Equity Instruments: Part I Discounted Cash Flow Valuation

Transcription

1 Equity Istrumets: Part I Discouted Cash Flow Valuatio B Aswath Damodara Aswath Damodara 1

2 Discouted Cashflow Valuatio: Basis for Approach Value = t = CF Â t t =1 (1+ r) t where CF t is the cash flow i period t, r is the discout rate appropriate give the riskiess of the cash flow ad t is the life of the asset. Propositio 1: For a asset to have value, the expected cash flows have to be positive some time over the life of the asset. Propositio 2: Assets that geerate cash flows early i their life will be worth more tha assets that geerate cash flows later; the latter may however have greater growth ad higher cash flows to compesate. Aswath Damodara 2

3 Equity Valuatio versus Firm Valuatio Value just the equity stake i the busiess Value the etire busiess, which icludes, besides equity, the other claimholders i the firm Aswath Damodara 3

4 I.Equity Valuatio The value of equity is obtaied by discoutig expected cashflows to equity, i.e., the residual cashflows after meetig all expeses, tax obligatios ad iterest ad pricipal paymets, at the cost of equity, i.e., the rate of retur required by equity ivestors i the firm. Value of Equity = t= Â t=1 CF to Equity t (1+ k e ) t where, CF to Equity t = Expected Cashflow to Equity i period t k e = Cost of Equity The divided discout model is a specialized case of equity valuatio, ad the value of a stock is the preset value of expected future divideds. Aswath Damodara 4

5 II. Firm Valuatio The value of the firm is obtaied by discoutig expected cashflows to the firm, i.e., the residual cashflows after meetig all operatig expeses ad taxes, but prior to debt paymets, at the weighted average cost of capital, which is the cost of the differet compoets of fiacig used by the firm, weighted by their market value proportios. Value of Firm = t= Â t =1 CF to Firm t (1+ WACC) t where, CF to Firm t = Expected Cashflow to Firm i period t WACC = Weighted Average Cost of Capital Aswath Damodara 5

6 Firm Value ad Equity Value o o o o o o o To get from firm value to equity value, which of the followig would you eed to do? Subtract out the value of log term debt Subtract out the value of all debt Subtract the value of all o-equity claims i the firm, that are icluded i the cost of capital calculatio Subtract out the value of all o-equity claims i the firm Doig so, will give you a value for the equity which is greater tha the value you would have got i a equity valuatio lesser tha the value you would have got i a equity valuatio equal to the value you would have got i a equity valuatio Aswath Damodara 6

7 Cash Flows ad Discout Rates Assume that you are aalyzig a compay with the followig cashflows for the ext five years. Year CF to Equity It Exp (1-t) CF to Firm 1 $ 50 $ 40 $ 90 2 $ 60 $ 40 $ $ 68 $ 40 $ $ 76.2 $ 40 $ $ $ 40 $ Termial Value $ $ Assume also that the cost of equity is % ad the firm ca borrow log term at 10%. (The tax rate for the firm is 50%.) The curret market value of equity is $1,073 ad the value of debt outstadig is $800. Aswath Damodara 7

8 Equity versus Firm Valuatio Method 1: Discout CF to Equity at Cost of Equity to get value of equity Cost of Equity = % PV of Equity = 50/ / / / ( )/ = $1073 Method 2: Discout CF to Firm at Cost of Capital to get value of firm Cost of Debt = Pre-tax rate (1- tax rate) = 10% (1-.5) = 5% WACC = % (1073/1873) + 5% (800/1873) = 9.94% PV of Firm = 90/ / / / ( )/ = $1873 PV of Equity = PV of Firm - Market Value of Debt = $ $ 800 = $1073 Aswath Damodara 8

9 First Priciple of Valuatio Never mix ad match cash flows ad discout rates. The key error to avoid is mismatchig cashflows ad discout rates, sice discoutig cashflows to equity at the weighted average cost of capital will lead to a upwardly biased estimate of the value of equity, while discoutig cashflows to the firm at the cost of equity will yield a dowward biased estimate of the value of the firm. Aswath Damodara 9

10 The Effects of Mismatchig Cash Flows ad Discout Rates Error 1: Discout CF to Equity at Cost of Capital to get equity value PV of Equity = 50/ / / / ( )/ = $1248 Value of equity is overstated by $175. Error 2: Discout CF to Firm at Cost of Equity to get firm value PV of Firm = 90/ / / / ( )/ = $1613 PV of Equity = $ $800 = $813 Value of Equity is uderstated by $ 260. Error 3: Discout CF to Firm at Cost of Equity, forget to subtract out debt, ad get too high a value for equity Value of Equity = $ 1613 Value of Equity is overstated by $ 540 Aswath Damodara 10

11 Discouted Cash Flow Valuatio: The Steps Estimate the discout rate or rates to use i the valuatio Discout rate ca be either a cost of equity (if doig equity valuatio) or a cost of capital (if valuig the firm) Discout rate ca be i omial terms or real terms, depedig upo whether the cash flows are omial or real Discout rate ca vary across time. Estimate the curret earigs ad cash flows o the asset, to either equity ivestors (CF to Equity) or to all claimholders (CF to Firm) Estimate the future earigs ad cash flows o the firm beig valued, geerally by estimatig a expected growth rate i earigs. Estimate whe the firm will reach stable growth ad what characteristics (risk & cash flow) it will have whe it does. Choose the right DCF model for this asset ad value it. Aswath Damodara 11

12 Geeric DCF Valuatio Model DISCOUNTED CASHFLOW VALUATION Cash flows Firm: Pre-debt cash flow Equity: After debt cash flows Expected Growth Firm: Growth i Operatig Earigs Equity: Growth i Net Icome/EPS Firm is i stable growth: Grows at costat rate forever Termial Value Value Firm: Value of Firm CF1 CF2 CF3 CF4 CF5 CF... Forever Equity: Value of Equity Legth of Period of High Growth Discout Rate Firm:Cost of Capital Equity: Cost of Equity Aswath Damodara 12

13 EQUITY VALUATION WITH DIVIDENDS Divideds Net Icome * Payout Ratio = Divideds Expected Growth Retetio Ratio * Retur o Equity Firm is i stable growth: Grows at costat rate forever Value of Equity Termial Value= Divided +1/(ke-g) Divided 1 Divided 2 Divided 3 Divided 4 Divided 5 Divided... Forever Discout at Cost of Equity Cost of Equity Riskfree Rate : - No default risk - No reivestmet risk - I same currecy ad i same terms (real or omial as cash flows + Beta - Measures market risk Type of Busiess Operatig Leverage X Fiacial Leverage Risk Premium - Premium for average risk ivestmet Base Equity Premium Coutry Risk Premium Aswath Damodara 13

