1 Learning About Intrinsic Valuation With the Help of an Integrated Valuation Model

8/9/2019 1 Learning About Intrinsic Valuation With the Help of an Integrated Valuation Model

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Learning About Intrinsic Valuation With the Help of an

Integrated Valuation Model

James A. GentryUniversity of Illinois at UrbanaChampaign

Frank K. Reilly Michael J. SandrettoUniversity of Notre Dame University of Illinois at UrbanaChampaign

Abstract

An integrated strategic financial management system provides students of finance an

invaluable learning experience in assessing the financial health of a company or estimating

the value of this company. We found students questions and misunderstanding about how to

assess a companys financial health or apply current valuation theories led to the

development an integrated valuation system (IVS). One objective of a dynamic valuation

system is to help students simulate changes in a firms financial strategies and discover howthese changes affect a firms credit health or its value. Additionally, an IVS provides a solid

conceptual foundation for a student to justify the credibility of a growth rate used to estimate

the terminal value of a project or stock. The IVS helps students learn why the intrinsic value

of a stock estimated by a dividend discount model (Vs[DIV]) may not equal the intrinsic

value of a stock estimated by discounting the free cash flow to equity (Vs[FCFE]), i.e.,

Vs[DIV] Vs[FCFE]. An IVS can also help a student to understand why the value of a firm

that is based on discounted free cash flow to the firm (Vf[FCFF]) may not equal discounted

free cash flow to equity (Vs[FCFE]) plus discounted free cash flow to debt (Vd[FCFD]), or

Vf[FCFF] [Vs[DIV] + Vd[FCFD]]. One reason for these valuation inconsistencies is thatthe underlying theories were developed independently in different time periods. Also inputs

for each of the models were unique because the models were not developed as a total

integrated system. Therefore, a valuation system was created that integrates the key

components needed to estimate the intrinsic value of a companys equity (Vs[FCFE]), debt

(Vd[FCFD]) and its firm value (Vf[FCFF]). The integrated valuation system helped reconcile

the valuation dilemmas by solving for an implied terminal growth rate of dividends [gDIV]


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Published: 2003

URL: http://www.business.uiuc.edu/Working_Papers/papers/030108.pdf
http://www.business.uiuc.edu/Working_Papers/papers/03-0108.pdf


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LEARNING ABOUT INTRINSIC VALUATION WITH THE HELP OF AN

INTEGRATED VALUATION MODEL

James A. Gentry

IBE Distinguished Professor of Finance

University of Illinois, Urbana-Champaign

[email protected]

Frank K. ReillyBernard J. Hank Professor of Business Administration

University of Notre Dame

[email protected]

and

Michael J. Sandretto

Visiting Associate Professor of Accountancy

University of Illinois, Urbana-Champaign

[email protected]
mailto:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]


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ABSTRACT

An integrated strategic financial management system provides students of finance aninvaluable learning experience in assessing the financial health of a company or estimating thevalue of this company. We found students questions and misunderstanding about how to assessa companys financial health or apply current valuation theories led to the development anintegrated valuation system (IVS). One objective of a dynamic valuation system is to helpstudents simulate changes in a firms financial strategies and discover how these changes affect

a firms credit health or its value. Additionally, an IVS provides a solid conceptual foundationfor a student to justify the credibility of a growth rate used to estimate the terminal value of aproject or stock. The IVS helps students learn why the intrinsic value of a stock estimated by adividend discount model (Vs[DIV]) may not equal the intrinsic value of a stock estimated by

discounting the free cash flow to equity (Vs[FCFE]), i.e., Vs[DIV] Vs[FCFE]. An IVS can also helpa student to understand why the value of a firm that isbased on discounted free cash flow to thefirm (Vf[FCFF]) may not equal discounted free cash flow to equity (Vs[FCFE]) plus discounted free

cash flow to debt (Vd[FCFD]), or Vf[FCFF] [Vs[DIV] + Vd[FCFD]]. One reason for these valuation

inconsistencies is that the underlying theories were developed independently in different timeperiods. Also inputs for each of the models were unique because the models were notdeveloped as a total integrated system. Therefore, a valuation system was created that integratesthe key components needed to estimate the intrinsic value of a companys equity (Vs[FCFE]), debt(Vd[FCFD]) and its firm value (Vf[FCFF]).

The integrated valuation system helped reconcile the valuation dilemmas by solving for animplied terminal growth rate of dividends [gDIV] that causes the Vs[DIV] = Vs[FCFE]. The IVS also

determines an implied terminal growth rate of the FCFF[(gFCFF), that causes the Vf[FCFF] =[Vs[FCFE] + Vd[FCFD]]. The challenge to the learners is to interpret accurately the informationconveyed via the implied terminal growth rate of dividends (gDIV) and the implied terminalgrowth rate of the FCFF (gFCFF).


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LEARNING ABOUT INTRINSIC VALUATION WITH THE HELP OF AN

INTEGRATED VALUATION MODEL

Students of financial analysis are constantly searching for the equivalent of HarryPotters magic wand to provide fresh insights into the process of interpreting the financialhealth of a company or estimating its intrinsic value. During the past seven decades severalmodels have been proposed to estimate the intrinsic value of a stock or a firm. For example, inthe 1930s and 1940s Graham and Dodd [1934, 1940] advocated using fundamental securityanalysis techniques to discover if the level of a stocks P/E multiple provides signals forinvestment opportunities, e.g., [P/E]x EPSt+1 = Pt+1. Interest in multipliers has continued to

expanded and today there are a variety of multipliers, such as Price/Book Value (P/B),Price/Sales (P/S) and Price/EBIT, used to estimate a stocks potential value, Damadoran [2001,Chapters 8-10]. Naturally, there are solid reasons for using multipliers to estimate the value ofa stock, but there are also shortcomings.

Near the end of the Great Depression, Williams [1938] introduced the classic dividenddiscount model [DIV] for estimating the value of a stock (Vs[DIV]). Later, Gordon [1962]extended the Williams model by introducing a dividend growth component in the late 1950s

and early 1960s. The DIV continues to be widely used to estimate the value of a stock, Vs[DIV].

In recent years the literature for estimating the value of a firm (Vf) and the value of astock (Vs) has expanded dramatically. Copeland, Koller and Murrin [1990, 1994, 2000],Rappaport [1988, 1998], Stewart [1991], and Hackel and Livnat [1992] were current pioneersin modeling the free cash flow to the firm [FCFF], which is widely used to derive the Vf.Recently, Copeland, Koller and Murrin [1994] and Damadoran [1998] introduced an equityvaluation model based on discounting a stream of free cash flows to equity [FCFE] at arequired rate of return to stockholders. Also Damadoran [2001] provides several approaches toestimate the value of a firm for which there are no comparable companies, no operatingearnings and a limited amount of cash flow data. Famas [1970] efficient market researchchallenged the validity of intrinsic valuation models.

Finally, a real options approach for valuing firms that have no comparables or operatingearnings and usually only limited data for analysis was launched in 1999. The leaders in

developing a real options approach to valuation were Amram and Kulatilaka [1999], Brennanand Trigeorgis [1999], Schwartz and Moon [2000], Copeland and Antikarov [2000] andDamadoran [2001, Chapter 11].

During the past decade we have been deeply involved in learning and teaching thetheory and practice of assessing the financial health of a company or estimating its intrinsic

l W f d t d t ti d i d t di b t h t


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Why are net operating cash inflows so important in the wealth creation processand/or in the assesment of a companys credit risk?

