Learning About Intrinsic Valuation With the Help of anIntegrated Valuation Model

James A. GentryUniversity of Illinois at Urbana−Champaign

Frank K. Reilly Michael J. SandrettoUniversity of Notre Dame University of Illinois at Urbana−Champaign

Abstract

An integrated strategic financial management system provides students of finance aninvaluable learning experience in assessing the financial health of a company or estimatingthe value of this company. We found students’ questions and misunderstanding about how toassess a company’s financial health or apply current valuation theories led to thedevelopment an integrated valuation system (IVS). One objective of a dynamic valuationsystem is to help students simulate changes in a firm’s financial strategies and discover howthese changes affect a firm’s credit health or its value. Additionally, an IVS provides a solidconceptual foundation for a student to justify the credibility of a growth rate used to estimatethe terminal value of a project or stock. The IVS helps students learn why the intrinsic valueof a stock estimated by a dividend discount model (Vs[DIV]) may not equal the intrinsicvalue 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 firmthat is based on discounted free cash flow to the firm (Vf[FCFF]) may not equal discountedfree cash flow to equity (Vs[FCFE]) plus discounted free cash flow to debt (Vd[FCFD]), orVf[FCFF] �‚ [Vs[DIV] + Vd[FCFD]]. One reason for these valuation inconsistencies is thatthe underlying theories were developed independently in different time periods. Also inputsfor each of the models were unique because the models were not developed as a totalintegrated system. Therefore, a valuation system was created that integrates the keycomponents needed to estimate the intrinsic value of a company’s equity (Vs[FCFE]), debt(Vd[FCFD]) and its firm value (Vf[FCFF]). The integrated valuation system helped reconcilethe valuation dilemmas by solving for an implied terminal growth rate of dividends [gDIV]that causes the Vs[DIV] = Vs[FCFE]. The IVS also determines an implied terminal growthrate of the FCFF[(gFCFF), that causes the Vf[FCFF] = [Vs[FCFE] + Vd[FCFD]]. Thechallenge to the learners is to interpret accurately the information conveyed via the impliedterminal growth rate of dividends (gDIV) and the implied terminal growth rate of the FCFF(gFCFF).

Published: 2003URL: http://www.business.uiuc.edu/Working_Papers/papers/03−0108.pdf

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 j-gentry@uiuc.edu

Frank K. Reilly Bernard J. Hank Professor of Business Administration

University of Notre Dame Frank.K.Reilly.1@nd.edu

and

Michael J. Sandretto Visiting Associate Professor of Accountancy University of Illinois, Urbana-Champaign

sandrett@uiuc.edu

FMA European Meetings

Dublin June 5, 2003

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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 company’s 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 firm’s financial strategies and discover how these changes affect a firm’s 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 that the 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 company’s 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] 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 information conveyed via the implied terminal growth rate of dividends (gDIV) and the implied terminal growth 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 Harry Potter’s magic wand to provide fresh insights into the process of interpreting the financial health of a company or estimating its intrinsic value. During the past seven decades several models have been proposed to estimate the intrinsic value of a stock or a firm. For example, in the 1930’s and 1940’s Graham and Dodd [1934, 1940] advocated using fundamental security analysis techniques to discover if the level of a stock’s P/E multiple provides signals for investment 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 stock’s potential value, Damadoran [2001, Chapters 8-10]. Naturally, there are solid reasons for using multipliers to estimate the value of a stock, but there are also shortcomings.

Near the end of the Great Depression, Williams [1938] introduced the classic dividend discount 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 a stock (Vs) has expanded dramatically. Copeland, Koller and Murrin [1990, 1994, 2000], Rappaport [1988, 1998], Stewart [1991], and Hackel and Livnat [1992] were current pioneers in 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 equity valuation model based on discounting a stream of free cash flows to equity [FCFE] at a required rate of return to stockholders. Also Damadoran [2001] provides several approaches to estimate the value of a firm for which there are no comparable companies, no operating earnings and a limited amount of cash flow data. Fama’s [1970] efficient market research challenged the validity of intrinsic valuation models.

Finally, a real options approach for valuing firms that have no comparables or operating

earnings 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], Brennan and Trigeorgis [1999], Schwartz and Moon [2000], Copeland and Antikarov [2000] and Damadoran [2001, Chapter 11].

