Valuing companies by discounted cash flows 10 methods and 1 solution 2

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Valuing companies by discounted cash flows 10 methods and 1 solution 2

  1. 1. INTERNATIONAL JOURNAL OF MANAGEMENT (IJM) International Journal of Management (IJM), ISSN 0976 – 6502(Print), ISSN 0976 – 6510(Online), Volume 4, Issue 2, March- April (2013)ISSN 0976-6502 (Print)ISSN 0976-6510 (Online)Volume 4, Issue 2, March- April (2013), pp. 63-77 IJM© IAEME: www.iaeme.com/ijm.asp ©IAEMEJournal Impact Factor (2013): 6.9071 (Calculated by GISI)www.jifactor.com VALUING COMPANIES BY DISCOUNTED CASH FLOWS: 10 METHODS AND 1 SOLUTION Nisarg A Joshi1, Jay Desai2, Arti Trivedi3 1 (M.B.A, Shri Chimanbhai Institute of Management & Research, Ahmedabad, Gujarat, India 2 (M.B.A, Shri Chimanbhai Institute of Management & Research, Ahmedabad, Gujarat, India 3 (M.B.A, Shri Chimanbhai Institute of Management & Research, Ahmedabad, Gujarat, India ABSTRACT This paper shows 10 valuation methods based on equity cash flow; free cash flow; capital cash flow; APV (Adjusted Present Value); businesss risk-adjusted free cash flow and equity cash flow; risk-free rate-adjusted free cash flow and equity cash flow; economic profit; and EVA. All 10 methods always give the same value. This result is logical, as all the methods analyze the same reality under the same hypotheses; they differ only in the cash flows or parameters taken as the starting point for the valuation. We present all ten methods, allowing the required return to debt to be different from the cost of debt. Seven methods require an iterative process. Only the APV and business risk-adjusted cash flows methods do not require iteration. Keywords: valuation, DCF, discounted cash flow, WACC, free cash flow 1. INTRODUCTION To value a company by cash flow discounting, we may use different cash flows, which will always have different risks and will require different discount rates. As in each case we are valuing the same company, we should get the same valuation, no matter which expected cash flows we use. In this paper we present ten different approaches to valuing companies by discounting cash flows. Although some authors argue that different methods may produce different valuations, we will show that all methods provide the same value under the same assumptions. 63
  2. 2. International Journal of Management (IJM), ISSN 0976 – 6502(Print), ISSN 0976 –6510(Online), Volume 4, Issue 2, March- April (2013) The most common method for valuing companies is the Free Cash Flow method. Inthat method, interest tax shields are excluded from the cash flows and the tax deductibility ofthe interest is treated as a decrease in the weighted average cost of capital (WACC). As theWACC depends on the capital structure, this method requires an iterative process: tocalculate the WACC, we need to know the value of the company, and to calculate the valueof the company, we need to know the WACC. Seven out of the ten methods presented requirean iterative process, while only three (APV and the two business risk-adjusted cash flowsmethods) do not. The prime advantage of these three methods is their simplicity. Wheneverthe debt is forecasted in levels, instead as a percentage of firm value, the APV is much easierto use because the value of the interest tax shields is quite easy to calculate. The two businessrisk-adjusted cash flows methods are also easy to use because the interest tax shields areincluded in the cash flows. The discount rate of these three methods is the required return toassets and, therefore, it does not change when capital structure changes.Section 1 shows the 10 most commonly used methods for valuing companies by discountedcash flows: 1. equity cash flows discounted at the required return to equity; 2. free cash flow discounted at the WACC; 3. capital cash flows discounted at the WACC before tax; 4. APV (Adjusted Present Value); 5. the businesss risk-adjusted free cash flows discounted at the required return to assets; 6. the businesss risk-adjusted equity cash flows discounted at the required return to assets; 7. economic profit discounted at the required return to equity; 8. EVA discounted at the WACC; 9. the risk-free rate-adjusted free cash flows discounted at the risk-free rate; and 10. The risk-free rate-adjusted equity cash flows discounted at the required return to assets. All ten methods always give the same value. This result is logical, since all themethods analyze the same reality