Valuation. Aswath Damodaran Aswath Damodaran 1

Transcription

1 Valuatio Aswath Damodara Aswath Damodara 1

2 Some Iitial Thoughts " Oe hudred thousad lemmigs caot be wrog" Graffiti Aswath Damodara 2

3 Miscoceptios about Valuatio Myth 1: A valuatio is a objective search for true value Truth 1.1: All valuatios are biased. The oly questios are how much ad i which directio. Truth 1.2: The directio ad magitude of the bias i your valuatio is directly proportioal to who pays you ad how much you are paid. Myth 2.: A good valuatio provides a precise estimate of value Truth 2.1: There are o precise valuatios Truth 2.2: The payoff to valuatio is greatest whe valuatio is least precise. Myth 3:. The more quatitative a model, the better the valuatio Truth 3.1: Oe s uderstadig of a valuatio model is iversely proportioal to the umber of iputs required for the model. Truth 3.2: Simpler valuatio models do much better tha complex oes. Aswath Damodara 3

4 Approaches to Valuatio Discouted cashflow valuatio, relates the value of a asset to the preset value of expected future cashflows o that asset. Relative valuatio, estimates the value of a asset by lookig at the pricig of 'comparable' assets relative to a commo variable like earigs, cashflows, book value or sales. Cotiget claim valuatio, uses optio pricig models to measure the value of assets that share optio characteristics. Aswath Damodara 4

5 Discouted Cash Flow Valuatio What is it: I discouted cash flow valuatio, the value of a asset is the preset value of the expected cash flows o the asset. Philosophical Basis: Every asset has a itrisic value that ca be estimated, based upo its characteristics i terms of cash flows, growth ad risk. Iformatio Needed: To use discouted cash flow valuatio, you eed to estimate the life of the asset to estimate the cash flows durig the life of the asset to estimate the discout rate to apply to these cash flows to get preset value Market Iefficiecy: Markets are assumed to make mistakes i pricig assets across time, ad are assumed to correct themselves over time, as ew iformatio comes out about assets. Aswath Damodara 5

6 Valuig a Firm 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= 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 6

7 DISCOUNTED CASHFLOW VALUATION 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 7

8 Avg Reivestmet rate = 25.59% Curret Cashflow to Firm EBIT(1-t) : Nt CpX 29 - Chg WC 10 = FCFF 115 Reivestmet Rate = 39/115=25% Tita Cemets: Status Quo Reivestmet Rate 25.59% Expected Growth i EBIT (1-t).2559*.1842= % Retur o Capital 18.42% Stable Growth g = 4.31%; Beta = 1.00; Coutry Premium= 0% Cost of capital = 7.20% ROC= 7.20%; Tax rate=33% Reivestmet Rate=59.85% Termial Value5= 78.4/( ) = 2713 Op. Assets 2,428 + Cash: 81 - Debt Mior. It. 101 =Equity 2,011 -Optios 0 Value/Share EBIT EBIT(1-t) Reivestmet = FCFF Discout at Cost of Capital (WACC) = 8.53% (.782) % (0.218) = 7.43% Term Yr Cost of Equity 8.53% Cost of Debt (4.31%+.5%+.22%)( ) = 3.50% Weights E = 78.2% D = 21.8% Riskfree Rate: Euro riskfree rate = 4.31% + Beta 0.96 X Risk Premium 4.44% Ulevered Beta for Sectors: 0.80 Firm s D/E Ratio: 27.9% Mature risk premium 4% Coutry Equity Prem 0.44% Aswath Damodara 8

9 Discouted Cash Flow Valuatio: High Growth with Negative Earigs Tax Rate - NOLs Curret Reveue EBIT Curret Operatig Margi Sales Turover Ratio Reveue Growth Reivestmet Competitive Advatages Expected Operatig Margi Stable Reveue Growth Stable Growth Stable Operatig Margi Stable Reivestmet Value of Operatig Assets + Cash & No-op Assets = Value of Firm - Value of Debt = Value of Equity - Equity Optios = Value of Equity i Stock FCFF = Reveue* Op Margi (1-t) - Reivestmet 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 9

10 NOL: 500 m Curret Reveue $ 1,117 EBIT -410m Curret Margi: % Sales Turover Ratio: 3.00 Reveue Growth: 42% Reivestmet: Cap ex icludes acquisitios Workig capital is 3% of reveues Competitive Advatages Expected Margi: -> 10.00% Stable Reveue Growth: 6% Stable Growth Stable Operatig Margi: 10.00% Stable ROC=20% Reivest 30% of EBIT(1-t) Termial Value= 1881/( ) =52,148 Value of Op Assets $ 14,910 + Cash $ 26 = Value of Firm $14,936 - Value of Debt $ 349 = Value of Equity $14,587 - Equity Optios $ 2,892 Value per share $ Reveues $2,793 5,585 9,774 14,661 19,059 23,862 28,729 33,211 36,798 39,006 EBIT -$373 -$94 $407 $1,038 $1,628 $2,212 $2,768 $3,261 $3,646 $3,883 EBIT (1-t) -$373 -$94 $407 $871 $1,058 $1,438 $1,799 $2,119 $2,370 $2,524 - Reivestmet $559 $931 $1,396 $1,629 $1,466 $1,601 $1,623 $1,494 $1,196 $736 FCFF -$931 -$1,024 -$989 -$758 -$408 -$163 $177 $625 $1,174 $1, Cost of Equity 12.90% 12.90% 12.90% 12.90% 12.90% 12.42% 12.30% 12.10% 11.70% 10.50% Cost of Debt 8.00% 8.00% 8.00% 8.00% 8.00% 7.80% 7.75% 7.67% 7.50% 7.00% AT cost of debt 8.00% 8.00% 8.00% 6.71% 5.20% 5.07% 5.04% 4.98% 4.88% 4.55% Cost of Capital 12.84% 12.84% 12.84% 12.83% 12.81% 12.13% 11.96% 11.69% 11.15% 9.61% Term. Year $41, % 35.00% $2,688 $ 807 $1,881 Forever Cost of Equity 12.90% Cost of Debt 6.5%+1.5%=8.0% Tax rate = 0% -> 35% Weights Debt= 1.2% -> 15% Riskfree Rate : T. Bod rate = 6.5% + Beta > 1.00 X Risk Premium 4% Amazo.com Jauary 2000 Stock Price = $ 84 Iteret/ Retail Operatig Leverage Curret D/E: 1.21% Base Equity Premium Coutry Risk Premium Aswath Damodara 10

11 I. Discout Rates:Cost of Equity 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* ( σequity/σcoutry bod) or Implied Premium Based o how equity market is priced today ad a simple valuatio model Aswath Damodara 11

12 A Simple Test You are valuig a Greek compay i Euros for a US istitutioal ivestor ad are attemptig to estimate a risk free rate to use i the aalysis. The risk free rate that you should use is o The iterest rate o a US $ deomiated treasury bod (4.25%) o The iterest rate o a Euro-deomiated Greek govermet bod (4.52%) o The iterest rate o a Euro-deomiated bod issued by the Germa govermet (4.31%) Aswath Damodara 12

13 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 % 6.54% 5.99% 4.82% % 4.70% 4.85% 3.82% % 4.87% 6.68% 3.57% Aswath Damodara 13

14 Assessig Coutry Risk Usig Currecy Ratigs: Wester Europe Coutry Ratig Default Spread over Germa Euro rate(i bp) Austria Aaa 9 Belgium Aaa 12 Frace Aaa 6 Germay Aaa 0 Greece A1 22 Irelad Aaa 3 Italy Aa2 22 Netherlads Aaa 9 Portugal Aa2 14 Spai Aaa 6 Aswath Damodara 14

15 Assessig Coutry Risk usig Ratigs: The Rest of Europe Coutry Ratig Default Spread Croatia Baa3 145 Cyprus A2 90 Czech Republic Baa1 120 Hugary A3 95 Latvia Baa2 130 Lithuaia Ba1 250 Moldova B3 650 Polad Baa1 120 Romaia B3 650 Russia B2 550 Slovakia Ba1 250 Sloveia A2 90 Turkey B1 450 Aswath Damodara 15

16 Usig Coutry Ratigs to Estimate Equity Spreads 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 Greek ASE(Equity) = 18% Stadard Deviatio i Greek Euro Bod = 9% Adjusted Equity Spread = 0.22% (18/9) = 0.44% Aswath Damodara 16

17 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 (US 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 (US premium + Coutry Spread) 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+ β (US premium) + λ (Coutry Spread) Aswath Damodara 17

18 Estimatig Compay Exposure to Coutry Risk Differet compaies should be exposed to differet degrees to coutry risk. For istace, a Greek firm that geerates the bulk of its reveues i the rest of Wester Europe should be less exposed to coutry risk tha oe that geerates all its busiess withi Greece. The factor λ measures the relative exposure of a firm to coutry risk. Oe simplistic solutio would be to do the followig: λ = % 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 λ = 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 18

19 Estimatig E(Retur) for Tita Cemets Assume that the beta for Tita Cemets is 0.95, ad that the riskfree rate used is 4.31%. Also assume that the historical premium for the US (4.82%) is a reasoable estimate of a mature market risk premium. Approach 1: Assume that every compay i the coutry is equally exposed to coutry risk. I this case, E(Retur) = 4.31% % (4.82%) = 9.33% Approach 2: Assume that a compay s exposure to coutry risk is similar to its exposure to other market risk. E(Retur) = 4.31% (4.82%+ 0.44%) = 9.31% 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)= 4.31% (4.82%) (0.44%) (3%) = 9.29% Tita is less exposed to Greek coutry risk tha the typical Greek firm sice it gets about 40% of its reveues i Greece; the average for Greek firms is 70%. I 2003, though, Tita got about 5% of it s reveues from the Balka states. Aswath Damodara 19

20 Implied Equity Premium for the S&P 500: Jauary 1, 2004 We ca use the iformatio i stock prices to back out how risk averse the market is ad how much of a risk premium it is demadig. I 2003, divideds & stock buybacks were 2.81% of the idex, geeratig i cashflows Aalysts expect earigs to grow 9.5% a year for the ext 5 years as the ecoomy comes out of a recessio After year 5, we will assume that earigs o the idex will grow at 4.25%, the same rate as the etire ecoomy Jauary 1, 2004 S&P 500 is at If you pay the curret level of the idex, you ca expect to make a retur of 7.94% o stocks (which is obtaied by solvig for r i the followig equatio) = (1+ r) (1+ r) (1+ r) (1+ r) (1+ r) (1.0425) (r.0425)(1+ r) 5 Implied Equity risk premium = Expected retur o stocks - Treasury bod rate = 7.94% % = 3.69% Aswath Damodara 20

21 Implied Premiums i the US Aswath Damodara 21

22 Implied Premiums: From Bubble to Bear Market Jauary 2000 to December 2002 Aswath Damodara 22

23 Choosig a Equity Risk Premium The historical risk premium of 4.82% for the Uited States is too high a premium to use i valuatio. It is much higher tha the actual implied equity risk premium i the market The curret implied equity risk premium requires us to assume that the market is correctly priced today. (If I were required to be market eutral, this is the premium I would use) The average implied equity risk premium betwee i the Uited States is about 4%. We will use this as the premium for a mature equity market. Aswath Damodara 23

24 Implied Premium for Greek Market: May 14, 2004 Level of the Idex = 2467 Divideds o the Idex = 3.18% of 2467 Other parameters Riskfree Rate = 4.31% (Euros) Expected Growth (i Euros) Next 5 years = 9% (Used expected growth rate i Earigs) After year 5 = 4.31% Solvig for the expected retur: Expected retur o Equity = 8.38% Implied Equity premium = 8.38% % = 4.07% Effect o valuatio Tita s value with historical premium (4%) + coutry (.44%) : Euros/share Tia s value with implied premium: Euros per share Aswath Damodara 24

25 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 25

26 Beta Estimatio: Amazo Aswath Damodara 26

27 Beta Estimatio for Tita Cemet: The Idex Effect Aswath Damodara 27

28 Determiats of Betas Beta of Equity Nature of product or service offered by compay: Other thigs remaiig equal, the more discretioary the product or service, the higher the beta. Beta of Firm Operatig Leverage (Fixed Costs as percet of total costs): Other thigs remaiig equal the greater the proportio of the costs that are fixed, the higher the beta of the compay. Fiacial Leverage: Other thigs remaiig equal, the greater the proportio of capital that a firm raises from debt,the higher its equity beta will be Implciatios Highly levered firms should have highe betas tha firms with less debt. Implicatios 1. Cyclical compaies should have higher betas tha ocyclical compaies. 2. Luxury goods firms should have higher betas tha basic goods. 3. High priced goods/service firms should have higher betas tha low prices goods/services firms. 4. Growth firms should have higher betas. Implicatios 1. Firms with high ifrastructure eeds ad rigid cost structures shoudl have higher betas tha firms with flexible cost structures. 2. Smaller firms should have higher betas tha larger firms. 3. Youg firms should have Aswath Damodara 28

29 I a perfect world we would estimate the beta of a firm by doig the followig Start with the beta of the busiess that the firm is i Adjust the busiess beta for the operatig leverage of the firm to arrive at the ulevered beta for the firm. Use the fiacial leverage of the firm to estimate the equity beta for the firm Levered Beta = Ulevered Beta ( 1 + (1- tax rate) (Debt/Equity)) Aswath Damodara 29

30 Bottom-up Betas Step 1: Fid the busiess or busiesses that your firm operates i. Step 2: Fid publicly traded firms i each of these busiesses ad obtai their regressio betas. Compute the simple average across these regressio betas to arrive at a average beta for these publicly traded firms. Ulever this average beta usig the average debt to equity ratio across the publicly traded firms i the sample. Ulevered beta for busiess = Average beta across publicly traded firms/ (1 + (1- t) (Average D/E ratio across firms)) Possible Refiemets If you ca, adjust this beta for differeces betwee your firm ad the comparable firms o operatig leverage ad product characteristics. Step 3: Estimate how much value your firm derives from each of the differet busiesses it is i. While reveues or operatig icome are ofte used as weights, it is better to try to estimate the value of each busiess. Step 4: Compute a weighted average of the ulevered betas of the differet busiesses (from step 2) usig the weights from step 3. Bottom-up Ulevered beta for your firm = Weighted average of the ulevered betas of the idividual busiess If you expect the busiess mix of your firm to chage over time, you ca chage the weights o a year-to-year basis. Step 5: Compute a levered beta (equity beta) for your firm, usig the market debt to equity ratio for your firm. Levered bottom-up beta = Ulevered beta (1+ (1-t) (Debt/Equity)) If you expect your debt to equity ratio to chage over time, the levered beta will chage over time. Aswath Damodara 30

31 Tita s Bottom-up Beta Busiess Ulevered D/E Ratio Levered beta Proportio of Value Cemet % % Levered Beta = Ulevered Beta ( 1 + (1- tax rate) (D/E Ratio) = 0.80 ( 1 + ( ) (.279)) = 0.95 A Hypothetical sceario: Assume that Tita had bee i two busiesses- cemet ad costructio. You could estimate a beta for the combied firm as follows Comparable firms Busiess Reveues Value/Sales Ulevered beta Value Weight Weight*Beta Cemet %.67*.80 Costruct %.33*1.20 Firm =.933 Aswath Damodara 31

32 Amazo s Bottom-up Beta Ulevered beta for firms i iteret retailig = 1.60 Ulevered beta for firms i specialty retailig = 1.00 Amazo is a specialty retailer, but its risk curretly seems to be determied by the fact that it is a olie retailer. Hece we will use the beta of iteret compaies to begi the valuatio By the fifth year, we are estimatig substatial reveues for Amazo ad we move the beta towards to beta of the retailig busiess. Aswath Damodara 32