During the past decade we have been deeply involved in learning and teaching the

theory and practice of assessing the financial health of a company or estimating its intrinsic value. We found students’ questions and misunderstandings about how to assess a company’s financial health or apply current valuation theories led to the development of an integrated financial system (IVS). The purpose of creating a dynamic valuation system was to stimulate student learning about complex issues that underlie the process of analyzing a company’s credit rating or estimating its value. A primary goal was to integrate the strategic information contained in a firm’s financial statements so that students could simulate various scenarios and thereby have a rich learning experience about valuation and credit analysis. We have discovered there are a few topics that generate big learning events, for example….

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• Why are net operating cash inflows so important in the wealth creation process and/or in the assesment of a company’s 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 firm

value 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 the

long-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 few

basic concepts used to estimate the market value of a firm (Vf) , a stock (Vs) and debt (Vd). A basic 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, and Vd 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 a firm’s weighted average cost capital (WACC) to discount to infinity its estimated free cash flows [FCFF]. It is possible to create forecasted inputs so that the Vf[FCFF] = Vf. On the right hand side of equation 1, a second theory assumes the Vs is estimated by discounting to infinity either the free cash flow to equity [FCFE] or the dividend flows [DIV] at the required rate of return 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., Vf* = [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 Vf – Vd = Vs , e.g., as shown in Rappaport and Mauboussin [2001, pp. 74-76]. Examples that use an all equity firm, or nearly all equity, avoid the complexities that occur when permanent debt is a significant part of a firm’s capital structure. On the positive side of using an all equity firm to illustrate a valuation argument, Solomon [1963, chapter 5] used an all equity firm to develop an insightful theoretical explanation of how growth in a firm occurs. An explanation of Solomon’s growth model is presented in Appendix 1. Finally, to the best of our knowledge, it has not been shown how to make the Vs[FCFE] = Vs[DIV]. Our thesis is that there is a learning gap in how valuation models are integrated. Thus one task is to connect these valuation theories so that the linkages are transparent.

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The primary objective of the paper is to present a valuation system that links the components 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 shows how to develop a forecast for integrated income statements and balance sheets. These forecasted financial statements provide information needed to estimate the intrinsic value of equity, debt and a firm. The two basic models for estimating the intrinsic value of equity are shown 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]]. Simulating various scenarios highlights the analytical power an integrated valuation system offers to students of financial analysis. The final section summarizes the most important contributions an integrated 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 concepts involved in estimating the intrinsic value of a stock, a bond and a firm. In the late 1930s Professor 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 the future cash flows that stockholders would receive. In the early 1960s, Gordon [1962] extended Williams DIV by allowing the stream of dividends to grow at a constant forecasted rate from time period zero to infinity. The Gordon constant growth model is widely used in the investment management profession. Also it has been extended to incorporate dividends growing at uneven rates. The estimation of bond value is similar to the dividend discount model (DIV), in that the bond value equals to a discounted stream of interest payments and the final 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 an intrinsic-value approach to equity valuation. In the 1962 edition they stated the most important single factor determining a stock’s value is now held to be the indicated average future earning 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 and then multiplying that prediction by an appropriate capitalization factor, Graham, Dodd and Cottle [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 of value 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 infinity. GDC concluded that the elements of uncertainty and risk assume a dominant position in the discounting of a future dividend stream. Second, they reached a practical conclusion, namely that investors in popular growth stocks do not explicitly think even vaguely in terms of discounting future dividends.

In the mid-1960s Fama [1965] found stock price performance resembled a random

walk. Fama later developed the efficient market theory in terms of a fair game model, that is the price of a security fully reflects all available information at a point in time, Reilly and Brown [1997, p. 210]. Fama divided the overall efficient market hypothesis (EMH) into three

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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]. Fama’s EMH raises serious questions concerning the validity of GDC’s earning power theory of value and Williams and Gordon’s DIV.

In the late 1980s and early 1990s several authors presented a valuation model based on

free 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 a bank. 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], by discounting the FCFE at the required rate of return on equity (ks). Thus it is possible to compare 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 equity discount 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 causes the 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 of FCFF assumes the estimated intrinsic Vs[FCFE] and Vd[FCFC] are correct. It is also assumed the gFCFF is positive and relatively constant throughout the life of the forecast. It is also assumed there 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 Vf be estimated? The answer is yes as shown by authors who focus on the using of real options to estimate Vf, e.g., Amram and Kulatilaka [1999], Brennan and Trigeorgis [1999], Schwartz and Moon [2000], Copeland and Antikarov [2000] and Damadoran [2001].