under the same hypotheses; they differ only in the cashflows taken as the starting point for the valuation.In section 2 the 10 methods and a theory are applied to an example. The theory is:1) Fernandez (2007)[6] assumes that the company will have a constant debt-to-equity ratio inbook value terms. In this scenario, the risk of the increases of debt is equal to the risk of thefree cash flow.2. LITERATURE REVIEW There is a considerable body of literature on the discounted cash flow valuation offirms. The main difference between all of these papers and the approach proposed in sectionsI and II is that most previous papers calculate the value of tax shields as the present value ofthe tax savings due to the payment of interest. 64
  3. 3. International Journal of Management (IJM), ISSN 0976 – 6502(Print), ISSN 0976 –6510(Online), Volume 4, Issue 2, March- April (2013) Myers (1974)[18] introduced the APV (adjusted present value) method, but proposedcalculating the VTS by discounting the tax savings (N T r) at the required return to debt (Kd).The argument is that the risk of the tax saving arising from the use of debt is the same as therisk of the debt. This approach has also been recommended in later papers in the literature,two being Taggart (1991)[22] and Luehrman (1997)[12]. One problem with the Myers (1974)[18]approach is that it does not always give a higher cost of equity than cost of assets and thishardly makes any economic sense. Harris and Pringle (1985)[9] propose that the present value of the tax saving due to thepayment of interest should be calculated by discounting the interest tax savings (N T r) at therequired return to unlevered equity (Ku), i.e. VTS = PV [Ku; N T r]. Their argument is thatthe interest tax shields have the same systematic risk as the firm’s underlying cash flows and,therefore, should be discounted at the required return to assets (Ku). Ruback (1995 and 2002)[19][20], Kaplan and Ruback (1995)[11], Brealey and Myers(2000, page 555)[23], and Tham and Vélez-Pareja (2001)[21], also claim that the appropriatediscount rate for tax shields is Ku, the required return to unlevered equity. Ruback (1995 and2002)[19][20] presents the Capital Cash Flow (CCF) method and claims that WACCBT = Ku.Based on this assumption, Ruback (1995 and 2002) [19][20] gets the same valuation as Harrisand Pringle (1985)[9]. A large part of the literature argues that the value of tax shields should be calculatedin a different manner depending on the debt strategy of the firm. Hence, a firm that wishes tokeep a constant D/E ratio must be valued in a different manner from a firm that has a presetlevel of debt. Miles and Ezzell (1980)[13] indicate that for a firm with a fixed debt target (i.e. aconstant [D/(D+E)] ratio), the correct rate for discounting the interest tax shields is Kd for thefirst year and Ku for the tax saving in later years. Inselbag and Kaufold (1997)[10] and Ruback(1995 and 2002) [19][20] argue that when the amount of debt is fixed, interest tax shields shouldbe discounted at the required return to debt. However, if the firm targets a constant debt/valueratio, the value of tax shields should be calculated according to Miles and Ezzell (1980)[13].Finally, Taggart (1991)[22] suggests using Miles & Ezzell (1985)[14] if the company adjusts toits target debt ratio once a year and Harris & Pringle (1985) [9] if the company adjusts to itstarget debt ratio continuously. Damodaran (1994, page 31)[3] argues that if all the business risk is borne by theequity, then the formula relating the levered beta (βL) to the asset beta (βu) is βL = βu +(D/E) βu (1– T). This formula is exactly formula (29) assuming that βd = 0. Oneinterpretation of this assumption is (see page 31 of Damodaran, 1994)[3] that “all of the firm’srisk is borne by the stockholders (i.e., the beta of the debt is zero)”. In some cases, it may bereasonable to assume that the debt has a zero beta, but then the required return to debt (Kd)should also be the risk-free rate. However, in several examples in his books Damodaran(1984 and 2002)[25] considers the required return to debt to be equal to the cost of debt, bothof which are higher than the risk-free rate. Fernandez (2007)[6] shows that for a company with a fixed book-value leverage ratio,the increase of debt is proportional to the increases of net assets and the risk of the increasesof debt is equal to the risk of the increases of assets. In that situation, when the debt value isequal to its book value, VTS0 = PV0 [Kut; Dt-1 Kut Tt]. This expression does not mean thatthe appropriate discount for tax shields is the unlevered cost of equity, since the amount beingdiscounted is higher than the tax shields (it is multiplied by the unlevered cost of equity andnot the cost of debt). This result arises as the difference of two present values. In the case ofno growth perpetuities, equation (12) is VTS = DT. The value of tax shields being DT for no 65