What can management do to improve the creation of operating cash inflows?

How does the investment in physical, human and working capital create firmvalue and/or change its credit risk?

How does depreciation and amortization contribute to the creation firm value?

What is the relationship between investment and financing?

Why does a long-run stable relationship between debt and equity contribute to thelong-run value of a company?

How does management develop the inputs used in a five-year forecast?

How does management know the inputs used to generate the forecast are correct? What assumptions are most important when preparing a cash flow forecast?

What is the relationship between the free cash flow (FCF) measures to equity(FCFE), debt (FCFD) and the firm (FCFF)?

Another contribution of this paper can best be explained with a brief review of a fewbasic concepts used to estimate the market value of a firm (Vf) , a stock (Vs) and debt (Vd). Abasic concept in the theory of finance is

Vf = [Vs + Vd], [1]

where: Vf is the market value of a firm,Vs is the market value of a stock, andVd is the market value of the long-term debt.

Separate theories are needed to estimate the intrinsic value on each side of equation 1.One theory assumes that the Vf, on the left hand side of equation 1, is estimated by using afirms weighted average cost capital (WACC) to discount to infinity its estimated free cashflows [FCFF]. It is possible to create forecasted inputs so that the Vf[FCFF] = Vf. On the righthand side of equation 1, a second theory assumes the Vs is estimated by discounting to infinityeither the free cash flow to equity [FCFE] or the dividend flows [DIV] at the required rate ofreturn on the equity (ks). With the appropriate forecasted inputs it is possible for the Vs[FCFE] =Vs or Vs[DIV] = Vs. When the Vd is added to the Vs[FCFE] or Vs[DIV], a separate intrinsic value of

the firm (Vf*) is estimated, as shown in equation 1, e.g., V f* = [Vs[FCFE] + Vd] and/or Vf* =[Vs[DIV] + Vd]. Theoretically, the components of the two sides of equation 1 can be equal, i.e.,Vf= Vf*. However, to the best of our knowledge, the linkages required to show that Vf[FCFF] =[Vs[FCFE] + Vd ] and/or Vf[FCFF] = [Vf[DIV] + Vd]has not been previously presented. In addition,equation 1 makes it possible for authors to assume the V f Vd = Vs , e.g., as shown in Rappaportand Mauboussin [2001, pp. 74-76]. Examples that use an all equity firm, or nearly all equity,


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The primary objective of the paper is to present a valuation system that links thecomponents used in estimating the intrinsic value of equity (Vs[FCFE] or Vs[DIV]), debt (Vd[FCFD])and a firm (Vf). In Section I a brief review of the valuation literature is presented, while

Section II develops a theoretical overview of an integrated valuation system. Section III showshow to develop a forecast for integrated income statements and balance sheets. Theseforecasted financial statements provide information needed to estimate the intrinsic value ofequity, debt and a firm. The two basic models for estimating the intrinsic value of equity areshown in Section IV, plus an implied terminal growth rate of dividends is developed. Likewise,Section V presents the linkage that makes the Vf[FCFF] = [Vs[FCFE] + Vd[FCFD]]. Simulatingvarious scenarios highlights the analytical power an integrated valuation system offers to

students of financial analysis. The final section summarizes the most important contributions anintegrated valuation system can make in estimating the long-run value of a firm.

I. LITERATURE REVIEW

A review of the valuation literature indicates there are several fundamental conceptsinvolved in estimating the intrinsic value of a stock, a bond and a firm. In the late 1930sProfessor John Burr Williams [1938] developed a theory for estimating the value of a stock

based on the idea of discounting a constant stream of dividends to infinity [DIV], that is thefuture cash flows that stockholders would receive. In the early 1960s, Gordon [1962] extendedWilliams DIV by allowing the stream of dividends to grow at a constant forecasted rate fromtime period zero to infinity. The Gordon constant growth model is widely used in theinvestment management profession. Also it has been extended to incorporate dividendsgrowing at uneven rates. The estimation of bond value is similar to the dividend discountmodel (DIV), in that the bond value equals to a discounted stream of interest payments and thefinal maturity value at the yield to maturity, Homer and Leibowitz [1972, Chapter 11].

Graham and Dodd [1934, 1940] and Graham, Dodd, and Cottle [1962] proposed anintrinsic-value approach to equity valuation. In the 1962 edition they stated the most importantsingle factor determining a stocks value is now held to be the indicated average futureearning power, i.e., the estimated average earnings for a future span of years. Furthermore,they indicated intrinsic value would then be found by first forecasting this earning power andthen multiplying that prediction by an appropriate capitalization factor, Graham, Dodd andCottle [1962, p. 28]. They wisely stated that any estimate of earning power extending over

future years may easily fall wide of the mark, since the major business factors of volume, price,and cost are all largely unpredictable. Graham, Dodd and Cottle (GDC) [1962, p. 29].

Graham, Dodd and Cottle [1962, p.741-742] reconciled their earning power theory ofvalue to the DIVvaluation models of Williams and Gordon, by discounting low-dividend-paying growth stocks in a manner comparable to discounting a stream of future dividends to


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sub-hypotheses depending on the information set involved: (1) weak-form EMH, (2)semistrong-form EMH and (3) strong-form EMH, Reilly and Brown [1997, p. 211]. FamasEMH raises serious questions concerning the validity of GDCs earning power theory of value

and Williams and Gordons DIV.

In the late 1980s and early 1990s several authors presented a valuation model based onfree cash flow to the firm (FCFF), e.g., Copeland, Koller and Murrin [1990,1994, 2000],Rappaport [1988, 1998], Stewart [1991] and Hackel and Livnant [1992]. Recently, Copeland,Koller and Murrin [1994, p. 500] presented a definition of free cash flow to the shareholder of abank. A few years later Damadoran [1998, 2001] and Reilly and Brown [2000, p. 797]presented a methodology for estimating the free cash that flows to equity shareholder [FCFE].This model opens the door to another approach for estimating the value of a stock, Vs[FCFE], bydiscounting the FCFE at the required rate of return on equity (ks). Thus it is possible tocompare the intrinsic estimates generated by two equity valuation models, Vs (FCFE to the Vs(DIV). Regardless, whether FCFE or dividends are used to estimate the Vs, the required equitydiscount rate (ks) is the same. Additionally, unless there is a 100 percent dividend payout, the

Vs[FCFE] Vs{DIV]. Therefore, this study creates an implied terminal dividend growth rate(gDIV)that makes the value of the discounted dividends equal to the value of the discounted FCFE, Vs

(DIV) = Vs (FCFE).

The preceding discussion briefly introduced the importance of the gDIV why it causesthe Vs[DIV] = Vs[FCFE]. Equally important, is an implied terminal growth rate of FCFF (gFCFF)that causes the Vf [FCFF] = [Vs[FCFE] + Vd[FCFD]]. Solving for an implied terminal growth rate ofFCFF assumes the estimated intrinsic Vs[FCFE] and Vd[FCFC] are correct. It is also assumed thegFCFF is positive and relatively constant throughout the life of the forecast. It is also assumedthere are positive operating cash flows, comparable companies and several years of estimated

cash flows. If these conditions do not exist, can the Vs or the Vfbe estimated? The answer isyes as shown by authors who focus on the using of real options to estimate Vf, e.g., Amram andKulatilaka [1999], Brennan and Trigeorgis [1999], Schwartz and Moon [2000], Copeland andAntikarov [2000] and Damadoran [2001].