This article is not about a real options approach to valuation, but rather the development of an integrated valuation system (IVS). An IVS provides a rich and stimulating foundation for 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 of the cash flow components to changes in the forecasted inputs. The IVS simulates the effect of using different growth rates of FCFF and FCFE in estimating the Vs[FCFE] and Vf[FCFF]. It also shows how changes in the [D / Vf] and [E / Vf] weights, and changes in ks and kd can affect WACC. The most challenging and important contribution of this paper is the sensitivity of the value 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 a static approach for a single point in time, where the current market value of the equity (Vs) and the 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 cash flows to a firm (FCFF) at the weighted average cost of capital (WACC). Vf[FCFF] is based on the 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 is an 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 / Vf kd = market interest rate on long-term debt, ws = Vs / Vf

ks = required rate of return on equity derived from CAPM Vd = 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 ∞ Although the FCFF looks like an innocent acronym, it is a very complex variable. It contains the net flows (inflows – outflows) related to operations (NOF), working capital (WCF) and investments (NIF). For example, these three net cash flow measures are based on many factors, such as a firm’s…

• corporate strategy and its implementation, • product markets served, its share of these markets and their growth potential, • competitive position within each of its product markets and its industry,

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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 firm’s growth rate, • performance of its operating, working capital and investment flows, • potential growth of a firm’s strategic investments, • expected long-run rates of return on a firm’s 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 annual FCFF for n periods, plus the inputs used in estimating the terminal value (TV). The estimate of terminal 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 firm’s estimated value. Finally the stability of the WACC is based on the stability of management’s target weights for debt (wd) and equity (ws), plus thestability of the economic outlook for the firm as reflected in the marketplace. Value of Equity (Vs)

Several methods are used to measure the value of a firm’s equity. If the current market Vf 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 equity

FCFEt = forecasted free cash flow to equity in periods 1 to n, = net incomet + depreciation expenset + ∆WCt + NIFt + principal increment of new debtt – principal repayment of debtt

where: -∆WCt or –NIFt is an outflow of cash and +∆WCt or +NIFt is an inflow of cash, ks = required rate of return on equity capital derived from the CAPM, TVn = terminal value of FCFEn = FCFEn (1 + gn) / (ks – gn), where: ks > gn, gn = estimated annual growth rate of FCFE from period n to ∞ .

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The discounted FCFE approach incorporates the cash flows directly associated with equity shareholders for an infinite time period. Theoretically, the FCFE reflects the net cash flows 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 cash inflow to equity holders, while a decrease in permanent debt reflects an outflow of cash. It is assumed 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 required by equity shareholders and does not explicitly include the costs associated with debt, wd, kd, (1-T), that are included in the WACC.

A dividend discount model (DIV) is a third approach used to estimate the intrinsic value of 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 forecasted inputs, Vs[DIV] = Vs [FCFE].

Value of Debt (Vd)

When estimating the value of the permanent debt, the conventional valuation practice is to assume the Vd equals the book value of the long-term debt. However, if the short-term debt is 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 include accounts payable and deferred taxes. Therefore, when a DCF infinite horizon model is used to estimate 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 bearing instruments. Practically speaking, it seems that a financial management staff would be best prepared to indicate the percentage of the short-term debt (including bank loans, notes payable and capitalized leases), that is considered to be permanent.

In a zero growth to infinity scenario, the value of the debt (Vd) can be estimated with

the following formula.

Vd = [INT1] / (1 + kd) + [INT2] / (1 + kd)2 + ….+ [INT + Maturity]∞ / (1 + kd)∞ [6] where:

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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 firm’s debt, where an infinite horizon is assumed, the value

of the debt would be equal the discounted stream of estimated interest payments (INT). For example, assuming a dynamic scenario, the level of permanent debt increases when a firm is forecasting real growth in its sales. The inference is that assets and debt will grow at the real rate needed to support the sales growth. The debt is assumed to be discounted at the current market 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 in equation 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 market value 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 the intrinsic 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 valuation equation. 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] Vs [FCFE] = Vf[FCFF] – Vd[FCFD], or DCF = DCF [11] Vs [DIV] = Vf[FCFF] – Vd[FCFD]. DCF = DCF [12] Vs[FCFE] = Vs[DIV] DCF = DCF [13] Vf[FCFF] = Vs[DIV] + Vd[FCFD], or DCF = DCF [14] Vf[FCFF] = Vs[FCFE] + Vd[FCFD] DCF = DCF [15]

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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 are developed. That is, the task is to highlight why Vf[FCFF] = [Vs[FCFE] + Vd[FCFD]]. Before explaining the linkages in equations 13 and 15, we focus on creating a financial forecast and the resulting cash flow metrics.