  4. 4. International Journal of Management (IJM), ISSN 0976 – 6502(Print), ISSN 0976 –6510(Online), Volume 4, Issue 2, March- April (2013)growth perpetuities is quite a standard result. It may be found, for example, in Bodie andMerton (2000)[24], Modigliani and Miller (1958 and 1963)[16,17], Myers (1974)[18], Damodaran(2002)[25] and Brealey and Myers (2000)[23]. In contrast, the Miller (1977)[15] view that T∗= 0corresponds to a CAPM where the intercept is RF(1 − TC). A similar effect can be seen in theformula for the required return on assets: It contains the most striking results of the valuationperformed on the company according to Fernández (2004)[4], Damodaran (1994)[3], Ruback(2002)[20] and Myers (1974)[18]. It may be seen that:1) Equity value (E) grows with residual growth (g), except according to Damodaran (1994)[3].2) Required return to equity (Ke) decreases with growth (g), except according to Damodaran(1994)[3] and Ruback (2002)[20].3) Required return to equity (Ke) is higher than the required return to assets (Ku), except forMyers (1974)[18] when g > 5%.Please note that these exceptions are counterintuitive.3. RESEARCH METHODOLOGY Ten discounted cash flow valuation methodsMethod 1: Using the expected equity cash flow (ECF) and the required return to equity(Ke).Equation (1) indicates that the value of the equity (E) is the present value of the expectedequity cash flows (ECF) discounted at the required return to equity (Ke).E0 = PV0 [Ket; ECFt] (1)The expected equity cash flow is the sum of all expected cash payments to shareholders,mainly dividends and share repurchases.Equation (2) indicates that the value of the debt (D) is the present value of the expected debtcash flows (CFd) discounted at the required return to debt (Kd). Dt is the increase in debt,and It is the interest paid by the company. CFdt = It - DtD0 = PV0 [Kdt; CFdt] (2)Definition of FCF: the free cash flow is the hypothetical equity cash flow when the companyhas no debt. The expression that relates the FCF with the ECF is:FCFt = ECFt - Dt + It (1 - T) (3)The expected debt cash flow in a given period is given by equation (4)CFd t = Nt-1 rt - (Nt - Nt-1) (4) 66
  5. 5. International Journal of Management (IJM), ISSN 0976 – 6502(Print), ISSN 0976 –6510(Online), Volume 4, Issue 2, March- April (2013)Where N is the book value of the financial debt and r is the cost of debt. Nt-1 rt is the interestpaid by the company in period t. (Nt - Nt-1) is the increase in the book value of debt in periodt. When the required return to debt (Kd) is different than the cost of debt (r), then the value ofdebt (D) is different than its book value (N). Note that if, for all t, rt = Kdt, then N0 = D0. Butthere are situations in which rt > Kdt (i.e. if the company has old fixed-rate debt and interestrates have declined, or if the company can only get expensive bank debt), and situations inwhich rt < Kdt (i.e. if the company has old fixed-rate debt and interest rates have increased).Method 2: Using the free cash flow and the WACC (weighted average cost of capital).Equation (5) indicates that the value of the debt (D) plus that of the shareholders equity (E) isthe present value of the expected free cash flows (FCF) discounted at the weighted averagecost of capital (WACC):E0 + D0 = PV0 [WACCt; FCFt] (5)The free cash flow is the hypothetical equity cash flow when the company has no debt. Theexpression that relates the FCF with the ECF is:ECFt = FCFt + (Nt - Nt-1) - Nt-1 rt (1 - Tt ) (6)Definition of WACC: the WACC is the rate at which the FCF must be discounted so thatequation (5) gives the same result as that given by the sum of (1) and (2). By doing so, theWACC is (7):WACCt = [Et-1 Ket + Dt-1 Kdt (1-T)] / [Et-1 + Dt-1] (7)T is the tax rate used in equation (3). Et-1 + Dt-1 are neither market values nor book values:in actual fact, Et-1 is the value obtained when the valuation is performed using formulae (1)or (4). Consequently, the valuation is an iterative process: the free cash flows are discounted atthe WACC to calculate the companys value (D+E) but, in order to obtain the WACC; we needto know the companys value (D+E).Some authors, one being Luehrman (1997)[12], argue that equation (4) does not give us thesame result as is given by the sum of (1) and (2). That usually happens as a result of an errorin calculating equation (6), which requires using the values of equity and debt (Et-1 and Dt-1)obtained in the valuation. The most common error when calculating the WACC is to usebook values of equity and debt, as in Luehrman (1997)[12] and in Arditti and Levy (1977)[1].Other common errors when calculating WACCt are:- Using Et and Dt instead of Et-1 and Dt-1.