Valuation Methods and Discount Rate Issues: A Comprehensive Example

Transcription

1 REV: NOVEMBER 1, 2006 MARC BERTONECHE FAUSTO FEDERICI Valuation Methods and Discount Rate Issues: A Comprehensive Example The objective of this note is to present a comprehensive review of valuation techniques and to show, through a simple example and straightforward how-to-do framework, the perfect consistency and identity of their results under similar assumptions. A special attention is given to the Adjusted Present Value (APV) method and the valuation of tax shields, raising the issue, discussed in the finance literature, of the discount rate that should be used to calculate the tax benefit of interest expenses. Unfortunately, finance theory does not tell us unequivocally which is the correct rate to use.... Many point to the original work by Modigliani and Miller which used the cost of debt. However, their purpose was to illustrate the tax impact of debt on value. They did not claim that their assumptions were realistic.... Similarly, Modigliani and Miller never addressed the issue of the riskiness of the tax shields from debt where a company is expected to grow and where there is uncertainty about the amount of debt that the company will have in the future. 1 According to Brealey & Myers 2, the discount rate to use in calculating the present value of the tax shields depends upon the financing rule the company follows: If debt is rebalanced (Financing rule 2, according to Brealey & Myers 3 ) every period to keep a constant debt-equity ratio, in market values, future debt levels are not known and shift up and down depending on the performance of the business. In other words, there will be a high correlation between the profits and cash flows and the interest tax shield, hence the risk will be similar. 4 As Brealey and Myers point out Interest tax shields therefore pick up the project s business risk. 5 They are just as risky as the business itself and should be discounted, following their financing rule 2 at the opportunity cost of capital, i.e. the unlevered cost of equity, defined as the risk-free rate plus the market risk premium multiplied by the asset beta (or unlevered beta ). 1 Copeland T.,T. Koller & J. Murrin, Valuation: Measuring and Managing the Value of Companies, 3 rd Edition, 2000, Appendix A, pp Brealey R. & S. Myers, Principles of Corporate Finance, McGraw Hill, 7 th Edition. 3 Brealey R. & S. Myers, op.cit., Chapter 19, p Copeland T. ibid. p Brealey R. & S. Myers, ibid p.541. Professor Marc Bertoneche and Fausto Federici prepared this note as the basis for class discussion. Copyright 2005 President and Fellows of Harvard College. To order copies or request permission to reproduce materials, call , write Harvard Business School Publishing, Boston, MA 02163, or go to No part of this publication may be reproduced, stored in a retrieval system, used in a spreadsheet, or transmitted in any form or by any means electronic, mechanical, photocopying, recording, or otherwise without the permission of Harvard Business School.

2 Valuation Methods and Discount Rate Issues: A Comprehensive Example If debt is not rebalanced, and therefore not kept at a constant debt-equity ratio, and repaid on a predetermined schedule, as it would be the case for example in a Leveraged Buyout (LBO), the tax shields are tied to fixed interest payments 6 and the cost of debt before taxes is considered, according to Brealey & Myers financing rule 1, as a reasonable discount rate since the tax shields bear the same risk than debt. The example is based on a firm with forecasted revenues of 20,000 in year 1, expecting to grow at 20% per year for the next two years, 10% the two following years and to experience no growth thereafter. The other assumptions used in the example are the following: margins (10% in year 1, 15% in year 2 and year 3, 20% after) corporate tax (35%) invested capital (60% of revenues in year 1, 55% in year 2 and 50% after, which means that the invested capital turnover ratio remains constant at a level of 2) cost of debt (6.4%, which given a risk-free rate of 4% and a market risk premium of 8% corresponds to a debt beta equal to.30) unlevered beta or asset beta (=1) Three different cases, associated with three different views on how to calculate the Present Value of the Tax Shields (PVTS), are presented. The case where debt is rebalanced (with PVTS calculated using the unlevered cost of capital) The case where debt is not rebalanced (with PVTS calculated using the cost of debt) The case where debt is not rebalanced (using a methodology based on the difference between the Present Value of taxes of the unlevered firm discounted at the unlevered cost of capital and the Present Value of taxes of the levered firm discounted at the cost of equity) In each case, the example shows the perfect consistency in results for any valuation methods (FCF / WACC, ECF/Cost of Equity, APV, EVA, SVA, CCF). The Case Where the Debt is Rebalanced (and the Tax Shields are discounted at the unlevered cost of capital) Exhibit 1 shows the calculations of the Free Cash Flows to the Firm (FCFF), the Free Cash Flows to Equity (FCFE) and the Weighted Average Cost of Capital (WACC) in the case the debt is rebalanced and the debt-equity ratio remains constant, in market values, at roughly 30% (29.9%exactly). Exhibit 2 shows the valuation results using the FCFF/ WACC method. The enterprise value, using the WACC of 11.33% shown in exhibit 1, is equal to 30,098 and the equity value, after deducting the value of debt, i.e. 9,000, is equal to 21, Brealey R. & S. Myers, ibid. 2