33 From Cost of Equity to 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 33

34 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 Tita s iterest coverage ratio, we used the iterest expeses ad EBIT from Iterest Coverage Ratio = 222/ 19.4 = Amazo.com has egative operatig icome; this yields a egative iterest coverage ratio, which should suggest a low ratig. We computed a average iterest coverage ratio of 2.82 over the ext 5 years. Aswath Damodara 34

35 Iterest Coverage Ratios, Ratigs ad Default Spreads If Iterest Coverage Ratio is Estimated Bod Ratig Default Spread(1/00) Default Spread(1/04) > 8.50 (>12.50) AAA 0.20% 0.35% ( ) AA 0.50% 0.50% ( ) A+ 0.80% 0.70% (6-7.5) A 1.00% 0.85% (4.5-6) A 1.25% 1.00% ( ) BBB 1.50% 1.50% (3.5-4) BB+ 1.75% 2.00% ((3-3.5) BB 2.00% 2.50% (2.5-3) B+ 2.50% 3.25% (2-2.5) B 3.25% 4.00% (1.5-2) B 4.25% 6.00% ( ) CCC 5.00% 8.00% ( ) CC 6.00% 10.00% ( ) C 7.50% 12.00% < 0.20 (<0.5) D 10.00% 20.00% For Tita, I used the iterest coverage ratio table for smaller/riskier firms (the umbers i brackets) which yields a lower ratig for the same iterest coverage ratio. Aswath Damodara 35

36 Estimatig the cost of debt for a firm The sythetic ratig for Tita Cemet is AA. Usig the 2004 default spread of 0.50%, we estimate a cost of debt of 5.03% (usig a riskfree rate of 4.31% ad addig i the coutry default spread of 0.22%): Cost of debt = Riskfree rate + Greek default spread + Compay default spread =4.31% %+ 0.50% = 5.03% The sythetic ratig for Amazo.com i 2000 was BBB. The default spread for BBB rated bod was 1.50% i 2000 ad the treasury bod rate was 6.5%. Pre-tax cost of debt = Riskfree Rate + Default spread = 6.50% % = 8.00% The firm is payig o taxes curretly. As the firm s tax rate chages ad its cost of debt chages, the after tax cost of debt will chage as well Pre-tax 8.00% 8.00% 8.00% 8.00% 8.00% 7.80% 7.75% 7.67% 7.50% 7.00% Tax rate 0% 0% 0% 16.13% 35% 35% 35% 35% 35% 35% After-tax 8.00% 8.00% 8.00% 6.71% 5.20% 5.07% 5.04% 4.98% 4.88% 4.55% Aswath Damodara 36

37 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 37

38 Estimatig Cost of Capital: Amazo.com Equity Cost of Equity = 6.50% (4.00%) = 12.90% Market Value of Equity = $ 84/share* mil shs = $ 28,626 mil (98.8%) Debt Cost of debt = 6.50% % (default spread) = 8.00% Market Value of Debt = $ 349 mil (1.2%) Cost of Capital Cost of Capital = 12.9 % (.988) % (1-0) (.012)) = 12.84% Aswath Damodara 38

39 Estimatig Cost of Capital: Tita Cemets Equity Cost of Equity = 4.31% (4%+ 0.44%) = 8.53% Market Value of Equity =1423 millio Euros (78.2%) Debt Cost of debt = 4.31% % %= 5.03% Market Value of Debt = 396 millio Euros (21.8%) Cost of Capital Cost of Capital = 8.53 % (.782) % ( ) (0.218)) = 7.43% The book value of equity at Tita Cemet is 498 millio Euros The book value of debt at Tita Cemet is 399 millio; Iterest expese is 19 mil; Average maturity of debt = 4 years Estimated market value of debt = 19 millio (PV of auity, 4 years, 5.03%) + $ 399 millio/ = 396 millio Euros Aswath Damodara 39

40 II. Estimatig Cash Flows to Firm Operatig leases - Covert ito debt - Adjust operatig icome R&D Expeses - Covert ito asset - Adjust operatig icome Update - Trailig Earigs - Uofficial umbers Normalize - History - Idustry Clease operatig items of - Fiacial Expeses - Capital Expeses - No-recurrig expeses Tax rate - ca be effective for ear future, but move to margial - reflect et operatig losses Iclude - R&D - Acquisitios Earigs before iterest ad taxes - Tax rate * EBIT = EBIT ( 1- tax rate) - (Capital Expeditures - Depreciatio) - Chage i o-cash workig capital = Free Cash flow to the firm (FCFF) Defied as No-cash CA - No-debt CL Aswath Damodara 40

41 The Importace of Updatig The operatig icome ad reveue that we use i valuatio should be updated umbers. Oe of the problems with usig fiacial statemets is that they are dated. As a geeral rule, it is better to use 12-moth trailig estimates for earigs ad reveues tha umbers for the most recet fiacial year. This rule becomes eve more critical whe valuig compaies that are evolvig ad growig rapidly. Last 10-K Trailig 12-moth Reveues $ 610 millio $1,117 millio EBIT - $125 millio - $ 410 millio The valuatio of Tita is dated because there have bee o fiacial statemets released sice the last 10K. Aswath Damodara 41

42 Normalizig Earigs: Amazo Year Reveues Operatig Margi EBIT Tr12m $1, % -$410 1 $2, % -$373 2 $5, % -$94 3 $9, % $407 4 $14, % $1,038 5 $19, % $1,628 6 $23, % $2,212 7 $28, % $2,768 8 $33, % $3,261 9 $36, % $3, $39, % $3,883 TY(11) $41, % $4,135 Idustry Average Aswath Damodara 42

43 Operatig Leases at The Home Depot i 1998 The pre-tax cost of debt at the Home Depot is 6.25% Yr Operatig Lease Expese Preset Value 1 $ 294 $ $ 291 $ $ 264 $ $ 245 $ $ 236 $ $ 270 $ 1,450 (PV of 10-yr auity) Preset Value of Operatig Leases =$ 2,571 Debt outstadig at the Home Depot = $1,205 + $2,571 = $3,776 mil (The Home Depot has other debt outstadig of $1,205 millio) Adjusted Operatig Icome = $2, ,571 (.0625) = $2,177 mil Aswath Damodara 43

44 Capitalizig R&D Expeses: Shire Pharmaceuticals 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...: R & D was assumed to have a 5-year life. Year R&D Uamortized R&D Amortizatio Curret Value of research asset = Amortizatio of research asset i 2000 = Adjustmet to Operatig Icome = + R&D - Amortizatio of R&D Adjusted Operatig Icome = = Aswath Damodara 44

45 The Effect of Net Operatig Losses: Amazo.com s Tax Rate Year EBIT -$373 -$94 $407 $1,038 $1,628 Taxes $0 $0 $0 $167 $570 EBIT(1-t) -$373 -$94 $407 $871 $1,058 Tax rate 0% 0% 0% 16.13% 35% NOL $500 $873 $967 $560 $0 After year 5, the tax rate becomes 35%. Aswath Damodara 45

46 Estimatig Actual FCFF: Tita Cemet EBIT = 222 millio Euros Tax rate = 30.44% Net Capital expeditures = Cap Ex - Depreciatio = = 28.6 millio Chage i Workig Capital = millio Estimatig FCFF Curret EBIT * (1 - tax rate) = 222 ( ) = Millio - (Capital Spedig - Depreciatio) Chage i Workig Capital 10.2 Curret FCFF Millio Euros Aswath Damodara 46

47 Estimatig FCFF: Amazo.com EBIT (Trailig 1999) = -$ 410 millio Tax rate used = 0% (Assumed Effective = Margial) Capital spedig (Trailig 1999) = $ 243 millio Depreciatio (Trailig 1999) = $ 31 millio No-cash Workig capital Chage (1999) = - 80 millio Estimatig FCFF (1999) Curret EBIT * (1 - tax rate) = (1-0) = - $410 millio - (Capital Spedig - Depreciatio) = $212 millio - Chage i Workig Capital = -$ 80 millio Curret FCFF = - $542 millio Aswath Damodara 47

48 IV. Expected Growth i EBIT ad Fudametals Reivestmet Rate ad Retur o Capital g EBIT = (Net Capital Expeditures + Chage i WC)/EBIT(1-t) * ROC = Reivestmet Rate * ROC Propositio: No firm ca expect its operatig icome to grow over time without reivestig some of the operatig icome i et capital expeditures ad/or workig capital. Propositio: The et capital expediture eeds of a firm, for a give growth rate, should be iversely proportioal to the quality of its ivestmets. Aswath Damodara 48

49 Normalizig Reivestmet: Tita Cemets Total Cp Ex $ $50.54 $81.00 $ $ $ Depreciatio $89.53 $39.26 $40.87 $80.94 $73.70 $ EBIT $ $ $ $ $ EBIT(1-t) $85.25 $ $ $ $ $ Net Cap Ex as % o 55.28% 9.96% 30.95% 23.19% 18.52% 25.64% Reveues No-cashh Curre $ No-debt curret l No-cash WC as % of reveues 23.00% 18.50% 16.87% 15.28% 14.20% 16.88% Aswath Damodara 49

50 Expected Growth Estimate: Tita Cemet Normalized Chage i workig capital = (Workig capital as percet of reveues) * Chage i reveues i 2003 =.1688 ( ) = 0 mil Euros Normalized Net Cap Ex = Net Cap ex as % of EBIT(1-t) * EBIT (1-t) i 2001 =.2564*(222 ( )) = millio Euros Normalized reivestmet rate = 39.59/(222( )) = 25.59% Retur o capital = 222 ( )/ ( ) = 18.42% The book value of debt ad equity from last year was used. Expected growth rate =.2559*.1842 = 4.71% Aswath Damodara 50

51 Reveue Growth ad Operatig Margis With egative operatig icome ad a egative retur o capital, the fudametal growth equatio is of little use for Amazo.com For Amazo, the effect of reivestmet shows up i reveue growth rates ad chages i expected operatig margis: Expected Reveue Growth i $ = Reivestmet (i $ terms) * (Sales/ Capital) The effect o expected margis is more subtle. Amazo s reivestmets (especially i acquisitios) may help create barriers to etry ad other competitive advatages that will ultimately traslate ito high operatig margis ad high profits. Aswath Damodara 51

52 Growth i Reveues, Earigs ad Reivestmet: Amazo Year Reveue Chg i Reivestmet Chg Rev/ Chg Reivestmet ROC Growth Reveue % $1,676 $ % % $2,793 $ % % $4,189 $1, % % $4,887 $1, % % $4,398 $1, % % $4,803 $1, % % $4,868 $1, % % $4,482 $1, % % $3,587 $1, % % $2,208 $ % Assume that firm ca ear high returs because of established ecoomies of scale. Aswath Damodara 52

53 V. Growth Patters A key assumptio i all discouted cash flow models is the period of high growth, ad the patter of growth durig that period. I geeral, we ca make oe of three assumptios: there is o high growth, i which case the firm is already i stable growth there will be high growth for a period, at the ed of which the growth rate will drop to the stable growth rate (2-stage) there will be high growth for a period, at the ed of which the growth rate will declie gradually to a stable growth rate(3-stage) Stable Growth 2-Stage Growth 3-Stage Growth Aswath Damodara 53

54 Determiats of Growth Patters Size of the firm Success usually makes a firm larger. As firms become larger, it becomes much more difficult for them to maitai high growth rates Curret growth rate While past growth is ot always a reliable idicator of future growth, there is a correlatio betwee curret growth ad future growth. Thus, a firm growig at 30% curretly probably has higher growth ad a loger expected growth period tha oe growig 10% a year ow. Barriers to etry ad differetial advatages Ultimately, high growth comes from high project returs, which, i tur, comes from barriers to etry ad differetial advatages. The questio of how log growth will last ad how high it will be ca therefore be framed as a questio about what the barriers to etry are, how log they will stay up ad how strog they will remai. Aswath Damodara 54

55 Stable Growth Characteristics I stable growth, firms should have the characteristics of other stable growth firms. I particular, The risk of the firm, as measured by beta ad ratigs, should reflect that of a stable growth firm. Beta should move towards oe The cost of debt should reflect the safety of stable firms (BBB or higher) The debt ratio of the firm might icrease to reflect the larger ad more stable earigs of these firms. The debt ratio of the firm might moved to the optimal or a idustry average If the maagers of the firm are deeply averse to debt, this may ever happe The reivestmet rate of the firm should reflect the expected growth rate ad the firm s retur o capital Reivestmet Rate = Expected Growth Rate / Retur o Capital Aswath Damodara 55

56 Tita ad Amazo.com: Stable Growth Iputs High Growth Stable Growth Tita Cemet Beta Debt Ratio 21.8% 21.8% Retur o Capital 18.42% 7.20% Cost of Capital 7.43% 7.20% Expected Growth Rate 4.71% 4.31% Reivestmet Rate 25.59% 4.31%/7.20% = 59.85% Amazo.com Beta Debt Ratio 1.20% 15% Retur o Capital Negative 20% Expected Growth Rate NMF 6% Reivestmet Rate >100% 6%/20% = 30% Aswath Damodara 56

57 Dealig with Cash ad Marketable Securities The simplest ad most direct way of dealig with cash ad marketable securities is to keep them out of the valuatio - the cash flows should be before iterest icome from cash ad securities, ad the discout rate should ot be cotamiated by the iclusio of cash. (Use betas of the operatig assets aloe to estimate the cost of equity). Oce the firm has bee valued, add back the value of cash ad marketable securities. If you have a particularly icompetet maagemet, with a history of overpayig o acquisitios, markets may discout the value of this cash. Aswath Damodara 57

58 Dealig with Cross Holdigs Whe the holdig is a majority, active stake, the value that we obtai from the cash flows icludes the share held by outsiders. While their holdig is measured i the balace sheet as a miority iterest, it is at book value. To get the correct value, we eed to subtract out the estimated market value of the miority iterests from the firm value. Whe the holdig is a miority, passive iterest, the problem is a differet oe. The firm shows o its icome statemet oly the share of divideds it receives o the holdig. Usig oly this icome will uderstate the value of the holdigs. I fact, we have to value the subsidiary as a separate etity to get a measure of the market value of this holdig. Propositio 1: It is almost impossible to correctly value firms with miority, passive iterests i a large umber of private subsidiaries. Aswath Damodara 58

59 Tita s Cash ad Cross Holdigs Tita has a majority iterest i aother compay ad the fiacial statemets of that compay are cosolidated with those of Tita. The miority iterests (represetig the equity i the subsidiary that does ot belog to Tita) are show o the balace sheet at millio Euros. Estimated market value of miority iterests = Book value of miority iterest * P/BV of sector that subsidiary belogs to = * 1.93 = millio Preset Value of FCFF i high growth phase = Preset Value of Termial Value of Firm = 1, =Value of operatig assets of the firm = 2, Value of Cash, Marketable Securities & No-operatig assets = = Value of Firm = 2, Market Value of outstadig debt = Value of Miority Iterests i Cosolidated Compay = = Market Value of Equity = 2, / Number of shares outstadig /38.18 = Market Value of Equity/share = Aswath Damodara 59

60 Amazo: Estimatig the Value of Equity Optios Details of optios outstadig Average strike price of optios outstadig = $ Average maturity of optios outstadig = 8.4 years Stadard deviatio i l(stock price) = 50.00% Aualized divided yield o stock = 0.00% Treasury bod rate = 6.50% Number of optios outstadig = 38 millio Number of shares outstadig = millio Value of optios outstadig (usig dilutio-adjusted Black-Scholes model) Value of equity optios = $ 2,892 millio Aswath Damodara 60