- Using market values of equity and debt, instead of the values of equity and debt (Et-1 andDt-1) obtained in the valuation. 67
  6. 6. International Journal of Management (IJM), ISSN 0976 – 6502(Print), ISSN 0976 –6510(Online), Volume 4, Issue 2, March- April (2013)Method 3: Using the capital cash flow (CCF) and the WACCBT (weighted average cost ofcapital, before tax).The capital cash flows are the cash flows available for all holders of the companyssecurities, whether these be debt or shares, and are equivalent to the equity cash flow(ECF) plus the cash flow corresponding to the debt holders (CFd).Equation (8) indicates that the value of the debt today (D) plus that of the shareholdersequity (E) is equal to the capital cash flow (CCF) discounted at the weighted average cost ofcapital before tax (WACCBT).E0 + D0 = PV[WACCBTt; CCFt] (8)Ruback (2002)[20] also proves in a different way that the CCF methos is equivalent to FCFmethod. Therefore the expression WACCBT shows the rate at which the CCF must bediscounted so that equation gives the same result as that given by the sum of (1) and (2).WACCBT t = [Et-1 Ket + Dt-1 Kdt] / [Et-1 + Dt-1] (9)The expression that relates the CCF with the ECF and the FCF is (9):CCFt = ECFt + CFdt = FCFt + It T. Dt = Dt - Dt-1 ; It = Dt-1 Kdt (10)Method 4: Adjusted present value (APV)Equation (11) indicates that the value of the debt (D) plus that of the shareholders equity (E) isequal to the value of the unlevered companys shareholders equity, Vu, plus the value of the taxshield (VTS):E0 + D0 = Vu0 + VTS0 (11)Ku is the required return to equity in the debt-free company. Vu is given by (12). Ku is therequired return to equity in the debt-free company (also called the required return to assets).Vu0 = PV0 [Ku t ; FCFt ] (12)Most descriptions of the APV suggest calculating the VTS by discounting the interest taxshields using some discount rate. Myers (1974)[18], Taggart (1991)[22] and Luehrman(1997)[12] propose using the cost of debt (based on the theory that tax shields are about asuncertain as principal and interest payments). However, Harris and Pringle (1985) [9], Kaplanand Ruback (1995)[11], Brealey and Myers (2000)[23] and Ruback (2002)[20] propose using therequired return to the unlevered equity as the discount rate.4 Copeland, Koller and Murrin(2000)[2] assert that “the finance literature does not provide a clear answer about whichdiscount rate for the tax benefit of interest is theoretically correct.” They further conclude“we leave it to the reader’s judgment to decide which approach best fits his or her situation.” 68
  7. 7. International Journal of Management (IJM), ISSN 0976 – 6502(Print), ISSN 0976 –6510(Online), Volume 4, Issue 2, March- April (2013)Fernández (2004)[4] shows that the value of tax shields is the difference between the presentvalues of two different cash flows, each with its own risk: the present value of taxes for theunlevered company, and the present value of taxes for the levered company. FollowingFernández (2007)[6], the value of tax shields without cost of leverage is:Method 5: Using the business risk-adjusted free cash flow and Ku (required return to assets).Equation (13) indicates that the value of the debt (D) plus equity (E) is the present value ofthe expected business risk-adjusted free cash flows (FCFKu), discounted at the requiredreturn to assets (Ku):E0 + D0 = PV0 [Kut ; FCFtKu] (13)The definition of the business risk-adjusted free cash flows (FCFKu) is (14):FCFtKu = FCFt - (Et-1 + Dt-1) [WACCt - Kut ] (14)Method 6: Using the business risk-adjusted equity cash flow and Ku (required return toassets).Equation (15) indicates that the value of the equity (E) is the present value of the expectedbusiness risk-adjusted equity cash flows (ECFKu) discounted at the required return to assets(Ku):E0 = PV0 [Kut; ECFt Ku] (15)The definition of the business risk-adjusted equity cash flows (ECFKu) is (16):ECFtKu = ECFt - Et-1 [Ket - Kut ] (16)Method 7: Using the economic profit and Ke (required return to equity).Equation (17) indicates that the value of the equity (E) is the equitys book value (Ebv) plusthe present value of the expected economic profit (EP) discounted at the required return toequity (Ke).E0 = Ebv0 + PV0 [Ket; EPt] (17)The term economic profit (EP) is used to define the accounting net income or profit after tax(PAT) less the equitys book value (Ebvt-1) multiplied by the required return to equity.EPt = PATt - Ke Ebvt-1 (18) 69