3 Valuation Methods and Discount Rate Issues: A Comprehensive Example Exhibit 3 shows the valuation results using the Adjusted Present Value method. APV is a valuation method by parts: First, it values the unlevered firm by discounting the Free Cash Flows to the Firm (FCFF) at the unlevered cost of capital and adds or subtracts the present value of the financing-side effects, such as the costs of issuing securities, the interest tax shields and any special financing opportunities tied to the project or the company (subsidized financing). In our example, we only consider interest tax shields. The value of the unlevered firm is equal to 28,010 and the present value of tax shields, discounted at the unlevered cost of equity (12%), is equal to 2,088, leading to an enterprise value of 30,098 and an equity value, after deducting the debt of 9,000, equal to 21,098. The results provided by APV are similar to the results given by the FCFF/ WACC method in Exhibit 2 since the latter assumes Brealey and Myers financing rule 2, that is debt rebalanced to a constant fraction which is the assumption used in APV when discounting the tax shields at the unlevered cost of equity. Exhibit 4 shows the results provided by the Equity Cash Flow method or Free Cash Flows to Equity (FCFE) discounted at the cost of equity. The equity value is equal to 21,098, the same result than in Exhibit 2 and 3. If the company s debt ratio is constant over time, the flow-to-equity method should give the same answer as discounting company cash flows at the WACC and subtracting debt. 7 Exhibit 5 describes the valuation process using the Economic Value Added (EVA) method. EVA is defined as NOPAT (Net Operating Profit) or EBIAT (Earnings Before Interest and After Tax) minus the invested capital multiplied by the WACC. EVA for the first period, given the NOPAT of 1,300 (Exhibit 1) the company s WACC of 11.33% (Exhibit 1), is equal to: EVA = 1,300 (12,000 x 11.33%) = - 60 It is also defined, which is exactly equivalent, by the spread between the company ROIC and its WACC multiplied by the invested capital. If in period 1, the company has generated a NOPAT of 1,300 (Exhibit 1) on an invested capital at the beginning of the period equal to 12,000, its return on invested capital (ROIC) is equal to 10.83% and the EVA of the first period, given the company s WACC of 11.33% (Exhibit 1), can be calculated as: EVA = (10.83% %) x 12,000 = - 60 The terminal value of EVA, given the assumption of no-growth after year 6 is equal to 2,556 /.1133 = 22,560. The present value of EVA from year 1 to 6 and the terminal value discounted at the WACC lead to an enterprise value of 30,098 and a value of equity, after deducting 9,000 of debt, equal to 21,098, a result similar to the one given by the previous methods. Exhibit 5 bis follows the same methodology but uses the unlevered cost of equity instead of the WACC to calculate the stream of EVA and its present value. The results are the same. 7 Brealey R. & S. Myers, ibid. p

4 Valuation Methods and Discount Rate Issues: A Comprehensive Example Exhibit 6 shows the valuation results following the Shareholder Value Added (SVA) proposed by A. Rappaport 8. Exhibit 7 illustrates the valuation method using the Capital Cash Flow (CCF) developed by Richard Ruback 9. Capital Cash Flows are equal to the Free Cash Flows to the Firm plus the interest tax shields. Because the interest tax shields are included in the cash flows, the appropriate discount rate is the WACC before taxes, which mathematically corresponds, only in the case of tax shields discounted at ku, to the unlevered cost of equity. It is important to remember that WACC before taxes (WACCbt) is different from the WACC without taxes which, in a world without taxes, does not change when leverage changes. In a world with taxes, WACCbt is different from the unlevered cost of capital, as we will see for the cases of debt not rebalanced, in Exhibits 15 and 22. This is because, in a world with taxes, in the calculation of ke (whether we use beta or Miller- Modigliani formulas), we do consider the impact of taxes. The results are consistent with the other methods, the Enterprise Value being equal to 30,098 and the Value of Equity to 21,098. Table 1 summarizes the formula used in this first case. Table 1 Exhibits 1 to 7 Cost of Debt (Kd) Cost of Capital (Ku) WACC WACC WACC Before Taxes Beta Levered (B Levered) B Levered for Constant Cash Flows Cost of Equity (Ke) Cost of Equity (Ke) Ke for Constant Cash Flows CASE OF DEBT REBALANCED PV of Tax Shields at Unlevered Cost of Capital Kd = Risk Free (Rf) + Debt Beta * Mkt Risk Premium Ku = Rf + Beta Unlevered * Mkt Risk Premium WACC = (Ke * E/(D+E)) + (Kd * D/(D+E) * (1-T)) WACC = Ku - Kd * D/(D+E) * T WACC = (Ke * E/(D+E)) + (kd * D/(D+E)) B Levered = Beta Unlevered + (Beta Unlev. - Beta Lev.) * (D/E) B Levered = Beta Unlevered + (Beta Unlev. - Beta Lev.) * (D/E) Ke = Rf + Beta Levered * Mkt Risk Premium Ke = Ku + D/E * (Ku - Kd) Ke = Ku + D/E * (Ku - Kd) Source: Copeland T., T. Koller & J. Murrin, Valuation: Measuring and Managing the Value of Companies; and Fernandez P., Valuation Methods and Shareholder Value Creation. 8 Alfred Rappaport, Creating Shareholder Value: The New Standard for Business Performance, Free Press 1986 and Creating Shareholder Value: A Guide for Managers and Investors, Free Press, Richard S. Ruback, Capital Cash Flows: A Simple Approach to Valuing Risky Cash Flows, Financial Management, Summer 2002, pp

5 Valuation Methods and Discount Rate Issues: A Comprehensive Example The Case Where Debt Is Not Rebalanced (and the tax shields are discounted at the cost of debt) Using the same basic assumptions than those shown in Exhibit 1 for growth, margins, corporate tax, invested capital turnover ratio, unlevered beta, but with a cost of debt decreasing as the debt is reduced, Exhibits 8 and 9 show the calculations of Free cash Flows to the Firm (FCFF), Free Cash Flows to Equity (FCFE), Cost of Equity and Weighted Average Cost of capital (WACC) in the case of a non-rebalanced, decreasing debt. The levered cost of equity, the cost of debt and the WACC are changing as financial leverage changes. Exhibit 10 shows the results of the FCFE / Cost of Equity and FCFF / WACC methods in the case of declining debt and therefore changing Cost of Equity and WACC 10. The enterprise value and the equity value are respectively equal to 28,755 and 19,755. Exhibits 11 provides the valuation results using APV with the tax shields discounted at the cost of debt, following Brealey and Myers financing rule 1.The value of the unlevered firm, discounting the FCFF at the unlevered cost of equity, i.e. 12%, is 28,010 and the present value of the tax shields, using the cost of debt as the discount rate, is equal to 745 (the sum of 595 and 150), which gives an Enterprise Value equal to 28,755 and a Value for Equity, after subtracting debt of 9,000, equal to 19,755. Exhibit 11 bis shows exactly the same results for FCFF / WACC using a backward calculation with APV to find out the changing WACC. 11 The equity valuation provided in Exhibit 12 by discounting the Free Cash Flows to the Equity Holders at the cost of equity is consistent with the other methods. Finally, Exhibit 13 (which applies the EVA approach), Exhibit 14 (which uses Rappaport s SVA methodology and Exhibit 15 (which follows the CCF method) show the consistency of these methods with the previous ones. Table 2 summarizes the formula used in this second case. 10 For a clear explanation of the iterations to find ke, step by step in the case of a LBO, see Damodaran A, Corporate Finance- Theory and Practice, John Wiley & Sons See in particular Pablo Fernandez, Valuation Methods and Shareholder Value Creation, Academic Press,

