ESTIMATING THE INTRINSIC VALUE OF AN ENTERPRISE WITH AN

INTEGRATED FINANCIAL MANAGEMENT SYSTEM

James A. Gentry Professor Emeritus of Finance &

University Distinguished Teacher Scholar University of Illinois, Urbana-Champaign

j-gentry@uiuc.edu

and

Frank K. Reilly

Bernard J. Hank Professor of Finance University of Notre Dame

Reilly.1@nd.edu

November 30, 2007

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ABSTRACT

Learning the process of estimating the intrinsic value of an enterprise can be extremely frustrating to students because it involves a deep understanding of numerous complex relationships. The teaching goals of this manuscript are to create a dynamic learning experience that underlies the valuation processs. To accomplish these goals we have created an integrated financial management system (IFMS). The IFMS provides a user friendly approach for preparing a financial forecast and, in turn, estimating the intrinsic value of an enterprise.

Our teaching experiences suggests students use the IFMS to simulate financial forecasts based on carefully researched inputs that reflect a company’s corporate and financial strategies. The simulations highlight the dynamic interplay of key quantitative and qualitative information on the value creation process. For example, students will observe why and how changes in credit policy decisions affect the long-run firm value. Furthermore, students can observe how changes in the target debt/ firm value ratios (D/V) can dramatically affect enterprise value. Additionally, an important event is learning if a firm’s strategic capital investment decisions result in an increase in enterprise value. Also, students will discover that the value of interest bearing debt (Vd[FCFD]) increases when management pursues a long run growth strategy versus a no growth strategy in which the value of debt (Vd) remains constant. Finally, the IFMS helps students discover how strategic forecasting errors related to operating, investment and/or financing decisions can affect the value of a firm.

One of the most important learning experiences created by the IFMS is the effect of a

long-run growth strategy on the free cash flow to the firm [FCFF] versus the free cash flow to the equity [FCFE] and the free cash flow to the debt [FCFD]. That is, the value of a firm based on a long-run growth strategy (Vf[FCFF]) will not equal the sum of discounted free cash flow to equity (Vs[FCFE]) plus the discounted free cash flow to debt (Vd[FCFD]). In reconciling this valuation dilemma, the solver routine in Excel generates an implied terminal growth rate of the FCFF (gFCFF) that causes the Vf[FCFF] = [Vs[FCFE] + Vd[FCFD]]. The gFCFF is a valuable financial tool for estimating a credible terminal growth rate.

Overall, the IFMS results in students having a deeper understanding of why and how changes in financial strategies affect the intrinsic value of a firm. Our teaching experiences suggests the IFMS provides a tool that enhances student understanding and retention of the valuation process. NOTE TO REVIEWERS

The authors have a minor disagreement concerning which discount rate to use in the valuation of debt on pages 9 and 10. One approach would use (1+kd)(1-t) and the other would use (1+kd). We would greatly appreciate participating in a discussion with the reviewer and audience as to which approach would be theoretically correct. Currently the paper uses the (1+kd)(1-t). For the June meeting in Prague, we shall prepare an example that show the results when (1+kd) is the discount rate for the debt. The authors are developing two additional approaches concerning the problem of what to do with the excess cash. Currently, the program uses all of the excess cash to retire debt. We are developing two other scenarios for the Prague meeting. (1) Transfer all of the excess cash to the account called “excess cash”. (2) Use a percent of the excess case (1 to 100 percent) to repurchase shares of stock and the remainder transferred to the excess cash account. We shall use a 100 percent repurchase plan for Prague.

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ESTIMATING THE INTRINSIC VALUE OF AN ENTERPRISE WITH AN

INTEGRATED FINANCIAL MANAGEMENT SYSTEM1 Many professional financial specialists, investors and academics are constantly searching for an equivalent to Harry Potter’s magic wand. The objectives are to gain fresh insights into the process of analyzing a company’s financial health and estimating its intrinsic value. In recent years our students have helped us to identify gaps in their understanding of credit risk and valuation theories. The result is the development of an integrated financial management system (IFMS). The IFMS uses forecasting assumptions to generate financial statements as the foundation for estimating a firm’s long-run value. The forecast reflects managements’ assumed corporate and financial strategies. As strategies change, the financial performance and the value of an enterprise can change. Based on the outcomes of various simulated scenarios, the IFMS identifies various performance patterns in the long-run intrinsic value of an enterprise. A careful analysis of financial statements highlights the variables that were closely associated with the changes in enterprise value. The IFMS helps students enhance their financial analysis skills in explaining possible causes in a firm’s financial health and changes in its intrinsic value.

Several models have been proposed to estimate the intrinsic value of a stock. 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 provided 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 [2006, Chapters 7-9]. 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 [DDM] for estimating the value of a stock (Vs[DDM]). Later, Gordon [1962] extended the Williams model by introducing a dividend constant growth model in the late 1950s and early 1960s, that is called the constant growth model (Vs[CGM]).

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. 1 The authors are very grateful to Mike Sandretto, Yiyi Zeng and Yerzhan Turkushev for their valuable programming assistance.

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Copeland, Koller and Murrin [1994, 2000] and Damadoran [1994, 206] 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].

A brief review of a few basic concepts used to estimate the market value of a firm

(Vf), its stock (Vs) and debt (Vd) will set the stage for this paper. . A basic concept in the theory of finance is… Vf = [Vs + Vd], [1] where: Vf is the estimated market value of a firm, Vs is the estimated market value of its stock, and Vd is the estimated market value of its interest-bearing 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], Brigham and Ehrhardt [2005, Chapter 15]. 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 and Vd are known or the intrinsic Vs can be estimated by discounting to infinity the free cash flow to equity [FCFE] at the required rate of return on the equity (ks), Damadoran [2006, Chapter 5] With the appropriate forecasted inputs it is possible for the Vs[FCFE] = Vs. 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 valuation complexities that occur when the interest bearing debt is allowed to increase as a firm pursues a long-run growth strategy2. 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. We have concluded that there is a gap in the explanation of how valuation models are integrated. Our challenge is to connect these valuation theories so that the linkages are transparent.

2 However, to the best of our knowledge a methodology has not been developed that estimates the value of debt for a firm with a long-run growth strategy. That is, discounting to infinity the free cash flow to interest-bearing debt [Vf[FCFD]] at a market determined rate of return on debt (1+kd (1-t)). Later, we shall develop the linkages that show Vf[FCFD] = Vs[FCFE] + Vd[FCFD].

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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])3, debt (Vd[FCFD]) and a firm (Vf) or an enterprise. 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. Likewise, Section V presents the linkages that make the Vf[FCFF] = [Vs[FCFE] + Vd[FCFD]]. Simulating various scenarios highlights the analytical power an integrated valuation system offers to professional financial specialist, investors and students of finance. 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 [DDM], that is the future cash flows that stockholders would receive. In the early 1960s, Gordon [1962] extended Williams DDM 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.

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 DDM valuation 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

3 We recognize the importance of the constant growth model is estimating the value of a firm’s equity, but we have chosen to focus on the free cash flow to equity approach and not develop the dividend model. in this article.

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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 sub-hypotheses depending on the information set involved: (1) weak-form EMH, (2) semi strong-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 William’s and Gordon’s dividend valuation models.

Late in the1980s 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 [1994, 2006] 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 (CGM)

4.