This article is not about a real options approach to valuation, but rather the developmentof an integrated valuation system (IVS). An IVS provides a rich and stimulating foundationfor teaching and learning about valuing a firm and an equity. The integrated valuation system

highlights the forecasting and discounting of FCFF and FCFE. Also it shows the sensitivity ofthe cash flow components to changes in the forecasted inputs. The IVS simulates the effect ofusing different growth rates of FCFF and FCFE in estimating the Vs[FCFE] and Vf[FCFF]. It alsoshows how changes in the [D / Vf] and [E / Vf] weights, and changes in ks and kd can affectWACC. The most challenging and important contribution of this paper is the sensitivity of thevalue of a firm (Vf[FCFF]) to the implied terminal growth rate of the FCFF


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II. AN OVERVIEW OF THE VALUATION PROCESS

Value of a Firm (Vf)

There are two widely methods employed to estimate the value of a firm. First, is astatic approach for a single point in time, where the current market value of the equity (Vs) andthe debt (Vd) are known. The market value of the firm is

Vf = Vs + Vd . [2]

A second approach estimates the intrinsic value of a firm by discounting the free cashflows to a firm (FCFF) at the weighted average cost of capital (WACC). Vf[FCFF] is based onthe following equation:

Vf[FCFF] = FCFF1 / (1 + WACC) + FCFF2 / (1 + WACC)2 +.+ [FCFFn + TVn] / [3]

(1 +WACC)n

where:

Vf = intrinsic value of a firm,FCFFt = forecasted annual free cash flows to a firm, periods 1 to n,

= [EBITt (1-T) + depreciationt] + [WCt] + [NIFt] + [OAt],

where: -WC or NIF is an outflow of cash and +WC or +NIF isan inflow of cash,

EBIT(1-T)t = Earnings before interest and taxes adjusted for tax shield,in each of n periods.

WCt = Receivablest + Inventoryt + OCAt + Payablest + OCLt,

NIFt = net fixed assetst + depreciaton expenset + other assetst

WACC = weighted average cost of capital,= wd kd (1- tax rate) + ws ks

wd = Vd / Vfkd = market interest rate on long-term debt,ws = Vs / Vfks = required rate of return on equity derived from CAPMVd = market value of permanent debt,Vs = market value of equity,

TVn = terminal value of FCFFn = FCFFn (1 + g) / [WACC g]where: WACC > g

gn = estimated annual growth in FCFF from period n to


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investment strategies for new and old product lines,

working capital strategies and their stability as a percent of sales,

financial strategies, e.g., dividend policy and target capital structure, and

internal operating efficiencies.

Additionally, when solving for the value of a firm, the role of its discount rate, WACC,and the expected growth in FCFF are impacted by

financial markets outlook for a firms growth rate,

performance of its operating, working capital and investment flows,

potential growth of a firms strategic investments, expected long-run rates of return on a firms equity and debt instruments,

stability of dividend policy and target capital structure,

terminal value (TV) of the FCFF.

Theoretically, financial analysts, portfolio managers and investors estimate annualFCFF for n periods, plus the inputs used in estimating the terminal value (TV). The estimate ofterminal value (TV) assumes the FCFF will grow at a constant growth rate from period n to

infinity. Frequently, the TV represents a major proportion of a firms estimated value. Finallythe stability of the WACC is based on the stability of managements target weights for debt (wd)and equity (ws), plus thestability of the economic outlook for the firm as reflected in themarketplace.

Value of Equity (Vs)

Several methods are used to measure the value of a firms equity. If the current marketVf and Vd are known, the current market equity value equals:

Vs = Vf - Vd. [4]

A second approach for estimating the intrinsic value of a stock is discounting the FCFE.The discounted FCFE provides a dynamic method for solving the intrinsic value of an equity:

Vs[FCFE] = FCFE1 / (1 + ks) + FCFE2 / (1 + ks)2+.+ [FCFEn + TVn ]]/ ( 1 + ks)

n[4]

where:Vs[FCFE] = intrinsic value of equityFCFEt = forecasted free cash flow to equity in periods 1 to n,

= net incomet + depreciation expenset + WCt + NIFt + principal


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The discounted FCFE approach incorporates the cash flows directly associated withequity shareholders for an infinite time period. Theoretically, the FCFE reflects the net cashflows that equity shareholders expect to receive throughout the life of the company. It includes

net income plus depreciation, and plus the outflows associated with capital investments (NIFt)and working capital (WCt). Additionally, an increase in permanent debt becomes a cashinflow to equity holders, while a decrease in permanent debt reflects an outflow of cash. It isassumed the permanent debt is used to finance capital investment projects, that, in turn,generate operating cash inflows. Likewise, the cost of equity (ks) reflects the returns requiredby equity shareholders and does not explicitly include the costs associated with debt, w d, kd, (1-T), that are included in the WACC.

A dividend discount model (DIV) is a third approach used to estimate the intrinsic valueof equity (Vs). In equation form it is:

Vs[DIV] = DIV0 (1 + g) / (1 + ks) + DIV0 (1 + g)2 / (1 + ks)

2 + . + DIV(1 + g)/

(l+ks) [5]

where:Vs = intrinsic value of equity,

DIV0 = annual dividend flows to shareholders in period zero,

1+ gn = estimated annual compound growth in DIV in period n,ks = required rate of return on equity derived from CAPM.

The DIV discounts the dividend flows to equity shareholders that estimates the Vs[DIV].The dividends are assumed to compound annually at a constant growth rate. Theoretically,with 100 percent dividend payout and DIV forecasted inputs identical with FCFE forecastedinputs, Vs[DIV] = Vs [FCFE].

Value of Debt (Vd)

When estimating the value of the permanent debt, the conventional valuation practice isto assume the Vd equals the book value of the long-term debt. However, if the short-term debtis rolled over each year or it increases annually, it is reasonable to assume that the total short-

term debt takes on the characteristics of permanent long-term debt, which would not includeaccounts payable and deferred taxes. Therefore, when a DCF infinite horizon model is used toestimate the Vf[FCFF] or Vs[FCFE], it seems reasonable to assume that the permanent debt(Vd[FCFD]) includes the sum of the long and the short-term debt, i.e., the interest bearinginstruments. Practically speaking, it seems that a financial management staff would be bestprepared to indicate the percentage of the short term debt (including bank loans notes payable


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Vd = value of debt in a zero growth to infinity scenario,INT = annual interest payments,kd = yield to maturity,

In estimating the value of a firms debt, where an infinite horizon is assumed, the valueof the debt would be equal the discounted stream of estimated interest payments (INT). Forexample, assuming a dynamic scenario, the level of permanent debt increases when a firm isforecasting real growth in its sales. The inference is that assets and debt will grow at the realrate needed to support the sales growth. The debt is assumed to be discounted at the currentmarket rate of return required by fixed income investors, that is the yield to maturity, i.e.,infinity. Thus, the Vd[FCFD] is an estimate of discounted interest flows to infinity, as reflected inequation 8, and the Vd[FCFD] is not equal to the market Vd in [7].

Vd[FCFD] = [INT1]/(1 + kd) + [INT2]/(1 + kd)2++ [INTn] /[kd g] / (1 + kd)

n [7]

where:Vd = intrinsic value of permanent debt,

INTn = annual interest payment for n time periods

kd = current market rate of return on permanent debt,gn = estimated annual growth in sales from period n to infinity.