6 Valuation Methods and Discount Rate Issues: A Comprehensive Example Table 2 Exhibits 8 to 15 Cost of Debt (Kd) Cost of Capital (Ku) WACC WACC (PVT = PV Tax Shields) WACC Before Taxes Beta Levered (B Levered) B Levered for Constant Cash Flows Cost of Equity (Ke) Cost of Equity (Ke) Ke for Constant Cash Flows CASE OF DEBT NOT REBALANCED PV of Tax Shields at Cost of Debt Kd = Risk Free (Rf) + Debt Beta * Mkt Risk Premium Ku = Rf + Beta Unlevered * Mkt Risk Premium WACC = (Ke * E/(D+E)) + (Kd * D/(D+E) * (1-T)) WACC = Ku - (Kd * D/(D+E) * T) - (PVT/(D+E) * (Ku - Kb) WACC = (Ke * E/(D+E)) + (kd * D/(D+E)) B Levered = Beta Unl. + (D - PVT) * (B Unl. - Beta D) / E B Levered = Beta Unlev.+(Beta Unlev.-Beta Lev.) * (D/E) * (1-T) Ke = Rf + Beta Levered * Mkt Risk Premium Ke = Ku + ((D - PVT) / E) * (Ku - Kd) Ke = Ku + D/E * (Ku - Kd) * (1-T) Source: Copeland T., T. Koller & J. Murrin, Valuation: Measuring and Managing the Value of Companies; and Fernandez P., Valuation Methods and Shareholder Value Creation. The Case Where Debt Is Not Rebalanced (using a methodology based on the difference between the Present Value of taxes of the unlevered firm at ku and the Present Value of taxes of the levered firm at ke) This section relies on the framework presented by P. Fernandez in his book 12. He claims that, in the calculation of the value of tax shields, we should not use either the unlevered cost of capital or the cost of debt. He says that PVT is not at all a Present Value of tax shield, but the difference between two cash flows, bearing different risk, the PV of taxes of the unlevered firm discounted at the unlevered cost of capital on the one hand and the PV of taxes of the levered firm discounted at the cost of equity on the other hand. Fernandez therefore claims that this is the correct method to use in all the cases, whether debt is rebalanced or not. Within the same general assumptions in terms of expected growth, margins, invested capital, corporate tax, unlevered beta and cost of debt, Exhibits 16 to 22 show the same results for the enterprise value (29,190) and for the value of equity (20,190) for the six different methods used in this note, i.e. FCF / WACC, APV, ECF, EVA, SVA and CCF. It is important to stress the fact that, in the case of debt not rebalanced, the difficult mechanics of finding the changing WACC can be solved through APV, working backward and calculating the enterprise value (unlevered value of the firm plus the value of tax shields) every year. Subtracting the value of debt every year, we obtain the value of equity every year. With these values and the appropriate formulas for each different framework, we can calculate ke, WACC, the debt- equity ratio and the levered beta, as shown in exhibits 11bis and Fernandez P. op.cit. 6

7 Valuation Methods and Discount Rate Issues: A Comprehensive Example or through iterations working backward, finding the appropriate levered beta for the given framework and the cost of equity, ke, every year. With the cost of equity, we can then compute the value of equity every year. Adding the value of debt, we get the enterprise value and consequently the debt-equity ratio and the WACC every year, as demonstrated in exhibits 10 and 17. Table 3 summarizes the formula used in this third case. Table 3 CASE OF DEBT NOT REBALANCED PV of Tax Shields (D*T*Ku) at Unlevered Cost of Capital (*) Exhibits 16 to 22 Cost of Debt (Kd) Cost of Capital (Ku) WACC WACC WACC Before Taxes Beta Levered (B Levered) B Levered for Constant Cash Flows Cost of Equity (Ke) Cost of Equity (Ke) Ke for Constant Cash Flows (* In this case PVTS is not the PV of Tax Shields but the difference between the PV at ku of the taxes of the unlevered company and the PV at ke of the taxes of the levered company) Kd = Risk Free (Rf) + Debt Beta * Mkt Risk Premium Ku = Rf + Beta Unlevered * Mkt Risk Premium WACC = (Ke * E/(D+E)) + (Kd * D/(D+E) * (1-T)) WACC = Ku * (1 - TD / (E + D)) WACC = (Ke * E/(D+E)) + (kd * D/(D+E)) B Levered = Beta Unlev.+(Beta Unlev.-Beta Lev.) * (D/E) * (1-T) B Levered = Beta Unlev.+(Beta Unlev.-Beta Lev.) * (D/E) * (1-T) Ke = Rf + Beta Levered * Mkt Risk Premium Ke = Ku + ((D*(1-T) / E) * (Ku - Kd) Ke = Ku + D/E * (Ku - Kd) * (1-T) Source: Copeland T., T. Koller & J. Murrin, Valuation: Measuring and Managing the Value of Companies; and Fernandez P., Valuation Methods and Shareholder Value Creation. Conclusion Through a comprehensive example, we have shown the PERFECT consistency in results under similar assumptions for six different valuation methods in three different frameworks for the value of tax shields and, in doing so, we have been able to improve our understanding of the valuation process and correct some misleading statements appearing in the literature. The different approaches have their own merits and the practitioner should choose the method which best fits his or her needs given the particular circumstances in which the valuation takes place. What is important, and what the example developed in this note is showing, is the consistency of the results as long as we use consistent formulas and consistent assumptions within each framework. 7

8 Valuation Methods and Discount Rate Issues: A Comprehensive Example This note relies, among numerous articles, books and papers, on the following fundamental references: Brealey R. & S. Myers, Principles of Corporate Finance, McGraw Hill, 7 th Edition, 2000, Chapter 19. Copeland T., T. Koller & J. Murrin, Valuation: Measuring and Managing the Value of Companies, Wiley, 3rd Edition, 2000, particularly Appendix A. Damodaran A. Corporate Finance- Theory and Practice, John Wiley and Sons, Fernandez P. Valuation Methods and Shareholder Value Creation, Academic Press 2002, Chapters 17, 19, 21. 8