14 Fiacig Weights Debt Ratio = DR EQUITY VALUATION WITH FCFE Cashflow to Equity Net Icome - (Cap Ex - Depr) (1- DR) - Chage i WC (!-DR) = FCFE Expected Growth Retetio Ratio * Retur o Equity Firm is i stable growth: Grows at costat rate forever Value of Equity Termial Value= FCFE +1/(ke-g) FCFE1 FCFE2 FCFE3 FCFE4 FCFE5 FCFE... Forever Discout at Cost of Equity Cost of Equity Riskfree Rate : - No default risk - No reivestmet risk - I same currecy ad i same terms (real or omial as cash flows + Beta - Measures market risk Type of Busiess Operatig Leverage X Fiacial Leverage Risk Premium - Premium for average risk ivestmet Base Equity Premium Coutry Risk Premium Aswath Damodara 14

15 VALUING A FIRM Cashflow to Firm EBIT (1-t) - (Cap Ex - Depr) - Chage i WC = FCFF Expected Growth Reivestmet Rate * Retur o Capital Firm is i stable growth: Grows at costat rate forever Value of Operatig Assets + Cash & No-op Assets = Value of Firm - Value of Debt = Value of Equity Termial Value= FCFF +1/(r-g) FCFF1 FCFF2 FCFF3 FCFF4 FCFF5 FCFF... Forever Discout at WACC= Cost of Equity (Equity/(Debt + Equity)) + Cost of Debt (Debt/(Debt+ Equity)) Cost of Equity Cost of Debt (Riskfree Rate + Default Spread) (1-t) Weights Based o Market Value Riskfree Rate : - No default risk - No reivestmet risk - I same currecy ad i same terms (real or omial as cash flows + Beta - Measures market risk Type of Busiess Operatig Leverage X Fiacial Leverage Risk Premium - Premium for average risk ivestmet Base Equity Premium Coutry Risk Premium Aswath Damodara 15

16 Discouted Cash Flow Valuatio: The Iputs Aswath Damodara Aswath Damodara 16

17 I. Estimatig Discout Rates DCF Valuatio Aswath Damodara 17

18 Estimatig Iputs: Discout Rates Critical igrediet i discouted cashflow valuatio. Errors i estimatig the discout rate or mismatchig cashflows ad discout rates ca lead to serious errors i valuatio. At a ituitive level, the discout rate used should be cosistet with both the riskiess ad the type of cashflow beig discouted. Equity versus Firm: If the cash flows beig discouted are cash flows to equity, the appropriate discout rate is a cost of equity. If the cash flows are cash flows to the firm, the appropriate discout rate is the cost of capital. Currecy: The currecy i which the cash flows are estimated should also be the currecy i which the discout rate is estimated. Nomial versus Real: If the cash flows beig discouted are omial cash flows (i.e., reflect expected iflatio), the discout rate should be omial Aswath Damodara 18

19 Cost of Equity The cost of equity should be higher for riskier ivestmets ad lower for safer ivestmets While risk is usually defied i terms of the variace of actual returs aroud a expected retur, risk ad retur models i fiace assume that the risk that should be rewarded (ad thus built ito the discout rate) i valuatio should be the risk perceived by the margial ivestor i the ivestmet Most risk ad retur models i fiace also assume that the margial ivestor is well diversified, ad that the oly risk that he or she perceives i a ivestmet is risk that caot be diversified away (I.e, market or o-diversifiable risk) Aswath Damodara 19

20 The Cost of Equity: Competig Models Model Expected Retur Iputs Needed CAPM E(R) = R f + b (R m - R f ) Riskfree Rate Beta relative to market portfolio Market Risk Premium APM E(R) = R f + S j=1 b j (R j - R f ) Riskfree Rate; # of Factors; Betas relative to each factor Factor risk premiums Multi E(R) = R f + S j=1,,n b j (R j - R f ) Riskfree Rate; Macro factors factor Betas relative to macro factors Macro ecoomic risk premiums Proxy E(R) = a + S j=1..n b j Y j Proxies Regressio coefficiets Aswath Damodara 20

21 The CAPM: Cost of Equity Cosider the stadard approach to estimatig cost of equity: Cost of Equity = R f + Equity Beta * (E(R m ) - R f ) where, R f = Riskfree rate E(R m ) = Expected Retur o the Market Idex (Diversified Portfolio) I practice, Short term govermet security rates are used as risk free rates Historical risk premiums are used for the risk premium Betas are estimated by regressig stock returs agaist market returs Aswath Damodara 21

22 Short term Govermets are ot riskfree i valuatio. O a riskfree asset, the actual retur is equal to the expected retur. Therefore, there is o variace aroud the expected retur. For a ivestmet to be riskfree, the, it has to have No default risk No reivestmet risk Thus, the riskfree rates i valuatio will deped upo whe the cash flow is expected to occur ad will vary across time A simpler approach is to match the duratio of the aalysis (geerally log term) to the duratio of the riskfree rate (also log term) I emergig markets, there are two problems: The govermet might ot be viewed as riskfree (Brazil, Idoesia) There might be o market-based log term govermet rate (Chia) Aswath Damodara 22

23 Estimatig a Riskfree Rate whe there are o default free etities. Estimate a rage for the riskfree rate i local terms: Approach 1: Subtract default spread from local govermet bod rate: Govermet bod rate i local currecy terms - Default spread for Govermet i local currecy Approach 2: Use forward rates ad the riskless rate i a idex currecy (say Euros or dollars) to estimate the riskless rate i the local currecy. Do the aalysis i real terms (rather tha omial terms) usig a real riskfree rate, which ca be obtaied i oe of two ways from a iflatio-idexed govermet bod, if oe exists set equal, approximately, to the log term real growth rate of the ecoomy i which the valuatio is beig doe. Do the aalysis i aother more stable currecy, say US dollars. Aswath Damodara 23

