Aswath Damodaran Discounted Cash Flow Valuation

Aswath Damodaran 1 Aswath Damodaran where CF Proposition 2: Assets that generate cash flows early in their life will Proposition 1: For an asset to have value, the expected cash flows Discounted Cashflow Valuation: Basis for compensate. may however have greater growth and higher cash flows to be worth more than assets that generate cash flows later; the latter have to be positive some time over the life of asset. given the riskiness of cash flow and t is life asset. t is the cash flow in period t, r discount rate appropriate au Value = Approach t=n t=1 ∑ 1 r) (1+ CF t

t 2 Aswath Damodaran I I Equity Valuation versus Firm

claimholders in the firm Value the entire business, which includes, besides equity, other Value just the equity stake in business 3 Aswath Damodaran I I value of a stock is the present expected future dividends. The dividend discount model is a specialized case of equity valuation, and the required by equity investors in the firm. interest and principal payments, at the cost of equity, i.e., rate return i.e., the residual cashflows after meeting all expenses, tax obligations and The value of equity is obtained by discounting expected cashflows to equity, where, k CF to Equity CF to e

= Cost of Equity au fEut = Value of Equity t = Expected Cashflow to Equity in period t I.Equity Valuation t=n ∑ t=1 CF to Equity 1+k + (1 e ) t

t 4 Aswath Damodaran I proportions. of financing used by the firm, weighted their market value average cost of capital, which is the different components expenses and taxes, but prior to debt payments, at the weighted the firm, i.e., residual cashflows after meeting all operating The value of the firm is obtained by discounting expected cashflows to where, CF to Firm CF to WACC = Weighted Average Cost of Capital au fFr = Value of Firm t

= Expected Cashflow to Firm in period t II. Firm Valuation ∑ t=n t=1 1 WACC) (1+ CF to Firm t

t 5 Aswath Damodaran J J J I J J J J I equal to the value you would have got in an equity valuation lesser than the value you would have got in an equity valuation greater than the value you would have got in an equity valuation Doing so, will give you a value for the equity which is Subtract out the value of all non-equity claims in firm included in the cost of capital calculation Subtract the value of all non-equity claims in firm, that are Subtract out the value of all debt Subtract out the value of long term debt you need to do? To get from firm value to equity value, which of the following would

Firm Value and Equity 6 Aswath Damodaran emnlVle$10. $ 2363.008 $ 1603.0 Terminal Value erC oEut n x 1t CF to Firm Int Exp (1-t) CF to Equity 1$Year I I I 5$ 4$ 3$2$ 60 is $800. The current market value of equity is $1,073 and the debt outstanding term at 10%. (The tax rate for the firm is 50%.) Assume also that the cost of equity is 13.625% and firm can borrow long the next five years. Assume that you are analyzing a company with the following cashflows for Cash Flows and Discount Rates 7. 0$ 116.2 40 $ 76.2

50 $ $ 50 8$4 $ 108 $ 40 68 34 0$ 123.49 $ 40 83.49 0$ 100 $ 40

0$ 90 40 7 Aswath Damodaran I I I Method 1: Discount CF to Equity at Cost of get value equity PV of Firm = 90/1.0994 + 100/1.0994 = 13.625% (1073/1873) + 5% (800/1873) 9.94% WACC Cost of Debt = Pre-tax rate (1- tax rate) 10% (1-.5) 5% Method 2: Discount CF to Firm at Cost of Capital get value firm 76.2/1.13625 Vo qiy= PV of Firm - Market Value Debt PV of Equity PV of Equity = 50/1.13625 + 60/1.13625 Cost of Equity = 13.625% (123.49+2363)/1.0994 Equity versus Firm Valuation 4 + (83.49+1603)/1.13625 = $ 1873 - 800 $1073 5 = $1873 2 + 108/1.0994 5 = $1073 2 + 68/1.13625 3 + 116.2/1.0994 3 + 4

+ 8 Aswath Damodaran I I The key error to avoid is mismatching cashflows and discount rates The key error to avoid is Never mix and match cash flows discount rates. a downward biased estimate of the value firm. while discounting cashflows to the firm at cost of equity will yield capital will lead to an upwardly biased estimate of the value equity, since discounting cashflows to equity at the weighted average cost of First Principle of Valuation

, 9 Aswath Damodaran The Effects of Mismatching Cash Flows and Error 3: Discount CF to Firm at Cost of Equity, forget subtract out debt, and Error 2: Discount CF to Firm at Cost of Equity get firm value Error 1: Discount CF to Equity at Cost of Capital get equity value get too high a value for equity Value of equity is overstated by $175. Value of Equity is overstated by $ 540 Value of Equity = $ 1613 PV of Firm = 90/1.13625 + 100/1.13625 PV of Equity = 50/1.0994 + 60/1.0994 Value of Equity is understated by $ 260. PV of Equity = $1612.86 - $800 $813 (83.49+1603)/1.0994 (123.49+2363)/1.13625 Discount Rates 5 = $1248 5 = $1613 2 + 68/1.0994 2 + 108/1.13625 3 + 76.2/1.0994 3 + 116.2/1.13625 4 + 4