61 NOL: 500 m Curret Reveue $ 1,117 EBIT -410m Curret Margi: % Sales Turover Ratio: 3.00 Reveue Growth: 42% Reivestmet: Cap ex icludes acquisitios Workig capital is 3% of reveues Competitive Advatages Expected Margi: -> 10.00% Stable Reveue Growth: 6% Stable Growth Stable Operatig Margi: 10.00% Stable ROC=20% Reivest 30% of EBIT(1-t) Termial Value= 1881/( ) =52,148 Value of Op Assets $ 14,910 + Cash $ 26 = Value of Firm $14,936 - Value of Debt $ 349 = Value of Equity $14,587 - Equity Optios $ 2,892 Value per share $ Reveues $2,793 5,585 9,774 14,661 19,059 23,862 28,729 33,211 36,798 39,006 EBIT -$373 -$94 $407 $1,038 $1,628 $2,212 $2,768 $3,261 $3,646 $3,883 EBIT (1-t) -$373 -$94 $407 $871 $1,058 $1,438 $1,799 $2,119 $2,370 $2,524 - Reivestmet $559 $931 $1,396 $1,629 $1,466 $1,601 $1,623 $1,494 $1,196 $736 FCFF -$931 -$1,024 -$989 -$758 -$408 -$163 $177 $625 $1,174 $1, Cost of Equity 12.90% 12.90% 12.90% 12.90% 12.90% 12.42% 12.30% 12.10% 11.70% 10.50% Cost of Debt 8.00% 8.00% 8.00% 8.00% 8.00% 7.80% 7.75% 7.67% 7.50% 7.00% AT cost of debt 8.00% 8.00% 8.00% 6.71% 5.20% 5.07% 5.04% 4.98% 4.88% 4.55% Cost of Capital 12.84% 12.84% 12.84% 12.83% 12.81% 12.13% 11.96% 11.69% 11.15% 9.61% Term. Year $41, % 35.00% $2,688 $ 807 $1,881 Forever Cost of Equity 12.90% Cost of Debt 6.5%+1.5%=8.0% Tax rate = 0% -> 35% Weights Debt= 1.2% -> 15% Riskfree Rate : T. Bod rate = 6.5% + Beta > 1.00 X Risk Premium 4% Amazo.com Jauary 2000 Stock Price = $ 84 Iteret/ Retail Operatig Leverage Curret D/E: 1.21% Base Equity Premium Coutry Risk Premium Aswath Damodara 61

62 Amazo.com: Break Eve at $84? 6% 8% 10% 12% 14% 30% $ (1.94) $ 2.95 $ 7.84 $ $ % $ 1.41 $ 8.37 $ $ $ % $ 6.10 $ $ $ $ % $ $ $ $ $ % $ $ $ $ $ % $ $ $ $ $ % $ $ $ $ $ Aswath Damodara 62

63 NOL: 1,289 m Curret Reveue $ 2,465 EBIT -853m Curret Margi: % Sales Turover Ratio: 3.02 Reveue Growth: 25.41% Reivestmet: Cap ex icludes acquisitios Workig capital is 3% of reveues Competitive Advatages Expected Margi: -> 9.32% Stable Reveue Growth: 5% Stable Growth Stable Operatig Margi: 9.32% Termial Value= 1064/( ) =$ 28,310 Stable ROC=16.94% Reivest 29.5% of EBIT(1-t) Value of Op Assets $ 7,967 + Cash & No-op $ 1,263 = Value of Firm $ 9,230 - Value of Debt $ 1,890 = Value of Equity $ 7,340 - Equity Optios $ 748 Value per share $ Reveues $4,314 $6,471 $9,059 $11,777 $14,132 $16,534 $18,849 $20,922 $22,596 $23,726 $24,912 EBIT -$703 -$364 $54 $499 $898 $1,255 $1,566 $1,827 $2,028 $2,164 $2,322 EBIT(1-t) -$703 -$364 $54 $499 $898 $1,133 $1,018 $1,187 $1,318 $1,406 $1,509 - Reivestmet $612 $714 $857 $900 $780 $796 $766 $687 $554 $374 $445 FCFF -$1,315 -$1,078 -$803 -$401 $118 $337 $252 $501 $764 $1,032 $1, Debt Ratio 27.27% 27.27% 27.27% 27.27% 27.27% 24.81% 24.20% 23.18% 21.13% 15.00% Beta Cost of Equity 13.81% 13.81% 13.81% 13.81% 13.81% 12.95% 12.09% 11.22% 10.36% 9.50% AT cost of debt 10.00% 10.00% 10.00% 10.00% 9.06% 6.11% 6.01% 5.85% 5.53% 4.55% Cost of Capital 12.77% 12.77% 12.77% 12.77% 12.52% 11.25% 10.62% 9.98% 9.34% 8.76% Term. Year $24,912 $2,322 $1,509 $ 445 $1,064 Forever Cost of Equity 13.81% Cost of Debt 5.1%+4.75%= 9.85% Tax rate = 0% -> 35% Weights Debt= 27.38% -> 15% Riskfree Rate : T. Bod rate = 5.1% + Beta 2.18-> 1.10 X Risk Premium 4% Amazo.com Jauary 2001 Stock price = $14 Iteret/ Retail Operatig Leverage Curret D/E: 37.5% Base Equity Premium Coutry Risk Premium Aswath Damodara 63

64 Avg Reivestmet rate = 25.59% Curret Cashflow to Firm EBIT(1-t) : Nt CpX 29 - Chg WC 10 = FCFF 115 Reivestmet Rate = 39/115=25% Tita Cemets: Status Quo Reivestmet Rate 25.59% Expected Growth i EBIT (1-t).2559*.1842= % Retur o Capital 18.42% Stable Growth g = 4.31%; Beta = 1.00; Coutry Premium= 0% Cost of capital = 7.20% ROC= 7.20%; Tax rate=33% Reivestmet Rate=59.85% Termial Value5= 78.4/( ) = 2713 Op. Assets 2,428 + Cash: 81 - Debt Mior. It. 101 =Equity 2,011 -Optios 0 Value/Share EBIT EBIT(1-t) Reivestmet = FCFF Discout at Cost of Capital (WACC) = 8.53% (.782) % (0.218) = 7.43% Term Yr Cost of Equity 8.53% Cost of Debt (4.31%+.5%+.22%)( ) = 3.50% Weights E = 78.2% D = 21.8% Riskfree Rate: Euro riskfree rate = 4.31% + Beta 0.96 X Risk Premium 4.44% Ulevered Beta for Sectors: 0.80 Firm s D/E Ratio: 27.9% Mature risk premium 4% Coutry Equity Prem 0.44% Aswath Damodara 64

65 Value Ehacemet: Back to Basics Aswath Damodara Aswath Damodara 65

66 Price Ehacemet versus Value Ehacemet Aswath Damodara 66

67 The Paths to Value Creatio Usig the DCF framework, there are four basic ways i which the value of a firm ca be ehaced: The cash flows from existig assets to the firm ca be icreased, by either icreasig after-tax earigs from assets i place or reducig reivestmet eeds (et capital expeditures or workig capital) The expected growth rate i these cash flows ca be icreased by either Icreasig the rate of reivestmet i the firm Improvig the retur o capital o those reivestmets The legth of the high growth period ca be exteded to allow for more years of high growth. The cost of capital ca be reduced by Reducig the operatig risk i ivestmets/assets Chagig the fiacial mix Chagig the fiacig compositio Aswath Damodara 67

68 A Basic Propositio For a actio to affect the value of the firm, it has to Affect curret cash flows (or) Affect future growth (or) Affect the legth of the high growth period (or) Affect the discout rate (cost of capital) Propositio 1: Actios that do ot affect curret cash flows, future growth, the legth of the high growth period or the discout rate caot affect value. Aswath Damodara 68

69 Value-Neutral Actios Stock splits ad stock divideds chage the umber of uits of equity i a firm, but caot affect firm value sice they do ot affect cash flows, growth or risk. Accoutig decisios that affect reported earigs but ot cash flows should have o effect o value. Chagig ivetory valuatio methods from FIFO to LIFO or vice versa i fiacial reports but ot for tax purposes Chagig the depreciatio method used i fiacial reports (but ot the tax books) from accelerated to straight lie depreciatio Major o-cash restructurig charges that reduce reported earigs but are ot tax deductible Usig poolig istead of purchase i acquisitios caot chage the value of a target firm. Decisios that create ew securities o the existig assets of the firm (without alterig the fiacial mix) such as trackig stock caot create value, though they might affect perceptios ad hece the price. Aswath Damodara 69

70 I. Ways of Icreasig Cash Flows from Assets i Place More efficiet operatios ad cost cutttig: Higher Margis Divest assets that have egative EBIT Reduce tax rate - movig icome to lower tax locales - trasfer pricig - risk maagemet Reveues * Operatig Margi = EBIT - Tax Rate * EBIT = EBIT (1-t) + Depreciatio - Capital Expeditures - Chg i Workig Capital = FCFF Live off past overivestmet Better ivetory maagemet ad tighter credit policies Aswath Damodara 70

71 II. Value Ehacemet through Growth Reivest more i projects Icrease operatig margis Reivestmet Rate * Retur o Capital = Expected Growth Rate Do acquisitios Icrease capital turover ratio Aswath Damodara 71

72 III. Buildig Competitive Advatages: Icrease legth of the growth period Icrease legth of growth period Build o existig competitive advatages Fid ew competitive advatages Brad ame Legal Protectio Switchig Costs Cost advatages Aswath Damodara 72

73 3.1: The Brad Name Advatage Some firms are able to sustai above-ormal returs ad growth because they have well-recogized brad ames that allow them to charge higher prices tha their competitors ad/or sell more tha their competitors. Firms that are able to improve their brad ame value over time ca icrease both their growth rate ad the period over which they ca expect to grow at rates above the stable growth rate, thus icreasig value. Aswath Damodara 73

74 Illustratio: Valuig a brad ame: Coca Cola Coca Cola Geeric Cola Compay AT Operatig Margi 18.56% 7.50% Sales/BV of Capital ROC 31.02% 12.53% Reivestmet Rate 65.00% (19.35%) 65.00% (47.90%) Expected Growth 20.16% 8.15% Legth 10 years 10 yea Cost of Equity 12.33% 12.33% E/(D+E) 97.65% 97.65% AT Cost of Debt 4.16% 4.16% D/(D+E) 2.35% 2.35% Cost of Capital 12.13% 12.13% Value $115 $13 Aswath Damodara 74

75 3.2: Patets ad Legal Protectio The most complete protectio that a firm ca have from competitive pressure is to ow a patet, copyright or some other kid of legal protectio allowig it to be the sole producer for a exteded period. Note that patets oly provide partial protectio, sice they caot protect a firm agaist a competitive product that meets the same eed but is ot covered by the patet protectio. Liceses ad govermet-sactioed moopolies also provide protectio agaist competitio. They may, however, come with restrictios o excess returs; utilities i the Uited States, for istace, are moopolies but are regulated whe it comes to price icreases ad returs. Aswath Damodara 75

76 3.3: Switchig Costs Aother potetial barrier to etry is the cost associated with switchig from oe firm s products to aother. The greater the switchig costs, the more difficult it is for competitors to come i ad compete away excess returs. Firms that devise ways to icrease the cost of switchig from their products to competitors products, while reducig the costs of switchig from competitor products to their ow will be able to icrease their expected legth of growth. Aswath Damodara 76

77 3.4: Cost Advatages There are a umber of ways i which firms ca establish a cost advatage over their competitors, ad use this cost advatage as a barrier to etry: I busiesses, where scale ca be used to reduce costs, ecoomies of scale ca give bigger firms advatages over smaller firms Owig or havig exclusive rights to a distributio system ca provide firms with a cost advatage over its competitors. Owig or havig the rights to extract a atural resource which is i restricted supply (The udeveloped reserves of a oil or miig compay, for istace) These cost advatages will show up i valuatio i oe of two ways: The firm may charge the same price as its competitors, but have a much higher operatig margi. The firm may charge lower prices tha its competitors ad have a much higher capital turover ratio. Aswath Damodara 77

78 Gaugig Barriers to Etry p p p p p p p p Which of the followig barriers to etry are most likely to work for Tita Cemet? Brad Name Patets ad Legal Protectio Switchig Costs Cost Advatages What about for Amazo.com? Brad Name Patets ad Legal Protectio Switchig Costs Cost Advatages Aswath Damodara 78

79 Reducig Cost of Capital Outsourcig Flexible wage cotracts & cost structure Reduce operatig leverage Chage fiacig mix Cost of Equity (E/(D+E) + Pre-tax Cost of Debt (D./(D+E)) = Cost of Capital Make product or service less discretioary to customers Match debt to assets, reducig default risk Chagig product characteristics More effective advertisig Swaps Derivatives Hybrids Aswath Damodara 79

80 Amazo.com: Optimal Debt Ratio Debt Ratio Beta Cost of Equity Bod Ratig Iterest rate o debt Tax Rate Cost of Debt (after-tax) WACC Firm Value (G) 0% % AAA 6.80% 0.00% 6.80% 12.82% $29,192 10% % D 18.50% 0.00% 18.50% 14.02% $24,566 20% % D 18.50% 0.00% 18.50% 15.22% $21,143 30% % D 18.50% 0.00% 18.50% 16.42% $18,509 40% % D 18.50% 0.00% 18.50% 17.62% $16,419 50% % D 18.50% 0.00% 18.50% 18.82% $14,719 60% % D 18.50% 0.00% 18.50% 20.02% $13,311 70% % D 18.50% 0.00% 18.50% 21.22% $12,125 80% % D 18.50% 0.00% 18.50% 22.42% $11,112 90% % D 18.50% 0.00% 18.50% 23.62% $10,237 Aswath Damodara 80

81 Tita : Optimal Capital Structure Debt Ratio Beta Cost of Equity Bod Ratig Iterest rate o debt Tax Rate Cost of Debt (after-tax) WACC Firm Value (G) 0% % AAA 4.88% 30.44% 3.39% 7.84% $1,658 10% % AAA 4.88% 30.44% 3.39% 7.64% $1,732 20% % A+ 5.23% 30.44% 3.64% 7.49% $1,793 30% % A- 5.53% 30.44% 3.85% 7.38% $1,841 40% % B+ 7.78% 30.44% 5.41% 7.85% $1,654 50% % B % 30.44% 7.32% 8.81% $1,371 60% % CC 14.53% 28.47% 10.39% 10.89% $1,001 70% % CC 14.53% 24.40% 10.98% 11.91% $883 80% % C 16.53% 18.77% 13.43% 14.61% $675 90% % C 16.53% 16.68% 13.77% 15.83% $609 Aswath Damodara 81

82 Tita Cemets: Restructured Curret Cashflow to Firm EBIT(1-t) : Nt CpX 29 - Chg WC 10 = FCFF 115 Reivestmet Rate = 39/115=25% Reivestmet Rate 50.00% Reivest more i lower retur projects Expected Growth i EBIT (1-t).50*.15= % Retur o Capital 15.00% Stable Growth g = 4.31%; Beta = 1.00; Coutry Premium= 0% Cost of capital = 6.78% ROC= 6.78%; Tax rate=33% Reivestmet Rate=63.5% Termial Value5= 81.2/( ) = 3283 Op. Assets 2,688 + Cash: 81 - Debt Mior. It. 101 =Equity 2,279 -Optios 0 Value/Share EBIT EBIT(1-t) Reivestmet = FCFF Discout at Cost of Capital (WACC) = 8.88% (.70) % (0.30) = 7.27% Optimize capital structure Term Yr Cost of Equity 8.88% Cost of Debt (4.31%+%+.22%)( ) =3.85% Weights E = 70%% D = 30% Riskfree Rate: Euro riskfree rate = 4.31% + Beta 1.03 X Risk Premium 4.44% Ulevered Beta for Sectors: 0.80 Firm s D/E Ratio: 42.9% Mature risk premium 4% Coutry Equity Prem 0.44% Aswath Damodara 82