9 Valuation Methods and Discount Rate Issues: A Comprehensive Example List of Exhibits Debt rebalanced Debt not rebalanced Debt not rebalanced Calculations of parameters Exhibit 1 Exhibit 8 Exhibit 9 FCF / WACC Exhibit 2 Exhibit 10 Exhibit 16 Exhibit 17 APV Exhibit 3 Exhibit 11 Exhibit 11bis Exhibit 18 ECF / ke Exhibit 4 Exhibit 12 Exhibit 19 EVA ( with WACC) Exhibit 5 Exhibit 13 Exhibit 20 EVA ( with ku) Exhibit 5bis SVA Exhibit 6 Exhibit 14 Exhibit 21 CCF Exhibit 7 Exhibit 15 Exhibit 22 9

10 Valuation Methods and Discount Rate Issues: A Comprehensive Example Exhibit 1 Calculations of Parameters (Debt Rebalanced) Revenues 20,000 24,000 28,800 31,680 34,848 34,848 EBIT 2,000 3,600 4,320 6,336 6,970 6,970 % On Revenues 10.00% 15.00% 15.00% 20.00% 20.00% 20.00% Interest Expense (576) (616) (664) (709) (738) (765) EBT 1,424 2,984 3,656 5,627 6,232 6,204 Taxes (498) (1,044) (1,279) (1,969) (2,181) (2,172) % On EBT 35.00% 35.00% 35.00% 35.00% 35.00% 35.00% Net Earnings 926 1,939 2,376 3,658 4,051 4,033 Invested Capital 12,000 12,000 13,200 14,400 15,840 17,424 17,424 % On Revenues 60.00% 55.00% 50.00% 50.00% 50.00% 50.00% Debt 9,000 9,631 10,381 11,077 11,531 11,956 11,956 Shareholders' Capital 3,000 3,000 3,000 3,000 3,000 3,000 3,000 Retained Earnings 0 (1,556) (2,121) (2,053) (2,348) (1,583) (1,565) Net Earnings ,939 2,376 3,658 4,051 4,033 Shareholders' Equity 3,000 2,369 2,819 3,323 4,309 5,468 5,468 Financial Sources 12,000 12,000 13,200 14,400 15,840 17,424 17,424 EBIT 2,000 3,600 4,320 6,336 6,970 6,970 Taxes On EBIT (700) (1,260) (1,512) (2,218) (2,439) (2,439) NOPAT 1,300 2,340 2,808 4,118 4,530 4,530 Change in Capital Invested - (1,200) (1,200) (1,440) (1,584) - Free Cash Flow 1,300 1,140 1,608 2,678 2,946 4,530 Interest Expense (576) (616) (664) (709) (738) (765) Tax Shield Change in Debt Residual Cash Flow 1,556 1,490 1,872 2,672 2,892 4,033 Cash Flow to Equity = 1,556 1,490 1,872 2,672 2,892 4,033 Dividends Market Value of Debt 9,000 9,631 10,381 11,077 11,531 11,956 11,956 Market Value of Equity 21,098 22,577 24,336 25,966 27,030 28,028 28,028 Enterprise Value 30,098 32,208 34,717 37,042 38,561 39,984 39,984 % Mkt Value of Debt 29.90% 29.90% 29.90% 29.90% 29.90% 29.90% 29.90% % Mkt Value of Equity 70.10% 70.10% 70.10% 70.10% 70.10% 70.10% 70.10% Corporate Taxes 35.00% 35.00% 35.00% 35.00% 35.00% 35.00% 35.00% Debt Beta Cost of Debt 6.40% 6.40% 6.40% 6.40% 6.40% 6.40% 6.40% Risk Free Rate 4.00% 4.00% 4.00% 4.00% 4.00% 4.00% 4.00% Market Risk 8.00% 8.00% 8.00% 8.00% 8.00% 8.00% 8.00% Debt/ Equity (Mkt Values) Beta Unlevered Beta Levered = Bu+(Bu-Bd)*D/E Cost of Equity Unlevered 12.00% 12.00% 12.00% 12.00% 12.00% 12.00% 12.00% Cost of Equity Levered 14.39% 14.39% 14.39% 14.39% 14.39% 14.39% 14.39% WACC 11.33% 11.33% 11.33% 11.33% 11.33% 11.33% 11.33% 10

11 Exhibit 2 FCF/WACC (Debt Rebalanced) PV of Free Cash Flow to the Firm 9,098 8,829 8,689 8,066 6,301 4,069-39,984 39,984 39,984 39,984 28,976 32,260 35,915 39,984 37,042 38,561 39,984 39,984 (11,077) (11,531) (11,956) (11,956 25,966 27,030 28,028 28,028 Terminal Value 39,984 39,984 39,984 PV of Terminal Value 20,999 23,379 26,027 Enterprise Value 30,098 32,208 34,717 Value of Debt (9,000) (9,631) (10,381) Equity Value 21,098 22,577 24,336 DCF Method PV of FCFF at WACC 9,098 PV of Terminal Value 20,999 Enterprise Value 30,098 Value of Debt (9,000) Equity Value 21,098 Exhibit 3 APV (Debt Rebalanced) APV Method - PVT At Ku Unlevered FCF 1,300 1,140 1,608 2,678 2,946 4,530 Terminal Value Unlevered 37,752 Terminal Value at Target Debt 39,984 Tax Shields in Terminal Value 2,232 Interest Tax Shields PV Interest Tax Shields at Ku PV FCF 1 to 6 8,883 PV of Unlevered Terminal Value 19,126 Total Unlevered Value 28,010 PV of Tax Shields 1 to PV of Tax Shields after 6 1,131 Enterprise Value 30,098 Value of Debt (9,000) Equity Value 21,098

12 Exhibit 4 ECF/ke (Debt Rebalanced) Equity Method Cash Flow to Equity 1,556 1,490 1,872 2,672 2,892 4,033 Terminal Value 28,028 Total Cash Flow 1,556 1,490 1,872 2,672 2,892 32,061 Equity Value 21,098 Exhibit 5 EVA with WACC (Debt Rebalanced) E.V.A. Method at WACC After Beginning Capital 12,000 12,000 13,200 14,400 15,840 17,424 17,424 NOPAT 1,300 2,340 2,808 4,118 4,530 4,530 4,530 ROIC 10.83% 19.50% 21.27% 28.60% 28.60% 26.00% 26.00% WACC 11.33% 11.33% 11.33% 11.33% 11.33% 11.33% 11.33% Charge on Capital 1,360 1,360 1,496 1,632 1,795 1,974 1,974 Spread -0.50% 8.17% 9.94% 17.27% 17.27% 14.67% 14.67% E.V.A. (60) 980 1,312 2,487 2,736 2,556 2,556 Terminal Value of E.V.A. 22,560 PV of E.V.A. at Year WACC (54) ,619 1,599 1,342 Total PV of E.V.A. 6,249 PV of Terminal Value 11,848 Market Value Added 18,098 Beginning Capital 12,000 Enterprise Value 30,098 Value of Debt (9,000) Equity Value 21,098