  8. 8. International Journal of Management (IJM), ISSN 0976 – 6502(Print), ISSN 0976 –6510(Online), Volume 4, Issue 2, March- April (2013)Method 8: Using the EVA (economic value added) and the WACC (weighted average cost ofcapital).Equation (19) indicates that the value of the debt (D) plus equity (E) is the book value of equityand the debt (Ebv0+ N0) plus the present value of the expected EVA, discounted at the WACC:E0 + D0 = (Ebv0+ N0) + PV0 [WACCt; EVAt] (19)The EVA (economic value added) is the NOPAT (Net Operating Profit After Tax) less thecompanys book value (Dt-1 + Ebvt-1) multiplied by the weighted average cost of capital(WACC). The NOPAT (Net Operating Profit After Taxes) is the profit of the unlevered company(debt-free).EVAt = NOPATt - (Dt-1 + Ebvt-1) WACC t (20)Method 9: Using the risk-free-adjusted free cash flows discounted at the risk-free rateEquation (21) indicates that the value of the debt (D) plus equity (E) is the present value of theexpected risk-free-adjusted free cash flows (FCF RF), discounted at the risk-free rate (RF):E0 + D0 = PV0 [RF t ; FCFtRF] (21)The definition of the risk-free-adjusted free cash flows (FCFRF) is (22):FCFtRF = FCFt - (Et-1 + Dt-1) [WACCt - RF t ] (22)Method 10: Using the risk-free-adjusted equity cash flows discounted at the risk-free rateEquation (23) indicates that the value of the equity (E) is the present value of the expected risk-free-adjusted equity cash flows (ECFRF) discounted at the risk-free rate (RF):E0 = PV0 [RF t; ECFt RF] (23)The definition of the risk-free-adjusted equity cash flows (ECFRF) is (24)ECFtRF = ECFt - Et-1 [Ket - RF t ] (24)We could also talk of an eleventh method; using the business risk-adjusted capital cash flow andKu (required return to assets), but the business risk-adjusted capital cash flow is identical to thebusiness risk-adjusted free cash flow (CCFKu = FCFKu). Therefore, this method would beidentical to Method 5.We could also talk of a twelfth method; using the risk-free-adjusted capital cash flow and RF(risk-free rate), but the risk-free-adjusted capital cash flow is identical to the risk-free-adjustedfree cash flow (CCFRF = FCFRF). Therefore, this method would be identical to Method 9. 70
  9. 9. International Journal of Management (IJM), ISSN 0976 – 6502(Print), ISSN 0976 –6510(Online), Volume 4, Issue 2, March- April (2013)4. SAMPLE DATA & ANALYSIS The fictitious company NJ Inc. has the balance sheet and income statement forecastsfor the next few years shown in Table II. After year 3, the balance sheet and the incomestatement are expected to grow at an annual rate of 3%. Although the statutory tax rate is40%, the effective tax rate will be zero in year 1 because the company is forecasting losses,and 36.36% in year 2 because the company will offset the previous year’s losses. The cost ofdebt (the interest rate that the bank will charge) is 9%. Using the balance sheet and incomestatement forecasts in Table II, we can readily obtain the cash flows given at the bottom ofTable II. Table III contains the valuation of the company NJ Inc. using the ten methodsdescribed in Section I. The unlevered beta (βu) is 1. The risk-free rate is 6%. The cost of debt(r) is 9%, but the company feels that it is too high. The company thinks that the appropriaterequired return to debt (Kd) is 8%. The market risk premium is 4%. Consequently, using theCAPM, the required return to assets is 10%. As the cost of debt (r) is higher than the requiredreturn to debt (Kd), the value of debt is higher than its nominal value. The value of debt alsofulfils equation. The first method used is the APV because it does not require an iterativeprocess and, therefore, is easier to implement. To calculate the value of the unlevered equityand the value of tax shields, we only need to compute two present values using Ku (10%) isthe enterprise value and the equity value. Next is the calculation of the equity value as thepresent value of the