Summary

The above analyses indicates there are several approaches used to estimate the value of

equity, debt and the firm. As shown below the marketvalue of equity (Vs), debt (Vd), or firm(Vf) can be on either or both sides of the valuation equation. Likewise, it is also shown that theintrinsic or discounted cash flow (DCF) value can be on either or both sides of the equation.Under certain conditions, market and intrinsic values can be on opposite sides of the valuationequation. In summary,

Valuation equations Market or Intrinsic (DCF)

Conditions

Vf= Vs + Vd , or market = market [8]

Vf [FCFF] = Vs + Vd, also DCF = market [9]

Vs = Vf [FCFF] Vd . market = DCF & market [10]


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These set of relationships provide the framework for the remainder of the paper. First,

the analysis focuses on explaining linkages between the two equity models in equation 13.

After 13 has been demonstrated, the linkages between the two sides of equation 15 aredeveloped. That is, the task is to highlight why Vf[FCFF] = [Vs[FCFE] + Vd[FCFD]]. Beforeexplaining the linkages in equations 13 and 15, we focus on creating a financial forecast andthe resulting cash flow metrics.

III. CREATING A FINANCIAL FORECAST

Explaining the assumptions underlying a financial forecast highlights the importantsteps involved in the valuation process. A financial forecast reflects the dynamics in a firmsproduct markets and its financial markets. Also good forecasting practices incorporate realisticassumptions concerning internal management efficiencies. The technical steps involved inpreparing a financial forecast are presented in Appendix 2. The outlook for economicconditions and the competitive environment are factored into the forecast along with the annualgrowth rate in sales. Initially, it is important to assume that a stable relationship exists between

sales and the related cost of sales, administrative expenses and other expenses. Alsodepreciation is assumed to be closely tied to the performance of a firms net fixed asset. Bestpractices in forecasting assume all assets and selected liabilities are a function of sales. That is,it is assumed

each asset is a function of sales, i.e., there is a relatively stable relationship between theith asset in the jth period and sales in the jth period;

selected liabilities are a function of sales, i.e., there exists a stable relationship between

salesj and accounts payablej, other current liabilitiesj and long and short term debt.

Also the percentage of earnings retained is stated explicitly and is assumed to maintaina stable relationship with net income.

When the forecasted assets are greater than forecasted liabilities, the shortfall infinancing, frequently called the additional funds needed (AFN), is offset first by increasing longterm debt in order to maintain a stable relationship with sales and also a target capital structure.

If further debt is needed to offset the shortfall, it is financed with short-term borrowing.Alternatively, if the forecasted assets (A) are less than the forecasted liabilities (L), A


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Growth rate of sales. The financial forecast program is driven by the growth rate ofsales. The growth of the several asset classes and accounts payable and other current liabilitiesare directly related to the growth of sales. The example assumes a stable 3 percent growth of

sales. However, if the growth rate of sales is assumed to be markedly higher or if it is assumedto be erratic and unstable, the outcomes of the forecast will look dramatically different andcreate uncertainty in the validity of the outcomes. It is extremely important to carefully trackthe cash flow results and discover why the forecasted results look vastly different from the baseforecast. The results of your forecast are correct, but it is the task of the user to understandwhat happened and why it happened.

Sales growing too fast. If the firms strategic plan is for sales to grow more rapidly than theoperating income or the net income during the next several years, the financial forecast willshow the total assets are more-than-likely growing more rapidly than the total liabilities. Tofinance this rapid growth strategy, where forecasted assets > liabilities, the firm will need toincrease it temporary and/or permanent financing. The financial forecasting model isprogrammed to first utilize the retained earning from the income statement, discretionary cashflow, before increasing its long-term debt to accomplish managements target debt/total marketvalue ratio. Short-term debt can be used to provide additional funds needed (AFN) until the

target capital structure is reached and forecasted total liabilities equal total assets. At this pointif additional funds are still needed to make liabilities = assets, the target debt ratio is overriddenand the debt ratio will expand causing the financial risk and the cost of capital to increase.From a planning perspective, a red flag appears because the capital structure is out of control.The financial forecast stops, because the firm either needs to reduce it growth of sales ordetermine a new set of inputs to accommodate the increase in market risk. The new inputswould be an increase in the cost of equity and debt because of market expectations havechanged, plus a revised target capital structure (Debt/Equity).

Growth inprofit margins > growth in sales. When profit margins are increasing morerapidly than sales, operating profits will be increasing at a rate greater than sales. According toSolomon [1963, chapter 5] this set of conditions reflects true growth. That is, when rate ofreturn on new capital investments (r) is greater than the weighted average cost of capital(WACC), r > WACC, a firm is experiencing true growth. If this condition is not permanent, itwill create some instability in forecasting future performance.

Sales in decline. If the forecast is for sales to decline over several years, the strategy of thefirm will change dramatically. The relationship between sales and assets will decline, and it iscrucial to track the return on operating income and/or net income vis--vis sales. Managementneeds a new strategic plan that where forecasted total assets to equal total liabilities. Keepingwithin the capital structure boundaries established and reducing debt if possible, would be theconservative strategy for the financial forecast to follow


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readjusted downward the WACC will likely increase as the percentage of equity approaches100 percent.

No growth, expansion and true growth. Solomon [1963] developed four scenarios thatwere related to the forecasted growth rate of net earnings or dividends. The scenarioshighlighted the effect that investment and how it was financed had on growth of earningsand/or dividends. If 100 percent of the net income was paid out in dividends, for an all equityfirm, there would be no growth in value over time. However, investing a portion of theearnings retained at exactly the WACC will result in an expansion of assets, but earning,debt/equity ratio and asset value of will experience a constant increase, as would the growth infirm value. The third condition occurred when a portion of earnings retained was invested at arate of return greater than WACC. Solomon referred to this condition as true growth and overtime equity would increase and the debt/equity ratio would decrease. True growth createscomplex issues in estimating the optimal capital structure, cost of equity (ks) and value of thestock. Likewise, the stability of the investment pattern can have a profound affect on the valueof the equity. Each of these conditions creates issues in estimating the value of a stock.

IV. DIFFERENCES BETWEEN EQUITY VALUATION THEORIES

In this illustration the basic inputs for estimating the equity value of AbbottLaboratories --free cash flow to equity [FCFE] and dividends [DIV]are presented in thepreformed income statement and balance sheet that is located in Exhibit 1. The sales of AbbottLaboratories are assumed to grow at 7.5 percent annually for five years. The forecastedrelationships between sales and income statement expenses, assets and selected liabilities arefound in first column of Exhibit 1. Other key assumptions relating sales to income statement

and balance sheet items are also located in column 1 of Exhibit 1. Exhibit 1A showsrelationships between FCFE, FCFD and FCFF in the financial forecast. Also Exhibit 1Aprovides an overview of the book and market value estimates of the debt/equity measures.These summary cash flow and debt/equity measures provide a valuable perspective of the long-run stability of the example company, Abbot Laboratories.

The FCFE is composed of cash flows associated with operations (CFFO), netinvestment (NIF), working capital (WCCF) and permanent debt (FCFD). The cash flows for

each of the three components of FCFE are presented in Exhibit 2. The FCFE is also shown inExhibit 3. Likewise, the annual dividend flows are shown at the top of Exhibit 4.

