,accrual components of income (value ows other thancash ows) are recognized in earnings. The rst featureis clearly desirable, for the perverse feature of free cashows is avoided. The second recognizes that value can begained or lost for shareholders without a cash ow. Paying wages with stock options is a good example ; others includepaying wages with pension promises (pension accruals)and recognizing revenue from a receivable (rather thanon payment of the receivable). A fundamental accountingequation states that:

Earnings (before interest) = Free cash ows +Investments + Accruals

This correction to free cash ows looks like a good basisfor measuring value added. General Electric, while reportingnegative free cash ows, reported a string of positive, growingearnings for 2000-2004 (see Table 1). Accrual accounting,in principle , aims to measure the value added from trading with customers and does that by an appropriate treatmentof investment (a cost of trading with future, not current,customers) and recognition of non-cash components ofvalued added in the trading process. I emphasizein prin-ciple because this does not mean that GAAP accounting iscompletely successful in the endeavor, but it is important toappreciate that accrual accountingin principle serves busi-

ness valuation well.Suppose one were reasonably condent of one’searnings forecasts for the next two years and felt thoseforecasts were something to anchor on. (Analysts typicallyforecast point estimates of earnings for only two yearsahead.) Then valuation with accrual accounting proceedsunder the following formula, the residual earnings model

(or residual income model). For a two-year forecastinghorizon,

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Residual earnings, REt = Earningst – (r × Bt-1), is earningsin excess of a charge against the book value of commonequity, B, which is the net assets employed in generatingthe earnings. Residual earnings can also be calculated asREt = (ROEt – r) × Bt-1, where ROE is expected earningsrelative to book value. If we forecast ROE = r for all futureperiods, then V 0 = B0 and the intrinsic price-to-book ratio,P/B, is 1.0; if we forecast ROE > r, then we conclude thatthe intrinsic P/B is greater than 1.0; and if we forecast ROE< r, then we conclude that the intrinsic P/B is less than 1.0.In contrast to the doubtful free cash ow concept, residualearnings is a logically consistent way to look at value added:a rm adds value to its book value only if it earns a rate ofreturn on book value greater than the required return.

As a point of theory, this valuation will always be equiva-lent to a dividend discount valuation and a DCF valuationif we somehow could forecast dividends and cash ow forvery long (innite) horizons, or if we somehow could get thecorrect (but different) growth rates for each model. However,in separating what we know from speculation, this modelbreaks down the components of the valuation differently. Wenow have a component (1), the book value, which we observe

in the present. If mark-to-market accounting is applied,the book value gives the complete valuation, as in the caseof an investment fund where one trades as net asset (book)value. More generally, book value is not sufcient so one addsforecasts of residual earnings for the near term, component(2), and speculation about the long term, component (3), toestimate the difference between value and book value.

It makes eminent sense to anchor the rst component onsomething in the (audited) nancial statements rather thana forecast of the future. In doing this, we are recognizing where the rm is now, before moving to the more tenta-tive task of adding value for the future. General Electric’s

per-share book value in its 2004 nancial statements was$10.47. In April, 2005, analysts were forecasting consen-sus earnings per share (EPS) of $1.71 for 2005 and $1.96for 2006. Using a required return, r, of 10 percent andsetting the long-term growth rate equal to the average GDPgrowth rate of 4% yields a valuation of $23.69.4 GE tradedat $36 at the time. Of course, if one had some condence in

4. The calculation goes as follows:

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where RE1 = $1.71 – (0.10 × 10.47) = $0.663, book value forecasted for the end of year1 = $10.47 + 1.71 – 0.91 = $11.27 (with a dividend of $0.91 per share indicated for2005), and RE

2 = $1.96 – (0.10 × 11.27) = $0.833.

Journal of Applied Corporate Finance• Volume 18 Number 2 A Morgan Stanley Publication• Spring 2006 51


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forecasting growth rates for the immediate term (over thethree to ve years for which analysts typically forecast EPSgrowth rates, for example), one could expand the forecasthorizon to incorporate these intermediate-term projectionsthat might differ from the GDP growth rate expected for

the very long term.