The preceding discussion briefly introduced 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[FCFD] are +relatively stable 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]. Also authors who developed the valuation of distressed and/or bankrupt companies, such as Gilson [1997], Grinblatt and Titman [1998], Gilson, Hotchkiss and Ruback [2000], Kaplan and Ruback [1995] and Ruback [2000].

An integrated financial management system (IFMS) provides a rich and stimulating foundation for teaching and learning about valuing a firm and its equity. The integrated valuation system highlights the forecasting and discounting of FCFF, FCFE and FCFD, that highlight the sensitivity of the cash flow components to changes in the forecasted inputs. It also illustrates how changes in the Vd / Vf and Vs / Vf weights, as well as changes in ks and kd, can affect WACC. Finally, as shown earlier, the IFMS develops an implied terminal growth rate of the FCFF (gFCFF), that results in the Vf[FCFF] = [Vs[FCFE] + Vd[FCFD].]

II. AN OVERVIEW OF THE VALUATION PROCESS

Value of a Firm (Vf)

4 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[CGM]. Therefore, to make the value of the discounted dividends equal to the value of the discounted FCFE, Vs (CGM) = Vs (FCFE), we created an implied terminal dividend growth rate (gDIV), but it is not reported in this study. A copy of this model is available upon request to j-gentry@uiuc.edu.

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There are two widely used methods 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 Vs + Vd equals the market value of the firm (Vf), i.e., Vf = Vs + Vd . [2]

A second approach estimates the intrinsic value of an enterprise 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[FCFF] = long-run intrinsic value of a firm,

FCFFt = forecasted annual free cash flows to a firm, periods 1 to n, = [EBITt (1-T) + depreciationt] + [ΔWCt] + [NIFt], where: -ΔWC or –NIF is an outflow of cash and +ΔWC 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.

ΔWCt = ΔReceivablest + ΔInventoryt + ΔOCAt + ΔPayablest + ΔOCLt, NIFt = Δnet fixed assetst + depreciation expenset + Δother assetst WACC = weighted average cost of capital, = wd kd (1- tax rate) + ws ks wd = Vd / Vf kd = market interest rate on interest-bearing 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 ∞ The FCFF 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, • 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, share repurchase policy and target capital

structure, and • internal operating efficiencies.

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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 significant proportion of a firm’s estimated value. Finally, the stability of WACC is based on the accuracy of the estimated target weights for debt (wd) and equity (ws), plus the outlook for the firm that is reflected in the marketplace. Value of Equity (Vs)5

Several methods are used to measure the value of a firm’s equity. If the current market price of a stock (P) is available, ks = P x N, where N is the number of shares outstanding. [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 [5] where: Vs[FCFE] = long-run intrinsic value of equity

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

where: -ΔWCt or –NIFt is an outflow of cash and +ΔWCt 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 ∞ .

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, plus the outflows associated with capital investments (NIFt) and working capital (ΔWCt). Additionally, an increase in permanent debt becomes a

5 This segment of the paper is based on Damadoran [2006 Chapter 5] and [1994 Chapter 7].

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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. The cost of equity (ks) reflects the returns required by equity shareholders. Finally, the FCFE does not include the costs associated with debt, wd, kd, (1-T), that are explicitly included in the WACC.6 Value of Debt (Vd)

When estimating the value of the permanent interest bearing debt, one approach is to assume the Vd equals the current book value of the long-term and short-term interest-bearing instruments.7 This approach to estimating Vd implicitly assumes management of the firm is pursuing a zero growth strategy. That is, there is no future growth in sales, assets, liablities or equity. Permanent sources of financing are long-term debt, short-term debt, current portion long-term debt, notes payable, bank loans, and capitalized leases. Therefore, when a DCF infinite horizon no growth model is used to estimate the Vf[FCFF] or Vs[FCFE], the permanent debt (Vd[FCFD]) includes the sum of all long and short-term interest-bearing debt.

When a firm is pursuing a zero economic growth policy, its sales, assets and

permanent debt are considered to be constant throughout time. Under these stable conditions, the value of its debt equals the stream of estimated interest payments (INT) discounted to infinity at 1 plus the current cost of debt (1 + kd) times (1- tax rate), as shown in [7].

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

with the following formula.

Vd = [INT1] / (1 + kd(1-t)) + [INT2] / (1 + kd(1-t))2 + ….+ [INT + Maturity]∞ / (1 + kd(1-t))∞ [7] where:

Vd = value of debt in a zero growth to infinity scenario, INT = annual interest payments based on a constant interest rate, (1 + kd(1-t)) = 1 + current market rate of return on debt times (1- tax rate),

The following explanation of the free cash flow to debt (FCFD) is presented as a conceptual companion to Damadoran’s [2006, Chapter 5] explanation of the FCFE. When an enterprise pursues a long-run growth strategy, it is assumed the growth rate of assets and the 6 A constant growth of dividends model (CGM) is a third approach used to estimate the intrinsic value of equity (Vs). In equation form it is: Vs[CGM] = DIV0 (1 + g)/ (1+ks) + DIV0(1+g)2/(1+ks) + ….+ DIV∞(1+g)∞/(1+ks)∞ [6] Where: Vs = intrinsic value of equity, DIV0 = annual dividend flows to shareholders in period zero, 1+gn = estimated annual compound grow in DIV in period n, ks = required rate of return on equity derived from CAPM. The CGM discounts the dividend flows to equity shareholders that estimates theVs[CGM]. The dividends are assumed to compound annually at a constant growth rate. Theoretically, with 100 percent dividend payout, the CGM forecasted inputs are identical with FCFE forecasted inputs, Vs[CGM] = Vs [FCFE]. 7 For example, textbooks that present this approach are: Brigham and Ehrhardt [2005, 514-515], Smart, Meggison and Gitman [2004, 143-144], and Stowe, Robinson and Pinto [2002, 170]

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growth rate of interest bearing debt will match the growth rate of its sales. Implicitly, it is assumed, the growth rate of the interest payments, hereafter called the free cash flow to debt (FCFD), are directly tied to the growth rate of sales. Thus the value of a firm’s debt (Vd[FCFD]) equals a stream of increasing FCFD being discounted to infinity at the current market rate of return (kd) times (1- tax rate). Therefore, when comparing the value of a no growth firm’s debt (Vd ) to the value of a firm pursuing a long-run growth strategy (Vd[FCFD]), it becomes apparent that the Vd is less than the Vd[FCFD] because the INT is constant for the no growth firm and the FCFD is increasing for the growth firm.

In the financial literature an accepted convention is to assume that the market Vf = Vs

+ Vd, shown in equation (1), and an algebraic restructuring of (1) becomes Vs = [Vf - Vd]. However, it was shown above, if a firm pursues a long-run growth strategy that the value of the forecasted debt (Vd[FCFD]) will be proportionally greater than its current market debt (Vd). Likewise, it is assumed if a firm pursues a long-run growth strategy that the value of its equity, Vs[FCFE] , would also be proportionally increased. Thus, theoretically, in a long-run growth strategy, the intrinsic enterprise value [Vf[FCFF]] would be proportionally greater than no growth value [Vf]. The difference between Vf and Vf[FCFF] occurs because the firm pursuing a no growth strategy is theoretically less the value of a growth firm, i.e., [Vs + Vd] < [Vs[FCFE] + Vd[FCFD]].