83 The Value of Cotrol? If the value of a firm ru optimally is sigificatly higher tha the value of the firm with the status quo (or icumbet maagemet), you ca write the value that you should be willig to pay as: Value of cotrol = Value of firm optimally ru - Value of firm with status quo Implicatios: The value of cotrol is greatest at poorly ru firms. Votig shares i poorly ru firms should trade at a premium o o-votig shares if the votes associated with the shares will give you a chace to have a say i a hostile acquisitio. Whe valuig private firms, your estimate of value will vary depedig upo whether you gai cotrol of the firm. For example, 49% of a private firm may be worth less tha 51% of the same firm. 49% stake = 49% of status quo value 51% stake = 51% of optimal value Aswath Damodara 83

84 Relative Valuatio Aswath Damodara Aswath Damodara 84

85 What is relative valuatio? I relative valuatio, the value of a asset is compared to the values assessed by the market for similar or comparable assets. To do relative valuatio the, we eed to idetify comparable assets ad obtai market values for these assets covert these market values ito stadardized values, sice the absolute prices caot be compared This process of stadardizig creates price multiples. compare the stadardized value or multiple for the asset beig aalyzed to the stadardized values for comparable asset, cotrollig for ay differeces betwee the firms that might affect the multiple, to judge whether the asset is uder or over valued Aswath Damodara 85

86 Relative valuatio is pervasive Most valuatios o Wall Street are relative valuatios. Almost 85% of equity research reports are based upo a multiple ad comparables. More tha 50% of all acquisitio valuatios are based upo multiples Rules of thumb based o multiples are ot oly commo but are ofte the basis for fial valuatio judgmets. While there are more discouted cashflow valuatios i cosultig ad corporate fiace, they are ofte relative valuatios masqueradig as discouted cash flow valuatios. The objective i may discouted cashflow valuatios is to back ito a umber that has bee obtaied by usig a multiple. The termial value i a sigificat umber of discouted cashflow valuatios is estimated usig a multiple. Aswath Damodara 86

87 Why relative valuatio? If you thik I m crazy, you should see the guy who lives across the hall Jerry Seifeld talkig about Kramer i a Seifeld episode A little iaccuracy sometimes saves tos of explaatio H.H. Muro If you are goig to screw up, make sure that you have lots of compay Ex-portfolio maager Aswath Damodara 87

88 So, you believe oly i itrisic value? Here s why you should still care about relative value Eve if you are a true believer i discouted cashflow valuatio, presetig your fidigs o a relative valuatio basis will make it more likely that your fidigs/recommedatios will reach a receptive audiece. I some cases, relative valuatio ca help fid weak spots i discouted cash flow valuatios ad fix them. The problem with multiples is ot i their use but i their abuse. If we ca fid ways to frame multiples right, we should be able to use them better. Aswath Damodara 88

89 Stadardizig Value You ca stadardize either the equity value of a asset or the value of the asset itself, which goes i the umerator. You ca stadardize by dividig by the Earigs of the asset Price/Earigs Ratio (PE) ad variats (PEG ad Relative PE) Value/EBIT Value/EBITDA Value/Cash Flow Book value of the asset Price/Book Value(of Equity) (PBV) Value/ Book Value of Assets Value/Replacemet Cost (Tobi s Q) Reveues geerated by the asset Price/Sales per Share (PS) Value/Sales Asset or Idustry Specific Variable (Price/kwh, Price per to of steel...) Aswath Damodara 89

90 The Four Steps to Uderstadig Multiples Defie the multiple I use, the same multiple ca be defied i differet ways by differet users. Whe comparig ad usig multiples, estimated by someoe else, it is critical that we uderstad how the multiples have bee estimated Describe the multiple Too may people who use a multiple have o idea what its cross sectioal distributio is. If you do ot kow what the cross sectioal distributio of a multiple is, it is difficult to look at a umber ad pass judgmet o whether it is too high or low. Aalyze the multiple It is critical that we uderstad the fudametals that drive each multiple, ad the ature of the relatioship betwee the multiple ad each variable. Apply the multiple Defiig the comparable uiverse ad cotrollig for differeces is far more difficult i practice tha it is i theory. Aswath Damodara 90

91 Defiitioal Tests Is the multiple cosistetly defied? Propositio 1: Both the value (the umerator) ad the stadardizig variable ( the deomiator) should be to the same claimholders i the firm. I other words, the value of equity should be divided by equity earigs or equity book value, ad firm value should be divided by firm earigs or book value. Is the multiple uiformly estimated? The variables used i defiig the multiple should be estimated uiformly across assets i the comparable firm list. If earigs-based multiples are used, the accoutig rules to measure earigs should be applied cosistetly across assets. The same rule applies with book-value based multiples. Aswath Damodara 91

92 Descriptive Tests What is the average ad stadard deviatio for this multiple, across the uiverse (market)? What is the media for this multiple? The media for this multiple is ofte a more reliable compariso poit. How large are the outliers to the distributio, ad how do we deal with the outliers? Throwig out the outliers may seem like a obvious solutio, but if the outliers all lie o oe side of the distributio (they usually are large positive umbers), this ca lead to a biased estimate. Are there cases where the multiple caot be estimated? Will igorig these cases lead to a biased estimate of the multiple? How has this multiple chaged over time? Aswath Damodara 92

93 Aalytical Tests What are the fudametals that determie ad drive these multiples? Propositio 2: Embedded i every multiple are all of the variables that drive every discouted cash flow valuatio - growth, risk ad cash flow patters. I fact, usig a simple discouted cash flow model ad basic algebra should yield the fudametals that drive a multiple How do chages i these fudametals chage the multiple? The relatioship betwee a fudametal (like growth) ad a multiple (such as PE) is seldom liear. For example, if firm A has twice the growth rate of firm B, it will geerally ot trade at twice its PE ratio Propositio 3: It is impossible to properly compare firms o a multiple, if we do ot kow the ature of the relatioship betwee fudametals ad the multiple. Aswath Damodara 93

94 Applicatio Tests Give the firm that we are valuig, what is a comparable firm? While traditioal aalysis is built o the premise that firms i the same sector are comparable firms, valuatio theory would suggest that a comparable firm is oe which is similar to the oe beig aalyzed i terms of fudametals. Propositio 4: There is o reaso why a firm caot be compared with aother firm i a very differet busiess, if the two firms have the same risk, growth ad cash flow characteristics. Give the comparable firms, how do we adjust for differeces across firms o the fudametals? Propositio 5: It is impossible to fid a exactly idetical firm to the oe you are valuig. Aswath Damodara 94

95 Price Earigs Ratio: Defiitio PE = Market Price per Share / Earigs per Share There are a umber of variats o the basic PE ratio i use. They are based upo how the price ad the earigs are defied. Price: is usually the curret price is sometimes the average price for the year EPS: earigs per share i most recet fiacial year earigs per share i trailig 12 moths (Trailig PE) forecasted earigs per share ext year (Forward PE) forecasted earigs per share i future year Aswath Damodara 95

96 PE Ratio: Distributio for the US: Jauary 2004 Aswath Damodara 96

97 PE: Decipherig the Distributio Curret PE Trailig PE Forward PE Mea Stadard Error Media Kurtosis Skewess Miimum Maximum Cout th largest th smallest Aswath Damodara 97

98 Comparig PE Ratios: Europe, Japa ad Emergig Markets Media PE Japa = US = Em. Mkts = Europe = Aswath Damodara 98

99 What about Greece? PE Ratio: Greece % of the stocks did ot have PE ratios because of egative earigs Lowest PE stocks Neorio Soros Shipyard: PE = 4.18 Techical Olympic: PE = >40 Aswath Damodara 99

100 PE Ratio: Uderstadig the Fudametals To uderstad the fudametals, start with a basic equity discouted cash flow model. With the divided discout model, P 0 = DPS 1 r g Dividig both sides by the earigs per share, If this had bee a FCFE Model, P 0 = PE = Payout Ratio * (1 + g ) EPS 0 r-g P 0 = FCFE 1 r g P 0 EPS 0 = PE = (FCFE/Earigs)* (1 + g ) r-g Aswath Damodara 100

101 PE Ratio ad Fudametals Propositio: Other thigs held equal, higher growth firms will have higher PE ratios tha lower growth firms. Propositio: Other thigs held equal, higher risk firms will have lower PE ratios tha lower risk firms Propositio: Other thigs held equal, firms with lower reivestmet eeds will have higher PE ratios tha firms with higher reivestmet rates. Of course, other thigs are difficult to hold equal sice high growth firms, ted to have risk ad high reivestmet rats. Aswath Damodara 101

102 Usig the Fudametal Model to Estimate PE For a High Growth Firm The price-earigs ratio for a high growth firm ca also be related to fudametals. I the special case of the two-stage divided discout model, this relatioship ca be made explicit fairly simply: (1+ g) EPS 0 * Payout Ratio *(1+ g)* 1 (1+ r) P 0 = r - g + EPS 0 * Payout Ratio *(1+ g) *(1+ g ) (r -g )(1+ r) For a firm that does ot pay what it ca afford to i divideds, substitute FCFE/Earigs for the payout ratio. Dividig both sides by the earigs per share: P 0 EPS 0 = (1 + g) Payout Ratio * (1 + g) * 1 (1+ r) r - g + Payout Ratio *(1+ g) * (1 + g ) (r - g )(1+ r) Aswath Damodara 102

103 Expadig the Model I this model, the PE ratio for a high growth firm is a fuctio of growth, risk ad payout, exactly the same variables that it was a fuctio of for the stable growth firm. The oly differece is that these iputs have to be estimated for two phases - the high growth phase ad the stable growth phase. Expadig to more tha two phases, say the three stage model, will mea that risk, growth ad cash flow patters i each stage. Aswath Damodara 103

104 A Simple Example Assume that you have bee asked to estimate the PE ratio for a firm which has the followig characteristics: Variable High Growth Phase Stable Growth Phase Expected Growth Rate 25% 8% Payout Ratio 20% 50% Beta Number of years 5 years Forever after year 5 Riskfree rate = T.Bod Rate = 6% Required rate of retur = 6% + 1(5.5%)= 11.5% 0.2 * (1.25) * 1 (1.25)5 (1.115) 5 PE = ( ) * (1.25)5 * (1.08) ( ) (1.115) 5 = Aswath Damodara 104

105 PE ad Growth: Firm grows at x% for 5 years, 8% thereafter PE Ratios ad Expected Growth: Iterest Rate Scearios PE Ratio r=4% r=6% r=8% r=10% % 10% 15% 20% 25% 30% 35% 40% 45% 50% Expected Growth Rate Aswath Damodara 105

106 PE Ratios ad Legth of High Growth: 25% growth for years; 8% thereafter Aswath Damodara 106

107 PE ad Risk: Effects of Chagig Betas o PE Ratio: Firm with x% growth for 5 years; 8% thereafter PE Ratios ad Beta: Growth Scearios PE Ratio g=25% g=20% g=15% g=8% Beta Aswath Damodara 107

108 PE ad Payout Aswath Damodara 108

109 I. Comparisos of PE across time: PE Ratio for the S&P 500 Aswath Damodara 109

110 Is low (high) PE cheap (expesive)? A market strategist argues that stocks are over priced because the PE ratio today is too high relative to the average PE ratio across time. Do you agree? q Yes q No If you do ot agree, what factors might explai the higher PE ratio today? Aswath Damodara 110

111 E/P Ratios, T.Bod Rates ad Term Structure Aswath Damodara 111

112 Regressio Results There is a strog positive relatioship betwee E/P ratios ad T.Bod rates, as evideced by the correlatio of 0.69 betwee the two variables., I additio, there is evidece that the term structure also affects the PE ratio. I the followig regressio, usig data, we regress E/P ratios agaist the level of T.Bod rates ad a term structure variable (T.Bod - T.Bill rate) E/P = 2.03% T.Bod Rate (T.Bod Rate-T.Bill Rate) (2.19) (6.38) (-1.38) R squared = 50.85% Aswath Damodara 112

113 II. Comparig PE Ratios across a Sector Compay Name PE Growth PT Idosat ADR Telebras ADR Telecom Corporatio of New Zealad ADR Telecom Argetia Stet - Frace Telecom SA ADR B Helleic Telecommuicatio Orgaizatio SA ADR Telecomuicacioes de Chile ADR Swisscom AG ADR Asia Satellite Telecom Holdigs ADR Portugal Telecom SA ADR Telefoos de Mexico ADR L Matav RT ADR Telstra ADR Gilat Commuicatios Deutsche Telekom AG ADR British Telecommuicatios PLC ADR Tele Damark AS ADR Telekomuikasi Idoesia ADR Cable & Wireless PLC ADR APT Satellite Holdigs ADR Telefoica SA ADR Royal KPN NV ADR Telecom Italia SPA ADR Nippo Telegraph & Telephoe ADR Frace Telecom SA ADR Korea Telecom ADR Aswath Damodara 113

114 PE, Growth ad Risk Depedet variable is: PE R squared = 66.2% R squared (adjusted) = 63.1% Variable Coefficiet SE t-ratio prob Costat Growth rate Emergig Market Emergig Market is a dummy: 1 if emergig market 0 if ot Aswath Damodara 114

115 Is Telebras uder valued? Predicted PE = (.075) (1) = 8.35 At a actual price to earigs ratio of 8.9, Telebras is slightly overvalued. What about Helleic Telecom? If viewed as a developed market telecom (0.12) (0) = It is dramatically udervalued at 12.8 times earigs If viewed as a emergig market telecom (0.12) (1) = It is close to fairly valued Aswath Damodara 115

116 Usig the etire crosssectio: A regressio approach I cotrast to the 'comparable firm' approach, the iformatio i the etire cross-sectio of firms ca be used to predict PE ratios. The simplest way of summarizig this iformatio is with a multiple regressio, with the PE ratio as the depedet variable, ad proxies for risk, growth ad payout formig the idepedet variables. Aswath Damodara 116

117 PE versus Growth Curret PE vs Expected Growth i EPS 120 Jauary 2004: US Compaies Curret PE Expected Growth i E PS: ext 5 y ears Aswath Damodara 117

118 PE Ratio: Stadard Regressio for US stocks - Jauary 2004 Model Summary Model 1 Adjusted R Std. Error of the R R Square Square Estimate.467 a a. Predictor s: ( Costat), PAYOUT, Regre ssio Be ta, Expected Gr owth i EPS: ext 5 years Co effici ets a,b Model 1 (Costat) Expected G rowth i EPS: ext 5 years Regr essio B eta PAYOUT a. Depedet Va riable: Curret PE Ustadardized Coefficiets B Std. Error Stadar dized Coefficiets Beta E b. Weighted Least Square s Regressio - Weighted by Mar ket Cap t Sig. Aswath Damodara 118

119 Problems with the regressio methodology The basic regressio assumes a liear relatioship betwee PE ratios ad the fiacial proxies, ad that might ot be appropriate. The basic relatioship betwee PE ratios ad fiacial variables itself might ot be stable, ad if it shifts from year to year, the predictios from the model may ot be reliable. The idepedet variables are correlated with each other. For example, high growth firms ted to have high risk. This multi-colliearity makes the coefficiets of the regressios ureliable ad may explai the large chages i these coefficiets from period to period. Aswath Damodara 119

120 The Multicolliearity Problem Correlatio s Expected G rowth i Reve ues: ext 5 year s Regressio Bet a PAYOUT Pear so Correlatio Sig. (2 -tailed) N Pear so Correlatio Sig. (2 -tailed) N Pear so Correlatio Sig. (2 -tailed) N Expected Growth i Reveues: Regr essio ext 5 years Beta PAYOUT ** ** ** -.183** **. Correlatio is sigificat at the 0.01 level (2-tailed). Aswath Damodara 120

121 Usig the PE ratio regressio Assume that you were give the followig iformatio for Dell. The firm has a expected growth rate of 10%, a beta of 1.20 ad pays o divideds. Based upo the regressio, estimate the predicted PE ratio for Dell. Predicted PE = Dell is actually tradig at 22 times earigs. What does the predicted PE tell you? Aswath Damodara 121