24 A Simple Test o o o o o You are valuig Ambev, a Brazilia compay, i U.S. dollars ad are attemptig to estimate a riskfree rate to use i the aalysis. The riskfree rate that you should use is The iterest rate o a Real deomiated log term bod issued by the Brazilia Govermet The iterest rate o a US $ deomiated log term bod issued by the Brazilia Govermet (C-Bod) The iterest rate o a US $ deomiated Brazilia Brady bod (which is partially backed by the US Govermet) The iterest rate o a dollar deomiated bod issued by Ambev The iterest rate o a US treasury bod Aswath Damodara 24

25 Everyoe uses historical premiums, but.. The historical premium is the premium that stocks have historically eared over riskless securities. Practitioers ever seem to agree o the premium; it is sesitive to How far back you go i history Whether you use T.bill rates or T.Bod rates Whether you use geometric or arithmetic averages. For istace, lookig at the US: Arithmetic average Geometric Average Stocks - Stocks - Stocks - Stocks - Historical Period T.Bills T.Bods T.Bills T.Bods % 6.25% 5.73% 4.53% % 3.66% 3.90% 2.76% % 2.15% 4.69% 0.95% Aswath Damodara 25

26 If you choose to use historical premiums. Go back as far as you ca. A risk premium comes with a stadard error. Give the aual stadard deviatio i stock prices is about 25%, the stadard error i a historical premium estimated over 25 years is roughly: Stadard Error i Premium = 25%/ 25 = 25%/5 = 5% Be cosistet i your use of the riskfree rate. Sice we argued for log term bod rates, the premium should be the oe over T.Bods Use the geometric risk premium. It is closer to how ivestors thik about risk premiums over log periods. Aswath Damodara 26

27 Risk Premium for a Mature Market Equity Risk Premiums - By Coutry 7.00% Average Risk Premium across all mature equity markets = 4% 6.00% Compouded Aual Risk Premium 5.00% 4.00% 3.00% 2.00% 1.00% 0.00% Australia Belgium Caada Demark Frace Germay Irelad Italy Japa Coutry Netherlads South Africa Spai Swede Switzerlad UK USA World Stocks - Log Term Govermet Retur Aswath Damodara 27

28 Effect of Chagig Tax Status of Divideds o Stock Prices Expected Retur o Stocks (Implied) = 7.91% Divided Yield i Jauary 2003 = 2.00% Assumig that divideds were taxed at 30% (o average) o 1/1/03 ad that capital gais were taxed at 15%. After-tax expected retur o stocks = 2%(1-.3)+5.91%(1-.15) = 6.42% If the tax rate o divideds drops to 15% ad the after-tax expected retur remais the same: 2% (1-.15) + X% (1-.15) = 6.42% New Pre-tax required rate of retur = 7.56% New equity risk premium = 3.75% Value of the S&P 500 at ew equity risk premium = Expected Icrease i idex due to divided tax chage = 9.69% Aswath Damodara 28

29 Coutry Risk Premiums Historical risk premiums are almost impossible to estimate with ay precisio i markets with limited history - this is true ot just of emergig markets but also of may Wester Europea markets. For such markets, we ca estimate a modified historical premium begiig with the U.S. premium as the base: Relative Equity Market approach: The coutry risk premium is based upo the volatility of the market i questio relative to U.S market. Coutry risk premium = Risk Premium US * s Coutry Equity / s US Equity Coutry Bod approach: I this approach, the coutry risk premium is based upo the default spread of the bod issued by the coutry. Coutry risk premium = Risk Premium US + Coutry bod default spread Combied approach: I this approach, the coutry risk premium icorporates both the coutry bod spread ad equity market volatility. Aswath Damodara 29

30 Step 1: Assessig Coutry Risk Usig Coutry Ratigs: Lati America - Jue 2003 Coutry Log-Term Ratig Typical Default Spread for Ratig Coutry bod spread (if available) Argetia Ca Bolivia B Brazil B Chile A Colombia Baa Costa Rica Ba Ecuador Caa El Salvador Baa Guatemala Ba Hoduras B Mexico Baa Nicaragua B Paama Ba Paraguay B Peru Baa Uruguay B Veezuela Caa Aswath Damodara 30

31 Step 2: From Bod Default Spreads to Equity Risk Premiums Coutry ratigs measure default risk. While default risk premiums ad equity risk premiums are highly correlated, oe would expect equity spreads to be higher tha debt spreads. Oe way to adjust the coutry spread upwards is to use iformatio from the US market. I the US, the equity risk premium has bee roughly twice the default spread o juk bods. Aother is to multiply the bod spread by the relative volatility of stock ad bod prices i that market. For example, Stadard Deviatio i Bovespa (Equity) = 36% Stadard Deviatio i Brazil C-Bod = 24% Adjusted Equity Spread = 7.50% (36/24) = 11.25% Aswath Damodara 31

32 From Coutry Spreads to Corporate Risk premiums Approach 1: Assume that every compay i the coutry is equally exposed to coutry risk. I this case, E(Retur) = Riskfree Rate + Coutry Spread + Beta (Mature Equity Premium) Implicitly, this is what you are assumig whe you use the local Govermet s dollar borrowig rate as your riskfree rate. Approach 2: Assume that a compay s exposure to coutry risk is similar to its exposure to other market risk. E(Retur) = Riskfree Rate + Beta (Mature Equity Premium + Coutry Equity premium) Approach 3: Treat coutry risk as a separate risk factor ad allow firms to have differet exposures to coutry risk (perhaps based upo the proportio of their reveues come from o-domestic sales) E(Retur)=Riskfree Rate+ b (Mature Equity Premium ) + l (Coutry Equity premium) Aswath Damodara 32

33 Estimatig Compay Exposure to Coutry Risk Differet compaies should be exposed to differet degrees to coutry risk. For istace, a Brazilia firm that geerates the bulk of its reveues i the Uited States should be less exposed to coutry risk i Brazil tha oe that geerates all its busiess withi Brazil. The factor l measures the relative exposure of a firm to coutry risk. Oe simplistic solutio would be to do the followig: l = % of reveues domestically firm / % of reveues domestically avg firm For istace, if a firm gets 35% of its reveues domestically while the average firm i that market gets 70% of its reveues domestically l = 35%/ 70 % = 0.5 There are two implicatios A compay s risk exposure is determied by where it does busiess ad ot by where it is located Firms might be able to actively maage their coutry risk exposures Aswath Damodara 33