The annual FCFE are discounted at the cost of equity capital (ks) and they are shown atthe top of Exhibit 3. The capital asset pricing model (CAPM) is used to estimate ks. TheCAPM is


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With the assumed CAPM inputs, the ks is 0.061 and the discounted FCFE for years 1 -5,PVFCFE, 1- 5, shown in Exhibit 3, are $7.931 billion. The terminal growth rate is assumed to be 3percent. The present value of the terminal value (PVTVFCFE) is $55.544 billion. That is,

PVTVFCFE = FCFE5 [(1 + growth rate) / (ks g)] / (1 + ks)5

[17]= [ $2.248 billion (1.03) / (0.061 0.03)] / (1 + 0.061)

5

= $55,544 billion

Thus the Vs[FCFE] = PVFCFE, 1 5 + PVTVFCFE , [18]= $7.931 billion + $57.544 billion= $63.475 billion

The annual flows to dividends (DIV) for years 1 5 are growing at a rate of 7.5 percentannually, the same as the growth rate of sales. Exhibit 4 shows discounting the dividends at ks,6.1 percent, for years 1 to 5 results in the PVDIV, 1-5 equaling $7.950 billion. Thus the PVDIV, 1-5are $0.019 billion greater the PVFCFE,1-5, $7.950 billion - $7.931 billion. In order to make thetotal PVDIV = PVFCFE the program calculates an implied terminal growth rate of dividends(gDIV).First, assuming equation 13, we find

Vs[FCFE] = Vs[DIV] [19]Vs[FCFE] = PVDIV, years 1- 5 + PVTVDIV, year 5$63.475 billion = $7.950 billion + PVTVDIV, year 5PVTVDIV, year 5 = $55.524 billion

To solve forgDIVthe next step is to find the future value of $55.524 billion, where ks is0.061 and terminal year in year 5 (FV0.061, year 5). That is, FV0.0610, year 5 = $55.524 / PVIF0.061, year

5 , thus FV0.061, year 5 = $55.524 billion / 0.74374 = $74.655 billion, as shown in Exhibit 4.

The third step is to find gDIV, assuming the numerals are in billions (B) $. Thefollowing is presented in Exhibit 4.

TVDIV, year 5 = $2.221 (1 +gDIV) / [0.061 gDIV] = $74.655 [20]where: $2.221 = DIVyear 5

0.061 = ks

$55,524 = FV0.061, year 5

therefore, applying algebra to [20]1, we findgDIVis

$74.655 (0.061 gDIV) = $2.221 + $2.221gDIV$4 55396 - $74 655 gDIV = $2 221 + $2 221 gDIV


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interpretation of the gDIV > gFCFE. First, if the estimated flows from DIV are considered abetter predictor of Vs than FCFE flows, the $63.475 billion intrinsic value of the equity

(Vs[FCFE])may be understated. This interpretation occurs because the $63.475 billion in equityvalue is achieved with only a 3.0 percent terminal growth rate of a FCFE to a companysshareholders, while a 3.03 percent terminal value of DIV flows is necessary to achieve the sameequity value of $63.475 billion. Why did this happen? One possible explanation for the gDIV >gFCFE , .0303 > .03, is that the undiscounted annual FCFE in years 1 to 5 are larger than theundiscounted annual DIV for the same period, as shown in Exhibits 3 and 4, respectively, e.g.,the FCFE is $2.248 billion, while the DIV5 is $2.221 billion. This relationship can occurbecause the payout ratio < 100 percent, and the higher retained earnings allows the FCFE inyears 1- 5 to increase more rapidly than the DIV in years 1-5. The dividends are based on thepercentage of net income disbursed to shareholders, and it is only indirectly related to balancesheet flows associated with FCFE. In closing, it is relatively common to find the present valueof the dividend stream being less-than the stream of free cash flows to equity (FCFE).

A second interpretation occurs because many investors consider the estimated flowsfrom DIV a better predictor of the value of equitythan the FCFE flows. That is, investors

physically receive dividends, while the flows associated with FCFE do not flow directly toinvestors. Namely, it is assumed that cash outflows associated with capital investments andworking capital earn at least the weighted average cost of capital (WACC), that in the futurebecome operating cash inflows. Likewise, it is assumed that the increase in debt will be used toinvest in investments that will earn at least theWACC.

V. DIFFERENCES BETWEEN FIRM AND EQUITY VALUATION

It was hypothesized in equation 15 that Vf[FCFF] = Vs[FCFE] + Vd[FCFD]. The objective ofthis section is to discover why the two sides of equation 15 differ. The first task is to examinethe Vf[FCFF], the left hand side of 15. The components of undiscounted free cash flows to a firm[FCFF] are presented at the bottom of Exhibit 2-- net operating flows (NOF), net investmentflows (NIF) and working capital flows (WCCF). The FCFF is shown in Exhibit 2 and 5. TheWACC is used to discount the FCFF and its components-- the equation for estimating themarket weights for debt (wd) and equity (ws), plus market costs of capital for debt (kd)(1-taxrate) and equity (ks)are shown at the bottom of Exhibit 3. The debt weight (Vd/Vf) and the

equity weight (Vs/Vf) are .152 and .848, respectively, and the kd and ks are 5.5 percent and 6.1percent, respectively. Inserting these components into the WACC equation creates a WACC of5.807 percent.

In estimating the Vs[FCFF], the annual FCFF are discounted at the WACC, as presented inExhibit 5. It is assumed the FCFF grows at a rate of 7.5 percent annually from years 1 to 5.


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Thus, summing the equity and debt components shows the Vf is $74.82 billion, as shown inExhibit 3. Equation 21 shows how to solve for the PVTVFCFF, year 5. Assume the numerals are

in billion $.

Vs[FCFE] + Vd[FCFD] = Vf [FCFF] [21]Vs[FCFE] + Vd[FCFD] = PVFCFF,years 1-10 + PVTVFCFF, year 10$63,475 + $11,345 = $ 9.382 + PVTVFCFF, year 10PVTVFCFF, year 5 = $65.438.

To solve for thegFCFF, it is necessary to determine the future value (FV) of $65,437

billion, shown in equation 21. The FV0.061, year 5 = [$65.438 billion / PVIF0.061, year 5] = [$65.437billion / .74374] = $87.983 billion. The next step is to findgFCFF, assuming numerals are inmillions $:

TVFCFF,year 10 = $2.732billion (1 +gFCFF) / [0.061 gFCFF] = $74.820billion [22]

Applying algebra similar to that used in equation 20 makes the two sides of equation 15equal. The result is the implied terminal growth rate of FCFF (g

FCFF), 0.02578, that equals 2.6

percent when rounded, as shown in Exhibit 5. Thus, at the beginning of year 6 the estimatedFCFF must grow at 2.6 percent annually to infinity in order for the intrinsic V f[FCFF] to equal$74.820 billion, where the estimated Vf[FCFF] = [Vs[FCFE] + Vd[FCFD]]. One possibleinterpretations of equation 15 is that the sum of the estimated discounted flows from FCFE andFCFD may be overstated. Exhibit 3 indicates the $74.820 billion intrinsic value of the firm isachieved with a 3 percent terminal growth of FCFE5 and FCFD5, while only a 2.6 percentgrowth in terminalFCFF10 was necessary to achieve a Vf[FCFF] equal to $74.820 billion. One

explanation for this occurrence is that the FCFF in years 1-5 is slighty greater than the sum ofFCFE + FCFD for years 1-5. In summary, the two sides of equation 15 are equal, but in orderfor this to occur, the growth rate of the FCFF had to be adjusted downward to make the Vf[FCFF]= [Vs[FCFE] + Vd[FCFD]].