Equation 8 introduces the equation used in the IFMS to estimate the Vd[FCFD]. To the

best of our knowledge this is the first time the Vd[FCFD] concept has been presented. Vd[FCFD] = [FCFD1]/(1+ kd(1-t)) + [FCFD2]/(1+ kd(1-t))2 +…+ [FCFDn +TVn] / ((1+kd) (1-t))n [8] where: Vd[FCFD] = intrinsic value of a growth firm’s permanent debt, FCFDn = annual interest payments based on a long-run growth strategy, TVn =terminal value of FCFDn = FCFDn (1+g)/((kd(1-t) – g), where kd (1-t) > g (1 +kd(1-t)) = 1 +current market rate of return on the debt times (1- tax rate), gn = estimated annual terminal growth rate of INT from period n to ∞. Summary

The above analyses indicates there are several approaches to estimating the value of equity, debt and the enterprise. As shown below, valuation equations (9-14) are listed in column 1 and the titles in column 2. The titles reflect two different valuation approaches-- market-determined (MD) and discounted cash flow (DCF), that are based on either a no growth (NG) or a long-run growth (LG) strategy. The three valuation strategies are entitled—(1) market-determined no-growth (MD-NG,), (2) DCF-no-growth (DCF-NG) or (3) DCF-long-run-growth (DCF-LG), as shown in column 2. For example, the left hand side of equation 10 is Vf[FCFF], and it represents a DCF valuation that is based on a no growth strategy. The right hand side of the equation 10, Vs + Vd, represents a market-determined valuation with a no growth strategy (MD-NG) for the equity (Vs) and the debt (Vd). Equations [13 and 14] reflect a DCF valuation that is based on long-run growth strategies on both sides of the equation. In summary,

Market-Determined No-Growth (MD-NG);

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Valuation equations DCF-No-Growth Strategy(DCF-NG); DCF-Long-run-Growth Strategy (DCF-LG).

(1) (2) Vf = Vs + Vd , MD-NG = MD-NG [9]

Vf [FCFF] = Vs + Vd, DCF-NG = MD-NG [10] Vs = Vf - Vd MD-NG = MD-NG [11] Vs = Vf [FCFF] – Vd . MD-NG = DCF-NG – MD-NG [12] Vs [FCFE] = Vf[FCFF] – Vd[FCFD] DCF- LG = DCF-LG [13] Vf[FCFF] = Vs[FCFE] + Vd[FCFD] DCF-LG = DCF-LG [14]

The above set of relationships provide the foundation for the remainder of the paper. The analysis will focus on the linkages between the two sides of equation 14, that is the conditions necessary for Vf[FCFF] = [Vs[FCFE] + Vd[FCFD]]. However, before explaining these linkages, we present an overview of the structure of the IFMS. Following the overview is a brief introduction to the process of preparing a financial forecast and critical assumptions that may create forecasting issues or problems of interpreting the results.

III. CREATING A FINANCIAL FORECAST An Overview of IFMS

The structure of the Integrated Financial Management System (IFMS) is best viewed via a flowchart that is shown in Figure 1. First, the historical information sources needed in preparing the financial forecast are introduced in Boxes 1 – 4. Next, Box 5 represents the assumptions needed for creating a financial forecast, i.e., the drives of the IFMS. The assumptions underlying a firm’s proforma income statement and balance sheet should reflect management’s realistic expectations about the future. Box 6 reflects the income statement and the balance sheet used in calculating the company’s free cash flow to debt (FCFD), free cash flow to equity (FCFE) and free cash flow to the firm (FCFF) that are reflected in Box 7.

Figure 1 utilizes Box 8 to highlight the estimation of cost of equity and debt; Box 9

to present an estimation of a company’s equity and its debt; and Box 10 to show the components of a firm’s weighted average cost of capital. The costs of capital are presented in Exhibit 3 and used to discount the FCFE and the FCFD. In turn, the sum of the Vs[FCFE] + Vd[FCFD] result in Vf[FCFF], that becomes the foundation against which the estimated value of the enterprise in Exhibits 4 and 5 are compared. The value of an enterprise (Vf[FCFF) in Exhibit 4 is based on FCFF discounted with a WACC based on the firm’s target capital structure, that is its target debt ratio (Vd/Vf) as shown in Box 11 of Figure 1. The next step, Box12, involves solving the implied terminal growth rate used in valuing the firm, that is shown in Exhibit 4. Boxes 14 repeats the valuation of the firm based on market-determined WACC and the calculation of the implied terminal value growth rate (gFCFF) is reflected in Box 15. Box 16 highlights the presentation of a comparative overview of the previous valuation results. This overview is presented in Exhibit 6.

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Financial Forecast

Recommendations for preparing the financial forecast are found in Appendix 2. That is, the recommendations provide the technical steps to follow when preparing the financial forecast for the income statement and the balance sheet.

The outlook for economic conditions and the competitive environment are factored

into the forecast along with the annual growth rate in sales. The IFMS assumes a relationship between sales and the related cost of sales, administrative expenses and other expenses. Also in the IFMS, depreciation is assumed to be closely related to the performance of a firm’s net fixed asset. Best practices in forecasting assume all assets, accounts payable and other current liabilities are a function of sales. The IFMS assumes … ..

• 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

sales and accounts payablej, other current liabilitiesj and all interest bearing debt. • the percentage of earnings retained is stated explicitly and is assumed to maintain a

stable relationship with net income. • the main data file shows the existing debt that will retire in the next five years;

based on these data, the remaining long-term debt for each year is calculated and is presented as continuous debt in each of the next five years. When forecasted assets are greater than forecasted liabilities in the IFMS, there a

shortfall in financing is discovered. This strategic financing gap is referred to as the additional funds needed (AFN). The AFN are offset first by retained earnings from the income statement. If the AFN are not satisfied with retained earnings, the next step is to use long-term debt. If the long-term debt limit is reached and the shortfall continues, the IFMS assumes the remaining shortfall 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 assets continue to be less than the total liabilities, the second step is to reduce the long-term debt. When the firm has no short or long-term debt, the remaining cash is programmed to an account called excess cash. However, repurchasing common stock could be achieved to reduce extra cash. Additional Insights Preparing different scenarios based on separate sets of conditions is a widely used technique to accommodate uncertainties in the financial forecast. The use of different scenarios provides valuable insights to the user. Initially, an example has been prepared that assumes a relatively stable long-run outlook for the example company, Archer Daniels Midlands Company (ADM). The ADM financial data were provided by the WRDS data sets, where the base data are provided by COMPUSTAT.

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Appendix 3 provides examples of critical assumptions associated with the financial forecast that can create problems in interpreting the financial health of a company or in deciding what may be the financial outcome.

IV. DIFFERENCES BETWEEN ENTERPRISE VALUATION THEORIES

Estimating Base Value of ADM—Discounted FCFE + Discounted FCFD We are now ready to interpret the valuation results presented in Exhibits 3-5. Previously it

has been shown that the value of an enterprise can be estimated in a variety of ways. The first step is to refer to Exhibit 3 and to find that the value of ADM was $25.404 billion, which was the sum of the present value of its free cash flow to equity, $14.207 billion, and the present value of the free cash flow to debt, $11.197 billion. The cost of equity was 6.9 percent and the cost of debt was 6.5 percent, with a terminal growth rate of 3.2 percent. The $25.404 billion valuation becomes the base value to be matched in Exhibits 4 and 5. It is important to note that the cash flow difference between the FCFE is primarily either the addition of debt financing--an inflow to the FCFE, or the repayment of debt—an outflow to the FCFE. Estimating Value ADM—Discounted FCFF

The next step involves estimating the value of ADM (Vf[FCFF]) by referring to Exhibit 4 . The task is to discount the free cash flows to the firm (FCFF) at the weighted average cost of capital (WAAC). The components of the FCFF for years 1-5 are presented in Exhibit 4 and originally presented at the bottom of Exhibit 2 The equation for estimating the WACC are shown at the bottom of Exhibit 3. The target debt weight (Vd/Vf) and the equity weight (Vs/Vf) are 20 and 80 percent, respectively. The cost of debt and equity, kd and ks, are 6.5 percent and 6.9 percent. Using these data results with a WACC of 6.439 percent, the annual FCFF for years 1-5 are presented in Exhibit 4, and the present value of this discounted stream of FCFF[1 to 5] is $3.650 billion.