III. CREATING A FINANCIAL FORECAST

Explaining the assumptions underlying a financial forecast highlights the important steps involved in the valuation process. A financial forecast reflects the dynamics in a firm’s product markets and its financial markets. Also good forecasting practices incorporate realistic assumptions concerning internal management efficiencies. The technical steps involved in preparing a financial forecast are presented in Appendix 2. The outlook for economic conditions and the competitive environment are factored into the forecast along with the annual growth 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. Also depreciation is assumed to be closely tied to the performance of a firm’s net fixed asset. Best practices 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 the

ith 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 maintain a stable relationship with net income.

When the forecasted assets are greater than forecasted liabilities, the shortfall in

financing, frequently called the additional funds needed (AFN), is offset first by increasing long term 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<L, the first step is to reduce the short-term debt. If the asset continue to be less than the total liabilities, the second step is to reduce the long-term debt. If there is no short or long-term debt, the remainder flows to excess cash. Additional Insights

The financial forecast program is an extremely valuable tool when you wish to simulate various scenarios of possible outcomes. Initially we have developed an example that assumes a relatively stable long-run outlook for the example company. Now, we wish to identify a few assumptions that can cause the forecast to be unstable and thereby create problems in interpreting the financial health of a company.

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Growth rate of sales. The financial forecast program is driven by the growth rate of sales. The growth of the several asset classes and accounts payable and other current liabilities are 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 assumed to be erratic and unstable, the outcomes of the forecast will look dramatically different and create uncertainty in the validity of the outcomes. It is extremely important to carefully track the cash flow results and discover why the forecasted results look vastly different from the base forecast. The results of your forecast are correct, but it is the task of the user to understand what happened and why it happened. Sales growing too fast. If the firm’s strategic plan is for sales to grow more rapidly than the operating income or the net income during the next several years, the financial forecast will show the total assets are more-than-likely growing more rapidly than the total liabilities. To finance this rapid growth strategy, where forecasted assets > liabilities, the firm will need to increase it temporary and/or permanent financing. The financial forecasting model is programmed to first utilize the retained earning from the income statement, discretionary cash flow, before increasing its long-term debt to accomplish management’s target debt/total market value 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 point if additional funds are still needed to make liabilities = assets, the target debt ratio is overridden and 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 or determine a new set of inputs to accommodate the increase in market risk. The new inputs would be an increase in the cost of equity and debt because of market expectations have changed, plus a revised target capital structure (Debt/Equity). Growth in profit margins > growth in sales. When profit margins are increasing more rapidly than sales, operating profits will be increasing at a rate greater than sales. According to Solomon [1963, chapter 5] this set of conditions reflects true growth. That is, when rate of return 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, it will create some instability in forecasting future performance. Sales in decline. If the forecast is for sales to decline over several years, the strategy of the firm will change dramatically. The relationship between sales and assets will decline, and it is crucial to track the return on operating income and/or net income vis-à-vis sales. Management needs a new strategic plan that where forecasted total assets to equal total liabilities. Keeping within the capital structure boundaries established and reducing debt if possible, would be the conservative strategy for the financial forecast to follow. Increasing operating profit margins. If new product markets result in and increase in operating profit margins (EBIT/Sales) and/or profit margins (NI/Sales), the FCFF and discretionary cash flow will likely rise, assuming other forecasted components remain unchanged. Under these conditions, equity in the balance sheet will rise and it is possible that forecasted liabilities > assets. An increase in equity can result in the debt ratio (debt/Vf) declining, and/or debt can be retired. Either of these acts can result in the debt ratio falling below the target established by management or to zero. If the cost of equity and debt is not