122 The value of growth Time Period Value of extra 1% of growth Equity Risk Premium Jauary % July % Jauary % July % Jauary % July % Jauary % July % Jauary % The value of growth is i terms of additioal PE Aswath Damodara 122

123 Value/Earigs ad Value/Cashflow Ratios While Price earigs ratios look at the market value of equity relative to earigs to equity ivestors, Value earigs ratios look at the market value of the firm relative to operatig earigs. Value to cash flow ratios modify the earigs umber to make it a cash flow umber. The form of value to cash flow ratios that has the closest parallels i DCF valuatio is the value to Free Cash Flow to the Firm, which is defied as: Value/FCFF = (Market Value of Equity + Market Value of Debt-Cash) Cosistecy Tests: EBIT (1-t) - (Cap Ex - Deprec) - Chg i WC If the umerator is et of cash (or if et debt is used, the the iterest icome from the cash should ot be i deomiator The iterest expeses added back to get to EBIT should correspod to the debt i the umerator. If oly log term debt is cosidered, oly log term iterest should be added back. Aswath Damodara 123

124 Value of Firm/FCFF: Determiats V 0 = Revertig back to a two-stage FCFF DCF model, we get: (1 + g) FCFF (1 + g) 1-0 (1+ WACC) FCFF + 0 (1+ g) (1+ g ) WACC - g (WACC - g )(1 + WACC) V 0 = Value of the firm (today) FCFF 0 = Free Cashflow to the firm i curret year g = Expected growth rate i FCFF i extraordiary growth period (first years) WACC = Weighted average cost of capital g = Expected growth rate i FCFF i stable growth period (after years) Aswath Damodara 124

125 Value Multiples Dividig both sides by the FCFF yields, V 0 FCFF 0 = (1 + g) 1- (1 + g) (1 + WACC) WACC - g + (1+ g) (1+ g ) (WACC - g )(1 + WACC) The value/fcff multiples is a fuctio of the cost of capital the expected growth Aswath Damodara 125

126 Value/FCFF Multiples ad the Alteratives o o o o Assume that you have computed the value of a firm, usig discouted cash flow models. Rak the followig multiples i the order of magitude from lowest to highest? Value/EBIT Value/EBIT(1-t) Value/FCFF Value/EBITDA What assumptio(s) would you eed to make for the Value/EBIT(1-t) ratio to be equal to the Value/FCFF multiple? Aswath Damodara 126

127 Illustratio: Usig Value/FCFF Approaches to value a firm: MCI Commuicatios MCI Commuicatios had earigs before iterest ad taxes of $3356 millio i 1994 (Its et icome after taxes was $855 millio). It had capital expeditures of $2500 millio i 1994 ad depreciatio of $1100 millio; Workig capital icreased by $250 millio. It expects free cashflows to the firm to grow 15% a year for the ext five years ad 5% a year after that. The cost of capital is 10.50% for the ext five years ad 10% after that. The compay faces a tax rate of 36%. V 0 FCFF 0 = (1.15) 1- (1.15)5 (1.105) (1.15) 5 (1.05) ( )(1.105) 5 = Aswath Damodara 127

128 Multiple Magic I this case of MCI there is a big differece betwee the FCFF ad short cut measures. For istace the followig table illustrates the appropriate multiple usig short cut measures, ad the amout you would overpay by if you used the FCFF multiple. Free Cash Flow to the Firm = EBIT (1-t) - Net Cap Ex - Chage i Workig Capital = 3356 (1-0.36) = $ 498 millio $ Value Correct Multiple FCFF $ EBIT (1-t) $2, EBIT $ 3, EBITDA $4, Aswath Damodara 128

129 Reasos for Icreased Use of Value/EBITDA 1. The multiple ca be computed eve for firms that are reportig et losses, sice earigs before iterest, taxes ad depreciatio are usually positive. 2. For firms i certai idustries, such as cellular, which require a substatial ivestmet i ifrastructure ad log gestatio periods, this multiple seems to be more appropriate tha the price/earigs ratio. 3. I leveraged buyouts, where the key factor is cash geerated by the firm prior to all discretioary expeditures, the EBITDA is the measure of cash flows from operatios that ca be used to support debt paymet at least i the short term. 4. By lookig at cashflows prior to capital expeditures, it may provide a better estimate of optimal value, especially if the capital expeditures are uwise or ear substadard returs. 5. By lookig at the value of the firm ad cashflows to the firm it allows for comparisos across firms with differet fiacial leverage. Aswath Damodara 129

130 Value/EBITDA Multiple The Classic Defiitio Value EBITDA = Market Value of Equity + Market Value of Debt Earigs before Iterest, Taxes ad Depreciatio The No-Cash Versio Eterprise Value EBITDA = Market Value of Equity + Market Value of Debt - Cash Earigs before Iterest, Taxes ad Depreciatio Whe cash ad marketable securities are etted out of value, oe of the icome from the cash ad securities should be reflected i the deomiator. Aswath Damodara 130

131 Value/EBITDA Distributio: Europe, Japa ad Emergig Markets Aswath Damodara 131

132 The Determiats of Value/EBITDA Multiples: Likage to DCF Valuatio Firm value ca be writte as: V 0 = FCFF 1 WACC - g The umerator ca be writte as follows: FCFF = EBIT (1-t) - (Cex - Depr) - Δ Workig Capital = (EBITDA - Depr) (1-t) - (Cex - Depr) - Δ Workig Capital = EBITDA (1-t) + Depr (t) - Cex - Δ Workig Capital Aswath Damodara 132

133 From Firm Value to EBITDA Multiples Now the Value of the firm ca be rewritte as, EBITDA (1- t) + Depr (t) - Cex - Δ Workig Capital Value = WACC - g Dividig both sides of the equatio by EBITDA, Value EBITDA = (1- t) WACC- g + Depr (t)/ebitda WACC -g - CEx/EBITDA WACC - g - Δ Workig Capital/EBITDA WACC - g Aswath Damodara 133

134 A Simple Example Cosider a firm with the followig characteristics: Tax Rate = 36% Capital Expeditures/EBITDA = 30% Depreciatio/EBITDA = 20% Cost of Capital = 10% The firm has o workig capital requiremets The firm is i stable growth ad is expected to grow 5% a year forever. Aswath Damodara 134

135 Calculatig Value/EBITDA Multiple I this case, the Value/EBITDA multiple for this firm ca be estimated as follows: Value EBITDA = (1-.36) + (0.2)(.36) = 8.24 Aswath Damodara 135

136 Value/EBITDA Multiples ad Taxes Aswath Damodara 136

137 Value/EBITDA ad Net Cap Ex Aswath Damodara 137

138 Value/EBITDA Multiples ad Retur o Capital Value/EBITDA ad Retur o Capital Value/EBITDA 6 WACC=10% WACC=9% WACC=8% % 7% 8% 9% 10% 11% 12% 13% 14% 15% Retur o Capital Aswath Damodara 138

139 Value/EBITDA Multiple: Truckig Compaies Compay Name Value EBITDA Value/EBITDA KLLM Tras. Svcs. $ $ Ryder System $ 5, $ 1, Rollis Truck Leasig $ 1, $ Cao Express Ic. $ $ Hut (J.B.) $ $ Yellow Corp. $ $ Roadway Express $ $ Marte Trasport Ltd. $ $ Kea Trasport Co. $ $ M.S. Carriers $ $ Old Domiio Freight $ $ Trimac Ltd $ $ Matlack Systems $ $ XTRA Corp. $ 1, $ Coveat Trasport Ic $ $ Builders Trasport $ $ Werer Eterprises $ $ Ladstar Sys. $ $ AMERCO $ 1, $ USA Truck $ $ Froze Food Express $ $ Arold Ids. $ $ Greyhoud Lies Ic. $ $ USFreightways $ $ Golde Eagle Group Ic. $ $ Arkasas Best $ $ Airlease Ltd. $ $ Celado Group $ $ Amer. Freightways $ $ Trasfiacial Holdigs $ $ Vitra Corp. 'A' $ $ Iterpool Ic. $ 1, $ Itreet Ic. $ $ Swift Trasportatio $ $ Ladair Services $ $ CNF Trasportatio $ 2, $ Budget Group Ic $ 1, $ Caliber System $ 2, $ Kight Trasportatio Ic $ $ Heartlad Express $ $ Greyhoud CDA Tras Corp $ $ Mark VII $ $ Coach USA Ic $ $ US 1 Ids Ic. $ 5.60 $ (0.17) NA Average 5.61 Aswath Damodara 139

140 A Test o EBITDA Ryder System looks very cheap o a Value/EBITDA multiple basis, relative to the rest of the sector. What explaatio (other tha misvaluatio) might there be for this differece? Aswath Damodara 140

141 Europe: Cross Sectioal Regressio Jauary 2004 Model 1 Model Summary Adjusted R R R Square Square Std. Er ror of the Estimate.542 a a. Predictors: (Costat), Tax Rate, Reiv Rate, Market Debt to Ca pital Coefficiets a,b Model 1 (Costat) Mar ket Debt to Capital Reiv Rate Tax Rat e a. Depedet Va riable: EV/EBITDA Ustadardized Coefficiets Stadardized Coefficiets B Std. Er ror Beta t Sig b. Weighted Least Square s Regressio - Weig hted by Market Capitalizatio Aswath Damodara 141

142 Price-Book Value Ratio: Defiitio The price/book value ratio is the ratio of the market value of equity to the book value of equity, i.e., the measure of shareholders equity i the balace sheet. Price/Book Value = Market Value of Equity Cosistecy Tests: Book Value of Equity If the market value of equity refers to the market value of equity of commo stock outstadig, the book value of commo equity should be used i the deomiator. If there is more that oe class of commo stock outstadig, the market values of all classes (eve the o-traded classes) eeds to be factored i. Aswath Damodara 142

143 Price to Book Value: Europe, Japa ad Emergig Markets Aswath Damodara 143

144 Price to Book: Greece i Jauary 2004 Price to Book: Greece Lowest PBV stocks ALTE TECHNICAL COMPANY:0.42 SHELMAN: 0.44 EMPEDOS SA: 0.45 Highest PBV stocks NEWSPHONE HELLAS SA FG EUROPE SA OLYMPIC CATERING S.A < >10 Aswath Damodara 144

145 Price Book Value Ratio: Stable Growth Firm Goig back to a simple divided discout model, P 0 = DPS 1 r g Defiig the retur o equity (ROE) = EPS 0 / Book Value of Equity, the value of equity ca be writte as: P 0 = BV 0 * ROE * Payout Ratio * (1 + g ) r-g P 0 = PBV = ROE * Payout Ratio * (1 + g ) BV 0 r-g If the retur o equity is based upo expected earigs i the ext time period, this ca be simplified to, P 0 BV 0 = PBV = ROE * Payout Ratio r-g Aswath Damodara 145

146 PBV/ROE: Europea Baks Bak Symbol PBV ROE Baca di Roma SpA BAHQE % Commerzbak AG COHSO % Bayerische Hypo ud Vereisbak AG BAXWW % Itesa Bci SpA BAEWF % Natexis Baques Populaires NABQE % Almaij NV Algemee Mij voor Nijver ALPK % Credit Idustriel et Commercial CIECM % Credit Lyoais SA CREV % BNL Baca Nazioale del Lavoro SpA BAEXC % Baca Mote dei Paschi di Siea SpA MOGG % Deutsche Bak AG DEMX % Skadiaviska Eskilda Bake SKHS % Nordea Bak AB NORDEA % DNB Holdig ASA DNHLD % ForeigsSparbake AB FOLG % Daske Bak AS DANKAS % Credit Suisse Group CRGAL % KBC Bakverzekerigsholdig KBCBA % Societe Geerale SODI % Satader Cetral Hispao SA BAZAB % Natioal Bak of Greece SA NAGT % Sa Paolo IMI SpA SAOEL % BNP Paribas BNPRB % Sveska Hadelsbake AB SVKE % UBS AG UBQH % Baco Bilbao Vizcaya Argetaria SA BBFUG % ABN Amro Holdig NV ABTS % UiCredito Italiao SpA UNCZA % Rolo Baca 1473 SpA ROGMBA % Dexia DECCT % Average % Aswath Damodara 146

147 PBV versus ROE regressio Regressig PBV ratios agaist ROE for baks yields the followig regressio: PBV = (ROE) R 2 = 46% For every 1% icrease i ROE, the PBV ratio should icrease by Aswath Damodara 147

148 Uder ad Over Valued Baks? Bak Actual Predicted Uder or Over Baca di Roma SpA % Commerzbak AG % Bayerische Hypo ud Vereisbak AG % Itesa Bci SpA % Natexis Baques Populaires % Almaij NV Algemee Mij voor Nijver % Credit Idustriel et Commercial % Credit Lyoais SA % BNL Baca Nazioale del Lavoro SpA % Baca Mote dei Paschi di Siea SpA % Deutsche Bak AG % Skadiaviska Eskilda Bake % Nordea Bak AB % DNB Holdig ASA % ForeigsSparbake AB % Daske Bak AS % Credit Suisse Group % KBC Bakverzekerigsholdig % Societe Geerale % Satader Cetral Hispao SA % Natioal Bak of Greece SA % Sa Paolo IMI SpA % BNP Paribas % Sveska Hadelsbake AB % UBS AG % Baco Bilbao Vizcaya Argetaria SA % ABN Amro Holdig NV % UiCredito Italiao SpA % Rolo Baca 1473 SpA % Dexia % Aswath Damodara 148

149 Lookig for udervalued securities - PBV Ratios ad ROE : The Valuatio Matrix MV/BV Overvalued Low ROE High MV/BV High ROE High MV/BV ROE-r Low ROE Low MV/BV Udervalued High ROE Low MV/BV Aswath Damodara 149

150 Price to Book vs ROE: Greek Stocks i Jauary NE WSPHONE HEL LAS SA OPAP SA 10 ELTON CHE MICALS-REG INTRALOT S.A.-INTE GR ATTICA PUBLICATI ONS 0 ELBISCO HOLDING SA POULIADIS ASSOCIATES DI AGNOS TIC & THERAPE TECHNI CAL OLYMPIC S. ATHE HELL. ENG. & TO PBV ROE Aswath Damodara 150

151 PBV Matrix: Telecom Compaies 12 TelAzteca 10 8 Carlto TelNZ Vimple 6 Teleglobe FraceTel Cable&W 4 2 DeutscheTel BritTel TelItalia BCE Nippo DamarkChiaTel Espaa TelArgFrace PhilTel Telmex TelArgetia Portugal Royal Helleic TelIdo TelPeru Televisas Idast HogKog AsiaSat APT CallNet Aoima GrupoCetro ROE Aswath Damodara 151

152 PBV, ROE ad Risk: Greek Stocks 30 OPAP GA Equity 20 NE WS GA Equity PBV 10 HYGEI A GA Equity MATHIO GA Equity FT GA Equity ROE Stad ard deviatio i st Aswath Damodara 152

153 IBM: The Rise ad Fall ad Rise Agai % % % % Price to Book % 0.00% Retur o Equity % % % Year % PBV ROE Aswath Damodara 153

154 PBV Ratio Regressio- Europe Jauary 2004 Model 1 Model Summary R R Square Squar e Std. Error of the Estimate a Adjusted R.830 b a. For regressio through the origi (the o-itercept model), R Squar e measur es the prop or tio of the variability i the depedet variable about the origi explaied by regressio. This CANNOT be compared to R Square for models which iclude a iter cept. b. Predictors: ROE, Payout Ra tio, B ETA Coefficiets a,b,c Model 1 Payout Ratio BE TA ROE a. Depedet Variable: PB V Ustadardized Coefficiets b. Liear Regr essio through the Origi Stadardized Coefficiets B Std. Er ror Beta t Sig. 8.E c. Weighted Least Squares R egre ssio - Weighted by Market Capitalizatio Aswath Damodara 154