In order for theVf[FCFF] in Exhibit 4 to equal the Vf[FCFE + FCFD] in Exhibit 3, the Solver routine in Excel was used to calculate an implied terminal value growth rate (gFCFF]). Instructions for using the Solver routine are presented in Appendix 4. After inserting the inputs, the Solver calculates the terminal growth rate that matches the present value of the discounted FCFF in Exhibit 4 to the present value of the firm in Exhibit 3, specifically, sum of the PVFCFE + PVFCFD. The Solver calculated implied terminal growth rate ( gFCFF) was 0.00329. Please see Appendix 5 and 6 for further interpretation of gFCFF. The present value of the terminal value of the FCFF is $21.753 billion, as reflected in Exhibit 4. That is, at the beginning of year 6, ADM’s estimated future FCFF must grow at 0.329 percent annually to infinity in order to achieve an intrinsic value of $21.753 billion. Finally, Vf = PVFCFF(2006-2010) + PVTVFCFF, or $25.404 billion = $3.650 billion + $21.753 billion.

Interpretation of implied terminal growth rate effect

There are several possible interpretations of the gFCFF < gFCFE & FCFD, 0.329 percent < 3.2 percent. Discounting the FCFF at WACC is considered a better predictor of Vf than the sum of the discounted FCFE at ks plus discounted FCFD at kd. As explained above, ADM’s valuation of $25.4 billion was achieved with a 3.2 percent terminal growth rate of the

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FCFE2010 and FCFD2010, as shown in Exhibit 3. However, Exhibit 4 shows that only a 0.329 percent implied terminal growth rate (gFCFF) was required in order to achieve a value of $25.4 billion. Also, Exhibit 5 provides a similar FCFF analysis with a lower WACC of 5.885 percent, that was based on market-determined D/E weights of 0.441for wd and 0.559 for ws. The resulting implied terminal growth rate was –0.367 percent. This lower gFCFF provides further confirmation that the growth rate required to achieve the value of $25.4 billion was substantially lower than 3.2 percent.

The current market value of ADM’s stock was $35.37 per share ($23.13 billion/0.64289 billion shares) compared to an estimated intrinsic value $22.10 per share ($14.207 billion/ 0.64289 billion shares). Likewise, ADM’s current debt was valued at $7.32 billion compared to an intrinsic debt valuation of $11.197 billion. Thus the implication being that the current value of ADM’s stock is currently overvalued by approximately 60 percent and the current debt is undervalued debt by approximately 53 percent. A summary of the preceding valuation data are found in Exhibit 6 and an interpretation of these data will provide a deeper interpretation of implied terminal value growth rate.

Exhibit 6 provides a comparison of the valuation results that were presented in Exhibits 3, 4 and 5. Column 3 in Exhibit 3 shows the present value of the FCFF1-5 being $3.557b compared to a FCFF1-5 of $3.650 in Exhibit 4 and 5, where the difference of approximately $0.2 billion is a relatively small difference. However, the difference between the FCFF5 in Exhibit 3 and Exhibit 4/5 is slightly greater than $1.0 billion ($1.810 b - $0.755 b), and has a dramatic affect on the respective terminal values. That is assuming a 3.2 percent terminal growth rate, the terminal value of FCFF5 in Exhibit 3 is $29.0 billion vis-à-vis the terminal FCFF5 in Exhibit 4 is $57.6 billion. However, when applying the implied terminal growth rate of 0.33 percent to the FCFF5 in Exhibit 4 the present value of the terminal value is $21.75 billion or nearly identical to the PVFCF5 of $21.85billion. The final result in Column 8 shows the present value of ADM is $25.4 billion in both Exhibit 3 and 4.

Finally, if the terminal growth rate of FCFF5 in Exhibit 4 had been 3.2 percent, as

shown in column 5 of Exhibit 6, a required terminal growth rate of 4.57 percent, in column 5 of Exhibit 6, would be required in order for the two terminal values be equal, as shown in column 6 for Exhibits 3 and 4, or $57,658 billion. If this were the case the intrinsic value of ADM's stock would be $55.50 per share, ($46.877 billion - $11.197 billion /0.64289).

CONCLUSIONS

The objective of this manuscript is to create an exciting teaching and learning tool for

professors and students. The paper presents a valuation system that integrates strategic and financial information. It is designed to allow users to simulate various financial management policies and discover how they affect the financial health and valuation of a company. It is requirement for students to learn how to create financial forecast and learn how to interpret the results of their forecast. Thus an integrated financial management system (IFMS) is presented that generates a five year forecast of a company’s financial statements, plus the terminal value forecast. The financial forecast provides a solid foundation for calculating cash flow measures and, in turn, estimate the value of an enterprise, its equity and debt. Also the system allows the user to observe the differences in the valuation of the enterprise that

15

uses a target capital structure weighted average cost of capital (WACC) versus a market determined WACC.

It is important to use an existing company and involve its corporate officers in the

discussion related to the inputs to be used in the IFMS. The inputs in forecasting the value of ADM generated conflicting information that created lively discussions within study groups and the classroom. For example, the financial forecast for ADM was relatively optimistic for years 1-5, but the intrinsic value of the stock was $22 per share compared to the market value of $36. What were the causes of the significant differences between intrinsic and market value of ADM? Or what were the causes of the overvaluation of ADM in the market place? Why did a low cost of capital not create a higher valuation of ADM? Why was the value of the forecasted debt substantially greater than the current debt value? Also there were many questions concerning ADM’s capital structure. For example why was the target value D/E .20/.80, but market-determined D/E was .44/.56 and the book D/E in 2006 was .34/.66 ? What is the correct capital structure? Other questions that always occur are: What is the correct growth rate of sales? What is the correct cost of goods/sales relationship? Is the company planning a large acquisition in the future? Does the company plan a major investment plan in the next few years? The IFMS creates a new approach in estimating the value of the debt that is used in calculating the value of an enterprise. The introduction of the concept of free cash flow to debt (FCFD) as a companion to the free cash flow to equity (FCFE) provides unique discussions and challenges to the concept of Vs + Vd = Vf. Historically, it is an accepted convention when estimating the value of a the firm to subtract the current value of the existing debt as an approach to determining the value of the equity. This paper suggests the practice of adding the current interest bearing debt to the discounted FCFE can results in understating the value of the firm. The discussion related to the valuation of debt are always lively. Valuation inconsistencies may occur because the underlying theories were developed independently in different time periods and they were not constructed as an integrated system. Also the inputs for each of the theoretical valuation models are unique. Additionally, the IFMS uses the Solver routine in Excel to generate an implied terminal growth rate of FCFF. What does the implied terminal growth rate tell the user? If the implied terminal growth rate of FCFF is less than the terminal growth rate of the FCFE and FCFD, it signals a scenario that the intrinsic value of the equity plus the debt is overvalued, or vice versa. The only time the Vf[FCFF] = Vf[FCFE+ FCFD] would be when there was an all equity firm with a 100 percent payout ratio and the return on investment equals the cost of equity. In closing, students have indicated the IFMS…

• helps identify the key pieces of the valuation puzzle and highlights the delicate tradeoffs decisions of management associated with operations, investments, working capital, financing and optimal capital structure;

• clarifies credit analysis linkages with cash flow, profitability, liquidity, efficiency, leverage and growth;

• highlights the interrelationships between academic disciplines such as marketing, production, accounting and finance;

• shows preparing the inputs requires informed inputs and analyzing the outcomes requires analytical skills and is not a mechanical process;

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• forces careful unbiased reasoning when comparing the derived intrinsic value of the firm to the market determined valuation;

• shows each company requires different inputs when searching for the intrinsic valuation;

• can be used in as a valuable learning tool in advanced courses in corporate finance, investments, accounting and strategic management.