34 Estimatig E(Retur) for Embraer Assume that the beta for Embraer is 0.88, ad that the dollar riskfree rate used is 4.5%. Assume that 4% is the premium for a mature equity market. Approach 1: Assume that every compay i the coutry is equally exposed to coutry risk. I this case, E(Retur) =4.5% % (4%) = 19.27% Approach 2: Assume that a compay s exposure to coutry risk is similar to its exposure to other market risk. E(Retur) = 4.5% (4% %) = 17.92% Approach 3: Treat coutry risk as a separate risk factor ad allow firms to have differet exposures to coutry risk (perhaps based upo the proportio of their reveues come from o-domestic sales) E(Retur)= 4.5% (4%) (11.25%) = 13.65% Embraer is less exposed to coutry risk tha the typical Brazilia firm sice much of its busiess is overseas. Aswath Damodara 34

35 Implied Equity Premiums If we use a basic discouted cash flow model, we ca estimate the implied risk premium from the curret level of stock prices. For istace, if stock prices are determied by a variatio of the simple Gordo Growth Model: Value = Expected Divideds ext year/ (Required Returs o Stocks - Expected Growth Rate) Divideds ca be exteded to icluded expected stock buybacks ad a high growth period. Pluggig i the curret level of the idex, the divideds o the idex ad expected growth rate will yield a implied expected retur o stocks. Subtractig out the riskfree rate will yield the implied premium. This model ca be exteded to allow for two stages of growth - a iitial period where the etire market will have earigs growth greater tha that of the ecoomy, ad the a stable growth period. Aswath Damodara 35

36 Estimatig Implied Premium for U.S. Market: Ja 1, 2003 Level of the idex = Treasury bod rate = 3.81% Expected Growth rate i earigs (ext 5 years) = 8% (Cosesus estimate for S&P 500 earigs) Expected growth rate after year 5 = 3.81% Divideds (2%)+ stock buybacks (1.29%)=3.29% of idex (latest year) Year 1 Year 2 Year 3 Year 4 Year 5 Expected Divideds = $31.25 $33.75 $36.45 $39.37 $ Stock Buybacks Expected divideds + buybacks i year 6 = (1.0381) = $ = 31.25/(1+r) /(1+r) /(1+r) /(1+r) 4 + (42.52+(44.14/(r-.0381))/(1+r) 5 Solvig for r, r = 7.91%. (Oly way to do this is trial ad error) Implied risk premium = 7.91% % = 4.10% Aswath Damodara 36

37 Implied Premiums: US Implied Premium for US Equity Market 7.00% 6.00% 5.00% Implied Premium 4.00% 3.00% 2.00% 1.00% 0.00% Year Aswath Damodara 37

38 Implied Premiums: US Implied Equity Risk Premiums: Mothly - Jauary 2000 to Jaury 2003 S&P S & P 500 Idex Implied Equity Risk Premium 5.00% 4.50% 4.00% 3.50% 3.00% 2.50% 2.00% 1.50% 1.00% 0.50% Implied Equity risk premium % Nov-02 Sep-02 Jul-02 May-02 Mar-02 Ja-02 Nov-01 Sep-01 Jul-01 May-01 Mar-01 Ja-01 Nov-00 Sep-00 Jul-00 May-00 3/1/00 1/1/00 Moth Idex Implied Premium Aswath Damodara 38

39 Implied Premium for Brazilia Market: Jue 2003 Level of the Idex = Divideds o the Idex = 4.50% of idex (Used weighted yield) Other parameters Riskfree Rate = 3.5% (real riskfree rate) Expected Growth Next 5 years = 8% (Used expected real growth rate i Earigs) After year 5 = 4% (real growth rate i log term) Solvig for the expected retur: Expected retur o Equity = 10.53% Implied Equity premium = 10.53% - 3.5% = 7.03%% Aswath Damodara 39

40 The Effect of Usig Implied Equity Premiums o Value Embraer s value per share (usig historical premium + coutry risk adjustmet) = BR Embraer s value per share (usig implied equity premium of 7.03%) = BR Embraer s stock price (at the time of the valuatio) = BR Aswath Damodara 40

41 Estimatig Beta The stadard procedure for estimatig betas is to regress stock returs (R j ) agaist market returs (R m ) - R j = a + b R m where a is the itercept ad b is the slope of the regressio. The slope of the regressio correspods to the beta of the stock, ad measures the riskiess of the stock. This beta has three problems: It has high stadard error It reflects the firm s busiess mix over the period of the regressio, ot the curret mix It reflects the firm s average fiacial leverage over the period rather tha the curret leverage. Aswath Damodara 41

42 Beta Estimatio: The Noise Problem Aswath Damodara 42

43 Beta Estimatio: The Idex Effect Aswath Damodara 43

44 Determiats of Betas Product or Service: The beta value for a firm depeds upo the sesitivity of the demad for its products ad services ad of its costs to macroecoomic factors that affect the overall market. Cyclical compaies have higher betas tha o-cyclical firms Firms which sell more discretioary products will have higher betas tha firms that sell less discretioary products Operatig Leverage: The greater the proportio of fixed costs i the cost structure of a busiess, the higher the beta will be of that busiess. This is because higher fixed costs icrease your exposure to all risk, icludig market risk. Fiacial Leverage: The more debt a firm takes o, the higher the beta will be of the equity i that busiess. Debt creates a fixed cost, iterest expeses, that icreases exposure to market risk. Aswath Damodara 44

45 Equity Betas ad Leverage The beta of equity aloe ca be writte as a fuctio of the ulevered beta ad the debt-equity ratio b L = b u (1+ ((1-t)D/E)) where b L = Levered or Equity Beta b u = Ulevered Beta (Asset Beta) t = Corporate margial tax rate D = Market Value of Debt E = Market Value of Equity While this beta is estimated o the assumptio that debt carries o market risk (ad has a beta of zero), you ca have a modified versio: b L = b u (1+ ((1-t)D/E)) - b debt (1-t) (D/E) Aswath Damodara 45

46 Solutios to the Regressio Beta Problem Modify the regressio beta by chagig the idex used to estimate the beta adjustig the regressio beta estimate, by brigig i iformatio about the fudametals of the compay Estimate the beta for the firm usig the stadard deviatio i stock prices istead of a regressio agaist a idex. accoutig earigs or reveues, which are less oisy tha market prices. Estimate the beta for the firm from the bottom up without employig the regressio techique. This will require uderstadig the busiess mix of the firm estimatig the fiacial leverage of the firm Use a alterative measure of market risk that does ot eed a regressio. Aswath Damodara 46