13 Exhibit 5 bis EVA with ku (Debt Rebalanced) E.V.A. Method at Cost of Equity Unlevered After Beginning Capital 12,000 12,000 13,200 14,400 15,840 17,424 17,424 NOPAT 1,300 2,340 2,808 4,118 4,530 4,530 4,530 ROIC 10.83% 19.50% 21.27% 28.60% 28.60% 26.00% 26.00% Cost of Equity Unlevered 12.00% 12.00% 12.00% 12.00% 12.00% 12.00% 12.00% Charge on Capital 1,440 1,440 1,584 1,728 1,901 2,091 2,091 Spread -1.17% 7.50% 9.27% 16.60% 16.60% 14.00% 14.00% E.V.A. (140) 900 1,224 2,390 2,629 2,439 2,439 Terminal Value of E.V.A. 20, PV of E.V.A. at Year Cost of Equity Unlevered (125) ,519 1,492 1,236 Total PV of E.V.A. 5,711 PV of Terminal Value 10,299 Market Value Added 16,010 Beginning Capital 12,000 PV of Tax Shields 1 to PV of Tax Shields after 6 1,131 Enterprise Value 30,098 Value of Debt (9,000) Equity Value 21,098

14 Exhibit 6 SVA (Debt Rebalanced) S.V.A. Method - A. Rappaport NOPAT 1,300 1,300 2,340 2,808 4,118 4,530 4,530 Change in NOPAT - 1, , Change in NOPAT/WACC - 9,179 4,131 11,566 3,635 - (Change in NOPAT/WACC)/(1+WACC)t-1-8,245 3,333 8,382 2,366 - Investment - (1,200) (1,200) (1,440) (1,584) - PV Investment - (968) (870) (937) (926) - Shareholder Value Added (SVA) - 7,277 2,463 7,444 1,440 - Cumulated SVA - 7,277 9,740 17,184 18,624 18,624 Baseline Value 11,474 Enterprise Value 30,098 Value of Debt (9,000) Equity Value 21,098 Exhibit 7 CCF (Debt Rebalanced) Capital Cash Flow Method - Ruback Equity Cash Flow 1,556 1,490 1,872 2,672 2,892 4,033 Terminal Value of Equity 28,028 Total Equity Cash Flow 1,556 1,490 1,872 2,672 2,892 32,061 Interest Expense (before taxes) Change in Debt (631) (750) (695) (454) (425) - Terminal Value of Debt 11,956 Total Debt Cash Flow (55) (134) (31) ,721 CAPITAL CASH FLOW 1,502 1,356 1,841 2,927 3,205 44, % 12.00% 12.00% 12.00% 12.00% 12.00% 12.00% WACC before taxes (Ke * E / V) + (Kd * D / V) Enterprise Value 30,098 Value of Debt (9,000) Equity Value 21,

15 Exhibit 8 Calculations of Parameters (Debt Not Rebalanced) Revenues 20,000 24,000 28,800 31,680 34,848 34,848 EBIT 2,000 3,600 4,320 6,336 6,970 6,970 % on Revenues 10.00% 15.00% 15.00% 20.00% 20.00% 20.00% Interest Expense (576) (484) (406) (307) (164) (23) EBT 1,424 3,116 3,914 6,029 6,805 6,946 Taxes (498) (1,090) (1,370) (2,110) (2,382) (2,431) % on EBT 35.00% 35.00% 35.00% 35.00% 35.00% 35.00% Net Earnings 926 2,025 2,544 3,919 4,423 4,515 Invested Capital 12,000 12,000 13,200 14,400 15,840 17,424 17,424 % on Revenues 60.00% 55.00% 50.00% 50.00% 50.00% 50.00% Debt 9,000 8,074 7,249 5,905 3,426 3,000 3,000 9,414 9,322 4,423 4,515 16,837 16,837 17,424 17,424 Shareholders' Capital 3,000 3,000 3,000 3,000 3,000 Retained Earnings ,951 5,495 Net Earnings ,025 2,544 3,919 Shareholders' Equity 3,000 3,926 5,951 8,495 12,414 Financial Sources 12,000 12,000 13,200 14,400 15,840 EBIT 2,000 3,600 4,320 6,336 6,970 6,970 Taxes on EBIT (700) (1,260) (1,512) (2,218) (2,439) (2,439) NOPAT 1,300 2,340 2,808 4,118 4,530 4,530 Change in Capital Invested - (1,200) (1,200) (1,440) (1,584) - Free Cash Flow 1,300 1,140 1,608 2,678 2,946 4,530 Interest Expense (576) (484) (406) (307) (164) (23) Tax Shield Dividends = Cash Flow To Equity (4,515) Residual Cash Flow ,344 2,479 2,839 - Change in Debt (926) (825) (1,344) (2,479) (2,839) - Corporate Taxes 35.00% 35.00% 35.00% 35.00% 35.00% 35.00% 35.00% Debt Beta Cost of Debt 6.40% 6.00% 5.60% 5.20% 4.80% 4.00% 4.00% Risk Free Rate 4.00% 4.00% 4.00% 4.00% 4.00% 4.00% 4.00% Market Risk Premium 8.00% 8.00% 8.00% 8.00% 8.00% 8.00% 8.00% Beta Unlevered Cost of Equity Unlevered 12.00% 12.00% 12.00% 12.00% 12.00% 12.00% 12.00%