+ 10 Aswath Damodaran Discounted Cash Flow Valuation: The Steps I I I I I equity investors (CF to Equity) or all claimholders Firm) Choose the Estimate Estimate the Estimate the Estimate the characteristics (risk & cash flow) it will have when does. valued, generally by estimating an expected growth rate in earnings. • • •D Discount rate can vary across time. whether the cash flows are nominal or real Discount rate can be in nominal terms or real terms, depending upon cost of capital (if valuing the firm) iscount rate can be either a cost of equity (if doing valuation) or when right DCF model for this asset and value it. future earnings and cash flows current earnings and discount rate or rates to use in the valuation the firm will reach “stable growth” “stable growth” cash flows on the firm being on the asset, to either

and what 11 Aswath Damodaran Equity: Value of Equity Firm: Value of Firm Value Generic DCF Valuation Model cash flows Equity: After debt flow Firm: Pre-debt cash Cash flows CF 1 DISCOUNTED CASHFLOW VALUATIO CF Length of Period High Growth 2 CF Equity: Cost of Equity Firm:Cost of Capital Discount Rate 3 CF Net Income/EPS Equity: Growth in Operating Earnings Firm: Growth in Expected Growth 4 CF 5 ...... N CF forever Grows at constant rate Firm is in stable growth: n Terminal Value

Forever 12 Aswath Damodaran Value of Equity nominal as cash flows in same terms (real or - In same currency and - No reinvestment risk - No default risk Riskfree Rate = Dividends * Payout Ratio Net Income Dividends Dividend : EQUITY VALUATION WITH DIVIDEND 1 Dividend +

Business Type of Discount at 2 - Measures market risk Beta Dividend Cost of Equity Leverage Operating Cost of Equit 3 Dividend Return on Equity Retention Ratio * Expected Growth Leverage Financial 4 y X Dividend risk investment - Premium for average Risk Premium ...... 5 Terminal Value= Dividend Dividend Premium Base Equity S forever Grows at constant rate Firm is in stable growth: n Premium Country Risk Forever n+1 /(k e

-g 13 n ) Aswath Damodaran Value of Equity Debt Ratio = DR Financing Weights nominal as cash flows in same terms (real or - In same currency and - No reinvestment risk - No default risk Riskfree Rate = FCFE - Change in WC (!-DR) - (Cap Ex Depr) (1- DR) Net Income Cashflow to Equity FCFE 1 : EQUITY VALUATION WITH FCF FCFE + 2

Business Type of Discount at - Measures market risk Beta FCFE Cost of Equity 3 Leverage Operating Cost of Equit FCFE 4 Return on Equity Retention Ratio * Expected Growth Leverage Financial y X FCFE risk investment - Premium for average Risk Premium 5 ...... E Terminal Value= FCFE FCFE Premium Base Equity n forever Grows at constant rate Firm is in stable growth: Premium Country Risk Forever n+1 /(k e -g n

) 14 Aswath Damodaran = Value of Equity - Value of Debt = Value of Firm + Cash & Non-op Assets Value of Operating Assets nominal as cash flows in same terms (real or - In same currency and - No reinvestment risk - No default risk Riskfree Rate : Cost of Equity = FCFF - Change in WC Depr) - (Cap Ex EBIT (1-t) Cashflow to Firm

+ Business Type of Discount at FCFF - Measures market risk Beta 1 WACC= Cost of Equity (Equity/(Debt + Equity)) Debt (Debt/(Debt+ Leverage Operating FCFF 2 VALUING A FIRM Cost of Debt + Default Spread) (1-t) (Riskfree Rate FCFF Leverage Financial X 3 risk investment - Premium for average Risk Premium FCFF * Return on Capital Reinvestment Rate Expected Growth Premium Base Equity 4 FCFF Terminal Value= FCFF Based on Market Value Weights 5 ...... Premium Country Risk FCFF forever Grows at constant rate Firm is in stable growth: n n+1 /(r-g Forever n