47 Bottom-up Betas The bottom up beta ca be estimated by : Takig a weighted (by sales or operatig icome) average of the ulevered betas of the differet busiesses a firm is i. j =k  j =1 b j È Operatig Icome j Í Î Operatig Icome Firm (The ulevered beta of a busiess ca be estimated by lookig at other firms i the same busiess) Lever up usig the firm s debt/equity ratio [ ] b levered = b ulevered 1+ (1- tax rate) (Curret Debt/Equity Ratio) The bottom up beta will give you a better estimate of the true beta whe It has lower stadard error (SE average = SE firm / ( = umber of firms) It reflects the firm s curret busiess mix ad fiacial leverage It ca be estimated for divisios ad private firms. Aswath Damodara 47

48 Bottom-up Beta: Firm i Multiple Busiesses Boeig i 1998 Segmet Estimated Value Ulevered Beta Segmet Weight Commercial Aircraft 30, % Defese 12, % Estimated Value = Reveues of divisio * Eterprise Value/Sales Busiess Ulevered Beta of firm = 0.91 (.7039) (.2961) = 0.88 Levered Beta Calculatio Market Value of Equity = $ 33,401 Market Value of Debt = $8,143 Market Debt/Equity Ratio = 24.38% Tax Rate = 35% Levered Beta for Boeig = 0.88 (1 + (1 -.35) (.2438)) = 1.02 Aswath Damodara 48

49 Embraer s Bottom-up Beta Embraer is a aerospace/defese compay. Busiess Value Proportio Ulevered Beta Aerospace/Defese % 0.90 Cash % 0.00 Compay Gross Debt outstadig = 2500 millio Equity = 9000 Tax rate = 33% Levered Beta = 0.74 (1 + (1-.33) (2500/9000)) = 0.88 Aswath Damodara 49

50 Comparable Firms? Ca a ulevered beta estimated usig U.S. aerospace compaies be used to estimate the beta for a Brazilia aerospace compay? q q Yes No What cocers would you have i makig this assumptio? Aswath Damodara 50

51 Dealig with Cash Approach 1: Gross Debt Approach Treat cash as a asset with a beta of zero ad compute the ulevered beta for the firm. Use the gross debt to equity ratio to lever up the beta Approach 2: Net Debt Approach Compute the ulevered beta for oly the o-cash assets Net cash out agaist debt to get a et debt ratio (which ca be egative) Use the et debt to equity ratio to lever up the beta For firms with little default risk, the two approaches will yield roughly the same fial levered beta. The et debt approach will usually yield a slightly higher beta sice it attaches the tax effect to both cash ad debt. Aswath Damodara 51

52 Usig the Net Debt Ratio Approach: Embraer Net Debt Calculatio Gross Debt = 2500 Cash = 2000 Net Debt = 500 Equity = 9000 Ulevered Beta = Ulevered beta of aerospace = 0.90 Levered Beta = 0.90 ( 1 + (1-.33) (500/9000)) = 0.93 Aswath Damodara 52

53 The Cost of Equity: A Recap Preferably, a bottom-up beta, based upo other firms i the busiess, ad firm s ow fiacial leverage Cost of Equity = Riskfree Rate + Beta * (Risk Premium) Has to be i the same currecy as cash flows, ad defied i same terms (real or omial) as the cash flows Historical Premium 1. Mature Equity Market Premium: Average premium eared by stocks over T.Bods i U.S. 2. Coutry risk premium = Coutry Default Spread* ( sequity/scoutry bod) or Implied Premium Based o how equity market is priced today ad a simple valuatio model Aswath Damodara 53

54 Estimatig the Cost of Debt The cost of debt is the rate at which you ca borrow at curretly, It will reflect ot oly your default risk but also the level of iterest rates i the market. The two most widely used approaches to estimatig cost of debt are: Lookig up the yield to maturity o a straight bod outstadig from the firm. The limitatio of this approach is that very few firms have log term straight bods that are liquid ad widely traded Lookig up the ratig for the firm ad estimatig a default spread based upo the ratig. While this approach is more robust, differet bods from the same firm ca have differet ratigs. You have to use a media ratig for the firm Whe i trouble (either because you have o ratigs or multiple ratigs for a firm), estimate a sythetic ratig for your firm ad the cost of debt based upo that ratig. Aswath Damodara 54

55 Estimatig Sythetic Ratigs The ratig for a firm ca be estimated usig the fiacial characteristics of the firm. I its simplest form, the ratig ca be estimated from the iterest coverage ratio Iterest Coverage Ratio = EBIT / Iterest Expeses For Embraer i 2003, the iterest coverage ratio is Iterest Coverage Ratio = 2166/474 = 4.70 Based upo the relatioship betwee iterest coverage ratios ad ratigs, we would estimate a ratig of A for Embraer with a default spread of 1.80% (give the ratig of A) Aswath Damodara 55

56 Iterest Coverage Ratios, Ratigs ad Default Spreads If Coverage Ratio is Estimated Bod Ratig Default Spread(1/99) Default Spread(1/01) > 8.50 AAA 0.20% 0.75% AA 0.50% 1.00% A+ 0.80% 1.50% A 1.00% 1.80% A 1.25% 2.00% BBB 1.50% 2.25% BB 2.00% 3.50% B+ 2.50% 4.75% B 3.25% 6.50% B 4.25% 8.00% CCC 5.00% 10.00% CC 6.00% 11.50% C 7.50% 12.70% < 0.20 D 10.00% 15.00% Aswath Damodara 56

57 Cost of Debt computatios Compaies i coutries with low bod ratigs ad high default risk might bear the burde of coutry default risk, especially if they are smaller or have all of their reveues withi the coutry. Larger compaies that derive a sigificat portio of their reveues i global markets may be less exposed to coutry default risk. I other words, they may be able to borrow at a rate lower tha the govermet. For Embraer, we will assume that oly half of the coutry risk is passed through ito it s cost of debt. Pre-tax Cost of Debt i US $ = US T.Bod rate + l*coutry default spread + Compay Default Spread = 4.50% + 0.5* 7.50% % = 10.05% Aswath Damodara 57

58 Sythetic Ratigs: Some Caveats The relatioship betwee iterest coverage ratios ad ratigs, developed usig US compaies, teds to travel well, as log as we are aalyzig large maufacturig firms i markets with iterest rates close to the US iterest rate They are more problematic whe lookig at smaller compaies i markets with higher iterest rates tha the US. Aswath Damodara 58