expected equity cash flows. Please note that they are calculated throughan iterative process because for equation (15) we need to know the result of equation (1), andfor equation (1) we need to know the result of equation (15). The equity value in lines 8 and 6is exactly the same. Next is the WACC according to equations (8), (14) and (19). Then thereis the calculation of the equity value as the present value of the expected free cash flowsminus the debt value. They are also calculated through an iterative process because forequations (8) and (19) we need to know the result of equation (7), and for equation (7) weneed to know the result of equation (8) or (19). Please note that in year 1 WACC = Ku = 10%because the effective tax rate is zero. The equity value is exactly the same. Next is theWACCBT according to equation (9). Thereafter is the calculation of the equity value as thepresent value of the expected capital cash flows minus the debt value. They are alsocalculated through an iterative process because for calculating the WACCBT we need toknow the equity value and vice-versa. Note that in year 1 WACCBT = WACC = Ku = 10%because the effective tax rate is zero. Next Line is the expected residual income according to equation. Next line is thecalculation of the equity value as the present value of the expected residual income plus thebook value of equity. They are calculated through an iterative process because for calculatingthe residual income we need to know the required return to equity, and for this, we need theequity value. Then the expected business’s risk-adjusted equity cash flows will be calculated. It isthe calculation of the equity value as the present value of the expected business’s risk-adjusted equity cash flows. As the present value is calculated using Ku (10%), there is noneed for an iterative process. Next is the expected business’s risk-adjusted free cash flows according. It is thecalculation of the equity value as the present value of the expected business’s risk-adjustedfree cash flows minus the value of debt. As the present value is calculated using Ku (10%),there is no need for an iterative process. 71
  10. 10. International Journal of Management (IJM), ISSN 0976 – 6502(Print), ISSN 0976 –6510(Online), Volume 4, Issue 2, March- April (2013) Next line is the expected risk-free-adjusted equity cash flows according to equation. Itis the calculation of the equity value as the present value of the risk-free rate adjusted equitycash flows. They are calculated through an iterative process because for calculating the risk-free-adjusted equity cash flows we need to know the required return to equity, and for that,we need the equity value. Finally it is the expected risk-free-adjusted free cash flows according to equation.Next is the calculation of the equity value as the present value of the risk free rate-adjustedfree cash flows minus the debt value. They are calculated through an iterative processbecause for calculating the risk-free-adjusted free cash flows we need to know the WACC,and for that, we need the equity value.5. RESULTS The method for calculating the company using cash flow is given in Table. 1. Thefigures of forecasted profit and loss account of a fictitious company NJ Inc. is given in Table2. Finally, the valuation of NJ Inc. using 10 methods is given in Table 3. Table I: Ten Valuation MethodsMethod Cash Flow Discount Rate Value 1 ECF (Equity Cash Flow) Ke (Cost of Levered Equity) E (Equity) CFd (Debt Cash Flow) Kd( Required Return to Debt) D (Debt) 2 FCF (Free Cash Flow) WACC E+D 3 CCF (Capital Cash Flows) WACCBT (Weighted Average E+D Cost of Capital Before Taxes) 4 FCF (Free Cash Flow) Ku (Cost of unlevered equity) Vu (Unlevered Equity) D T Ku Ku (Cost of unlevered equity) VTS (Value of Tax Shields) 5 RI (Residual Income) Ke E – Ebv 6 EVA (Economic Value WACC E + D – Ebv – N Added) 7 FCF//ku (Business risk- Ku E+D adjusted free cash flow) 8 ECF//ku (Business risk- Ku E adjusted equity cash flow) 9 FCF//Rf (Risk free-adjusted Rf E+D free cash flow) 10 ECF//Rf (Risk free-adjusted Rf E equity cash flow) 72