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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 ® 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 ® 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.

8 Percentage of sales 4 Percentage of net assets 5 All assets, accounts payable and other current liabilities are a percentage of sales.

8 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

INPUTS REQUIRED FOR PREPARING A FINANCIAL FORECAST The objective of Appendix 2 is to explain the key steps involved in preparing a percentage of sales forecast for an income statement and balance sheet. The information is to be inserted in Exhibit 1.

Inputs required for Income Statement forecast, where percentage of sales method for inputs are used, except where explanation is shown.

• Annual growth rate of sales ( F5 to J5) [e.g., 7.5%] • Cost of Sales/Sales (F6 to J6) • Administrative expenses/ Sales (F7 to J7) • Depreciation/Net Fixed Assets (D11) • Interest Expense C126 [determined by program and inserted in G13 to J13 • Other expenses/Sales (D14) [may be a used as a balancing entry] • Tax rate (D16) • Net Income (F17 to J17) [calculated by program] • Payout Ratio Dividends/Net Income (D18) • Change in retained earnings [net income – dividends is calculated by program].

Inputs required for Balance Sheet forecast

• Excess Cash [If: (Total Liabilities + Equity) > Total Assets] (see row 22) • Cash/Sales (D23) • Accounts Receivable/Sales (D24) • Inventories/Sales (D25) • Other Current Assets/Sales (D26) sometimes may be a plug value for years 1 to 5 • Net Fixed Assets/Sales (D28) • Other Assets/Sales (D29) sometimes may be a plug value for 1 to5 years. • Accounts Payable/Sales (D32) • Notes Payable (row 33) determined internally [increases if: Total Assets > Total

Liabilities + Equity, decreases if opposite occurs] • Other Current Liabilities/Sales (D34) sometimes may be a plug value for years 1 to 5 • Other liabilities/Sales (D36) sometimes may be a plug value for years 1 to 5 • Book value Long Term Debt/Sales (D37). • Common Stock (Row 38) [Constant all years] • Retained earnings + change in retained earnings in income statement (Row 39)

Inputs required for valuation assumptions. These inputs are referred to in Exhibits 3 of

the financial forecast worksheet. • Cost of equity (ks) [Exhibit 3 (C115)] • Terminal growth rate of FCFE & FCFD [Exhibit 3 (C116)] • Cost of debt (kd) [Exhibits 3 (C126)]

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APPENDIX 3

Financial Forecasting Assumptions That Can Create Problems In The Forecasted Results

Growth rate of sales. The financial forecast program is driven by the growth rate of sales. The growth of receivables, inventories and accounts payable are directly related to the growth of sales. The financial forecast in Exhibit 1 assumes a 7.5 percent growth of sales for years 1 through 4.. However, if the growth rate of sales is assumed to be markedly lower or if it is assumed to be erratic and unstable, the cash flow components will look dramatically different from the standard forecast.. It is extremely important to track the cash flow results and discover why they changed. The results of the forecast are based on the inputs. It is the user’s responsibility to interpret the data and explain what happened and why it happened. Sensitivity of CGS / Sales and SG&A /Sales. The operating income of a company is highly sensitive to increases or decreases in Cost of Goods Sold or Selling, General and Administrative Expenses as a percent of Sales. What appears to be minor percentage changes in CGS/Sales or SG&A/Sales ratios can have a profound effect on operating income. At a minimum a forecast should simulate most likely and worst case scenarios for CGS/Sales and SG&A/Sales. Sensitivity of working capital cash flows to changes in sales. For example, when current asset components are increasing more rapidly than the growth of sales, the free cash flow and management’s discretionary cash flow can decline significantly. Likewise, when the growth rate of accounts payables are less than the growth of sales, the free cash flow and management’s discretionary cash flow [MDCF] can decline rapidly. In summary, working capital components have a significant effect on the financial performance of a company. Sales growing too fast. If the firm’s strategic plan calls for sales to grow more rapidly than the operating income or the net income during the next few 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 its temporary and/or permanent financing. The IFMS 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, the capital structure is out of control. The financial forecast stops, because the user either needs to reduce the growth of sales or determine a new set of inputs to offset the increase in market risk. Under these conditions, the cost of equity and debt are increased because market expectations and credit risk have increased. Naturally, there is an increase in the debt/ equity mix. Growth in operating profit margins > growth in sales. When operating profit margins increase more rapidly than sales, operating profits are growing at a rate greater than the growth of sales. According to Solomon [1963, chapter 5] this set of conditions reflects true

22

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 in the IFMS. Sales in decline. If the forecast is for sales to decline over several years, the strategy of a distressed or bankrupt firm is markedly different than a non-distressed company The relationship between sales and assets will decline, as will the return on operating income and/or net income. The target capital structure will be mostly debt. Management needs a new strategic plan. Increasing operating profit margins. If new product markets result in an 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 (D0/Vf) declining, and/or debt can be retired. Either of these events 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 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 showed how investment and its financing affected the 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 earnings, debt/equity ratios and asset value 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. Finally, 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. Capital Structure inputs and growth rates. The valuation of a firm is highly sensitive to the assumed capital structure,Vd /Vf and the Vs/Vf, and the terminal growth rate. It is recommended that the first task in creating a financial forecast is to create a most likely income statement and balance sheet, the financial forecast in Exhibit 1. When you are comfortable with the forecasted financial statements, you can make adjustments to the target capital structure in Exhibit 4.

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APPENDIX 4

USING THE SOLVER ROUTINE IN EXCEL

Inputs required to solve for growth rate of terminal value (TV) using Solver

• To find the implied growth rate of TV of free cash flow to firm in Exhibit 4 …

Go to Tools and select Solver and follow instructions by inserting… 1. Set Target Cell …… $E$162 (present value of FCFF in Exhibit 4) 2. Equal to Value of…. Dollar Value in cell E136 (PV of FCFF in Exhibit 3) 3. By changing cell…… $C$155 (implied growth of TV of FCFF in Exhibit 4)

• To discover the implied growth rate of TV of FCFF, in Exhibit 5…

Go to Tools and select Solver and follow instructions by inserting… 1. Set Target Cell….. $E$176 (present value of FCFF in Exhibit 5) 2. Equal to Value of.. Dollar value in cell E136 (PV of FCFF in Exhibit 3) 3. By changing cell…. $C$168 (implied growth of TV of FCFF in Exhibit 5)

APPENDIX 5 Equation 14 hypothesizes that Vf[FCFF] = Vs[FCFE] + Vd[FCFD]. An objective of this section

is to discover why the two sides of [14] may differ. The first task is to examine the right hand side of [14]. In this illustration the basic inputs for estimating the free cash flow to equity [FCFE] and free cash flow to debt [FCFD] are presented in the proforma income statement and balance sheet located in Exhibit 1. The sales of Archer Daniels Midland Company (ADM) are assumed to grow at 4.5 percent annually for the period 2006-2010. The forecasted relationships between income statement expenses, assets and selected liabilities as a percentage-of-sales are found in third column of Exhibit 1. Appendix 2 provides the inputs used in the Excel spread sheet in preparing the financial forecast.