59 Weights for the Cost of Capital Computatio The weights used to compute the cost of capital should be the market value weights for debt ad equity. There is a elemet of circularity that is itroduced ito every valuatio by doig this, sice the values that we attach to the firm ad equity at the ed of the aalysis are differet from the values we gave them at the begiig. As a geeral rule, the debt that you should subtract from firm value to arrive at the value of equity should be the same debt that you used to compute the cost of capital. Aswath Damodara 59

60 Estimatig A U.S. Dollar Cost of Capital: Embraer Equity Cost of Equity = $ Riskfree Rate + b *Mature Equity Premium + l * Coutry Equity Premium = 4.5% (4%) (11.25%) = 13.65% (See page 34) Market Value of Equity = 9 billio BR Debt Cost of debt = $ Riskfree Rate + l * Coutry Default Spread + Compay Default Spread = 4.50% + 0.5* 7.50% % = 10.05% (See page 57) Market Value of Gross Debt = 2.5 billio BR Cost of Capital Cost of Capital = % (9/11.5) % (1-.33) (2.5/11.5)) = 12.15% What would you do if you caot estimate lambda? Aswath Damodara 60

61 Covertig a Dollar Cost of Capital ito a omial BR cost of capital Approach 1: Use a BR riskfree rate i all of the calculatios above. For istace, if the BR riskfree rate was 8%, the cost of capital would be computed as follows: Cost of Equity )= 8% (4%) (11.25%) = 17.15% Cost of Debt = 8% + 0.5* 7.50% % = 13.55% (This assumes the peso riskfree rate has o coutry risk premium embedded i it.) Approach 2: Use the differetial iflatio rate to estimate the cost of capital. For istace, if the iflatio rate i BR is 6% ad the iflatio rate i the U.S. is 2% È Cost of capital= (1+ Cost of Capital $ ) 1+ Iflatio BR Í Î 1+ Iflatio $ = (1.06/1.02)-1 =.1655 or 16.55% Aswath Damodara 61

62 Dealig with Hybrids ad Preferred Stock Whe dealig with hybrids (covertible bods, for istace), break the security dow ito debt ad equity ad allocate the amouts accordigly. Thus, if a firm has $ 125 millio i covertible debt outstadig, break the $125 millio ito straight debt ad coversio optio compoets. The coversio optio is equity. Whe dealig with preferred stock, it is better to keep it as a separate compoet. The cost of preferred stock is the preferred divided yield. (As a rule of thumb, if the preferred stock is less tha 5% of the outstadig market value of the firm, lumpig it i with debt will make o sigificat impact o your valuatio). Aswath Damodara 62

63 Recappig the Cost of Capital Cost of borrowig should be based upo (1) sythetic or actual bod ratig (2) default spread Cost of Borrowig = Riskfree rate + Default spread Margial tax rate, reflectig tax beefits of debt Cost of Capital = Cost of Equity (Equity/(Debt + Equity)) + Cost of Borrowig (1-t) (Debt/(Debt + Equity)) Cost of equity based upo bottom-up beta Weights should be market value weights Aswath Damodara 63

64 II. Estimatig Cash Flows DCF Valuatio Aswath Damodara 64

65 Steps i Cash Flow Estimatio Estimate the curret earigs of the firm If lookig at cash flows to equity, look at earigs after iterest expeses - i.e. et icome If lookig at cash flows to the firm, look at operatig earigs after taxes Cosider how much the firm ivested to create future growth If the ivestmet is ot expesed, it will be categorized as capital expeditures. To the extet that depreciatio provides a cash flow, it will cover some of these expeditures. Icreasig workig capital eeds are also ivestmets for future growth If lookig at cash flows to equity, cosider the cash flows from et debt issues (debt issued - debt repaid) Aswath Damodara 65

66 Measurig Cash Flows Cash flows ca be measured to All claimholders i the firm Just Equity Ivestors EBIT (1- tax rate) - ( Capital Expeditures - Depreciatio) - Chage i o-cash workig capital = Free Cash Flow to Firm (FCFF) Net Icome - (Capital Expeditures - Depreciatio) - Chage i o-cash Workig Capital - (Pricipal Repaid - New Debt Issues) - Preferred Divided Divideds + Stock Buybacks Aswath Damodara 66

67 Measurig Cash Flow to the Firm EBIT ( 1 - tax rate) - (Capital Expeditures - Depreciatio) - Chage i Workig Capital = Cash flow to the firm Where are the tax savigs from iterest paymets i this cash flow? Aswath Damodara 67

68 From Reported to Actual Earigs Firm s history Comparable Firms Operatig leases - Covert ito debt - Adjust operatig icome R&D Expeses - Covert ito asset - Adjust operatig icome Normalize Earigs Clease operatig items of - Fiacial Expeses - Capital Expeses - No-recurrig expeses Measurig Earigs Update - Trailig Earigs - Uofficial umbers Aswath Damodara 68

69 I. Update Earigs Whe valuig compaies, we ofte deped upo fiacial statemets for iputs o earigs ad assets. Aual reports are ofte outdated ad ca be updated by usig- Trailig 12-moth data, costructed from quarterly earigs reports. Iformal ad uofficial ews reports, if quarterly reports are uavailable. Updatig makes the most differece for smaller ad more volatile firms, as well as for firms that have udergoe sigificat restructurig. Time saver: To get a trailig 12-moth umber, all you eed is oe 10K ad oe 10Q (example third quarter). Use the Year to date umbers from the 10Q: Trailig 12-moth Reveue = Reveues (i last 10K) - Reveues from first 3 quarters of last year + Reveues from first 3 quarters of this year. Aswath Damodara 69

70 II. Correctig Accoutig Earigs Make sure that there are o fiacial expeses mixed i with operatig expeses Fiacial expese: Ay commitmet that is tax deductible that you have to meet o matter what your operatig results: Failure to meet it leads to loss of cotrol of the busiess. Example: Operatig Leases: While accoutig covetio treats operatig leases as operatig expeses, they are really fiacial expeses ad eed to be reclassified as such. This has o effect o equity earigs but does chage the operatig earigs Make sure that there are o capital expeses mixed i with the operatig expeses Capital expese: Ay expese that is expected to geerate beefits over multiple periods. R & D Adjustmet: Sice R&D is a capital expediture (rather tha a operatig expese), the operatig icome has to be adjusted to reflect its treatmet. Aswath Damodara 70