Dealing with the Speculative Componentin a ValuationIn making the $23.69 valuation for GE, we have refused tospeculate about the long-term growth rate. We have set itsolely on what we know from the past, the average for theeconomy. In Grahamite fashion, we might well choose toanchor on the 4% and refuse to speculate further. However, we recognize that individual rm’s growth rates may vary.Before retiring, there is something else we can do: we canreverse engineer the model to get an understanding of the

growth rate implicit in the market price of $36, and thenchallenge the market’s expectation.Figure 1 displays the three components that make up

the market price of $36.5 The book value component of$10.47 we know for certain. We are reasonably sure of the$8.18 component (and would be even more condent ifthis were calculated from our own forecasts rather than theanalysts’ consensus). Component (3), consisting of $17.35of the $36, is speculative value, corresponding to the last

term in the two-period residual model. Anchoring on what we know in components (1) and (2), we can solve for thegrowth rate: g = 7.0%. We may not know the long-termgrowth rate but, with an exercise in reverse engineering, wecan understand the growth rate that the market sees at a

price of $36. We understand what we are buying if we buyat the market price. We can now turn to challenge the market’s speculation:

given what we know, is the market’s growth forecast a reason-able one, or is it out of line? We might conclude (or not) thatGE can maintain a growth rate, perpetually, in excess of theGDP rate. Or we might put in some effort to pro forma thegrowth under alternative “reasonable scenarios” to challengethe 7.0% rate. Note that the calculated growth rate refersto growth in residual earnings, not earnings, but with aforecast of dividends, a residual earnings forecast can readilybe converted to an earnings per share forecast. The 7.0%

growth rate translates to an EPS forecast of $2.11 for 2007,and so on for subsequent years.6 The analyst asks herself: doI see it differently?

In anchoring on book value and two years of earningsforecasts, we have explained $18.65, or 51.8%, of GE’s marketprice (in the rst two building blocks). If we had anchoredon two years of forecast cash ows and they were negative (as with GE in Table 1), we would have had a calculated negativeamount, with over 100% of the market value identied with

5. The second component is calculated as follows:

Two-year-ahead residual earnings, $0.833, are capitalized as a perpetuity, that is, with no

growth. The speculative growth has been shifted to the third component.6. The calculation reverse engineers the residual earnings formula:Earnings for 2007 = (Book value for 2006 × 0.10) + Residual earnings forecasted

for 2007.

Figure 1 Building Blocks of a Valuation for General Electric, April 2005

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the speculative component.7 But that would not incorporate what we know from the accrual accounting. Accrual account-ing in principleeffectively brings value forward in time; cashaccounting defers it to the speculative future. This is theprinciple reason for moving from discounted cash ow valua-tion to residual earnings valuation.

That move to accrual accounting valuation, of course,begs the question of what is the appropriate accrual account-ing. For GE, we have observed some advantages in usingGAAP accounting. However, the quality of GAAP account-ing is suspect on a number of dimensions. For example,GAAP accounting expenses investments in R&D; GAAPapplies cash accounting to R&D, resulting in low earningsand even reported losses for (valuable) R&D rms, and thusintroduces the same valuation problems we have observed with cash accounting. But what constitutes the appropriateaccrual accounting is a question for another day.

Reverse Engineering and Enhanced ScreeningIf one wishes to engage in stock screening, one mightscreen on implied growth rates rather than simple P/Bor P/E ratios. This builds what we know in the rst twobuilding blocks into the screen and isolates the most spec-ulative component of the price that is presumably subjectto mispricing. However, there is another aspect of thevaluation model that is also subject to speculation, onethat we have overlooked to this point: we do not knowthe required return. If we had set the required return for

GE at 9% (a risk premium of 4.5% over the 4.5% yieldon the 10-year treasury note at the time) rather than the10% in the valuation above (a risk premium of 5.5%), we would have calculated a per-share value of $28.53, closerto the money, and the implied growth rate would havebeen 5.5%. If we are condent in our estimate of the riskpremium, we might proceed on this basis, but risk premi-ums are very much a guess.

Alternatively, we might admit our ignorance andproceed (as a fundamentalist would) on the basis of what we know, grouping rms into perceived risk classes basedon an analysis of their fundamental risk characteristics. This

ordinal grouping into risk classes admits (honestly) that we cannot distinguish risk within a class, only differences

between classes; this is as ne an identication as our knowl-edge will allow. Then, to complete the screen, rank rms onimplied growth rates within risk classes. With this controlfor perceived risk, one reasonably screens out stocks wherethe market might be overly speculative.

Enhancements in Challenging GrowthSpeculationsForecasting a constant growth rate after two years is somewhatunsatisfactory; one typically thinks of higher growth in theintermediate term, declining to normal growth in the longterm. This view can be implemented by extending the horizonfor forecasting residual earnings (to ve years, for example),and then estimating an implied long-term growth rate there-after. However, there is another way to go about it.