CONCLUSIONS

An integrated valuation system (IVS) is presented that reflects a companys strategicfinancial forecast. The IVS and makes is possible to simulate changes in a companys financialstrategies and discover how they affect the firms financial health and/or valuation. Thisintegrated valuation system (IVS) generates a five year forecast of a companys financialstatements and creates a solid foundation for calculating cash flow measures used to estimatethe value of a firm its equity and it permanent debt The cash flow components can also be


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when there was an all equity firm with a 100 percent payout ratio and the return on investmentequals the cost of equity. Many investors believe dividends provide a more accurate measureof equity value than FCFE because dividends are physically distributed to its stockholders,

while FCFE are an indirect measure equity value.

Another contribution of this research is the development of an implied terminal growth rateof free cash flows to the firm. This implied growth rate causes the value of a firm based on itsfree cash flows (Vf[FCFF]) to equal the value of a firm based on the sum of its free cash flow toequity and debt [Vs]FCFE] + Vd[FCFD]]. If the implied terminal growth rate of FCFF is less thanthe growth rate of the FCFE and FCFD, it suggests the equity is likely to be overvalued. Theinputs for these two models are also substantially different. The challenge to the learner is to

develop an understanding of a companys financial health based on the inputs used in thefinancial forecast and information conveyed in the implied terminal growth rate of FCFF.


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APPENDIX 1

ALL EQUITY FINANCED FIRM WITH THREE SEPARATE STRATEGIESNO

GROWTH, EXPANSION AND TRUE GROWTH

Solomon [1963, Chapter 5] recognized the importance of growth in firm value and how

it was created. In the modern context, he identified an all equity strategy that would generate

true growth. Solomon used an all equity financed firm to develop three separate strategies

no growth, expansion and true growth-- to illustrate how wealth or growth was created. The

definitions of the three all equity strategies were:

Zero Growth is represented by 100 percent payout of earnings and the rate ofreturn on capital investments (r) equals the cost of equity capital (ks), r = ks.

Expansion reflects a firm that increases its size, by investing incapital investment projects that earn the cost of equity, r = ks, and these projectswere financed with the retention of earnings, thus payout ratio is ks, and they projects were financed with retained earnings.

The first of two exhibits presents the three strategies and shows the inputs used to createa firms pro forma income statement and a balance sheet. Note the inputs for the three allequity strategies are nearly the same with the exception of the cost of goods sold and thepercent of earnings paid out in dividends for the true growth firm and the payout ratio for theexpansion strategy. The inputs are used in the same financial forecasting model used in

generating Exhibits 1-6 in the text.

The second exhibit highlights the simulated financial results for each of the strategies.The Dupont System results are identical with the exception of the profit margin in the truegrowth strategy. The weighted average cost of capital inputs are identical. The market valuesfor the zero growth and expansion strategy are identical, while the value of the stock, firm andvalue per share are greater for the true growth strategy. The value of the dividends and freecash flow are the same forzero growth and expansion,but they are larger for the true growthscenario. Finally, the implied terminal value for the free cash flow to equity are identical forthezero growth and expansion,but greater for the true growth strategy.


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APPENDIX 1 (continued)

ALL EQUITY FINANCED FIRMS WITH THREE STRATEGIESNO GROWTH,

EXPANSION AND TRUE GROWTH

Percentage of Sales Forecast Method

Financial Input Zero Growth Expansion1

True Growth2

I. Income Statement1. Growth of Sales 0% 0% 0%2. Cost of Goods Sold

350% 50% 46%

3. Administrative Expenses3 15% 15% 15%4. Other Expenses3 5% 5% 5%5. Depreciation Expense

410% 10% 10%

6. Percent of Earnings Paid Out 100% 88.095% 89.583%

Assets

7. Cash5

3% 3% 3%8. Accounts Receivable 20% 20% 20%9. Inventories 20% 20% 20%10. Other Current Assets 2% 2% 2%11. Net Fixed Assets 20% 20% 20%

12. Other Assets 0% 0% 0%

Liabilities and Equity

13. Accounts Payable 0% 0% 0%14. Notes Payable $0 $0 $015. Other Current Liabilities 0% 0% 0%16. Other Liabilities $0 $0 $0

17. Long Term Debt $0 $0 $018. Common Stock

6$12.50 $12.50 $12.50

19. Retained Earnings6

$20.00 $20.00 $20.00

1 Expansion occurs when the retention of earnings is sufficient to finance a firms capitalinvestments and the return on the investments (r) equals cost of equity (k ) r = k


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APPENDIX 1 (continued)

SIMULATED FINANCIAL RESULTS FOR EACH OF THE GROWTH STRATEGIES

Financial Results Zero Growth Expansion True Growth

Dupont System

1. Profit Margin (%) 0.1680 0.1680 0.19702. Asset Turnover (X) 1.5385 1.5873 1.5873

3. Rate of Return on Assets 0.2585 0.2667 0.30484. Leverage Multiplier 1.0 1.0 1.05. Rate of Return on Equity 0.2585 0.2667 0.3048

WACC Components

6. Weight in debt (wd) 0.0 0.0 0.07. Cost of debt (kd) 0.07 0.07 0.078. (1 Tax Rate) 0.60 0.60 0.609. Weight in equity (we) 100.0% 100.0% 100.0%10. WACC 0.10 0.10 0.10

Market Values l

11. Value of Stock (Vs) $84 M $ 84M $96M12. Value of Debt (Vd) 0.0 0.0 0.0

13. Value of Firm (Vf) $84M $84M $96M14. Value per share $1.0 $1.0 $1.142915 Number of Shares 84M 84M 84M

Dividend and FCFE

16. Dividends $8.40M $7.4M $8.6M17. Rate of Return on Div. 0.10 0.10

70.1429

8

18. Free Cash Flow to Equity $8.40M $8.40M 9.60M

19. Rate of Return on FCFE 0.10 0.10 0.1429

Implied Terminal Growth (TV) Rate

20. Implied TV Div. Growth 0.0 0.02416 0.0215921. Implied TV FCFE Growth 0.0 0.0 0.02159


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APPENDIX 2

The objective of Appendix 2 is to explain the key assumptions and steps involved inpreparing a percentage of sales forecast for an income statement and balance sheet. Theexplanation is based on the information provided in Exhibit 1 for years 0 and 1 . The growth ofsales is assumed to be 7.5 percent annually.

Income Statement

0 1 Explanation for Period 11. Sales $17.68 $19,01 Sales1 increased 7.5 percent, $17.68(1.075

2. Cost of Sales 7.33 7.79 C0S1 = 0.414 (Sales1): 0.414($19.01)3. Administrative Expenses 3.98 4.28 AE1 = 0.225 (Sales1): 0.225 ($19.01)4. Other Expenses 1.67 1.81 OE1 = 0.095 (Sales1): 0.095 ($19.01)5. Depreciation 1.18 0.59 Depr. = 0.102 (NFA1): 0.102($6.274)6. EBIT $3.53 $4.54 EBIT1 = Sales COS AE OE Depr.7.Interest Income 0.00 0.00 II1 = 0.008. Interest Expense -0.143 0.33 IE1 = i [NP0 + LTD0] = 0.055 [1.71 + $4.60]9. Net Income before taxes 3.67 4.21 NIBT1= EBIT1 + II1 IE1: $4.54 + 0.0 - 0.3310.Taxes 0.88 1.02 T1 = (TR)NIBT1: 0.242 ($4.21)11.Net Income $2.79 $3.19 NI1 = NIBT1 T1: $4.21 $1.0212.Dividends 1.43 1.63 DIV = [DIV/NI] (NI): 0.51 ($3.19)