71 The Magitude of Operatig Leases Operatig Lease expeses as % of Operatig Icome 60.00% 50.00% 40.00% 30.00% 20.00% 10.00% 0.00% Market Apparel Stores Furiture Stores Restaurats Aswath Damodara 71

72 Dealig with Operatig Lease Expeses Operatig Lease Expeses are treated as operatig expeses i computig operatig icome. I reality, operatig lease expeses should be treated as fiacig expeses, with the followig adjustmets to earigs ad capital: Debt Value of Operatig Leases = Preset value of Operatig Lease Commitmets at the pre-tax cost of debt Whe you covert operatig leases ito debt, you also create a asset to couter it of exactly the same value. Adjusted Operatig Earigs Adjusted Operatig Earigs = Operatig Earigs + Operatig Lease Expeses - Depreciatio o Leased Asset As a approximatio, this works: Adjusted Operatig Earigs = Operatig Earigs + Pre-tax cost of Debt * PV of Operatig Leases. Aswath Damodara 72

73 Operatig Leases at The Gap i 2003 The Gap has covetioal debt of about $ 1.97 billio o its balace sheet ad its pre-tax cost of debt is about 6%. Its operatig lease paymets i the 2003 were $978 millio ad its commitmets for the future are below: Year Commitmet (millios) Preset Value (at 6%) 1 $ $ $ $ $ $ $ $ $ $ &7 $ each year $1, Debt Value of leases = $4, (Also value of leased asset) Debt outstadig at The Gap = $1,970 m + $4,397 m = $6,367 m Adjusted Operatig Icome = Stated OI + OL exp this year - Deprec = $1,012 m m m /7 = $1,362 millio (7 year life for assets) Approximate OI = $1,012 m + $ 4397 m (.06) = $1,276 m Aswath Damodara 73

74 The Effects of Capitalizig Operatig Leases Debt : will icrease, leadig to a icrease i debt ratios used i the cost of capital ad levered beta calculatio Operatig icome: will icrease, sice operatig leases will ow be before the imputed iterest o the operatig lease expese Net icome: will be uaffected sice it is after both operatig ad fiacial expeses ayway Retur o Capital will geerally decrease sice the icrease i operatig icome will be proportioately lower tha the icrease i book capital ivested Aswath Damodara 74

75 The Magitude of R&D Expeses R&D as % of Operatig Icome 60.00% 50.00% 40.00% 30.00% 20.00% 10.00% 0.00% Market Petroleum Computers Aswath Damodara 75

76 R&D Expeses: Operatig or Capital Expeses Accoutig stadards require us to cosider R&D as a operatig expese eve though it is desiged to geerate future growth. It is more logical to treat it as capital expeditures. To capitalize R&D, Specify a amortizable life for R&D (2-10 years) Collect past R&D expeses for as log as the amortizable life Sum up the uamortized R&D over the period. (Thus, if the amortizable life is 5 years, the research asset ca be obtaied by addig up 1/5th of the R&D expese from five years ago, 2/5th of the R&D expese from four years ago...: Aswath Damodara 76

77 Capitalizig R&D Expeses: Cisco i 1999 R & D was assumed to have a 5-year life. Year R&D Expese Uamortized portio Amortizatio this year 1999 (curret) $ $ $ $ $17.80 Total $ 3, $ Value of research asset = $ 3,035.4 millio Amortizatio of research asset i 1998 = $ millio Adjustmet to Operatig Icome = $ 1,594 millio millio = 1,109.4 millio Aswath Damodara 77

78 The Effect of Capitalizig R&D Operatig Icome will geerally icrease, though it depeds upo whether R&D is growig or ot. If it is flat, there will be o effect sice the amortizatio will offset the R&D added back. The faster R&D is growig the more operatig icome will be affected. Net icome will icrease proportioately, depedig agai upo how fast R&D is growig Book value of equity (ad capital) will icrease by the capitalized Research asset Capital expeditures will icrease by the amout of R&D; Depreciatio will icrease by the amortizatio of the research asset; For all firms, the et cap ex will icrease by the same amout as the after-tax operatig icome. Aswath Damodara 78

79 III. Oe-Time ad No-recurrig Charges Assume that you are valuig a firm that is reportig a loss of $ 500 millio, due to a oe-time charge of $ 1 billio. What is the earigs you would use i your valuatio? o o A loss of $ 500 millio A profit of $ 500 millio Would your aswer be ay differet if the firm had reported oe-time losses like these oce every five years? o o Yes No Aswath Damodara 79

80 IV. Accoutig Malfeasace. Though all firms may be govered by the same accoutig stadards, the fidelity that they show to these stadards ca vary. More aggressive firms will show higher earigs tha more coservative firms. While you will ot be able to catch outright fraud, you should look for warig sigals i fiacial statemets ad correct for them: Icome from uspecified sources - holdigs i other busiesses that are ot revealed or from special purpose etities. Icome from asset sales or fiacial trasactios (for a o-fiacial firm) Sudde chages i stadard expese items - a big drop i S,G &A or R&D expeses, for istace. Aswath Damodara 80

81 V. Dealig with Negative or Abormally Low Earigs A Framework for Aalyzig Compaies with Negative or Abormally Low Earigs Why are the earigs egative or abormally low? Temporary Problems Cyclicality: Eg. Auto firm i recessio Life Cycle related reasos: Youg firms ad firms with ifrastructure problems Leverage Problems: Eg. A otherwise healthy firm with too much debt. Log-term Operatig Problems: Eg. A firm with sigificat productio or cost problems. Normalize Earigs If firm s size has ot chaged sigificatly over time Average Dollar Earigs (Net Icome if Equity ad EBIT if Firm made by the firm over time If firm s size has chaged over time Use firm s average ROE (if valuig equity) or average ROC (if valuig firm) o curret BV of equity (if ROE) or curret BV of capital (if ROC) Value the firm by doig detailed cash flow forecasts startig with reveues ad reduce or elimiate the problem over time.: (a) If problem is structural: Target for operatig margis of stable firms i the sector. (b) If problem is leverage: Target for a debt ratio that the firm will be comfortable with by ed of period, which could be its ow optimal or the idustry average. (c) If problem is operatig: Target for a idustry-average operatig margi. Aswath Damodara 81

82 What tax rate? o o o o o o The tax rate that you should use i computig the after-tax operatig icome should be The effective tax rate i the fiacial statemets (taxes paid/taxable icome) The tax rate based upo taxes paid ad EBIT (taxes paid/ebit) The margial tax rate for the coutry i which the compay operates The weighted average margial tax rate across the coutries i which the compay operates Noe of the above Ay of the above, as log as you compute your after-tax cost of debt usig the same tax rate Aswath Damodara 82