155 PBV Regressio: Greece Lookig at 141 Greek stocks with PBV ratios ad returs o equity available o them: PBV = Retur o Equity (24.49) R squared for regressio = 85.2% Aswath Damodara 155

156 Price Sales Ratio: Defiitio The price/sales ratio is the ratio of the market value of equity to the sales. Price/ Sales= Market Value of Equity Cosistecy Tests Total Reveues The price/sales ratio is iterally icosistet, sice the market value of equity is divided by the total reveues of the firm. Aswath Damodara 156

157 Price to Sales: Europe, Japa ad Emergig Markets Aswath Damodara 157

158 Price to Sales: Greece Price to Sales: Greece 25 Lowest Price to Sales stocks POULIADIS ASSOCIATES CORP.: 0.17 LAVIPHARM S.A.: 0.21 EMPEDOS SA: 0.23 Highest Price to Sales stocks REDS SA N.B.G. REAL ESTATE DEV CO IONIAN HOTEL ENT. KERAMIA-ALLATINI < >10 Aswath Damodara 158

159 Price/Sales Ratio: Determiats The price/sales ratio of a stable growth firm ca be estimated begiig with a 2-stage equity valuatio model: P 0 = DPS 1 r g Dividig both sides by the sales per share: P 0 Sales 0 = PS = Net Profit Margi* Payout Ratio *(1+ g ) r-g Aswath Damodara 159

160 PS/Margis: Europea Retailers - March PS Ratio vs Net Margi: Europea Retailers ROFBF 6 5 HEUG 4 FIIV HEPU GUFQ 3 BEUHS CLOHSN DUWG 2 NAFBC 1 MOFPB ARTA MAOVG GRRC RNBRET JEEG 10 BIDQ 12 GIAG Net Margi Aswath Damodara 160

161 Regressio Results: PS Ratios ad Margis Regressig PS ratios agaist et margis, PS = (Net Margi) R 2 = 45% Thus, a 1% icrease i the margi results i a icrease of 0.23 i the price sales ratios. The regressio also allows us to get predicted PS ratios for these firms Aswath Damodara 161

162 Curret versus Predicted Margis Oe of the limitatios of the aalysis we did i these last few pages is the focus o curret margis. Stocks are priced based upo expected margis rather tha curret margis. For most firms, curret margis ad predicted margis are highly correlated, makig the aalysis still relevat. For firms where curret margis have little or o correlatio with expected margis, regressios of price to sales ratios agaist curret margis (or price to book agaist curret retur o equity) will ot provide much explaatory power. I these cases, it makes more sese to ru the regressio usig either predicted margis or some proxy for predicted margis. Aswath Damodara 162

163 Curret versus Predicted Margis Oe of the limitatios of the aalysis we did i these last few pages is the focus o curret margis. Stocks are priced based upo expected margis rather tha curret margis. For most firms, curret margis ad predicted margis are highly correlated, makig the aalysis still relevat. For firms where curret margis have little or o correlatio with expected margis, regressios of price to sales ratios agaist curret margis (or price to book agaist curret retur o equity) will ot provide much explaatory power. I these cases, it makes more sese to ru the regressio usig either predicted margis or some proxy for predicted margis. Aswath Damodara 163

164 A Case Study: The Iteret Stocks 30 PKSI 20 INTM SCNT LCOS MMXI SPYG A d j P S 10-0 INTW RAMP MQST CNET CSGP NETO APNT SONE CLKS PCLN SPLN EDGR PSIX BIDS ATHY AMZN ALOY ACOM BIZZ EGRP IIXL ITRA ONEM FATB ABTL INFO ANET RMII TMNT GEEK TURF PPOD GSVI BUYX ELTX ROWE CBIS FFIV ATHM DCLK NTPA AdjMargi Aswath Damodara 164

165 PS Ratios ad Margis are ot highly correlated Regressig PS ratios agaist curret margis yields the followig PS = (Net Margi) R 2 = 0.04 (0.49) This is ot surprisig. These firms are priced based upo expected margis, rather tha curret margis. Aswath Damodara 165

166 Solutio 1: Use proxies for survival ad growth: Amazo i early 2000 Hypothesizig that firms with higher reveue growth ad higher cash balaces should have a greater chace of survivig ad becomig profitable, we ra the followig regressio: (The level of reveues was used to cotrol for size) PS = l(rev) (Rev Growth) (Cash/Rev) R squared = 31.8% (0.66) (2.63) (3.49) Predicted PS = (7.1039) (1.9946) (.3069) = Actual PS = Stock is udervalued, relative to other iteret stocks. Aswath Damodara 166

167 Solutio 2: Use forward multiples You ca always estimate price (or value) as a multiple of reveues, earigs or book value i a future year. These multiples are called forward multiples. For youg ad evolvig firms, the values of fudametals i future years may provide a much better picture of the true value potetial of the firm. There are two ways i which you ca use forward multiples: Look at value today as a multiple of reveues or earigs i the future (say 5 years from ow) for all firms i the comparable firm list. Use the average of this multiple i cojuctio with your firm s earigs or reveues to estimate the value of your firm today. Estimate value as a multiple of curret reveues or earigs for more mature firms i the group ad apply this multiple to the forward earigs or reveues to the forward earigs for your firm. This will yield the expected value for your firm i the forward year ad will have to be discouted back to the preset to get curret value. Aswath Damodara 167

168 Solutio 2: Use forward multiples Global Crossig lost $1.9 billio i 2001 ad is expected to cotiue to lose moey for the ext 3 years. I a discouted cashflow valuatio (see otes o DCF valuatio) of Global Crossig, we estimated a expected EBITDA for Global Crossig i five years of $ 1,371 millio. The average eterprise value/ EBITDA multiple for healthy telecomm firms is 7.2 curretly. Applyig this multiple to Global Crossig s EBITDA i year 5, yields a value i year 5 of Eterprise Value i year 5 = 1371 * 7.2 = $9,871 millio Eterprise Value today = $ 9,871 millio/ = $5,172 millio (The cost of capital for Global Crossig is 13.80%) The probability that Global Crossig will ot make it as a goig cocer is 77%. Expected Eterprise value today = 0.23 (5172) = $1,190 millio Aswath Damodara 168

169 PS Regressio: Europe i Jauary 2004 Model 1 Model Summary R R Square a Square Adjusted R Std. Error of the Estimate.757 b a. For regressio through the origi (the o-itercept model), R Sq uare measures the proportio of the variab ility i the depedet varia ble about the origi explaied by regressio. This CANNOT be compar ed to R Square for models which iclude a itercept. b. Predictors: Net Mar gi, Payout Ratio, BETA Coefficiets a,b,c Model 1 Payout Ratio BE TA Net Margi a. Depedet Va riable: PS Ustadardized Coefficiets b. Liear Regr essio through the Origi Stadardized Coefficiets B Std. Er ror Beta t Sig. 5.E c. Weighted Least Squares R egre ssio - Weighted by Market Capitalizatio Aswath Damodara 169

170 Choosig Betwee the Multiples As preseted i this sectio, there are dozes of multiples that ca be potetially used to value a idividual firm. I additio, relative valuatio ca be relative to a sector (or comparable firms) or to the etire market (usig the regressios, for istace) Sice there ca be oly oe fial estimate of value, there are three choices at this stage: Use a simple average of the valuatios obtaied usig a umber of differet multiples Use a weighted average of the valuatios obtaied usig a mber of differet multiples Choose oe of the multiples ad base your valuatio o that multiple Aswath Damodara 170

171 Pickig oe Multiple This is usually the best way to approach this issue. While a rage of values ca be obtaied from a umber of multiples, the best estimate value is obtaied usig oe multiple. The multiple that is used ca be chose i oe of two ways: Use the multiple that best fits your objective. Thus, if you wat the compay to be udervalued, you pick the multiple that yields the highest value. Use the multiple that has the highest R-squared i the sector whe regressed agaist fudametals. Thus, if you have tried PE, PBV, PS, etc. ad ru regressios of these multiples agaist fudametals, use the multiple that works best at explaiig differeces across firms i that sector. Use the multiple that seems to make the most sese for that sector, give how value is measured ad created. Aswath Damodara 171

172 A More Ituitive Approach Maagers i every sector ted to focus o specific variables whe aalyzig strategy ad performace. The multiple used will geerally reflect this focus. Cosider three examples. I retailig: The focus is usually o same store sales (turover) ad profit margis. Not surprisigly, the reveue multiple is most commo i this sector. I fiacial services: The emphasis is usually o retur o equity. Book Equity is ofte viewed as a scarce resource, sice capital ratios are based upo it. Price to book ratios domiate. I techology: Growth is usually the domiat theme. PEG ratios were iveted i this sector. Aswath Damodara 172

173 I Practice As a geeral rule of thumb, the followig table provides a way of pickig a multiple for a sector Sector Multiple Used Ratioale Cyclical Maufacturig PE, Relative PE Ofte with ormalized earigs High Tech, High Growth PEG Big differeces i growth across firms High Growth/No Earigs PS, VS Assume future margis will be good Heavy Ifrastructure VEBITDA Firms i sector have losses i early years ad reported earigs ca vary depedig o depreciatio method REITa P/CF Geerally o cap ex ivestmets from equity earigs Fiacial Services PBV Book value ofte marked to market Retailig PS If leverage is similar across firms VS If leverage is differet Aswath Damodara 173

174 Reviewig: The Four Steps to Uderstadig Multiples Defie the multiple Check for cosistecy Make sure that they are estimated uiformly Describe the multiple Multiples have skewed distributios: The averages are seldom good idicators of typical multiples Check for bias, if the multiple caot be estimated Aalyze the multiple Idetify the compaio variable that drives the multiple Examie the ature of the relatioship Apply the multiple Aswath Damodara 174

175 Real Optios: Fact ad Fatasy Aswath Damodara Aswath Damodara 175

176 Uderlyig Theme: Searchig for a Elusive Premium Traditioal discouted cashflow models uder estimate the value of ivestmets, where there are optios embedded i the ivestmets to Delay or defer makig the ivestmet (delay) Adjust or alter productio schedules as price chages (flexibility) Expad ito ew markets or products at later stages i the process, based upo observig favorable outcomes at the early stages (expasio) Stop productio or abado ivestmets if the outcomes are ufavorable at early stages (abadomet) Put aother way, real optio advocates believe that you should be payig a premium o discouted cashflow value estimates. Aswath Damodara 176

177 Three Basic Questios Whe is there a real optio embedded i a decisio or a asset? Whe does that real optio have sigificat ecoomic value? Ca that value be estimated usig a optio pricig model? Aswath Damodara 177

178 Whe is there a optio embedded i a actio? A optio provides the holder with the right to buy or sell a specified quatity of a uderlyig asset at a fixed price (called a strike price or a exercise price) at or before the expiratio date of the optio. There has to be a clearly defied uderlyig asset whose value chages over time i upredictable ways. The payoffs o this asset (real optio) have to be cotiget o a specified evet occurrig withi a fiite period. Aswath Damodara 178

179 Payoff Diagram o a Call Net Payoff o Call Strike Price Price of uderlyig asset Aswath Damodara 179

180 Payoff Diagram o Put Optio Net Payoff O Put Strike Price Price of uderlyig asset Aswath Damodara 180

181 Whe does the optio have sigificat ecoomic value? For a optio to have sigificat ecoomic value, there has to be a restrictio o competitio i the evet of the cotigecy. I a perfectly competitive product market, o cotigecy, o matter how positive, will geerate positive et preset value. At the limit, real optios are most valuable whe you have exclusivity - you ad oly you ca take advatage of the cotigecy. They become less valuable as the barriers to competitio become less steep. Aswath Damodara 181

182 Determiats of optio value Variables Relatig to Uderlyig Asset Value of Uderlyig Asset; as this value icreases, the right to buy at a fixed price (calls) will become more valuable ad the right to sell at a fixed price (puts) will become less valuable. Variace i that value; as the variace icreases, both calls ad puts will become more valuable because all optios have limited dowside ad deped upo price volatility for upside. Expected divideds o the asset, which are likely to reduce the price appreciatio compoet of the asset, reducig the value of calls ad icreasig the value of puts. Variables Relatig to Optio Strike Price of Optios; the right to buy (sell) at a fixed price becomes more (less) valuable at a lower price. Life of the Optio; both calls ad puts beefit from a loger life. Level of Iterest Rates; as rates icrease, the right to buy (sell) at a fixed price i the future becomes more (less) valuable. Aswath Damodara 182

183 Whe ca you use optio pricig models to value real optios? The otio of a replicatig portfolio that drives optio pricig models makes them most suited for valuig real optios where The uderlyig asset is traded - this yield ot oly observable prices ad volatility as iputs to optio pricig models but allows for the possibility of creatig replicatig portfolios A active marketplace exists for the optio itself. The cost of exercisig the optio is kow with some degree of certaity. Whe optio pricig models are used to value real assets, we have to accept the fact that The value estimates that emerge will be far more imprecise. The value ca deviate much more dramatically from market price because of the difficulty of arbitrage. Aswath Damodara 183

184 Creatig a replicatig portfolio The objective i creatig a replicatig portfolio is to use a combiatio of riskfree borrowig/ledig ad the uderlyig asset to create the same cashflows as the optio beig valued. Call = Borrowig + Buyig Δ of the Uderlyig Stock Put = Sellig Short Δ o Uderlyig Asset + Ledig The umber of shares bought or sold is called the optio delta. The priciples of arbitrage the apply, ad the value of the optio has to be equal to the value of the replicatig portfolio. Aswath Damodara 184

185 The Biomial Optio Pricig Model Stock Price Call Optio Details K = $ 40 t = 2 r = 11% 100 D B = D B = 10 D = 1, B = Call = 1 * = D B = D B = 4.99 D = , B = Call = * = Call = Call = Call = D B = D B = 0 D = 0.4, B = 9.01 Call = 0.4 * = 4.99 Aswath Damodara

186 The Limitig Distributios. As the time iterval is shorteed, the limitig distributio, as t -> 0, ca take oe of two forms. If as t -> 0, price chages become smaller, the limitig distributio is the ormal distributio ad the price process is a cotiuous oe. If as t->0, price chages remai large, the limitig distributio is the poisso distributio, i.e., a distributio that allows for price jumps. The Black-Scholes model applies whe the limitig distributio is the ormal distributio, ad explicitly assumes that the price process is cotiuous ad that there are o jumps i asset prices. Aswath Damodara 186

187 The Black-Scholes Model The versio of the model preseted by Black ad Scholes was desiged to value Europea optios, which were divided-protected. The value of a call optio i the Black-Scholes model ca be writte as a fuctio of the followig variables: S = Curret value of the uderlyig asset K = Strike price of the optio t = Life to expiratio of the optio r = Riskless iterest rate correspodig to the life of the optio σ 2 = Variace i the l(value) of the uderlyig asset Aswath Damodara 187

188 The Black Scholes Model Value of call = S N (d 1 ) - K e -rt N(d 2 ) where, l S K + (r + σ 2 2 ) t d 1 = σ t d 2 = d 1 - σ t The replicatig portfolio is embedded i the Black-Scholes model. To replicate this call, you would eed to Buy N(d1) shares of stock; N(d1) is called the optio delta Borrow K e -rt N(d 2 ) Aswath Damodara 188

189 The Normal Distributio N(d1) d1 d N(d) d N(d) d N(d) Aswath Damodara 189

190 Adjustig for Divideds If the divided yield (y = divideds/ Curret value of the asset) of the uderlyig asset is expected to remai uchaged durig the life of the optio, the Black-Scholes model ca be modified to take divideds ito accout. C = S e -yt N(d 1 ) - K e -rt N(d 2 ) where, d 1 = l S K + (r - y + σ2 2 ) t σ t d 2 = d 1 - σ t The value of a put ca also be derived: P = K e -rt (1-N(d 2 )) - S e -yt (1-N(d 1 )) Aswath Damodara 190