13.Change to retained. earn. 1.36 1.56 RE = NI DIV: $3.19 - $1.63

Balance Sheet

Assets14.Excess Cash 0.00 0.0015.Cash $0.97 $1.05 CASH = i [Sales1]: 0.055 ($19.01)16.Accounts Receivable 2.93 3.16 AR = %Sales1 [Sales1]: 0.167 ($19.01)17.Inventory 2.44 2.62 INV = %Sales1 [Sales1]: 0.138 ($19.01)18.Other Current Assets 2.79 3.00 OCA = % Sales1 [Sales1]: 0.158 ($19.01)19.Net Fixed Assets 5.83 6.27 NFA = % Sales1 [Sales1]: 0.33 ($19.01)20.Other Assets 9.31 10.0 OA = %Sales1[Sales1]: 0.526 ($19.01)

21.Total Assets $24.26 $26.10 TA = MS1 + AR1 + INV1 + OCA1 + NFA1 +OA1

Liabilities22.Accounts Payable 1.93 2.07 AP = %Sales1 [Sales1]: 0.109 ($19.01))23 Notes Payable 1 66 1 71 NP= TA- [AP + OCL +LTD + CS+ RE]


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REFERENCES

Amram, Martha and Nalin Lulatilaka [1999],Real Options: Managing Strategic InvestmentOptions in an Uncertain World, Boston, Harvard Business School Press.

Block, Stanley B. and Geoffrey A. Hirt [2001],Foundations of Financial Management, TenthEdition, New York, The McGraw-Hill Companies, Inc.

Brealey, Richard A. and Stewart C. Myers [1996], Principles of Corporate Finance, Fifth

Edition, New York, The McGraw-Hill Companies, Inc.

Brennan, Michael J. and L. Trigeorgis [1999],Project Flexibility, Agency and Competition;New Developments in the Theory and Applications of Real Options, New York, OxfordPress.

Brigham, Eugene F., Louis C. Gapenski and Michael C. Ehrhardt [1999],FinancialManagement: Theory and Practice,Ninth Edition, Fort Worth, The Dryden Press.

Copeland, Tom, Tim Koller and Jack Murin [2000], Valuation: Measuring and Managing theValue of Companies, Third edition, New York, John Wiley & Sons, Inc.

__________[1995], Valuation: Measuring and Managing the Value of Companies, SecondEdition, New York, John Wiley & Sons, Inc.

__________[1990], Valuation: Measuring and Managing the Value of Companies, First

Edition, New York, John Wiley & Sons, Inc.

Damadoran, Aswath [2001], Corporate Finance: Theory and Practice, Second Edition, NewYork, John Wiley & Sons, Inc.

__________[2001], The Dark Side of Valuation, Upper Saddle River, NJ, Financial TimesPrentice Hall.

Fama, Eugene F. [January 1965], The Behavior of Stock Market Prices, Journal of Business,Vol. 38, No. 1, 34-105.

Fama, Eugene F. [May 1970], Efficient Capital Markets: A Review of Theory and EmpiricalWork, Journal of Finance, Vol. 25, No. 2, 383-417.


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Hawawini, Gabriel and Claude Viallet [1999], Finance for Executives: Managing for Value

Creation, Cincinnati, South-Western College Publishing.

Hackel, Kenneth S. and Joshua Livnat [1992], Cash Flow and Security Analysis, Homewood,Business One Irwin.

Homer, Sidney and Martin L. Leibowitz [1972], Inside the Yield Book, Englewood Cliffs, N. J.,Prentice-Hall Inc.

Palepu, Krishna G., Paul M. Healy and Victor L. Bernard [2000],Business Analysis &

Valuation, Second Edition, Cincinnati, South-Western College Publishing.

Rappaport, Alfred [1988, 1998], Creating Shareholder Value, New York, The Free Press.

Rappaport, Alfred and Michael J. Mauboussin [2001],Expectations Investing, Boston, HarvardBusiness School Press.

Reilly, Frank K. and Keith C. Brown [1997],Investment Analysis and Portfolio, Fort Worth,The Dryden Press.

Solomon, Ezra [1963], The Theory of Financial Management, New York, Columbia UniversityPress.

Stewart, G. Bennett III [1991], The Quest for Value, New York, HarperBusiness.

Stickney, Clyde P. and Paul R. Brown [1999],Financial Reporting and Statement Analysis, FortWorth, The Dryden Press.

Williams, J. B. [1938], The Theory of Investment Value, Cambridge, Mass., Harvard UniversityPress.


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Exhibit 1A: Financial Statement reasonableness tests (in millions)


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Year ended Dec 31, year: 0 1 2 3 4 5Free cash flow to firm, FCFF $1,412.05 $2,199.01 $2,363.93 $2,541.23 $2,731.82

Free cash flow to equity, FCFE $1,535.71 $1,761.82 $1,919.75 $2,077.54 $2,247.70Free cash flow to debt, FCFD $326.46 $346.87 $337.29 $326.92 $315.04

FCFE + FCFD $1,862.16 $2,108.69 $2,257.04 $2,404.46 $2,562.74

FCFF - (FCFE + FCFD) -$450.12 $90.32 $106.90 $136.77 $169.08

Total debt $6,306.74 $6,132.48 $5,943.96 $5,728.07 $5,482.75

Total equit $12,229.00 $13,793.44 $15,476.40 $17,298.81 $19,271.15

BV Debt/BV Equity 51.57% 44.46% 38.41% 33.11% 28.45%

BV Debt/BV Firm 34.02% 30.78% 27.75% 24.88% 22.15%BV Equity/BV Firm 65.98% 69.22% 72.25% 75.12% 77.85%

PCFCFD/PVFCFE 17.87%PVFCFD/PV Firm 15.16%

PVFCFE/PV Firm 84.84%

% increase in dividends 7.576% 8.286% 8.227% 8.185%

% increase in debt -2.763% -3.074% -3.632% -4.283%

% increase in equit 12.793% 12.201% 11.775% 11.402%% increase in FCFE 8.964% 8.219% 8.190%

% increase in FCFD -2.763% -3.074% -3.632%% increase in FCFF 7.500% 7.500% 7.500%

hibit 2: Calculation of free cash flow to equity (FCFE), free cash flow to debt (FCFD), and free cash flow to the firm (FCFF) (in millions)


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Year ended Dec 31, year: 0 1 2 3 4 5

Working CapitalCurrent assets - (excess cash + cash) $8,156.65 $8,783.09 $9,441.82 $10,149.95 $10,911.20 $11,729.54Current liabilities - Debt in CL $5,340.55 $5,075.94 $5,456.64 $5,865.88 $6,305.82 $6,778.76Net working capital (NWC) $2,816.10 $3,707.15 $3,985.18 $4,284.07 $4,605.38 $4,950.78

Change in working capital (WCCF) $891.05 $278.04 $298.89 $321.31 $345.40

Change in net fixed assets (NFA) $445.51 $470.52 $505.81 $543.75 $584.53(+) Depreciation $594.47 $639.91 $687.90 $739.50 $794.96

Change in Other Assets $691.58 $749.98 $806.23 $866.70 $931.70

Net investment flow (NIF) $1,731.56 $1,860.42 $1,999.95 $2,149.94 $2,311.19

Net income $3,192.73 $3,434.62 $3,719.20 $4,025.18 $4,354.65

(+) Depreciation $594.47 $639.91 $687.90 $739.50 $794.96CFFO $3,787.20 $4,074.53 $4,407.11 $4,764.67 $5,149.61