83 The Right Tax Rate to Use The choice really is betwee the effective ad the margial tax rate. I doig projectios, it is far safer to use the margial tax rate sice the effective tax rate is really a reflectio of the differece betwee the accoutig ad the tax books. By usig the margial tax rate, we ted to uderstate the after-tax operatig icome i the earlier years, but the after-tax tax operatig icome is more accurate i later years If you choose to use the effective tax rate, adjust the tax rate towards the margial tax rate over time. While a argumet ca be made for usig a weighted average margial tax rate, it is safest to use the margial tax rate of the coutry Aswath Damodara 83

84 A Tax Rate for a Moey Losig Firm Assume that you are tryig to estimate the after-tax operatig icome for a firm with $ 1 billio i et operatig losses carried forward. This firm is expected to have operatig icome of $ 500 millio each year for the ext 3 years, ad the margial tax rate o icome for all firms that make moey is 40%. Estimate the after-tax operatig icome each year for the ext 3 years. Year 1 Year 2 Year 3 EBIT Taxes EBIT (1-t) Tax rate Aswath Damodara 84

85 Net Capital Expeditures Net capital expeditures represet the differece betwee capital expeditures ad depreciatio. Depreciatio is a cash iflow that pays for some or a lot (or sometimes all of) the capital expeditures. I geeral, the et capital expeditures will be a fuctio of how fast a firm is growig or expectig to grow. High growth firms will have much higher et capital expeditures tha low growth firms. Assumptios about et capital expeditures ca therefore ever be made idepedetly of assumptios about growth i the future. Aswath Damodara 85

86 Capital expeditures should iclude Research ad developmet expeses, oce they have bee recategorized as capital expeses. The adjusted et cap ex will be Adjusted Net Capital Expeditures = Net Capital Expeditures + Curret year s R&D expeses - Amortizatio of Research Asset Acquisitios of other firms, sice these are like capital expeditures. The adjusted et cap ex will be Adjusted Net Cap Ex = Net Capital Expeditures + Acquisitios of other firms - Amortizatio of such acquisitios Two caveats: 1. Most firms do ot do acquisitios every year. Hece, a ormalized measure of acquisitios (lookig at a average over time) should be used 2. The best place to fid acquisitios is i the statemet of cash flows, usually categorized uder other ivestmet activities Aswath Damodara 86

87 Cisco s Acquisitios: 1999 Acquired Method of Acquisitio Price Paid GeoTel Poolig $1,344 Fibex Poolig $318 Setiet Poolig $103 America Iteret Purchase $58 Summa Four Purchase $129 Clarity Wireless Purchase $153 Selsius Systems Purchase $134 PipeLiks Purchase $118 Amteva Tech Purchase $159 $2,516 Aswath Damodara 87

88 Cisco s Net Capital Expeditures i 1999 Cap Expeditures (from statemet of CF) = $ 584 mil - Depreciatio (from statemet of CF) = $ 486 mil Net Cap Ex (from statemet of CF) = $ 98 mil + R & D expese = $ 1,594 mil - Amortizatio of R&D = $ 485 mil + Acquisitios = $ 2,516 mil Adjusted Net Capital Expeditures = $3,723 mil (Amortizatio was icluded i the depreciatio umber) Aswath Damodara 88

89 Workig Capital Ivestmets I accoutig terms, the workig capital is the differece betwee curret assets (ivetory, cash ad accouts receivable) ad curret liabilities (accouts payables, short term debt ad debt due withi the ext year) A cleaer defiitio of workig capital from a cash flow perspective is the differece betwee o-cash curret assets (ivetory ad accouts receivable) ad o-debt curret liabilities (accouts payable) Ay ivestmet i this measure of workig capital ties up cash. Therefore, ay icreases (decreases) i workig capital will reduce (icrease) cash flows i that period. Whe forecastig future growth, it is importat to forecast the effects of such growth o workig capital eeds, ad buildig these effects ito the cash flows. Aswath Damodara 89

90 Workig Capital: Geeral Propositios Chages i o-cash workig capital from year to year ted to be volatile. A far better estimate of o-cash workig capital eeds, lookig forward, ca be estimated by lookig at o-cash workig capital as a proportio of reveues Some firms have egative o-cash workig capital. Assumig that this will cotiue ito the future will geerate positive cash flows for the firm. While this is ideed feasible for a period of time, it is ot forever. Thus, it is better that o-cash workig capital eeds be set to zero, whe it is egative. Aswath Damodara 90

91 Volatile Workig Capital? Amazo Cisco Motorola Reveues $ 1,640 $12,154 $30,931 No-cash WC % of Reveues % -3.32% 8.23% Chage from last year $ (309) ($700) ($829) Average: last 3 years-15.16% -3.16% 8.91% Average: idustry 8.71% -2.71% 7.04% Assumptio i Valuatio WC as % of Reveue 3.00% 0.00% 8.23% Aswath Damodara 91

92 Divideds ad Cash Flows to Equity I the strictest sese, the oly cash flow that a ivestor will receive from a equity ivestmet i a publicly traded firm is the divided that will be paid o the stock. Actual divideds, however, are set by the maagers of the firm ad may be much lower tha the potetial divideds (that could have bee paid out) maagers are coservative ad try to smooth out divideds maagers like to hold o to cash to meet uforesee future cotigecies ad ivestmet opportuities Whe actual divideds are less tha potetial divideds, usig a model that focuses oly o divideds will uder state the true value of the equity i a firm. Aswath Damodara 92

93 Measurig Potetial Divideds Some aalysts assume that the earigs of a firm represet its potetial divideds. This caot be true for several reasos: Earigs are ot cash flows, sice there are both o-cash reveues ad expeses i the earigs calculatio Eve if earigs were cash flows, a firm that paid its earigs out as divideds would ot be ivestig i ew assets ad thus could ot grow Valuatio models, where earigs are discouted back to the preset, will over estimate the value of the equity i the firm The potetial divideds of a firm are the cash flows left over after the firm has made ay ivestmets it eeds to make to create future growth ad et debt repaymets (debt repaymets - ew debt issues) The commo categorizatio of capital expeditures ito discretioary ad o-discretioary loses its basis whe there is future growth built ito the valuatio. Aswath Damodara 93