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readjusted downward the WACC will likely increase as the percentage of equity approaches 100 percent. No growth, expansion and true growth. Solomon [1963] developed four scenarios that were related to the forecasted growth rate of net earnings or dividends. The scenarios highlighted the effect that investment and how it was financed had on growth of earnings and/or dividends. If 100 percent of the net income was paid out in dividends, for an all equity firm, there would be no growth in value over time. However, investing a portion of the earnings 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 in firm value. The third condition occurred when a portion of earnings retained was invested at a rate of return greater than WACC. Solomon referred to this condition as true growth and over time equity would increase and the debt/equity ratio would decrease. True growth creates complex issues in estimating the optimal capital structure, cost of equity (ks) and value of the stock. Likewise, the stability of the investment pattern can have a profound affect on the value of 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 Abbott Laboratories --free cash flow to equity [FCFE] and dividends [DIV]—are presented in the preformed income statement and balance sheet that is located in Exhibit 1. The sales of Abbott Laboratories are assumed to grow at 7.5 percent annually for five years. The forecasted relationships between sales and income statement expenses, assets and selected liabilities are found 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 shows relationships between FCFE, FCFD and FCFF in the financial forecast. Also Exhibit 1A provides 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), net investment (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 in Exhibit 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 at the top of Exhibit 3. The capital asset pricing model (CAPM) is used to estimate ks. The CAPM is… ks = rf + β [MRP] [16] where: rf = risk free rate = 0.044 β = beta = 0.85 MRP = market risk premium = 0.02

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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 3 percent. 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 percent annually, 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, 1-5 are $0.019 billion greater the PVFCFE,1-5, $7.950 billion - $7.931 billion. In order to make the total 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 5 PVTVDIV, year 5 = $55.524 billion

To solve for gDIV the next step is to find the future value of $55.524 billion, where ks is 0.061 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) $. The following 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 find gDIV is… $74.655 (0.061 – gDIV) = $2.221 + $2.221gDIV $4.55396 - $74.655 gDIV = $2.221 + $2.221 gDIV gDIV* = [$4.55396 - $2.221] / [$74.655 + $2.221] gDIV* = 0.030348775

Thus, the implied terminal value growth rate of dividends is 3.03 percent, which is shown as 3.0 percent in Exhibit 4. That is, at the beginning of year 6, the estimated future dividends must grow at 3.03 percent annually to infinity in order to achieve an intrinsic value of $63.475 billion, thereby making the estimated Vs[DIV] = Vs[FCFE]. There are two possible _____ 1 This calculation can be accomplished in Excel by using Solver under Tools.

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interpretation of the gDIV > gFCFE. First, if the estimated flows from DIV are considered a better 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 equity value is achieved with only a 3.0 percent terminal growth rate of a FCFE to a company’s shareholders, while a 3.03 percent terminal value of DIV flows is necessary to achieve the same equity 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 the undiscounted 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 occur because the payout ratio < 100 percent, and the higher retained earnings allows the FCFE in years 1- 5 to increase more rapidly than the DIV in years 1-5. The dividends are based on the percentage of net income disbursed to shareholders, and it is only indirectly related to balance sheet flows associated with FCFE. In closing, it is relatively common to find the present value of 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 flows

from DIV a better predictor of the value of equity than the FCFE flows. That is, investors physically receive dividends, while the flows associated with FCFE do not flow directly to investors. Namely, it is assumed that cash outflows associated with capital investments and working capital earn at least the weighted average cost of capital (WACC), that in the future become operating cash inflows. Likewise, it is assumed that the increase in debt will be used to invest 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 of this section is to discover why the two sides of equation 15 differ. The first task is to examine the 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 investment flows (NIF) and working capital flows (WCCF). The FCFF is shown in Exhibit 2 and 5. The WACC is used to discount the FCFF and its components-- the equation for estimating the market weights for debt (wd) and equity (ws), plus market costs of capital for debt (kd)(1-tax rate) 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 6.1 percent, respectively. Inserting these components into the WACC equation creates a WACC of 5.807 percent.

In estimating the Vs[FCFF], the annual FCFF are discounted at the WACC, as presented in

Exhibit 5. It is assumed the FCFF grows at a rate of 7.5 percent annually from years 1 to 5. When the annual FCFF for years 1 to 5 are discounted at 5.807 percent, the present value is $9.382 billion, as shown in Exhibit 5.

By comparison, the Vs[FCFE] is $63,475 billion and the Vf[FCFD] is $11.345 billion.2 _____ 2 Note the book value of debt in year 1 was $6.307 billion. It is common practice to solve for the Vf by adding the book value of debt in year 1 to the present value of the FCFE (Vs[FCFE]). The estimated value of Abbott Laboratories would be understated by approximately $5 billion and the wd in the WACC would be 9.04 percent vis-à-vis the 15.16 percent in Exhibit 3.