  11. 11. International Journal of Management (IJM), ISSN 0976 – 6502(Print), ISSN 0976 –6510(Online), Volume 4, Issue 2, March- April (2013) Table II: Balance Sheet and Income Statement Forecasts of NJ Inc. Balance Sheet 0 1 2 3 4 5 Working Capital Requirements 800 890 1,000 1,100 1,133 1,166.99 Gross Fixed Assets 1,200 1,300 1,450 1,660 1,895.10 2,134.90 - Accumulated Depriciation -200 -405 -615 -818.2 1,026.20 Net Fixed Assets 1,200 1,100 1,045 1,045 1,076.90 1,108.70 TOTAL ASSETS 2,000 1,990 2,045 2,145 2,209.90 2,275.69 Debt 1,500 1,500 1,500 1,550 1,597 1,644.40 Equity (Book Value) 500 490 545 595 612.9 631.29 TOTAL LIABILITIES 2,000 1,990 2,045 2,145 2,209.90 2,275.69 Income Statement 1 2 3 4 5 EBIDTA 325 450 500 515 530.45 Depriciation 200 205 210 216.3 222.79 Interest Payments 135 135 135 139.5 142.29 PBT -10 110 155 159.2 165.37 Taxes 0 40 62 63.68 66.15 PAT -10 70 93 95.52 99.22 Taxes 0% 36.36% 40% 40% 40% Cash Flows 1 2 3 4 5 PAT -10 70 93 95.52 99.22 Depreciation 200 205 210 216.3 222.79 Increase of Debt 0 0 50 46.5 47.9 Increase in Working Capital -90 -110 -100 -33 -33.99 Investment in Fixed Assets -100 -150 -210 -235.1 -239.8 ECF (Equity Cash Flow) 0 15 43 90.22 96.12 FCF (Free Cash Flow) 135 100.91 74 127.42 133.59 CFd (Debt Cash Flow) 135 135 85 93 94.39 CCF (Capital Cash Flow) 135 150 128 183.22 190.51 73
  12. 12. International Journal of Management (IJM), ISSN 0976 – 6502(Print), ISSN 0976 –6510(Online), Volume 4, Issue 2, March- April (2013) Table III: Valuation of NJ Inc. Formula 0 1 2 3 4 5 Ku 10.00% 10.00% 10.00% 10.00% 10.00% D = PV(Kd; CFd) 1,743.73 1,748.23 1,753.09 1,808.33 1,844.50 1,881.39 Vu = PV (Ku; FCF) 1,525.62 1,543.18 1,596.59 1,682.25 1,715.90 1,750.21 VTS = PV[Ku; D T Ku + T (Nr - DKd)] 762.09 838.3 860.33 878.33 895.9 913.82 E + D = VTS + Vu 2,287.71 2,381.48 2,456.92 2,560.58 2,611.80 2,664.03 E = VTS + Vu – D 543.98 633.25 703.83 752.25 767.29 782.64 Ke 16.41% 13.51% 12.99% 12.88% 12.88% E = PV(Ke; ECF) 543.98 633.25 703.83 752.25 767.29 782.64 WACC 10% 7.41% 7.23% 7.26% 7.26% E = PV(WACC; FCF) – D 543.98 633.25 703.83 752.25 767.29 782.64 WACCBT 10% 9.47% 9.43% 9.44% 9.44% E = PV(WACCBT; CCF) - D 543.98 633.25 703.83 752.25 767.29 782.64 RI -92.05 3.78 22.21 17.12 17.46 E = PV(Ke; RI) + Ebv 543.98 633.25 703.83 752.25 767.29 782.64 EVA -75 8.55 26.12 21.84 22.28 E = Ebv - (D-N) + PV(WACC; EVA) 543.98 633.25 703.83 752.25 767.29 782.64 ECF//Ku -34.87 -7.25 21.95 60.18 61.38 E = PV(Ku; ECF//Ku) 543.98 633.25 703.83 752.25 767.29 782.64 FCF//Ku 135 162.71 142.02 204.85 208.94 E = PV(Ku; FCF//Ku) – D 543.98 633.25 703.83 752.25 767.29 782.64 ECF//RF -56.63 -32.58 -6.19 30.09 30.69 E = PV(RF; ECF//RF) 543.98 633.25 703.83 752.25 767.29 782.64 FCF//RF 43.49 67.46 43.75 102.42 104.47 E = PV(RF; FCF//RF) – D 543.98 633.25 703.83 752.25 767.29 782.64 74
  13. 13. International Journal of Management (IJM), ISSN 0976 – 6502(Print), ISSN 0976 –6510(Online), Volume 4, Issue 2, March- April (2013)6. CONCLUSION The paper shows that ten commonly used discounted cash flow valuation methodsalways give the same value. This result is logical, since all the methods analyze the samereality under the same hypotheses; they differ only in the cash flows taken as the startingpoint for the valuation. We present all ten methods, allowing the required return to debt to be different fromthe cost of debt. Seven methods require an iterative process. Only APV and the business riskadjusted cash flows methods do not require iteration; that makes them the easiest methods touse. The relevant tax rate is not the statutory tax rate, but the effective tax rate applied toearnings in the levered company on each year. The value of tax shields is not the present value of tax shields using either the cost ofequity or debt to discount the tax write-offs. It is the difference between the present values oftwo different cash flows, each with its own risk: the present value of taxes for the unleveredcompany and the present value of taxes for the levered company.Abbreviationsβd = Beta of debtβL = Beta of levered equityβu = Beta of unlevered equity = beta of assetsD = Value of debtE = Value of equityEbv = Book value of equityECF = Equity cash flowECF//Ku = business risk-adjusted equity cash flowsECF//RF = expected risk-free-adjusted equity cash flowsRI = Residual incomeEVA = Economic value addedFCF = Free cash flowFCF//Ku = business risk-adjusted free cash flowsFCF//RF = risk-free-adjusted free cash flowsg = Growth rate of the constant growth caseI = Interest paidKu = Cost of unlevered equity (required return to unlevered equity)Ke = Cost of levered equity (required return to levered equity)Kd = Required return to debtN = Book value of the debtNOPAT = Net Operating Profit After Tax = profit after tax of the unlevered companyPAT = Profit after taxPBT = Profit before taxPM = Market premium = E (RM - RF)PV = Present valuer = Cost of debtRF = Risk-free rateRM = Market return 75