) 15 Aswath Damodaran Discounted Cash Flow Valuation: The Inputs

Aswath Damodaran 16 Aswath Damodaran I. Estimating Discount Rates

DCF Valuation 17 Aswath Damodaran I I both the At an intuitive level, the discount rate used should be consistent with rates can lead to serious errors in valuation. estimating the discount rate or mismatching cashflows and Critical ingredient • • • Estimating Inputs: Discount Rates flows (i.e., reflect expected inflation), the discount rate should be nominal Currency capital. are cash flows to the firm, appropriate discount rate is cost of equity, the appropriate discount rate is a cost of equity. If cash flows Equity versus Firm Nominal versus Real be the currency in which discount rate is estimated. riskiness : The currency in which the cash flows are estimated should also and the in discounted cashflow valuation. Errors : If the cash flows being discounted are to : If the cash flows being discounted are nominal type of cashflow

being discounted. 18 Aswath Damodaran I I I market or non-diversifiable risk) market or non-diversifiable perceives in an investment is risk that cannot be diversified away (I.e, for safer investments investor is well diversified investor is Most risk and return models in finance also assume that the marginal in the investment rate) in valuation should be the risk perceived by marginal investor that the risk should be rewarded (and thus built into discount around an expected return, risk and return models in finance assume While risk is usually defined in terms of the variance actual returns investments riskier for higher The cost of equity should be Cost of Equity , and that the only risk he or she

and lower 19 Aswath Damodaran rx E(R) = a + Proxy factor ut E(R) = R Multi AME(R) = R Expected Return CAPM Model P E(R) = R APM The Cost of Equity: Competing Models f f f + + + Σ β Σ j=1..N j=1..N Σ

j=1 (R j=1,,N β m b j - R (R β j Y j (R f j ) - R j j - R f ) f )

Inputs Needed Macro economic risk premiums Riskfree Rate; Macro factors Regression coefficients Proxies Factor risk premiums Betas relative to each factor Riskfree Rate; # of Factors; Market Risk Premium Beta relative to market portfolio Riskfree Rate Betas relative to macro factors 20 Aswath Damodaran I I where, R In practice, R Cost of Equity = Consider the standard approach to estimating cost of equity: E(R Betas are estimated by regressing stock returns against market • • • f = Riskfree rate Short term government security rates Historical risk premiums m ) = Expected Return on the Market Index (Diversified Portfolio) The CAPM: Cost of Equity f + Equity Beta * (E(R are used for the risk premium are used as risk free rates m ) - R f

) 21 Aswath Damodaran I I I I I Short term Governments are not riskfree In emerging markets, there are two problems: long term) to the duration of riskfree rate (also A simpler approach is to match the duration of analysis (generally flow is expected to occur and will vary across time Thus, the riskfree rates in valuation will depend upon when cash For an investment to be riskfree, then, it has have Therefore, there is no variance around the expected return. On a riskfree asset, the actual return is equal to expected return. • • • •

There might be no market-based long term government rate (China) The government might not be viewed as riskfree (Brazil, Indonesia) No reinvestment risk No default risk 22 Aswath Damodaran I I I Do the analysis in another more stable currency, say US dollars. riskfree rate, which can be obtained in one of two ways – Do the analysis in real terms (rather than nominal terms) using a Estimate a range for the riskfree rate in local terms: • •f • Government bond rate in local currency terms - Default spread for • in which the valuation is being done. set equal, approximately, to the long term real growth rate of economy (say Euros or dollars) to estimate the riskless rate in local currency. Approach 2: Use forward rates and the riskless rate in an index currency Government in local currency Approach 1: Subtract default spread from local government bond rate: rom an inflation-indexed government bond, if one exists

Estimating a Riskfree Rate 23 Aswath Damodaran J J J J I The interest rate on a US treasury bond is partially backed by the US Government) The interest rate on a US $ denominated Brazilian Brady bond (which Bond) The interest rate on a US $ denominated Brazilian long term bond (C- Government bond The interest rate on a Brazilian Real denominated long term riskfree rate that you should use is attempting to estimate a riskfree rate use in the analysis. The Ambev, a Brazilian company, in U.S. dollars and are You are valuing

A Simple Test 24 Aswath Damodaran I I I 9120 06%69%94%6.17% 3.90% 9.44% 4.74% 5.17% 6.21% 6.90% 10.62% 4.68% 5.89% 6.84% 8.09% T.Bonds T.Bills 1991-2001 T.Bonds 1962-2001 T.Bills 1928-2001 Historical Period Everyone uses historical premiums, but.. For instance, looking at the US: Practitioners never seem to agree on the premium; it is sensitive earned over riskless securities. The historical premium is the that stocks have historically • • • Whether you use geometric or arithmetic averages. Whether you use T.bill rates or T.Bond How far back you go in history…

rtmtcaeaeGeometric Average Arithmetic average 25 Aswath Damodaran If you choose to use historical premiums…. I I I about risk premiums over long periods. Use the geometric risk premium. It is closer to how investors think term bond rates, the premium should be one over T.Bonds Be consistent in your use of the riskfree rate. Since we argued for long years is roughly: 25%, the standard error in a historical premium estimated over 25 error. Given the annual standard deviation in stock prices is about Go back as far you can. A risk premium comes with a standard Standard Error in Premium = 25%/