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Thus, summing the equity and debt components shows the Vf is $74.82 billion, as shown in Exhibit 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 10

PVTVFCFF, year 5 = $65.438. To solve for the gFCFF, 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] = [$65.437 billion / .74374] = $87.983 billion. The next step is to find gFCFF, assuming numerals are in millions $:

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 15 equal. The result is the implied terminal growth rate of FCFF (gFCFF), 0.02578, that equals 2.6 percent when rounded, as shown in Exhibit 5. Thus, at the beginning of year 6 the estimated FCFF must grow at 2.6 percent annually to infinity in order for the intrinsic Vf[FCFF] to equal $74.820 billion, where the estimated Vf[FCFF] = [Vs[FCFE] + Vd[FCFD]]. One possible interpretations of equation 15 is that the sum of the estimated discounted flows from FCFE and FCFD may be overstated. Exhibit 3 indicates the $74.820 billion intrinsic value of the firm is achieved with a 3 percent terminal growth of FCFE5 and FCFD5, while only a 2.6 percent growth in terminal FCFF10 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 of FCFE + FCFD for years 1-5. In summary, the two sides of equation 15 are equal, but in order for 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 company’s strategic financial forecast. The IVS and makes is possible to simulate changes in a company’s financial strategies and discover how they affect the firm’s financial health and/or valuation. This integrated valuation system (IVS) generates a five year forecast of a company’s financial statements and creates a solid foundation for calculating cash flow measures used to estimate the value of a firm, its equity and it permanent debt. The cash flow components can also be used to assess the financial health of a company. The IVS allows a student to discover why the intrinsic value of stock based on a free cash flow to equity valuation model (Vs{FCFE] ) does not equal the value generated by a dividend discount model (Vs[DIV]). Additionally, the IVS generates an implied terminal growth rate of dividends where a discounted stream of dividends is to equal a discounted stream of free cash flows to equity. When the implied terminal growth rate of dividends is greater than the growth rate of the FCFE, it signals a scenario where the intrinsic value of the equity is underestimated by the dividend discount model or vice versa. The only time the Vs[DIV] = Vs[FCFE] would be

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when there was an all equity firm with a 100 percent payout ratio and the return on investment equals the cost of equity. Many investors believe dividends provide a more accurate measure of 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 rate of free cash flows to the firm. This implied growth rate causes the value of a firm based on its free cash flows (Vf[FCFF]) to equal the value of a firm based on the sum of its free cash flow to equity and debt [Vs]FCFE] + Vd[FCFD]]. If the implied terminal growth rate of FCFF is less than the growth rate of the FCFE and FCFD, it suggests the equity is likely to be overvalued. The inputs for these two models are also substantially different. The challenge to the learner is to develop an understanding of a company’s financial health based on the inputs used in the financial 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 STRATEGIES—NO 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 of return on capital investments (r) equals the cost of equity capital (ks), r = ks.

Expansion reflects a firm that increases its size, by investing in capital investment projects that earn the cost of equity, r = ks, and these projects were financed with the retention of earnings, thus payout ratio is <100 percent.

True Growth occurs when the firm invests in projects that earn more than the cost of equity, r>ks, and they projects were financed with retained earnings. The first of two exhibits presents the three strategies and shows the inputs used to create a firm’s pro forma income statement and a balance sheet. Note the inputs for the three all equity strategies are nearly the same with the exception of the cost of goods sold and the percent of earnings paid out in dividends for the true growth firm and the payout ratio for the expansion 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 true growth strategy. The weighted average cost of capital inputs are identical. The market values for the zero growth and expansion strategy are identical, while the value of the stock, firm and value per share are greater for the true growth strategy. The value of the dividends and free cash flow are the same for zero growth and expansion, but they are larger for the true growth scenario. Finally, the implied terminal value for the free cash flow to equity are identical for the zero growth and expansion, but greater for the true growth strategy.

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APPENDIX 1 (continued)

ALL EQUITY FINANCED FIRMS WITH THREE STRATEGIES—NO GROWTH, EXPANSION AND TRUE GROWTH Percentage of Sales Forecast Method

Financial Input Zero Growth Expansion1 True Growth2

I. Income Statement

1. Growth of Sales 0% 0% 0% 2. Cost of Goods Sold3 50% 50% 46% 3. Administrative Expenses3 15% 15% 15% 4. Other Expenses3 5% 5% 5% 5. Depreciation Expense4 10% 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 $0 15. Other Current Liabilities 0% 0% 0% 16. Other Liabilities $0 $0 $0 17. Long Term Debt $0 $0 $0 18. Common Stock6 $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 firm’s capital investments and the return on the investments (r) equals cost of equity (ks), r = ks. 2 True growth occurs when the retention of earnings is sufficient to finance the firm’s capital investments and the investments earn more than the cost of equity (ks), r>ks. 3 Percentage of sales 4 Percentage of net assets 5 All assets, accounts payable and other current liabilities are a percentage of sales. 6 Common Stock and Retained earnings are in millions of dollars