By recognizing that the change in book value is deter-mined by (comprehensive) earnings before net dividends,the two-period residual earnings model can be written as

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where RE2 is the change in residual earnings in year 2 overyear 1. This presents the valuation in the form of a P/E ratiorather than a P/B ratio. Investors and analysts tend to talk interms of P/E ratios rather than P/B ratios: value is based onforward earnings, capitalized, plus a premium for growth.That growth comes from growth forecast two years ahead

plus a long-term growth rate.8 With some reorganization,the formula expresses this idea more clearly:

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where G2 is the forecast EPS growth rate two years ahead.9

This version, known as the Ohlson-Juettner model after itsarchitects, explicitly identies the forward earnings multi-plier.10

Figure 2 applies this model to Cisco Systems. In Septem-ber 2004, Cisco traded at $21 per share and analysts were

forecasting EPS of $0.89 for scal year ending July, 2005and $1.02 for 2006. Since Cisco pays no dividends, forecast

7. To be fair, GE is a particular (but not unusual) case. DCF valuation works OK forcases where cash ows are aligned with the value generation. The Coca Cola Company,for example, regularly produces positive free cash ows that grow at about the same rateas residual earnings from their operations.

When applying DCF valuation, analysts sometimes make adjustments to cash ows(distinguishing maintenance investments from growth investments, for example) to dealwith the investment problem. These adjustments are really a form of accrual accountingand beg the question as to the appropriate accrual accounting for valuation. From afundamentalist’s point of view, accrual accounting should not embrace too much specula-tion. “Maintenance capex” is notoriously hard to identify, so one must ask whether apply-ing such an accrual concept builds too much speculation into the accounting.

8. The transformation of the residual earnings model to the P/E form here recognizesthat

That is, anchoring on book value plus forward residual earnings capitalized (withoutgrowth) is the same as anchoring on capitalized forward earnings (without growth). In thespirit of anchoring on something in the nancial statements, the modeling permits anchor-ing on reported earnings rather than book value, in which case the focus is on the trailingP/E rather than the forward P/E:

In this case, the current EPS0 should be a measure of core EPS to purge the earningsof transitory items that do not produce growth.

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EPS growth for 2006 was $1.02/$0.89 = 14.6%. Once againsetting the required return at 10% and the long-term growthrate at the GDP growth rate of 4%, the calculated forward(intrinsic) P/E is 17.68 which, when applied to forward EPSof $0.89, yields a per-share value of $15.73. Moving intoreverse engineering mode, one could set r = 10% and calcu-

late the long-term growth rate implied by the market priceof $21: g = 6.6%. The EPS growth rates that this implies,for years beyond 2006, are plotted in Figure 2. From the14.6% growth forecast by analysts for 2006, we see a gradualdecay in the growth rate. A geometric decay is built into themodel and suitably so, for we typically expect high earningsgrowth to decline over years as growth rms become lessprotable under competition and their P/E ratios revert tonormal levels. Indeed, if we were to extrapolate these EPSgrowth rates out to the very long run, we would see that theyconverge to the 6.6% long-term growth rate implied by themarket price.

The projected EPS growth path distinguishes buy andsell regions in Figure 2. If, on the basis of our own analysis, we feel that Cisco cannot maintain this growth path that themarket sees, we must sell. If we see growth rates above thepath, we buy.

However, we have again built in speculation about therequired return. Do both GE and Cisco have the samerequired return of 10%? (With a beta of 0.4 for GE and 1.6

for Cisco, we might give them a different required return,though we would be speculating about how much thatdifference should be.) This formulation of the model doesgive us another degree of freedom to work with, however. We do have a grasp on the average GDP growth rate, so if we are willing to put this into the set of “what we know,” we

can set g = 4%. Then, anchoring on everything else in theformula, we can reverse engineer to get the implied r in themarket price rather than the implied g. For Cisco at $21, aG2 of 14.6%, and g set to 4%, the implied r = 9.0%. It isimportant to note that this implied r is the required returnonly if the market price is a fair (efcient) one. Rather, itis the implied rate of return to be earned from buying thestock at the market price, and a higher price yields a lowerreturn. If we were looking for a higher return for the riskborne (say 10%), we would sell Cisco. In screening mode, we would rank rms on their implied r and buy those with highr and sell those with low r. Before ranking, we might group

rms into fundamental risk classes, and then rank withinrisk class, so that Cisco (with a beta of 1.6) would demanda higher implied return than GE (with a beta of 0.4). Thisapproach serves us well if we deem the (very) long-termgrowth rate to be the same for all rms: we have anchoredon near-term forecasts about which we felt comfortable andon a long-term growth rate that must correspond to averageGDP growth.

Figure 2 Projected EPS Growth Forecast Implicit in the Market Price of $21 forCisco Systems Inc., September 2004

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9. Strictly, G2 is the forecasted growth rate in cum-dividend earnings, that is, with thereinvestment of any dividends expected to be paid in year 1:

This recognizes that dividends can be reinvested to earn further earnings (by buyingthe stock with the dividend, for example).