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, ADM.

The annual FCFE and FCFD for years 1-5 FCFE are presented in Exhibit 2. 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 = 0.05 β = beta = 0.80 MRP = market risk premium = 0.0238

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With the assumed CAPM inputs above, the ks is 0.069 and the discounted FCFE for

years 1 –5, PVFCFE, 1- 5, shown in Exhibit 3, are $2.571 billion. The terminal growth rate is assumed to be 3.2 percent. The present value of the terminal value (PVTVFCFE) is $11.636 billion and the intrinsic value of ADM is $14.2 billion or $22.10 per share

Thus the Vs[FCFE] = PVFCFE, 1 –5 + PVTVFCFE , [18] = $2.571 billion + $11.636 billion = $14.207 billion The current value of ADM stock was approximately $36 per share at the time this example was created. Also there were approximately 642.89 million shares of ADM stock outstanding at this time, which makes the current market value of the stock (Vs) equals to $23.14 billion.

The annual FCFD(1-T) for years 1-5 are shown in Exhibit 2 and they are discounted at

the current cost of debt (kd)(1-t), and the PVFCFD equal $0.986 billion, as shown in Exhibit 3. The PVTVFCFD is $10.211 billion, and the Vd[FCFD] equals $11.197 billion, as presented in the middle of Exhibit 3. Thus the intrinsic estimated enterprise (present) value of the ADM (Vf[FCFE + FCFD]) based on the sum of PVFCFE and PVFCFD equals $25.4 billion, as shown in Exhibit 3. The current market value of the permanent debt at this time was approximately $7.32billion or approximately $3.9 billion less than the $11.2 billion intrinsic value of the debt.

APPENDIX 6

To find gFCFF, assuming the numerals are in billions (B) $. The following is presented in Exhibit 4.

TVFCFF, year 5 = $1.810 B (1 + gFCFF) / [0.06439 – gFCFF] = $25.404 B [20]

where: $1.810 = FCFFyear 5 0.06439 = WACC $25.404 B = TV0.06722, year 5 therefore, applying algebra to [20]8, we find gFCFF is… $25.404 B (0.06439 – gFCFF) = $1.810 B + $1.810 B gFCFF $1.6358 B- $25.404B gFCFF = $1.810 B + $1.810 B gFCFF gFCFF* = [$1.6358 B - $1.810 B] / [$25.404 B + $1.810 B]

gFCFF* = 0.0032948

8 This calculation is accomplished by Solver in Excel, as shown below. Differences are related to rounding estimates.

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IMPLIED TERMINAL GROWTH RATES: INSIGHTS The implied growth of the terminal value of free cash flow to firm (gFCFF) in C155 or C168 should be compared to the growth rate of free cash flow to equity and debt (gFCFE & FCFD), that is found in C116. For example, if the implied growth rate of the terminal value of FCFF (gFCFF) in C155 is less than the annual terminal growth rate of FCFE and FCFD (gFCFE & FCFD) in C116, it shows that the terminal FCFF in year 5 of Exhibit 4 is greater than the sum of the terminal values of FCFE and FCFD in Exhibit 3. Thus the slope of the TV gFCFF<slope of gFCFE & FCFD, 0.0033<0.032. Because the gFCFF is consider a better proxy for the terminal growth rate, it means that the Vs and Vd in Exhibit 3 are more-than-likely undervalued. The opposite occurs if C155 is greater-than C116. Exhibits 4 and 5 provide a comparison of the value of ADM based on different capital structures. The percentage of the capital structure in Exhibit 4 is based on management’s perception of a target D/V equal to 20 percent, while Exhibit 5 uses a market determined D/V of 44.1 percent. The target debt ratio created a WACC of 6.439 percent compared to an 5.885 percent for the market determined debt ratio. This difference between the two WACCs resulted in the terminal growth in FCFF being 0.00329 percent for the target debt ratio and –0.00367 percent for the market determined debt proportion.

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REFERENCES Amram, Martha and Nalin Lulatilaka [1999], Real Options: Managing Strategic Investment

Options in an Uncertain World, Boston, Harvard Business School Press. Block, Stanley B. and Geoffrey A. Hirt [2001], Foundations of Financial Management, Tenth

Edition, 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, Oxford Press.

Brigham, Eugene F. and Michael C. Ehrhardt [2005], Financial Management: Theory and

Practice, 11th Edition, Fort Worth, The Dryden Press. Copeland, Tom, Tim Koller and Jack Murin [2000], Valuation: Measuring and Managing the

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

Edition, 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 [1994], Damadoran on Valuation, New York, John Wiley & Sons, Inc. ________, [2001], The Dark Side of Valuation, Upper Saddle River, NJ, Financial Times

Prentice Hall. Damadoran, Aswath [2006], Damadoran on Valuation, Second Edition, New York, John Wiley & Sons, Inc. 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

Empirical Work,” Journal of Finance, Vol. 25, No. 2, 383-417. Gordon, Myron J. [1962], The Investment, Financing, and Valuation of the Corporation, Homewood, IL, Irwin. Graham, Benjamin and David L. Dodds [1934, 1940], Security Analysis: Principles and

Technique, First and Second Editions, New York, McGraw-Hill Book Company, Inc.

27

Graham, Benjamin, David L. Dodds, Sidney Cottle with the collaboration of Charles Tatham [1962], Security Analysis: Principles and Technique, Fourth Edition, New York, McGraw-Hill Book Company, Inc.

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,

Harvard Business School Press. Reilly, Frank K. and Keith C. Brown [1997], Investment Analysis and Portfolio, Fort Worth,

The Dryden Press. Smart, Scott B., William L. Megginson and Lawrence J. Gitman [2004], Corporate Finance,

Mason, OH, South-Western. Solomon, Ezra [1963], The Theory of Financial Management, New York, Columbia

University Press. 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,

Fort Worth, The Dryden Press. Williams, J. B. [1938], The Theory of Investment Value, Cambridge, Mass., Harvard

University Press. Stowe, John D., Thomas R. Robinson, Jerald E. Pinto, Dennis W. McLeavey [2002], Analysis

of Equity Investments; Valuation, Charlottesville, VA, Association of Investment Management.

Figure 1: A Flowchart Showing the Structure of the Integrated Financial Management System

1) Six years of company data and

ratio analysis (Main Data)

Figure 1: A Flowchart Showing the Structure of the Integrated Financial Management System

2) Balance Sheet and Income Statement

(B.S.+I.S.)