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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 0.1970 2. Asset Turnover (X) 1.5385 1.5873 1.5873 3. Rate of Return on Assets 0.2585 0.2667 0.3048 4. Leverage Multiplier 1.0 1.0 1.0 5. Rate of Return on Equity 0.2585 0.2667 0.3048 WACC Components 6. Weight in debt (wd) 0.0 0.0 0.0 7. Cost of debt (kd) 0.07 0.07 0.07 8. (1 – Tax Rate) 0.60 0.60 0.60 9. 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 $96M 12. Value of Debt (Vd) 0.0 0.0 0.0 13. Value of Firm (Vf) $84M $84M $96M 14. Value per share $1.0 $1.0 $1.1429 15 Number of Shares 84M 84M 84M Dividend and FCFE 16. Dividends $8.40M $7.4M $8.6M 17. Rate of Return on Div. 0.10 0.107 0.14298 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 0.02159 21. Implied TV FCFE Growth 0.0 0.0 0.02159 ___ 7 Dividend return = 0.08810 and capital gain=0.0119, total return = 0.10

8 0.1429 = $96M / 84M.

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APPENDIX 2 The objective of Appendix 2 is to explain the key assumptions and steps involved in preparing a percentage of sales forecast for an income statement and balance sheet. The explanation is based on the information provided in Exhibit 1 for years 0 and 1 . The growth of sales is assumed to be 7.5 percent annually. Income Statement 0 1 Explanation for Period 1 1. 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 = 0.00 8. 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 - 0.33 10.Taxes 0.88 1.02 T1 = (TR)NIBT1: 0.242 ($4.21) 11.Net Income $2.79 $3.19 NI1 = NIBT1 – T1: $4.21 – $1.02 12.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 Assets 14.Excess Cash 0.00 0.00 15.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 Liabilities 22.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] 24.Other Current Liabilities 3.41 3.00 OCL = % Sales1 [Sales1]: 0.158 [$19.01] 25.Other Liabilities 7.00 6.78 OL = % Sales1 [Sales1]: 0.131 [$19.01] 26.Long Term Debt 4.27 4.66 LTD = See paragraph 3 on page 11. 27.Common Stock 2.89 2.89 CS = no change 28.Retained Earnings 7.77 9.34 RE = RE0 + ∆RE: 7.77 + 1.57 29.Total Liabilities+Equity $24.26 $26.10 TL+E=AP+NP+OCL+LTD+CS+RE

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Press.

Exhibit 1: Financial Statements (in millions)Example Analyst

Income Statement % of Sales % of Sales ForecastYear ended Dec 31, year: Historical Base % of Sales 2001 +1 +2 +3 +4 +5Growth of Sales (Last 5 yrs) Year & Others Base YR 7.5% 7.5% 7.5% 7.5% 7.5%Cost of Sales /Sales 41.0% 41.0% 41.0% 41.0% 41.0%Admin. Exp. /Sales 22.5% 22.5% 22.5% 22.5% 22.5%Sales $17,684.66 $19,011.01 $20,436.84 $21,969.60 $23,617.32 $25,388.62Cost of sales 6.83% 41.4% $7,328.91 $7,794.51 $8,379.10 $9,007.54 $9,683.10 $10,409.33Administrative expenses 0.00% 22.5% $3,978.91 $4,277.48 $4,598.29 $4,943.16 $5,313.90 $5,712.44Other expenses 9.11% 9.4% 9.5% $1,669.49 $1,806.05 $1,941.50 $2,087.11 $2,243.65 $2,411.92Depreciation (% of net fixe 70.0% 10.2% 10.2% $1,177.35 $594.47 $639.91 $687.90 $739.50 $794.96Earnings before interest and taxes $3,530.00 $4,538.50 $4,878.03 $5,243.89 $5,637.18 $6,059.97Net Interest expense 13.66% -0.8% -$143.27 $326.46 $346.87 $337.29 $326.92 $315.04Net income before tax $3,673.27 $4,212.05 $4,531.16 $4,906.60 $5,310.26 $5,744.92Taxes 23.54% 5.0% 24.2% $879.57 $1,019.31 $1,096.54 $1,187.40 $1,285.08 $1,390.27Net Income $2,793.70 $3,192.73 $3,434.62 $3,719.20 $4,025.18 $4,354.65Dividends 57.09% 8.1% 51.0% $1,427.85 $1,628.29 $1,751.66 $1,896.79 $2,052.84 $2,220.87Change to retained earnings $1,365.85 $1,564.44 $1,682.97 $1,822.41 $1,972.34 $2,133.78