10. See J. Ohlson and B. Juettner-Nauroth, “Expected EPS and EPS Growth as Determi-nants of Value,”Review of Accounting Studies , Vol. 10 (2005), pp. 350-365. See also thediscussion of the model by S. Penman on pp. 368-378 of the same issue of the Reviewof Accounting Studies .

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The View from Corporate FinanceSo far, this paper has been written from the point of view ofan investor evaluating a buy or sell of a stock. The tools read-ily translate to corporate nance, however. The CFO andthe rm’s banker need to understand the market’s pricing ofthe rm’s stock. An implied growth rate turns the price intoan earnings forecast that the CFO can evaluate as realistic ornot; it articulates the market’s expectations. (For the calcula-tions, he or she anchors onthe rm’s near-term forecasts, ofcourse, not those of analysts.)

With these tools, the CFO can get a sense of the under-or overpricing of the rm’s shares for such decisions as timingshare offerings and share repurchases, or choosing betweendebt and equity offerings. He or she understands value inacquisitions, not only the valuation of the target, but alsothe valuation of the rm’s own shares to decide whether(overpriced) those shares should be offered in exchange.The CFO, along with the associated investment banker,can also challenge due diligence valuations used to justifyprices. For acquisitions, the methods here, though maintain-ing some simplicity, surely dominate too-simple relative P/Eapproaches; indeed, the methods are essentially a renementof the relative P/E approach using more information.

A CFO with a dened hurdle rate may choose to usethat rate for r in the analysis and focus on implied growthrates. Implied r ts naturally into corporate nance, however,because it is essentially the internal rate of return (IRR) sofamiliar in project nance. The CFO has some advantage in

developing an “accounting for value” rather than relying onGAAP accounting, for presumably he has better information with which to capitalize and amortize R&D and other invest-ments, and to evaluate when GAAP rules are arbitrary andmisleading with respect to his rm. (Be careful about buildingin too much speculation into the accounting, however!)

In corporate nance we usually work with enterprisevaluations rather than the equity valuations above, but theresidual earnings model can be adapted to enterprise valua-tions. With a two-year forecasting horizon, the value of theequity can be expressed as

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where ReOIt = Operating incomet – (r × Net Operating Assetst-1) and r is now the weighted-average cost of capital.Operating income is income from the business (earningsbefore interest) and net operating assets is the capitalinvested in the business—that is, equity plus net debt. All ofthe analysis can be done with operating income substitutedfor EPS and residual operating income (ReOI) substitutedfor residual earnings (RE) in the formulas above.11 Reverse

engineering proceeds with enterprise market price (equityprice + net debt) substituted for equity price.

ConclusionsValuation is a question of handling uncertainty. Valuationmodels supposedly accomplish this by specifying expectedgrowth rates and discount rates that discount for uncertainty(risk). However, growth rates—and the discount rate itself—are highly uncertain, even speculative, leading to BenjaminGraham’s objection to valuation models at the head of thispaper. Valuation models, expressed as mathematical formu-las, look precise, but can be abused to convey fake precision.To handle uncertainty, we need a means of handling theuncertainty embedded in valuation models.

This paper has attempted to nesse the problems withvaluation models that so concerned Benjamin Graham, andin a way that honors the fundamentalist creed from whichthose concerns arise. Valuation models are implementedunder a discipline that separates what we know, based on solidfundamental information, from speculation. Accounting isimportant, for accounting discovers what we know about abusiness. Accordingly, accrual accounting methods of valuation(and residual earnings methods) are preferred to cash accounting(and discounted cash ow methods). These models are imple-mented in a rather unconventional way, however. They are usedto incorporate “what we know” and then turn that knowledgearound to identify the speculative component of market prices.Further, they express that speculation in the form of earnings

forecasts that can be challenged with fundamental analysis. And, with additional input about fundamental risk characteris-tics, uncertainty about discount rates can also be handled.

Equity investing is not a game against nature and valua-tion models should not be seen as identifying a true intrinsicvalue. Rather, equity investing is a game against other inves-tors and valuation models should be used to understand howan investor thinks differently from the market. Thus the rightquestion is not what the “right” value is, but rather whether amodel can help an investor understand what perceptions bestexplain the market price, and then compare those perceptionsto his own. The paper shows how to handle valuation models

under this approach, and in a way that meets the objections inthe Graham quote at the top of the paper.

stephen penman is the George O. May Professor of Accounting atColumbia’s Graduate School of Business, as well as co-director, withTrevor Harris, of the school’s Center for Excellence in Accounting andSecurity Analysis. He is widely recognized as one of the leading scholarsin nancial statement analysis, having published numerous papers onthe subject along with a well-received book entitledFinancial StatementAnalysis and Security Valuation .

11. For details, see S. Penman, Financial Statement Analysis and Valuation , referenced above, Chapters 13-14.



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