(-)NIF $1,731.56 $1,860.42 $1,999.95 $2,149.94 $2,311.19(-) WCCF $891.05 $278.04 $298.89 $321.31 $345.40

Principal increase (repayment) in debt $371.12 -$174.26 -$188.52 -$215.88 -$245.32

Change in excess cash $0.00 $0.00 $0.00 $0.00 $0.00Free cash flow to equity (FCFE) $1,535.71 $1,761.82 $1,919.75 $2,077.54 $2,247.70

(+) Interest on total interest bearing deb $326.46 $346.87 $337.29 $326.92 $315.04Free cash to debt FCFD $326.46 $346.87 $337.29 $326.92 $315.04

Earnings before interest and taxes (EBIT) $4,538.50 $4,878.03 $5,243.89 $5,637.18 $6,059.97

EBIT(1 - tax rate) $3,440.19 $3,697.55 $3,974.87 $4,272.98 $4,593.46

(+) Depreciation expense $594.47 $639.91 $687.90 $739.50 $794.96Net operating flow (NOF) $4,034.65 $4,337.46 $4,662.77 $5,012.48 $5,388.41

(-) NIF $1,731.56 $1,860.42 $1,999.95 $2,149.94 $2,311.19

(+) WCCF $891.05 $278.04 $298.89 $321.31 $345.40Free cash flow to firm (FCFF) $1,412.05 $2,199.01 $2,363.93 $2,541.23 $2,731.82

Exhibit 3: Calculation of the value of free cash flow to equity (FCFE) and free cash flow to debt (in millions)


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Year ended Dec 31, year: 0 1 2 3 4 5Cost of Equity (Ks) 6.1%

Growth rate in FCFE, years 1 to 5 3.0%

Free cash flows to equity (FCFE) $1,535.71 $1,761.82 $1,919.75 $2,077.54 $2,247.70

Terminal value: (1+ g)/(Ks - g) x $2,247.70 $0.00 $0.00 $0.00 $0.00 $74,681.51Total: FCFE + terminal value of FCF $1,535.71 $1,761.82 $1,919.75 $2,077.54 $76,929.21

Present value of free cash flows to equit $7,930.90Present value of terminal value $55,543.88

Present value of free cash flows to equity $63,474.78

Cost of Debt (Kd) 5.5%Growth in free cash flow to debt (FCFD) 3.0%

Free cash flows to debt (FCFD) $326.46 $346.87 $337.29 $326.92 $315.04

Terminal value: (1+g)/(Kd - g) x $315.04 $0.00 $0.00 $0.00 $0.00 $12,979.82

Total: FCFD + terminal value of FCFD $326.46 $346.87 $337.29 $326.92 $13,294.86Present value of cash flows to debt $1,413.27

Present value of terminal value $9,931.30Present value of free cash flows to debt $11,344.57

Present value of the firm (Value of equity + debt) $74,819.35

Weighted average cost of capital (WACC)(value of debt / value of firm) x Kd x (1 - Tax rate) + (value of equity / value of firm) x K

Wd 15.2%

Kd 5.5%

(1 - T) 75.8%

Ws 84.8%Ks 6.1%

Debt portion 0.63%Equity portion 5.18%

WACC 5.807%

Exhibit 4: Calculation of the value of dividends and free cash flow to debt (in millions)

Y d d D 31 0 1 2 3 4 5


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Year ended Dec 31, year: 0 1 2 3 4 5Cost of Equity (Ks) 6.1%

Growth rate in DIV, years 1 to 5 3.0%

Implied growth rate in TVof DIV 3.0%

Dividends $1,628.29 $1,751.66 $1,896.79 $2,052.84 $2,220.87Terminal value: (1+ g)/(Ks - g) x $2,220.87 $0.00 $0.00 $0.00 $0.00 $74,655.20

Total: dividends + terminal value of dividends $1,628.29 $1,751.66 $1,896.79 $2,052.84 $76,876.07Present value of dividends $7,950.47Present value of terminal value $55,524.31

Present value of dividends $63,474.78

Cost of Debt (Kd) 5.5%

Growth rate in FCFD, years 1 to 5 3.0%

Free cash flows to debt (FCFD) $326.46 $346.87 $337.29 $326.92 $315.04

Terminal value: (1+g)/(Kd - g) x $315.04 $0.00 $0.00 $0.00 $0.00 $12,979.82Total: FCFD + terminal value of FCFD $326.46 $346.87 $337.29 $326.92 $13,294.86

Present value of free cash flows to debt $1,413.27Present value of terminal value $9,931.30

Present value of free cash flows to debt $11,344.57

Present value of the firm (Value of equity + debt) $74,819.35

Weighted average cost of capital (WACC)(value of debt / value of firm) x Kd x (1 - Tax rate) + (value of equity / value of firm) x KDebt portion 0.63%

Equity portion 5.18%

WACC 5.807%

Exhibit 5: Calculation of the value of free cash flow to firm using WACC from Exhibit 3 (in millioins)

Year ended Dec 31 year: 0 1 2 3 4 5


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Year ended Dec 31, year: 0 1 2 3 4 5WACC, Exhibit 3 (Kf) 5.807%

Growth in Free cash flows (FCFF) 3.0%

Implied growth in terminal value of Free c 2.6% $0.00

Free cash flows to the firm (FCFF) $1,412.05 $2,199.01 $2,363.93 $2,541.23 $2,731.82Terminal value: (1+ g)/(Kf - g) x $2,731.82 $0.00 $0.00 $0.00 $0.00 $86,776.33

Total: FCFF + terminal value of FCF $1,412.05 $2,199.01 $2,363.93 $2,541.23 $89,508.15Present value of free cash flows to firm $9,382.11Present value of terminal value $65,437.24

Present value of free cash flows to firm (FCFF) $74,819.35

Exhibit 6: Calculation of the value of free cash flow to firm using WACC from Exhibit 4 (in millions)

Year ended Dec 31 year: 0 1 2 3 4 5


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Year ended Dec 31, year: 0 1 2 3 4 5WACC, Exhibit 4 (Kf) 5.807%

Growth in Free cash flows (FCFF) 3.0%

Implied growth in terminal value of Free c 2.6%

Free cash flows to the firm (FCFF) $1,412.05 $2,199.01 $2,363.93 $2,541.23 $2,731.82Terminal value: (1+ g)/(Kf - g) x $2,731.82 $0.00 $0.00 $0.00 $0.00 $86,776.33

Total: FCFF + terminal value of FCF $1,412.05 $2,199.01 $2,363.93 $2,541.23 $89,508.15Present value of free cash flows to firm $9,382.11Present value of terminal value $65,437.24

Present value of free cash flows to firm $74,819.35

Exhibit 7: Comparisons, Exhibits 3, 4, 5, and 6 (in millions)

Exhibit 3 Exhibit 4 Exhibit 5 Exhibit 6


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FCFE Dividends FCF, Exh 3 FCF, Exh 4

+ FCD + FCD WACC WACC

Present value of cash flows $9,344.17 $9,363.74 $9,382.11 $9,382.11

Present value of terminal values $65,475.18 $65,455.61 $65,437.24 $65,437.24Present value of the firm $74,819.35 $74,819.35 $74,819.35 $74,819.35

Difference, Exhibit 5 - Exhibit 3Cash flows $37.94

Terminal values -$37.94

Firm value $0.00

Difference, Exhibit 6 - Exhibit 4Cash flows $18.37

Terminal values -$18.37

Firm value $0.00

1 Learning About Intrinsic Valuation With the Help of an Integrated Valuation Model

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