Balance SheetExcess Cash $0.00 $0.00 $0.00 $0.00 $0.00 $0.00Cash #VALUE! 5.5% 5.5% $966.12 $1,045.61 $1,124.03 $1,208.33 $1,298.95 $1,396.37Accounts Receivable 0.01% 16.6% 16.6% $2,927.37 $3,155.83 $3,392.51 $3,646.95 $3,920.47 $4,214.51Inventory 0.00% 13.8% 13.8% $2,441.30 $2,623.52 $2,820.28 $3,031.80 $3,259.19 $3,503.63Other current assets 123.69% 15.8% 15.8% $2,787.98 $3,003.74 $3,229.02 $3,471.20 $3,731.54 $4,011.40Total current assets $9,122.77 $9,828.69 $10,565.84 $11,358.28 $12,210.15 $13,125.91Net fixed assets 27.18% 33.0% 33.0% $5,828.12 $6,273.63 $6,744.16 $7,249.97 $7,793.71 $8,378.24Other assets 123.69% 52.6% 52.6% $9,308.21 $9,999.79 $10,749.78 $11,556.01 $12,422.71 $13,354.41 Total Assets $24,259.10 $26,102.12 $28,059.77 $30,164.26 $32,426.58 $34,858.57

Accounts payable 46.86% 10.9% 10.9% $1,927.54 $2,072.20 $2,227.62 $2,394.69 $2,574.29 $2,767.36Notes payable $1,661.65 $1,706.07 $1,186.76 $627.31 $12.68 $0.00Other current liabilities 0.00% 19.3% 15.8% $3,413.01 $3,003.74 $3,229.02 $3,471.20 $3,731.54 $4,011.40Total current liabilities $7,002.20 $6,782.01 $6,643.40 $6,493.20 $6,318.51 $6,778.76Other Liabilities 88.80% 13.1% 13.1% $2,318.37 $2,490.44 $2,677.23 $2,878.02 $3,093.87 $3,325.91Long term debt 290.52% 24.2% 24.2% $4,273.97 $4,600.66 $4,945.71 $5,316.64 $5,715.39 $5,482.75Common Stock $2,891.27 $2,891.27 $2,891.27 $2,891.27 $2,891.27 $2,891.27Retained Earnings $7,773.29 $9,337.73 $10,902.17 $12,585.13 $14,407.54 $16,379.88 Total Liabilities + Equity $24,259.10 $26,102.12 $28,059.77 $30,164.26 $32,426.58 $34,858.57

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

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 $315.04FCFE + 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 $5,482.75Total equity $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 equity 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%

xhibit 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)

Year ended Dec 31, year: 0 1 2 3 4 5Working 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 (ΔNWC) $2,816.10 $3,707.15 $3,985.18 $4,284.07 $4,605.38 $4,950.78Change 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 $794.96Change in Other Assets $691.58 $749.98 $806.23 $866.70 $931.70Net 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 $345.40Principal increase (repayment) in debt $371.12 -$174.26 -$188.52 -$215.88 -$245.32Change 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 debt $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 $6,059.97EBIT(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)

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 $2,247.70Terminal value: (1+ g)/(Ks - g) x $2,247.70 $0.00 $0.00 $0.00 $0.00 $74,681.51Total: FCFE + terminal value of FCFE $1,535.71 $1,761.82 $1,919.75 $2,077.54 $76,929.21Present value of free cash flows to equity $7,930.90Present value of terminal value $55,543.88Present 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 $315.04Terminal 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 $13,294.86Present value of cash flows to debt $1,413.27Present 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 Ke

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)

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 $74,655.20Total: 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 $55,524.31Present 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 $315.04Terminal 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 $13,294.86Present value of free cash flows to debt $1,413.27Present 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 KeDebt 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 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 $86,776.33Total: FCFF + terminal value of FCFF $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 $65,437.24Present 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 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 $86,776.33Total: FCFF + terminal value of FCFF $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 $65,437.24Present 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 6FCFE 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 $9,382.11Present 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 3 Cash flows $37.94 Terminal values -$37.94 Firm value $0.00

Difference, Exhibit 6 - Exhibit 4 Cash flows $18.37 Terminal values -$18.37 Firm value $0.00