  14. 14. International Journal of Management (IJM), ISSN 0976 – 6502(Print), ISSN 0976 –6510(Online), Volume 4, Issue 2, March- April (2013)ROA = Return on Assets = NOPATt / (Nt-1+Ebvt-1)ROE = Return on Equity = PATt / Ebvt-1T = Corporate tax rateVTS = Value of the tax shieldsVu = Value of shares in the unlevered companyWACC = Weighted average cost of capitalWACCBT = Weighted average cost of capital before taxesWCR = Working capital requirements = net current assetsREFERENCES[1]. Arditti, F.D. and H. Levy (1977), "The Weighted Average Cost of Capital as a CutoffRate: A Critical Examination of the Classical Textbook Weighted Average", FinancialManagement (Fall), pp. 24-34.[2]. Copeland, T.E., T. Koller and J. Murrin (2000), Valuation: Measuring and Managingthe Value of Companies. Third edition. New York: Wiley.[3]. Damodaran, A (1994), Damodaran on Valuation, John Wiley and Sons, New York.[4]. Fernandez, P. (2004), "The value of tax shields is NOT equal to the present value oftax shields", Journal of Financial Economics, Vol. 73/1 (July), pp. 145-165.[5]. Fernandez, P. (2007). "A More Realistic Valuation: APV and WACC with constantbook leverage ratio", Journal of Applied Finance, Fall/Winter, Vol.17 No 2, pp. 13-20.[6]. Fernandez, P. (2007b), "Equity Premium: Historical, Expected, Required andImplied"[7]. Fernandez, P. (2008), Equivalence of Ten Different Methods for Valuing Companiesby Cash Flow Discounting, International Journal of Finance Education, Vol. 1 Issue 1, pp.141-168. 2005.[8]. Fernandez, P. (2002), Valuation Methods and Shareholder Value Creation. (AcademicPress, San Diego, CA.).[9]. Harris, R.S. and J.J. Pringle (1985), "Risk-Adjusted Discount Rates Extensions formthe Average-Risk Case", Journal of Financial Research (Fall), pp. 237-244.[10]. Inselbag, I. and H. Kaufold (1997), "Two DCF Approaches for Valuing Companiesunder Alternative Financing Strategies (and How to Choose Between Them)", Journal ofApplied Corporate Finance (Spring), pp. 114- 122.[11]. Kaplan, S. and R. Ruback (1995), "The Valuation of Cash Flow Forecasts: AnEmpirical Analysis", Journal of Finance, Vol 50, No 4, September.[12]. Luehrman, T. A. (1997), "Whats It Worth: A General Managers Guide to Valuation",and "Using APV: A Better Tool for Valuing Operations", Harvard Business Review, (May-June), pp. 132-154.[13]. Miles, J.A. and J.R. Ezzell (1980), "The Weighted Average Cost of Capital, PerfectCapital Markets and Project Life: A Clarification," Journal of Financial and QuantitativeAnalysis (September), pp. 719-730.[14]. Miles, J.A. and J.R. Ezzell, (1985), "Reequationing Tax Shield Valuation: A Note",Journal of Finance, Vol XL, 5 (December), pp. 1485-1492.[15]. Miller, M. H. (1977), "Debt and Taxes", Journal of Finance (May), pp. 261-276.[16]. Modigliani, F. and M. Miller (1958), "The Cost of Capital, Corporation Finance andthe Theory of Investment", American Economic Review 48, 261-297. 76
  15. 15. International Journal of Management (IJM), ISSN 0976 – 6502(Print), ISSN 0976 –6510(Online), Volume 4, Issue 2, March- April (2013)[17]. Modigliani, F. and M. Miller (1963), "Corporate Income Taxes and the Cost ofCapital: A Correction", American Economic Review (June), pp. 433-443.[18]. Myers, S.C. (1974), "Interactions of Corporate Financing and Investment Decisions -Implications for Capital Budgeting", Journal of Finance (March), pp. 1-25.[19]. Ruback, R. S. (1995), "A Note on Capital Cash Flow Valuation", Harvard BusinessSchool, 9-295-069.[20]. Ruback, R. (2002), "Capital Cash Flows: A Simple Approach to Valuing Risky CashFlows", Financial Management 31, pp. 85-103.[21]. Tham, J. and I. Vélez-Pareja (2001), "The Correct Discount Rate for the Tax Shield:the N-period Case", SSRN Working Paper.[22]. Taggart, Robert A, 1991, Consistent valuation and cost of capital expressions withcorporate and personal taxes, Financial Management, Autumn 1991, 8-20.[23]. Brealey, Richard A and Stewart C Myers, 2000, Principles of Corporate Finance,McGraw-Hill.[24]. Bodie, Z., Merton, R.C. (2000), Finance, Prantice Hall, Upper Saddle River, NJ.[25]. Damodaran, A. (2002), Investment Valuation. (John Wiley and Sons, New York,second edition).[26]. V.Anandavel and Dr.A.Selvarasu, “Economic Value Added Performance of BSE--Sensex Companies Against its Equity Capital” International Journal of Management (IJM),Volume 3, Issue 2, 2012, pp. 108 - 123, ISSN Print: 0976-6502, ISSN Online: 0976-6510. 77

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