191 Choice of Optio Pricig Models Most practitioers who use optio pricig models to value real optios argue for the biomial model over the Black-Scholes ad justify this choice by otig that Early exercise is the rule rather tha the exceptio with real optios Uderlyig asset values are geerally discotious. If you ca develop a biomial tree with outcomes at each ode, it looks a great deal like a decisio tree from capital budgetig. The questio the becomes whe ad why the two approaches yield differet estimates of value. Aswath Damodara 191

192 The Decisio Tree Alterative Traditioal decisio tree aalysis teds to use Oe cost of capital to discout cashflows i each brach to the preset Probabilities to compute a expected value These values will geerally be differet from optio pricig model values If you modified decisio tree aalysis to Use differet discout rates at each ode to reflect where you are i the decisio tree (This is the Copelad solutio) (or) Use the riskfree rate to discout cashflows i each brach, estimate the probabilities to estimate a expected value ad adjust the expected value for the market risk i the ivestmet Decisio Trees could yield the same values as optio pricig models Aswath Damodara 192

193 Key Tests for Real Optios Is there a optio embedded i this asset/ decisio? Ca you idetify the uderlyig asset? Ca you specify the cotigecy uder which you will get payoff? Is there exclusivity? If yes, there is optio value. If o, there is oe. If i betwee, you have to scale value. Ca you use a optio pricig model to value the real optio? Is the uderlyig asset traded? Ca the optio be bought ad sold? Is the cost of exercisig the optio kow ad clear? Aswath Damodara 193

194 Optio Pricig Applicatios i Ivestmet/Strategic Aalysis Aswath Damodara 194

195 Optios i Projects/Ivestmets/Acquisitios Oe of the limitatios of traditioal ivestmet aalysis is that it is static ad does ot do a good job of capturig the optios embedded i ivestmet. The first of these optios is the optio to delay takig a ivestmet, whe a firm has exclusive rights to it, util a later date. The secod of these optios is takig oe ivestmet may allow us to take advatage of other opportuities (ivestmets) i the future The last optio that is embedded i projects is the optio to abado a ivestmet, if the cash flows do ot measure up. These optios all add value to projects ad may make a bad ivestmet (from traditioal aalysis) ito a good oe. Aswath Damodara 195

196 The Optio to Delay Whe a firm has exclusive rights to a project or product for a specific period, it ca delay takig this project or product util a later date. A traditioal ivestmet aalysis just aswers the questio of whether the project is a good oe if take today. Thus, the fact that a project does ot pass muster today (because its NPV is egative, or its IRR is less tha its hurdle rate) does ot mea that the rights to this project are ot valuable. Aswath Damodara 196

197 Valuig the Optio to Delay a Project PV of Cash Flows from Project Iitial Ivestmet i Project Project has egative NPV i this sectio Project's NPV turs positive i this sectio Preset Value of Expected Cash Flows o Product Aswath Damodara 197

198 Isights for Ivestmet Aalyses Havig the exclusive rights to a product or project is valuable, eve if the product or project is ot viable today. The value of these rights icreases with the volatility of the uderlyig busiess. The cost of acquirig these rights (by buyig them or spedig moey o developmet, for istace) has to be weighed off agaist these beefits. Aswath Damodara 198

199 Example 1: Valuig product patets as optios A product patet provides the firm with the right to develop the product ad market it. It will do so oly if the preset value of the expected cash flows from the product sales exceed the cost of developmet. If this does ot occur, the firm ca shelve the patet ad ot icur ay further costs. If I is the preset value of the costs of developig the product, ad V is the preset value of the expected cashflows from developmet, the payoffs from owig a product patet ca be writte as: Payoff from owig a product patet = V - I if V> I = 0 if V I Aswath Damodara 199

200 Payoff o Product Optio Net Payoff to itroductio Cost of product itroductio Preset Value of cashflows o product Aswath Damodara 200

201 Obtaiig Iputs for Patet Valuatio Iput Estimatio Process 1. Value of the Uderlyig Asset Preset Value of Cash Iflows from takig project ow This will be oisy, but that adds value. 2. Variace i value of uderlyig asset Variace i cash flows of similar assets or firms Variace i preset value from capital budgetig simulatio. 3. Exercise Price o Optio Optio is exercised whe ivestmet is made. Cost of makig ivestmet o the project ; assumed to be costat i preset value dollars. 4. Expiratio of the Optio Life of the patet 5. Divided Yield Cost of delay Each year of delay traslates ito oe less year of value-creatig cashflows Aual cost of delay = 1 Aswath Damodara 201

202 Valuig a Product Patet: Avoex Bioge, a bio-techology firm, has a patet o Avoex, a drug to treat multiple sclerosis, for the ext 17 years, ad it plas to produce ad sell the drug by itself. The key iputs o the drug are as follows: PV of Cash Flows from Itroducig the Drug Now = S = $ billio PV of Cost of Developig Drug for Commercial Use = K = $ billio Patet Life = t = 17 years Riskless Rate = r = 6.7% (17-year T.Bod rate) Variace i Expected Preset Values =σ 2 = (Idustry average firm variace for bio-tech firms) Expected Cost of Delay = y = 1/17 = 5.89% d1 = N(d1) = d2 = N(d2) = Call Value= 3,422 exp ( )(17) (0.8720) - 2,875 (exp (-0.067)(17) (0.2076)= $ 907 millio Aswath Damodara 202

203 Valuig a firm with patets The value of a firm with a substatial umber of patets ca be derived usig the optio pricig model. Value of Firm = Value of commercial products (usig DCF value + Value of existig patets (usig optio pricig) + (Value of New patets that will be obtaied i the future Cost of obtaiig these patets) The last iput measures the efficiecy of the firm i covertig its R&D ito commercial products. If we assume that a firm ears its cost of capital from research, this term will become zero. If we use this approach, we should be careful ot to double cout ad allow for a high growth rate i cash flows (i the DCF valuatio). Aswath Damodara 203

204 Value of Bioge s existig products Bioge had two commercial products (a drug to treat Hepatitis B ad Itro) at the time of this valuatio that it had licesed to other pharmaceutical firms. The licese fees o these products were expected to geerate $ 50 millio i after-tax cash flows each year for the ext 12 years. To value these cash flows, which were guarateed cotractually, the pre-tax cost of debt of the guarators (6.7%) was used: Preset Value of Licese Fees = $ 50 millio (1 (1.067) -12 )/.067 = $ millio Aswath Damodara 204

205 Value of Bioge s Future R&D Bioge cotiued to fud research ito ew products, spedig about $ 100 millio o R&D i the most recet year. These R&D expeses were expected to grow 20% a year for the ext 10 years, ad 5% thereafter. It was assumed that every dollar ivested i research would create $ 1.25 i value i patets (valued usig the optio pricig model described above) for the ext 10 years, ad break eve after that (i.e., geerate $ 1 i patet value for every $ 1 ivested i R&D). There was a sigificat amout of risk associated with this compoet ad the cost of capital was estimated to be 15%. Aswath Damodara 205

206 Value of Future R&D Yr Value of R&D Cost Excess Value Preset Value Patets (at 15%) 1 $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ Aswath Damodara 206

207 Value of Bioge The value of Bioge as a firm is the sum of all three compoets the preset value of cash flows from existig products, the value of Avoex (as a optio) ad the value created by ew research: Value = Existig products + Existig Patets + Value: Future R&D = $ millio + $ 907 millio + $ millio = $ millio Sice Bioge had o debt outstadig, this value was divided by the umber of shares outstadig (35.50 millio) to arrive at a value per share: Value per share = $ 1, millio / 35.5 = $ Aswath Damodara 207

208 The Real Optios Test: Patets ad Techology The Optio Test: Uderlyig Asset: Product that would be geerated by the patet Cotigecy: If PV of CFs from developmet > Cost of developmet: PV - Cost If PV of CFs from developmet < Cost of developmet: 0 The Exclusivity Test: Patets restrict competitors from developig similar products Patets do ot restrict competitors from developig other products to treat the same disease. The Pricig Test Uderlyig Asset: Patets are ot traded. Not oly do you therefore have to estimate the preset values ad volatilities yourself, you caot costruct replicatig positios or do arbitrage. Optio: Patets are bought ad sold, though ot as frequetly as oil reserves or mies. Cost of Exercisig the Optio: This is the cost of covertig the patet for commercial productio. Here, experiece does help ad drug firms ca make fairly precise estimates of the cost. Coclusio: You ca estimate the value of the real optio but the quality of your estimate will be a direct fuctio of the quality of your capital budgetig. It works best if you are valuig a publicly traded firm that geerates most of its value from oe or a few patets - you ca use the market value of the firm ad the variace i that value the i your optio pricig model. Aswath Damodara 208

209 Example 2: Valuig Natural Resource Optios I a atural resource ivestmet, the uderlyig asset is the resource ad the value of the asset is based upo two variables - the quatity of the resource that is available i the ivestmet ad the price of the resource. I most such ivestmets, there is a cost associated with developig the resource, ad the differece betwee the value of the asset extracted ad the cost of the developmet is the profit to the ower of the resource. Defiig the cost of developmet as X, ad the estimated value of the resource as V, the potetial payoffs o a atural resource optio ca be writte as follows: Payoff o atural resource ivestmet = V - X if V > X = 0 if V X Aswath Damodara 209

210 Payoff Diagram o Natural Resource Firms Net Payoff o Extractio Cost of Developig Reserve Value of estimated reserve of atural resource Aswath Damodara 210

211 Estimatig Iputs for Natural Resource Optios Iput Estimatio Process 1. Value of Available Reserves of the Resource Expert estimates (Geologists for oil..); The preset value of the after-tax cash flows from the resource are the estimated. 2. Cost of Developig Reserve (Strike Price) Past costs ad the specifics of the ivestmet 3. Time to Expiratio Reliqushmet Period: if asset has to be reliquished at a poit i time. Time to exhaust ivetory - based upo ivetory ad capacity output. 4. Variace i value of uderlyig asset based upo variability of the price of the resources ad variability of available reserves. 5. Net Productio Reveue (Divided Yield) Net productio reveue every year as percet of market value. 6. Developmet Lag Calculate preset value of reserve based upo the lag. Aswath Damodara 211

212 Valuig a Oil Reserve Cosider a offshore oil property with a estimated oil reserve of 50 millio barrels of oil, where the preset value of the developmet cost is $12 per barrel ad the developmet lag is two years. The firm has the rights to exploit this reserve for the ext twety years ad the margial value per barrel of oil is $12 per barrel curretly (Price per barrel - margial cost per barrel). Oce developed, the et productio reveue each year will be 5% of the value of the reserves. The riskless rate is 8% ad the variace i l(oil prices) is Aswath Damodara 212

213 Iputs to Optio Pricig Model Curret Value of the asset = S = Value of the developed reserve discouted back the legth of the developmet lag at the divided yield = $12 * 50 /(1.05) 2 = $ (If developmet is started today, the oil will ot be available for sale util two years from ow. The estimated opportuity cost of this delay is the lost productio reveue over the delay period. Hece, the discoutig of the reserve back at the divided yield) Exercise Price = Preset Value of developmet cost = $12 * 50 = $600 millio Time to expiratio o the optio = 20 years Variace i the value of the uderlyig asset = 0.03 Riskless rate =8% Divided Yield = Net productio reveue / Value of reserve = 5% Aswath Damodara 213

214 Valuig the Optio Based upo these iputs, the Black-Scholes model provides the followig value for the call: d1 = N(d1) = d2 = N(d2) = Call Value= exp (-0.05)(20) (0.8498) -600 (exp (-0.08)(20) (0.6030)= $ millio This oil reserve, though ot viable at curret prices, still is a valuable property because of its potetial to create value if oil prices go up. Aswath Damodara 214

215 Extedig the optio pricig approach to value atural resource firms Sice the assets owed by a atural resource firm ca be viewed primarily as optios, the firm itself ca be valued usig optio pricig models. The preferred approach would be to cosider each optio separately, value it ad cumulate the values of the optios to get the firm value. Sice this iformatio is likely to be difficult to obtai for large atural resource firms, such as oil compaies, which ow hudreds of such assets, a variat is to value the etire firm as oe optio. A purist would probably disagree, arguig that valuig a optio o a portfolio of assets (as i this approach) will provide a lower value tha valuig a portfolio of optios (which is what the atural resource firm really ow). Nevertheless, the value obtaied from the model still provides a iterestig perspective o the determiats of the value of atural resource firms. Aswath Damodara 215

216 Iputs to the Model Iput to model Correspodig iput for valuig firm Value of uderlyig asset Value of cumulated estimated reserves of the resource owed by the firm, discouted back at the divided yield for the developmet lag. Exercise Price Estimated cumulated cost of developig estimated reserves Time to expiratio o optio Average reliquishmet period across all reserves owed by firm (if kow) or estimate of whe reserves will be exhausted, give curret productio rates. Riskless rate Riskless rate correspodig to life of the optio Variace i value of asset Variace i the price of the atural resource Divided yield Estimated aual et productio reveue as percetage of value of the reserve. Aswath Damodara 216

217 Valuig Gulf Oil Gulf Oil was the target of a takeover i early 1984 at $70 per share (It had millio shares outstadig, ad total debt of $9.9 billio). It had estimated reserves of 3038 millio barrels of oil ad the average cost of developig these reserves was estimated to be $10 a barrel i preset value dollars (The developmet lag is approximately two years). The average reliquishmet life of the reserves is 12 years. The price of oil was $22.38 per barrel, ad the productio cost, taxes ad royalties were estimated at $7 per barrel. The bod rate at the time of the aalysis was 9.00%. Gulf was expected to have et productio reveues each year of approximately 5% of the value of the developed reserves. The variace i oil prices is Aswath Damodara 217

218 Valuig Udeveloped Reserves Iputs for valuig udeveloped reserves Value of uderlyig asset = Value of estimated reserves discouted back for period of developmet lag= 3038 * ($ $7) / = $42, Exercise price = Estimated developmet cost of reserves = 3038 * $10 = $30,380 millio Time to expiratio = Average legth of reliquishmet optio = 12 years Variace i value of asset = Variace i oil prices = 0.03 Riskless iterest rate = 9% Divided yield = Net productio reveue/ Value of developed reserves = 5% Based upo these iputs, the Black-Scholes model provides the followig value for the call: d1 = N(d1) = d2 = N(d2) = Call Value= 42, exp (-0.05)(12) (0.9510) -30,380 (exp (-0.09)(12) (0.8542)= $ 13,306 millio Aswath Damodara 218

219 Valuig Gulf Oil I additio, Gulf Oil had free cashflows to the firm from its oil ad gas productio of $915 millio from already developed reserves ad these cashflows are likely to cotiue for te years (the remaiig lifetime of developed reserves). The preset value of these developed reserves, discouted at the weighted average cost of capital of 12.5%, yields: Value of already developed reserves = 915 ( )/.125 = $ Addig the value of the developed ad udeveloped reserves Value of udeveloped reserves Value of productio i place Total value of firm Less Outstadig Debt Value of Equity = $ 9,900 millio = $ 13,306 millio = $ 5,066 millio = $ 18,372 millio = $ 8,472 millio Value per share = $ 8,472/165.3 = $51.25 Aswath Damodara 219

220 Puttig Natural Resource Optios to the Test The Optio Test: Uderlyig Asset: Oil or gold i reserve Cotigecy: If value > Cost of developmet: Value - Dev Cost If value < Cost of developmet: 0 The Exclusivity Test: Natural resource reserves are limited (at least for the short term) It takes time ad resources to develop ew reserves The Optio Pricig Test Uderlyig Asset: While the reserve or mie may ot be traded, the commodity is. If we assume that we kow the quatity with a fair degree of certaity, you ca trade the uderlyig asset Optio: Oil compaies buy ad sell reserves from each other regularly. Cost of Exercisig the Optio: This is the cost of developig a reserve. Give the experiece that commodity compaies have with this, they ca estimate this cost with a fair degree of precisio. Real optio pricig models work well with atural resource optios. Aswath Damodara 220