3) Statements of cashflows (CFL)

4) Cashflow analysis (Cash

Flow)

5) Assumptions for Financial Forecast Financial Forecast

(Exhibit 1)

6)

Pro forma BS and IS (Exhibit 1)

7)Calculation of FCFE, FCFD,

FCFF (Exhibit 2)

8)

Estimation of Ks and Kd (Exhibit 3)

9)PV of the Firm

(FCFE + FCFD) (Exhibit 3)

10) Estimation of WACC using target capital

structure (Exhibit FCFF (Exhibit 2) (Exhibit 3) structure (Exhibit 3)

11)PV of the Firm

with target

12) Solve for implied terminal growth

rate for FCFF

13)Estimation on WACC using

14) PV of the Firm with market

values of D/E

15) Solve for implied terminal growth

rate for FCFF using capital structure

(FCFF) (Exhibit 4)using value of the firm from Exhibit

3 (Exhibit 4)

market values of D/E (Exhibit 5)

values of D/E (FCFF) (Exhibit

5)

gvalue of the firm from Exhibit 3

(Exhibit 5)

16)Compare results

(Exhibit 6)(Exhibit 6)

Exhibit 1: Financial Statements (in millions)HER-DANIELS-MIDLAND CO AnalystIncome Statement Mean % of Sales ForecastYear ended Dec 31, year: % of Sales Base % of Sales 2005 2006 2007 2008 2009 2010Growth of Sales (Last 5 yrs) Year & Others Base YR 1.8% 8.0% 8.0% 7.0% 7.0%Cost of Sales /Sales 90.1% 88.0% 87.0% 86.0% 86.0%Admin. Exp. /Sales 3.0% 1.2% 1.2% 1.2% 1.2%Sales $35,943.81 $36,594.39 $39,521.94 $42,683.70 $45,671.56 $48,868.57Cost of sales - Depreciation 91.53% 91.4% $32,847.82 $32,971.55 $34,779.31 $37,134.82 $39,277.54 $42,026.97Administrative expenses 3.14% 3.0% $1,080.81 $1,108.81 $1,197.51 $1,293.32 $1,383.85 $1,480.72Depreciation (% of net fixed assets 12.2% 12.8% 12.4% $664.65 $772.03 $833.79 $900.50 $963.53 $1,030.98Earnings before interest and taxes $1,350.53 $1,742.00 $2,711.32 $3,355.07 $4,046.64 $4,329.90Net Interest expense 1.25% 0.9% $337.58 $271.63 $386.00 $363.90 $321.38 $244.66Other expenses -0.86% -1.40% -0.8% -$503.43 -$283.61 -$306.30 -$330.80 -$353.95 -$378.73Net income before tax $1,516.38 $1,753.98 $2,631.62 $3,321.97 $4,079.22 $4,463.98Taxes 0.83% 31.1% 29.3% $471.99 $513.57 $770.54 $972.67 $1,194.39 $1,307.05Net Income $1,044.39 $1,240.42 $1,861.08 $2,349.29 $2,884.82 $3,156.92Dividends 0.00% 20.1% 15.4% $209.43 $191.52 $287.35 $362.73 $445.42 $487.43Change to retained earnings $834 96 $1 048 90 $1 573 73 $1 986 56 $2 439 40 $2 669 50Change to retained earnings $834.96 $1,048.90 $1,573.73 $1,986.56 $2,439.40 $2,669.50

Balance SheetExcess Cash $0.00 $0.00 $0.00 $0.00 $0.00 $0.00Cash 4.07% 4.0% 6.4% $1,430.42 $2,334.72 $2,521.50 $2,723.22 $2,913.85 $3,117.81Accounts Receivable 11.43% 11.4% 12.2% $4,102.26 $4,475.49 $4,833.53 $5,220.22 $5,585.63 $5,976.63Inventory 12.26% 10.9% 12.8% $3,906.70 $4,680.42 $5,054.86 $5,459.25 $5,841.39 $6,250.29Other current assets 0.94% 0.8% 0.9% $271.32 $343.99 $371.51 $401.23 $429.31 $459.36Total current assets $9,710.70 $11,834.63 $12,781.40 $13,803.91 $14,770.18 $15,804.09Net fixed assets 17.58% 14.4% 17.0% $5,184.38 $6,221.05 $6,718.73 $7,256.23 $7,764.17 $8,307.66Other assets 11.76% 10.3% 11.4% $3,703.02 $4,153.46 $4,485.74 $4,844.60 $5,183.72 $5,546.58 Total Assets $18,598.11 $22,209.14 $23,985.87 $25,904.74 $27,718.07 $29,658.33

Accounts payable 9.30% 9.5% 11.0% $3,399.35 $4,018.06 $4,339.51 $4,686.67 $5,014.74 $5,365.77Notes payable $648.75 $449.35 $0.00 $0.00 $0.00 $0.00Other current liabilities 3.98% 3.7% 4.2% $1,318.77 $1,522.33 $1,644.11 $1,775.64 $1,899.94 $2,032.93Total current liabilities $5,366.86 $5,989.74 $5,983.62 $6,462.31 $6,914.67 $7,398.70Other Liabilities 1.31% 3.5% 3.4% $1,267.63 $1,247.87 $1,347.70 $1,455.51 $1,557.40 $1,666.42Long term debt 12.03% 9.8% 15.0% $3,530.14 $5,489.16 $5,598.45 $4,944.25 $3,763.93 $2,441.65Common Stock $5,385.84 $5,385.84 $5,385.84 $5,385.84 $5,385.84 $5,385.84Retained Earnings $3,047.63 $4,096.53 $5,670.26 $7,656.82 $10,096.22 $12,765.72Other equity $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 Total Liabilities + Equity $18,598.11 $22,209.14 $23,985.87 $25,904.74 $27,718.07 $29,658.33

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

Year ended Dec 31, year: 2005 2006 2007 2008 2009 2010Free cash flow to firm, FCFF -$652.51 $770.73 $1,134.24 $1,691.44 $1,809.84

Free cash flow to equity, FCFE $1,115.58 $374.30 $456.64 $534.16 $582.38Free cash flow to debt, FCFD $192.10 $272.98 $257.35 $227.28 $173.02FCFE + FCFD $1,307.68 $647.28 $713.98 $761.43 $755.40

FCFF - (FCFE + FCFD) -$1,960.19 $123.45 $420.26 $930.00 $1,054.44

Continuous debt $2,881.39 $3,458.14 $3,460.14 $3,494.14 $3,487.14Cumulative new debt (repayment) $2,607.76 $2,140.31 $1,484.11 $269.79 -$1,045.49Total debt $5,938.51 $5,598.45 $4,944.25 $3,763.93 $2,441.65Total equity $9,482.37 $11,056.10 $13,042.66 $15,482.06 $18,151.56

BV Debt/BV Equity 62.63% 50.64% 37.91% 24.31% 13.45%BV Debt/BV Firm 38.51% 33.62% 27.49% 19.56% 11.86%BV Equity/BV Firm 61.49% 66.38% 72.51% 80.44% 88.14%

PCFCFD/PVFCFE 78.81%PVFCFD/PV Firm 44.08%PVFCFE/PV Firm 55.92%

% increase in dividends 50.04% 26.23% 22.80% 9.43%% increase in debt -5.73% -11.69% -23.87% -35.13%% increase in equity 16.60% 17.97% 18.70% 17.24%% increase in FCFE -66.45% 22.00% 16.98% 9.03%% increase in FCFD 42.11% -5.73% -11.69% -23.87%% increase in FCFF -218.12% 47.17% 49.12% 7.00%

Exhibit 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: 2005 2006 2007 2008 2009 2010Working CapitalCurrent assets - (excess cash + cash) $8,280.28 $9,499.90 $10,259.90 $11,080.69 $11,856.34 $12,686.28Current liabilities - Debt in CL $4,718.12 $5,540.39 $5,983.62 $6,462.31 $6,914.67 $7,398.70Net working capital (ΔNWC) $3,562.16 $3,959.51 $4,276.27 $4,618.38 $4,941.66 $5,287.58Change in working capital (WCCF) $397.35 $316.76 $342.10 $323.29 $345.92