16 Exhibit 9 Calculations of Parameters (Debt Not Rebalanced) Calculating WACC with discrete cash flows when Tax Shields are discounted at Kd (Valuation III Ed.- T. Copeland) Cost of Equity Unlevered (Ku) 12.00% 12.00% 12.00% 12.00% 12.00% 12.00% 12.00% Cost of Debt (Kd) 6.40% 6.00% 5.60% 5.20% 4.80% 4.00% 4.00% Value of Debt (D) 9,000 8,074 7,249 5,905 3, Enterprise Value (V) 28,755 30,662 32,996 35,177 36,589 37,957 37,957 Debt / Value Corporate Taxes 35.00% 35.00% 35.00% 35.00% 35.00% 35.00% 35.00% PV Interest Tax Shields (PVT) WACC = Ku - (Kb * D/V * t) - (PVT/V * (Ku - Kb)) 11.15% 11.33% 11.48% 11.63% 11.79% 11.94% 11.94% Calculating Ke with discrete cash flows when Tax Shields are discounted at Kd (Valuation Methods - P. Fernandez) Cost of Equity Unlevered (Ku) 12.00% 12.00% 12.00% 12.00% 12.00% 12.00% 12.00% Cost of Debt (Kd) 6.40% 6.00% 5.60% 5.20% 4.80% 4.00% 4.00% Value of Debt (D) 9,000 8,074 7,249 5,905 3, Equity Value (E) 19,755 22,588 25,747 29,271 33,162 37,370 37,370 PV Interest Tax Shields (PVT) Ke = Ku + ((D - PVT) / E) * (Ku - Kd) 14.34% 13.99% 13.69% 13.29% 12.69% 12.08% 12.08% Beta L with discrete cash flows when Tax Shields are discounted at Kd (Valuation Methods - P. Fernandez) Beta Unlevered Value of Debt (D) 9,000 8,074 7,249 5,905 3, PV Interest Tax Shields (PVT) Debt Beta Equity Value (E) 19,755 22,588 25,747 29,271 33,162 37,370 37,370 Beta L = Bu + (D - PVT) * (Bu - Bd) / E Ke = Risk Free + (BetaL * Mkt Premium) 14.34% 13.99% 13.69% 13.29% 12.69% 12.08% 12.08% Source: Copeland T., T. Koller & J. Murrin, Valuation: Measuring and Managing the Value of Companies; and Fernandez P., Valuation Methods and Shareholder Value Creation.

17 Exhibit 10 FCF/WACC (Debt Not Rebalanced) Working backward and bottom-up with iterations for Ke Corporate Taxes 35.00% 35.00% 35.00% 35.00% 35.00% 35.00% 35.00% Cost of Debt 6.40% 6.00% 5.60% 5.20% 4.80% 4.00% 4.00% Risk Free Rate 4.00% 4.00% 4.00% 4.00% 4.00% 4.00% 4.00% Market Risk Premium 8.00% 8.00% 8.00% 8.00% 8.00% 8.00% 8.00% Beta Unlevered Cost of Equity Unlevered (Ku) 12.00% 12.00% 12.00% 12.00% 12.00% 12.00% 12.00% Value of Debt (D) 9,000 8,074 7,249 5,905 3, PV Interest Tax Shields (PVT) Debt Beta Beta Equity = Bu + (D - PVT) * (Bu - Bd) / E Cost of Equity Levered (Ke) 14.34% 13.99% 13.69% 13.29% 12.69% 12.08% 12.08% Iteration Cells for Beta Equity 19,755 22,588 25,747 29,271 33,162 37,370 37,370 EQUITY VALUE at Ke 19,755 22,588 25,747 29,271 33,162 37,370 37,370 Equity Value 19,755 22,588 25,747 29,271 33,162 37,370 37,370 Debt 9,000 8,074 7,249 5,905 3, ENTERPRISE VALUE 28,755 30,662 32,996 35,177 36,589 37,957 37,957 % Equity 68.70% 73.67% 78.03% 83.21% 90.64% 98.45% 98.45% % Debt 31.30% 26.33% 21.97% 16.79% 9.36% 1.55% 1.55% WACC 11.15% 11.33% 11.48% 11.63% 11.79% 11.94% 11.94% ENTERPRISE VALUE at WACC 28,755 30,662 32,996 35,177 36,589 37,957 37,957

18 Exhibit 11 APV (Debt Not Rebalanced) APV Method - PV Tax Shields At Kd Unlevered FCF 1,300 1,140 1,608 2,678 2,946 4,530 Terminal Value Unlevered 37,752 Tax Shields in Terminal Value 205 Interest Tax Shields PV Interest Tax Shields at Kd PV FCF1 to 6 8,883 PV of Unlevered Terminal Value 19,126 Total Unlevered Value 28,010 PV of Tax Shields 1 to PV of Tax Shields after Enterprise Value 28,755 Value of Debt (9,000) Equity Value 19,

19 Exhibit 11 Bis (Working Backward with APV) Unlevered FCF 1,300 1,140 1,608 2,678 2,946 4,530 Terminal Value Unlevered 37,752 Total Unlevered FCF 1,300 1,140 1,608 2,678 2,946 42,282 Total Unlevered Value Every Year 28,010 30,071 32,539 34,836 36,338 37,752 37,752 IRR Per Year = Cost of Capital Unleveraged 12.00% 12.00% 12.00% 12.00% 12.00% 12.00% 12.00% Interest Tax Shields Tax Shields in Terminal Value 205 Total Tax Shields Total Value of Tax Shields Every Year IRR Per Year = Cost of Debt 6.40% 6.00% 5.60% 5.20% 4.80% 4.00% 4.00% Enterprise Value Every Year 28,755 30,662 32,996 35,177 36,589 37,957 37,957 IRR Per Year = WACC Per Year (*) 11.15% 11.33% 11.48% 11.63% 11.79% 11.94% 11.94% (*) See also Exhibit 10 for Direct WACC Calculation Unlevered FCF 1,300 1,140 1,608 2,678 2,946 4,530 Terminal Value at Target Debt 37,957 Total FCF And Terminal Value at Target Debt 1,300 1,140 1,608 2,678 2,946 42,488 PV of FCF And Terminal Value at Year WACC 1, ,166 1,739 1,711 22,048 Enterprise Value 28,755 Value of Debt (9,000) Equity Value 19,755