221 The Optio to Expad/Take Other Projects Takig a project today may allow a firm to cosider ad take other valuable projects i the future. Thus, eve though a project may have a egative NPV, it may be a project worth takig if the optio it provides the firm (to take other projects i the future) provides a more-tha-compesatig value. These are the optios that firms ofte call strategic optios ad use as a ratioale for takig o egative NPV or eve egative retur projects. Aswath Damodara 221

222 The Optio to Expad PV of Cash Flows from Expasio Additioal Ivestmet to Expad Firm will ot expad i this sectio Expasio becomes attractive i this sectio Preset Value of Expected Cash Flows o Expasio Aswath Damodara 222

223 A Example of a Expasio Optio Ambev is cosiderig itroducig a soft drik to the U.S. market. The drik will iitially be itroduced oly i the metropolita areas of the U.S. ad the cost of this limited itroductio is $ 500 millio. A fiacial aalysis of the cash flows from this ivestmet suggests that the preset value of the cash flows from this ivestmet to Ambev will be oly $ 400 millio. Thus, by itself, the ew ivestmet has a egative NPV of $ 100 millio. If the iitial itroductio works out well, Ambev could go ahead with a fullscale itroductio to the etire market with a additioal ivestmet of $ 1 billio ay time over the ext 5 years. While the curret expectatio is that the cash flows from havig this ivestmet is oly $ 750 millio, there is cosiderable ucertaity about both the potetial for the drik, leadig to sigificat variace i this estimate. Aswath Damodara 223

224 Valuig the Expasio Optio Value of the Uderlyig Asset (S) = PV of Cash Flows from Expasio to etire U.S. market, if doe ow =$ 750 Millio Strike Price (K) = Cost of Expasio ito etire U.S market = $ 1000 Millio We estimate the stadard deviatio i the estimate of the project value by usig the aualized stadard deviatio i firm value of publicly traded firms i the beverage markets, which is approximately 34.25%. Stadard Deviatio i Uderlyig Asset s Value = 34.25% Time to expiratio = Period for which expasio optio applies = 5 years Call Value= $ 234 Millio Aswath Damodara 224

225 Cosiderig the Project with Expasio Optio NPV of Limited Itroductio = $ 400 Millio - $ 500 Millio = - $ 100 Millio Value of Optio to Expad to full market= $ 234 Millio NPV of Project with optio to expad = - $ 100 millio + $ 234 millio = $ 134 millio Ivest i the project Aswath Damodara 225

226 The Real Optios Test for Expasio Optios The Optios Test Uderlyig Asset: Expasio Project Cotigecy If PV of CF from expasio > Expasio Cost: PV - Expasio Cost If PV of CF from expasio < Expasio Cost: 0 The Exclusivity Test Barriers may rage from strog (exclusive liceses grated by the govermet) to weaker (brad ame, kowledge of the market) to weakest (first mover). The Pricig Test Uderlyig Asset: As with patets, there is o tradig i the uderlyig asset ad you have to estimate value ad volatility. Optio: Liceses are sometimes bought ad sold, but more diffuse expasio optios are ot. Cost of Exercisig the Optio: Not kow with ay precisio ad may itself evolve over time as the market evolves. Usig optio pricig models to value expasio optios will ot oly yield extremely oisy estimates, but may attach iappropriate premiums to discouted cashflow estimates. Aswath Damodara 226

227 Opportuities ad ot Optios Aswath Damodara 227

228 Iteret Firms as Optios Some aalysts have justified the valuatio of iteret firms o the basis that you are buyig the optio to expad ito a very large market. What do you thik of this argumet? Is there a optio to expad embedded i these firms? Is it a valuable optio? Aswath Damodara 228

229 The Optio to Abado A firm may sometimes have the optio to abado a project, if the cash flows do ot measure up to expectatios. If abadoig the project allows the firm to save itself from further losses, this optio ca make a project more valuable. PV of Cash Flows from Project Cost of Abadomet Preset Value of Expected Cash Flows o Project Aswath Damodara 229

230 Valuig the Optio to Abado Embraer is cosiderig a joit veture with Lear Aircraft to produce a small commercial airplae (capable of carryig passegers o short haul flights) Embraer will have to ivest $ 500 millio for a 50% share of the veture Its share of the preset value of expected cash flows is 480 millio. Lear Aircraft, which is eager to eter ito the deal, offers to buy Embraer s 50% share of the ivestmet aytime over the ext five years for $ 400 millio, if Embraer decides to get out of the veture. A simulatio of the cash flows o this time share ivestmet yields a variace i the preset value of the cash flows from beig i the partership is The project has a life of 30 years. Aswath Damodara 230

231 Project with Optio to Abado Value of the Uderlyig Asset (S) = PV of Cash Flows from Project = $ 480 millio Strike Price (K) = Salvage Value from Abadomet = $ 400 millio Variace i Uderlyig Asset s Value = 0.16 Time to expiratio = Life of the Project =5 years Divided Yield = 1/Life of the Project = 1/30 = (We are assumig that the project s preset value will drop by roughly 1/ each year ito the project) Assume that the five-year riskless rate is 6%. The value of the put optio ca be estimated as follows: Aswath Damodara 231

232 Should Embraer eter ito the joit veture? Value of Put =Ke -rt (1-N(d2))- Se -yt (1-N(d1)) =400 (exp (-0.06)(5) ( ) exp (-0.033)(5) ( ) = $ millio The value of this abadomet optio has to be added o to the et preset value of the project of -$ 20 millio, yieldig a total et preset value with the abadomet optio of $ millio. Aswath Damodara 232

233 Implicatios for Ivestmet Aalysis Havig a optio to abado a project ca make otherwise uacceptable projects acceptable. Actios that icrease the value of the abadomet optio iclude More cost flexibility, that is, makig more of the costs of the projects ito variable costs as opposed to fixed costs. Fewer log-term cotracts/obligatios with employees ad customers, sice these add to the cost of abadoig a project Fidig parters i the ivestmet, who are willig to acquire your ivestmet i the future These actios will udoubtedly cost the firm some value, but this has to be weighed off agaist the icrease i the value of the abadomet optio. Aswath Damodara 233

234 Optio Pricig Applicatios i Valuatio Equity Value i Deeply Troubled Firms Value of Udeveloped Reserves for Natural Resource Firm Value of Patet/Licese Aswath Damodara 234

235 Optio Pricig Applicatios i Equity Valuatio Equity i a troubled firm (i.e. a firm with high leverage, egative earigs ad a sigificat chace of bakruptcy) ca be viewed as a call optio, which is the optio to liquidate the firm. Natural resource compaies, where the udeveloped reserves ca be viewed as optios o the atural resource. Start-up firms or high growth firms which derive the bulk of their value from the rights to a product or a service (eg. a patet) Aswath Damodara 235

236 Valuig Equity as a optio The equity i a firm is a residual claim, i.e., equity holders lay claim to all cashflows left over after other fiacial claim-holders (debt, preferred stock etc.) have bee satisfied. If a firm is liquidated, the same priciple applies, with equity ivestors receivig whatever is left over i the firm after all outstadig debts ad other fiacial claims are paid off. The priciple of limited liability, however, protects equity ivestors i publicly traded firms if the value of the firm is less tha the value of the outstadig debt, ad they caot lose more tha their ivestmet i the firm. Aswath Damodara 236

237 Equity as a call optio The payoff to equity ivestors, o liquidatio, ca therefore be writte as: where, Payoff to equity o liquidatio = V - D if V > D V = Value of the firm = 0 if V D D = Face Value of the outstadig debt ad other exteral claims A call optio, with a strike price of K, o a asset with a curret value of S, has the followig payoffs: Payoff o exercise = S - K if S > K = 0 if S K Aswath Damodara 237

238 Payoff Diagram for Liquidatio Optio Net Payoff o Equity Face Value of Debt Value of firm Aswath Damodara 238

239 Applicatio to valuatio: A simple example Assume that you have a firm whose assets are curretly valued at $100 millio ad that the stadard deviatio i this asset value is 40%. Further, assume that the face value of debt is $80 millio (It is zero coupo debt with 10 years left to maturity). If the te-year treasury bod rate is 10%, how much is the equity worth? What should the iterest rate o debt be? Aswath Damodara 239

240 Model Parameters Value of the uderlyig asset = S = Value of the firm = $ 100 millio Exercise price = K = Face Value of outstadig debt = $ 80 millio Life of the optio = t = Life of zero-coupo debt = 10 years Variace i the value of the uderlyig asset = σ 2 = Variace i firm value = 0.16 Riskless rate = r = Treasury bod rate correspodig to optio life = 10% Aswath Damodara 240

241 Valuig Equity as a Call Optio Based upo these iputs, the Black-Scholes model provides the followig value for the call: d1 = N(d1) = d2 = N(d2) = Value of the call = 100 (0.9451) - 80 exp (-0.10)(10) (0.6310) = $75.94 millio Value of the outstadig debt = $100 - $75.94 = $24.06 millio Iterest rate o debt = ($ 80 / $24.06) 1/10-1 = 12.77% Aswath Damodara 241

242 The Effect of Catastrophic Drops i Value o o o Assume ow that a catastrophe wipes out half the value of this firm (the value drops to $ 50 millio), while the face value of the debt remais at $ 80 millio. What will happe to the equity value of this firm? It will drop i value to $ millio [ $ 50 millio - market value of debt from previous page] It will be worth othig sice debt outstadig > Firm Value It will be worth more tha $ millio Aswath Damodara 242

243 Illustratio : Value of a troubled firm Assume ow that, i the previous example, the value of the firm were reduced to $ 50 millio while keepig the face value of the debt at $80 millio. This firm could be viewed as troubled, sice it owes (at least i face value terms) more tha it ows. The equity i the firm will still have value, however. Aswath Damodara 243

244 Valuig Equity i the Troubled Firm Value of the uderlyig asset = S = Value of the firm = $ 50 millio Exercise price = K = Face Value of outstadig debt = $ 80 millio Life of the optio = t = Life of zero-coupo debt = 10 years Variace i the value of the uderlyig asset = σ 2 = Variace i firm value = 0.16 Riskless rate = r = Treasury bod rate correspodig to optio life = 10% Aswath Damodara 244

245 The Value of Equity as a Optio Based upo these iputs, the Black-Scholes model provides the followig value for the call: d1 = N(d1) = d2 = N(d2) = Value of the call = 50 (0.8534) - 80 exp (-0.10)(10) (0.4155) = $30.44 millio Value of the bod= $50 - $30.44 = $19.56 millio The equity i this firm drops by, because of the optio characteristics of equity. This might explai why stock i firms, which are i Chapter 11 ad essetially bakrupt, still has value. Aswath Damodara 245

246 Equity value persists.. Value of Equity as Firm Value Chages Value of Equity Value of Firm ($ 80 Face Value of Debt) Aswath Damodara 246

247 Valuig equity i a troubled firm The first implicatio is that equity will have value, eve if the value of the firm falls well below the face value of the outstadig debt. Such a firm will be viewed as troubled by ivestors, accoutats ad aalysts, but that does ot mea that its equity is worthless. Just as deep out-of-the-moey traded optios commad value because of the possibility that the value of the uderlyig asset may icrease above the strike price i the remaiig lifetime of the optio, equity will commad value because of the time premium o the optio (the time util the bods mature ad come due) ad the possibility that the value of the assets may icrease above the face value of the bods before they come due. Aswath Damodara 247

248 Obtaiig optio pricig iputs - Some real world problems The examples that have bee used to illustrate the use of optio pricig theory to value equity have made some simplifyig assumptios. Amog them are the followig: (1) There were oly two claim holders i the firm - debt ad equity. (2) There is oly oe issue of debt outstadig ad it ca be retired at face value. (3) The debt has a zero coupo ad o special features (covertibility, put clauses etc.) (4) The value of the firm ad the variace i that value ca be estimated. Aswath Damodara 248

249 Real World Approaches to Gettig iputs Iput Value of the Firm Variace i Firm Value Estimatio Process Cumulate market values of equity ad debt (or) Value the assets i place usig FCFF ad WACC (or) Use cumulated market value of assets, if traded. If stocks ad bods are traded, σ2 firm = we 2 σe 2 + wd 2 σd we wd ρed σe σd where σe 2 = variace i the stock price we = MV weight of Equity Value of the Debt Maturity of the Debt σd 2 = the variace i the bod price w d = MV weight of debt If ot traded, use variaces of similarly rated bods. Use average firm value variace from the idustry i which compay operates. If the debt is short term, you ca use oly the face or book value of the debt. If the debt is log term ad coupo bearig, add the cumulated omial value of these coupos to the face value of the debt. Face value weighted duratio of bods outstadig (or) If ot available, use weighted maturity Aswath Damodara 249

250 Valuig Equity as a optio - Eurotuel i early 1998 Eurotuel has bee a fiacial disaster sice its opeig I 1997, Eurotuel had earigs before iterest ad taxes of - 56 millio ad et icome of millio At the ed of 1997, its book value of equity was millio It had 8,865 millio i face value of debt outstadig The weighted average duratio of this debt was years Debt Type Face Value Duratio Short term year year Loger Total 8,865 mil years Aswath Damodara 250

251 The Basic DCF Valuatio The value of the firm estimated usig projected cashflows to the firm, discouted at the weighted average cost of capital was 2,312 millio. This was based upo the followig assumptios Reveues will grow 5% a year i perpetuity. The COGS which is curretly 85% of reveues will drop to 65% of reveues i yr 5 ad stay at that level. Capital spedig ad depreciatio will grow 5% a year i perpetuity. There are o workig capital requiremets. The debt ratio, which is curretly 95.35%, will drop to 70% after year 5. The cost of debt is 10% i high growth period ad 8% after that. The beta for the stock will be 1.10 for the ext five years, ad drop to 0.8 after the ext 5 years. The log term bod rate is 6%. Aswath Damodara 251

252 Other Iputs The stock has bee traded o the Lodo Exchage, ad the aualized std deviatio based upo l (prices) is 41%. There are Eurotuel bods, that have bee traded; the aualized std deviatio i l(price) for the bods is 17%. The correlatio betwee stock price ad bod price chages has bee 0.5. The proportio of debt i the capital structure durig the period ( ) was 85%. Aualized variace i firm value = (0.15) 2 (0.41) 2 + (0.85) 2 (0.17) (0.15) (0.85)(0.5)(0.41)(0.17)= The 15-year bod rate is 6%. (I used a bod with a duratio of roughly 11 years to match the life of my optio) Aswath Damodara 252

253 Valuig Eurotuel Equity ad Debt Iputs to Model Value of the uderlyig asset = S = Value of the firm = 2,312 millio Exercise price = K = Face Value of outstadig debt = 8,865 millio Life of the optio = t = Weighted average duratio of debt = years Variace i the value of the uderlyig asset = σ 2 = Variace i firm value = Riskless rate = r = Treasury bod rate correspodig to optio life = 6% Based upo these iputs, the Black-Scholes model provides the followig value for the call: d1 = N(d1) = d2 = N(d2) = Value of the call = 2312 (0.2023) - 8,865 exp (-0.06)(10.93) (0.0751) = 122 millio Appropriate iterest rate o debt = (8865/2190) (1/10.93) -1= 13.65% Aswath Damodara 253

254 I Closig There are real optios everywhere. Most of them have o sigificat ecoomic value because there is o exclusivity associated with usig them. Whe optios have sigificat ecoomic value, the iputs eeded to value them i a biomial model ca be used i more traditioal approaches (decisio trees) to yield equivalet value. The real value from real optios lies i Recogizig that buildig i flexibility ad escape hatches ito large decisios has value Isights we get o uderstadig how ad why compaies behave the way they do i ivestmet aalysis ad capital structure choices. Aswath Damodara 254

255 Back to Lemmigs... Aswath Damodara 255