Net Investment Flow (NIF)Change in net fixed assets (NFA) $1,036.67 $497.68 $537.50 $507.94 $543.49(+) Depreciation $772.03 $833.79 $900.50 $963.53 $1,030.98Change in Other Assets $450.44 $332.28 $358.86 $339.12 $362.86Net investment flow (NIF) $2,259.14 $1,663.76 $1,796.86 $1,810.59 $1,937.33

Free Cash Flow To Equity (FCFE)Net income $1,240.42 $1,861.08 $2,349.29 $2,884.82 $3,156.92(+) Depreciation $772.03 $833.79 $900.50 $963.53 $1,030.98CFFO $2 012 45 $2 694 87 $3 249 79 $3 848 35 $4 187 91CFFO $2,012.45 $2,694.87 $3,249.79 $3,848.35 $4,187.91(-)NIF $2,259.14 $1,663.76 $1,796.86 $1,810.59 $1,937.33(-) WCCF $397.35 $316.76 $342.10 $323.29 $345.92Principal increase (repayment) in debt $1,759.62 -$340.06 -$654.20 -$1,180.32 -$1,322.28Change in excess cash $0.00 $0.00 $0.00 $0.00 $0.00Free cash flow to equity (FCFE) $1,115.58 $374.30 $456.64 $534.16 $582.38

Free Cash To Debt (FCFD)(+) Interest on total interest bearing debt $192.10 $272.98 $257.35 $227.28 $173.02Free cash to debt (FCFD) $192.10 $272.98 $257.35 $227.28 $173.02

Free Cash Flow To Firm (FCFF)Earnings before interest and taxes (EBIT) $1,742.00 $2,711.32 $3,355.07 $4,046.64 $4,329.90EBIT(1 - tax rate) $1,231.94 $1,917.45 $2,372.70 $2,861.78 $3,062.11(+) Depreciation expense $772.03 $833.79 $900.50 $963.53 $1,030.98Net operating flow (NOF) $2,003.98 $2,751.24 $3,273.20 $3,825.31 $4,093.09(-) NIF $2,259.14 $1,663.76 $1,796.86 $1,810.59 $1,937.33(+) WCCF $397.35 $316.76 $342.10 $323.29 $345.92Free cash flow to firm (FCFF) -$652.51 $770.73 $1,134.24 $1,691.44 $1,809.84

Exhibit 3: Valuation of FCFE and FCFD ($ in millions), target Wd and Ws

Year ended Dec 31, year: 2005 2006 2007 2008 2009 2010Cost of Equity (Ks) 6.9%Growth rate in FCFE, end year 5 to inf. 3.2%Implied Growth Rate FCFE

Free cash flows to equity (FCFE) $1,115.58 $374.30 $456.64 $534.16 $582.38Terminal value: (1+ g)/(Ks - g) x $582.38 $0.00 $0.00 $0.00 $0.00 $16,243.69Total: FCFE + terminal value of FCFE $1,115.58 $374.30 $456.64 $534.16 $16,826.07Present value of free cash flows to equity $2,571.12Present value of terminal value $11,635.80Present value of free cash flows to equity $14,206.92

Cost of Debt (Kd) 6.5%Growth in free cash flow to debt (FCFD) 3.2%

Free cash flows to debt (FCFD) $192.10 $272.98 $257.35 $227.28 $173.02Terminal value: (1+g)/(Kd - g) x $173.02 $0.00 $0.00 $0.00 $0.00 $12,783.29

$ $ $ $ $Total: FCFD + terminal value of FCFD $192.10 $272.98 $257.35 $227.28 $12,956.31Present value of cash flows to debt $986.14Present value of terminal value $10,210.59Present value of free cash flows to debt $11,196.72

Present value of the firm (Value of equity + debt) $25,403.64

Weighted average cost of capital (WACC) = (target Wd) x Kd x (1 - Tax rate) + (target Ws) x Ks

Wd [target] 20.0%Kd 6.5%(1 - T) 70.7%

Ws [target] 80.0%Ks 6.9%

Debt portion 14.28%Equity portion 85.72%WACC 6.439%

Exhibit 4: Valuation of FCFF using WACC from Exhibit 3 ($ in millions), target Wd and Ws

Year ended Dec 31, year: 2005 2006 2007 2008 2009 2010WACC, Exhibit 3 (Kf) 6.439%Implied terminal growth rate of FCFF 0.3% 20.0%

Free cash flows to the firm (FCFF) -$652.51 $770.73 $1,134.24 $1,691.44 $1,809.84Terminal value: (1+ g)/(Kf - g) x $1,809.84 $0.00 $0.00 $0.00 $0.00 $29,719.11Total: FCFF + terminal value of FCFF -$652.51 $770.73 $1,134.24 $1,691.44 $31,528.95Present value of free cash flows to firm $3,650.37Present value of terminal value $21,753.27Present value of free cash flows to firm (FCFF) $0.00 $25,403.64

Exhibit 5: Valuation of FCFF using WACC from Exhibit 3 ($ in millions), market Wd and Ws

Year ended Dec 31, year: 2005 2006 2007 2008 2009 2010WACC, Exhibit 5 (Kf) 5.885% $0.15Implied terminal growth rate 0f FCFF -0.4%

Free cash flows to the firm (FCFF) -$652.51 $770.73 $1,134.24 $1,691.44 $1,809.84Terminal value: (1+ g)/(Kf - g) x $1,809.84 $0.00 $0.00 $0.00 $0.00 $28,844.33Total: FCFF + terminal value of FCFF -$652.51 $770.73 $1,134.24 $1,691.44 $30,654.17Present value of free cash flows to firm $3,732.03Present value of terminal value $21,671.61Present value of free cash flows to firm $25,403.64

Weighted average cost of capital (WACC) = (market Wd) x Kd x (1 - Tax rate) + (market Ws) x Ks

Wd [market = D/V] 44.1%Kd 6.5%(1 - T) 70.7%

Ws [market = E/V] 55.9%Ks 6.9%

Debt portion (D/V) 34.43%Equity portion (E/V) 65.57%WACC 5.885%

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

Exhibit # Target of valuation

PV of Cashflows

FCF in 5th year of forecast TV growth (%) Terminal

Value

PV of Terminal

Value

Sum of PV of CF and PV of

TV(1) (2) (3) (4) (5) (6) (7=6/(1+r)^5) (8=7+3)

Exhibit 3 EQUITY $2,571.12 $582.38 3.20% $16,243.69 $11,635.80 $14,206.92Exhibit 3 DEBT $986.14 $173.02 3.20% $12,783.29 $10,210.59 $11,196.72Exhibit 3 FIRM $3,557.26 $755.40 $21,846.39 $25,403.64Exhibit 3 FIRM $3,557.26 $755.40 4.57% $57,658.08 $43,320.24 $46,877.50

Exhibit 4 FIRM $3,650.37 $1,809.84 0.33% $29,719.11 $21,753.27 $25,403.64Exhibit 4 FIRM $3,650.37 $1,809.84 3.20% $57,658.08 $42,203.54 $45,853.91

Exhibit 5 FIRM $3,732.03 $1,809.84 -0.37% $28,844.33 $21,671.61 $25,403.64Exhibit 5 FIRM $3,732.03 $1,809.84 3.20% $69,566.16 $52,267.14 $55,999.17