20 Exhibit 12 ECF / ke (Debt Not Rebalanced) Equity Method Enterprise Value every year 28,755 30,662 32,996 35,177 36,589 37,957 37,957 Value of Debt every year (9,000) (8,074) (7,249) (5,905) (3,426) (587) (587) Equity Value every year 19,755 22,588 25,747 29,271 33,162 37,370 37, % 1.55% 90.64% 1.55% 98.45% 98.45% % Mkt Value of Debt 31.30% 26.33% 21.97% 16.79% % Mkt Value of Equity 68.70% 73.67% 78.03% 83.21% WACC 11.15% 11.33% 11.48% 11.63% 11.79% 11.94% 11.94% Cost of Equity Levered 14.34% 13.99% 13.69% 13.29% 12.69% 12.08% 12.08% Cash Flow to Equity ,515 Terminal Value 37,370 Total Cash Flow to Equity ,885 Equity Value 19,755

21 Exhibit 13 EVA with WACC (Debt Not Rebalanced) E.V.A. Method at WACC After Beginning Capital 12,000 12,000 13,200 14,400 15,840 17,424 17,424 NOPAT 1,300 2,340 2,808 4,118 4,530 4,530 4,530 ROIC 10.83% 19.50% 21.27% 28.60% 28.60% 26.00% 26.00% WACC 11.15% 11.33% 11.48% 11.63% 11.79% 11.94% 11.94% Charge on Capital 1,338 1,360 1,515 1,675 1,868 2,080 2,080 Spread -0.32% 8.17% 9.79% 16.97% 16.81% 14.06% 14.06% E.V.A. (38) 980 1,293 2,444 2,662 2,451 2,451 Terminal Value of E.V.A. 20,533 PV of E.V.A. at Year WACC (35) ,587 1,546 1,272 Total PV of E.V.A. 6,099 PV of Terminal Value 10,655 Market Value Added 16,755 Beginning Capital 12,000 Enterprise Value 28,755 Value of Debt (9,000) Equity Value 19,755

22 Exhibit 14 SVA (Debt Not Rebalanced) S.V.A. Method TV NOPAT 1,300 2,340 2,808 4,118 4,530 4,530 Change in NOPAT 1, , Investment - (1,200) (1,200) (1,440) (1,584) - Framework PVT at Kd WACC 11.15% 11.33% 11.48% 11.63% 11.79% 11.94% 11.94% Baseline NOPAT Stream 1,300 1,300 1,300 1,300 1,300 1,300 10,892 Change in NOPAT - Stream t=2 1,040 1,040 1,040 1,040 1,040 8,714 Change in NOPAT - Stream t= ,921 Change in NOPAT - Stream t=4 1,310 1,310 1,310 10,979 Change in NOPAT - Stream t= ,451 Discount Factor PV PV Baseline NOPAT Stream 11,089 1,170 1, ,327 PV Change in NOPAT - Stream t=2 7, ,061 PV Change in NOPAT - Stream t=3 3, ,278 PV Change in NOPAT - Stream t=4 7, ,377 PV Change in NOPAT - Stream t=5 2, ,004 7,990 2,244 PV of Change in NOPAT 7,935 3, PV Investment 0 (970) (870) (935) (920) Shareholder Value Added (SVA) 0 6,965 2,323 7,054 1,323 Cumulated SVA 0 6,965 9,288 16,343 17,666 17,666 Baseline Value 11,089 Enterprise Value 28,755 Value of Debt (9,000) Equity value 19,755

23 Exhibit 15 CCF (Debt Not Rebalanced) Capital Cash Flow Method - Ruback Equity Cash Flow ,515 Terminal Value of Equity 37,370 Total Equity Cash Flow ,885 Interest Expense (before taxes) Change in Debt ,344 2,479 2,839 - Terminal Value of Debt 587 Total Debt Cash Flow 1,502 1,310 1,750 2,786 3, CAPITAL CASH FLOW 1,502 1,310 1,750 2,786 3,004 42,496 WACC Before Taxes (Ke * E / V) + (Kd * D / V) 11.85% 11.88% 11.91% 11.93% 11.95% 11.96% 11.96% (framework: PVT at Kd) PV of Capital Cash Flow at WACC bt 1,342 1,046 1,250 1,777 1,712 21,628 Enterprise Value 28,755 Value of Debt (9,000) Equity Value 19,755

24 Exhibit 16 PV of FCF at WACC Unlevered FCF 1,300 1,140 1,608 2,678 2,946 4,530 Terminal Value Unlevered 37,752 Total Unlevered FCF 1,300 1,140 1,608 2,678 2,946 42,282 Total Unlevered Value every year 28,010 30,071 32,539 34,836 36,338 37,752 37,752 IRR per year = Cost of Capital Unlevered 12.00% 12.00% 12.00% 12.00% 12.00% 12.00% 12.00% Interest Tax Shields (D * T * Ku) Tax shields in Terminal Value 205 Total Tax Shields Total Value of Tax Shields every year 1, IRR per year = Cost of Capital Unlevered 12.00% 12.00% 12.00% 12.00% 12.00% 12.00% 12.00% Enterprise Value every year 29,190 31,015 33,257 35,336 36,650 37,957 37,957 IRR per year = WACC per year 10.71% 10.91% 11.08% 11.30% 11.61% 11.94% 11.94% Unlevered FCF 1,300 1,140 1,608 2,678 2,946 4,530 Terminal Value at Target Debt 37,957 Total FCF and Terminal Value at Target Debt 1,300 1,140 1,608 2,678 2,946 42,488 PV of FCF and Terminal Value at Year WACC 1, ,179 1,764 1,739 22,405 Enterprise Value 29,190 Value of Debt (9,000) Equity Value 20,190

25 Exhibit 17 Working backward and bottom-up with iterations for Ke Corporate Taxes 35.00% 35.00% 35.00% 35.00% 35.00% 35.00% 35.00% Cost of Debt 6.40% 6.00% 5.60% 5.20% 4.80% 4.00% 4.00% Risk Free Rate 4.00% 4.00% 4.00% 4.00% 4.00% 4.00% 4.00% Market Risk Premium 8.00% 8.00% 8.00% 8.00% 8.00% 8.00% 8.00% Beta Unlevered Cost of Equity Unlevered (Ku) 12.00% 12.00% 12.00% 12.00% 12.00% 12.00% 12.00% Beta Debt Beta Equity Cost of Equity Levered (Ke) 13.62% 13.37% 13.16% 12.89% 12.48% 12.08% 12.08% Iteration Cells for Beta Equity 20,190 22,940 26,008 29,431 33,223 37,370 37,370 EQUITY VALUE at Ke 20,190 22,940 26,008 29,431 33,223 37,370 37,370 Equity Value 20,190 22,940 26,008 29,431 33,223 37,370 37,370 Debt 9,000 8,074 7,249 5,905 3, ENTERPRISE VALUE 29,190 31,015 33,257 35,336 36,650 37,957 37,957 % Equity 69.17% 73.97% 78.20% 83.29% 90.65% 98.45% 98.45% % Debt 30.83% 26.03% 21.80% 16.71% 9.35% 1.55% 1.55% WACC 10.71% 10.91% 11.08% 11.30% 11.61% 11.94% 11.94% ENTERPRISE VALUE at WACC 29,190 31,015 33,257 35,336 36,650 37,957 37,957

26 Exhibit 18 APV with Tax Shield (D*T*Ku) and PV of Tax Shields at Ku Unlevered FCF 1,300 1,140 1,608 2,678 2,946 4,530 Terminal Value Unlevered 37,752 Tax Shields in Terminal Value 205 Interest Tax Shields (D * T * Ku) PV Interest Tax Shields at Ku PV FCF1 to 6 8,883 PV of Unlevered Terminal Value 19,126 Total Unlevered Value 28,010 PV of Tax Shields 1 to 6 1,076 PV of Tax Shields after Enterprise Value 29,190 Value of Debt (9,000) Equity Value 20,

27 Exhibit 19 PV of ECF at Ke Enterprise Value every year 29,190 31,015 33,257 35,336 36,650 37,957 37,957 Value of Debt every year (9,000) (8,074) (7,249) (5,905) (3,426) (587) (587) Equity Value every year 20,190 22,940 26,008 29,431 33,223 37,370 37,370 % Mkt Value of Debt 30.83% 26.03% 21.80% 16.71% 9.35% 1.55% 1.55% % Mkt Value of Equity 69.17% 73.97% 78.20% 83.29% 90.65% 98.45% 98.45% Beta Levered = Bu+(Bu-Bd)*D/E*(1-T) Cost of Equity Levered ( Ke ) 13.62% 13.37% 13.16% 12.89% 12.48% 12.08% 12.08% WACC 10.71% 10.91% 11.08% 11.30% 11.61% 11.94% 11.94% Ke = Ku + ((D*(1-T)) / E) * (Ku - Kd) 13.62% 13.37% 13.16% 12.89% 12.48% 12.08% 12.08% Cash Flow to Equity ,515 Terminal Value 37,370 Total Cash Flow to Equity ,885 Equity Value 20,190

28 Exhibit 20 EVA with WACC (Debt Not Rebalanced) Framework PVT = ( D * T * Ku) at Ku After E.V.A. Method at WACC Beginning Capital 12,000 12,000 13,200 14,400 15,840 17,424 17,424 NOPAT 1,300 2,340 2,808 4,118 4,530 4,530 4,530 ROIC 10.83% 19.50% 21.27% 28.60% 28.60% 26.00% 26.00% WACC 10.71% 10.91% 11.08% 11.30% 11.61% 11.94% 11.94% Charge on Capital 1,285 1,309 1,463 1,627 1,839 2,080 2,080 Spread 0.13% 8.59% 10.19% 17.30% 16.99% 14.06% 14.06% E.V.A. 15 1,031 1,345 2,491 2,692 2,451 2,451 Terminal Value of E.V.A. 20,533 PV of E.V.A. at Year WACC ,641 1,589 1,292 Total PV of E.V.A. 6,362 PV of Terminal Value 10,828 Market Value Added 17,190 Beginning Capital 12,000 Enterprise Value 29,190 Value of Debt (9,000) Equity Value 20,190

29 Exhibit 21 SVA (Debt Not Rebalanced) TV NOPAT 1,300 2,340 2,808 4,118 4,530 4,530 Change in NOPAT 1, , Investment - (1,200) (1,200) (1,440) (1,584) - WACC 10.71% 10.91% 11.08% 11.30% 11.61% 11.94% 11.94% Baseline NOPAT Stream 1,300 1,300 1,300 1,300 1,300 1,300 10,892 Change in NOPAT - Stream t=2 1,040 1,040 1,040 1,040 1,040 8,714 Change in NOPAT - Stream t= ,921 Change in NOPAT - Stream t=4 1,310 1,310 1,310 10,979 Change in NOPAT - Stream t= , Discount Factor (DF) Baseline NOPAT Stream DF Change in NOPAT - Stream t= DF Change in NOPAT - Stream t= DF Change in NOPAT - Stream t= DF Change in NOPAT - Stream t= PV PV Baseline NOPAT Stream 11,239 1,174 1, ,429 PV Change in NOPAT - Stream t=2 8, ,143 PV Change in NOPAT - Stream t=3 3, ,315 PV Change in NOPAT - Stream t=4 8, ,481 PV Change in NOPAT - Stream t=5 2, ,037 PV of Change in NOPAT 8,052 3,242 8,117 2,280 PV Investment (977) (880) (949) (935) Shareholder Value Added (SVA) 7,075 2,362 7,169 1,345 Cumulated SVA 7,075 9,437 16,606 17,951 17,951 Baseline Value 11,239 Enterprise Value 29,190 Value of Debt (9,000) Value of Equity 20,190

30 Exhibit 22 CCF (Debt Not Rebalanced) Capital Cash Flow Method - Ruback Equity Cash Flow ,515 Terminal Value of Equity 37,370 Total Equity Cash Flow ,885 Interest Expense (before taxes) Change in Debt ,344 2,479 2,839 - Terminal Value of Debt 587 Total Debt Cash Flow 1,502 1,310 1,750 2,786 3, CAPITAL CASH FLOW 1,502 1,310 1,750 2,786 3,004 42, % 11.45% 11.51% 11.60% 11.76% 11.96% 11.96% WACC before taxes (Ke * E / V) + (Kd * D / V) (framework: PVT = ( D * T * Ku) at Ku PV of Capital Cash Flow at WACC bt 1,348 1,055 1,264 1,803 1,739 21,981 Enterprise Value 29,190 Value of Debt (9,000) Equity Value 20,