√ 25 = 25%/5 5% 26 Aswath Damodaran I I beginning with the U.S. premium as base: For such markets, we can estimate a modified historical premium emerging markets but also of many Western European markets. precision in markets with limited history - this is true not just of Historical risk premiums are almost impossible to estimate with any • Country risk premium = Risk Premium Country risk premium = Risk • Premium Country risk premium = Risk • incorporates both the country bond spread and equity market volatility. Combined approach based upon the default spread of bond issued by country. Country Bond approach upon the volatility of market in question relative to U.S market. Relative Equity Market approach Country Risk Premiums : In this approach, the country risk premium : In this approach, the country risk premium is : The country risk premium is based US US + Country bond default spread * σ Country Equity / σ

US Equity 27 Aswath Damodaran

Step 1: Assessing Country Risk Using Mexico Baa3 Honduras B2 Guatemala Ba2 Ecuador 550 Colombia Ba2 300 Brazil B1 Bolivia B1 300 Argentina B1 Country 450 450 450 Venezuela B2 Uruguay Baa3 550 Peru Ba3 Paraguay B2 145 550

Ratings: Latin America - March 2001 a2750 5 Caa2 7 Spread Market Typical Spread Rating 145 400

563 331 235 193 7 8 7 581 361 537 551 631 601 455 28 Aswath Damodaran Step 2: From Bond Default Spreads to Equity I I and building in risk. Ratings agencies make mistakes. They are often late in recognizing spreads to be higher than debt spreads. equity risk premiums are highly correlated, one would expect Country ratings measure default risk. While risk premiums and • One way to adjust the country spread upwards is use information from • and bond prices in that market. For example, Another is to multiply the bond spread by relative volatility of stock the default spread on junk bonds. the US market. In US, equity risk premium has been roughly twice – – – Adjusted Equity Spread = 5.37% (32.6/17.1%) Standard Deviation in Brazil C-Bond = 17.1% Bovespa Standard Deviation in Spreads (Equity) = 32.6%

10.24% 29 Aswath Damodaran • •S • • • • • • • • • • • •B • • Another Example: Assessing Country Risk Using Currency Ratings: Western Europe pi a 030 55 30 60 0 35 50 95 0 70 Aa1 Aaa 0 65 95 A3 Aaa Aa3 0 0 Switzerland 0 Aaa AA2 Spain A3 0 Portugal 0 Norway Aaa Aaa Netherlands Actual Spread Aaa Typical Spread Italy Ireland Aaa Greece Aaa Germany Rating France Finland Denmark Austria Country

ee a 025 60 Aa1 weden

limAa0 Aaa elgium 30 Aswath Damodaran I I and building in risk. Ratings agencies make mistakes. They are often late in recognizing spreads to be higher than debt spreads. equity risk premiums are highly correlated, one would expect Country ratings measure default risk. While risk premiums and • One way to adjust the country spread upwards is use information from • and bond prices in that market. For example, Another is to multiply the bond spread by relative volatility of stock the default spread on junk bonds. the US market. In US, equity risk premium has been roughly twice – – – Greek Country Risk Premium Adjusted Equity Spread = 0.95% (40.5%/26.1%) Standard Deviation in Greek GDr Bond = 26.1% Standard Deviation in Greek ASE(Equity) = 40.5%

1.59% 31 Aswath Damodaran I I I From Country Spreads to Corporate Risk the proportion of their revenues come from non-domestic sales) firms to have different exposures country risk (perhaps based upon Approach 3: Treat country risk as a separate factor and allow similar to its exposure other market risk. exposure to country risk is Approach 2: Assume that a company’s exposed to country risk. In this case, Approach 1: Assume that every company in the country is equally E(Return) = Riskfree Rate + Beta (US premium Country Spread) E(Return) = Riskfree Rate + Country Spread Beta (US premium) E(Return)=Riskfree Rate+ E(Return)=Riskfree Implicitly, this is what you are assuming when use the local Government’s dollar borrowing rate as your riskfree rate. Government’s premiums β (US premium) + λ (

Country Spread) 32 Aswath Damodaran Estimating Company Exposure to Country Risk I I I There are two implications firm in that market gets 70% of its revenues domestically For instance, if a firm gets 35% of its revenues domestically while the average λ = simplistic solution would be to do the following: “ The factor generates all its business within Brazil. United States should be less exposed to country risk in Brazil than one that For instance, a Brazilian firm that generates the bulk of its revenues in Different companies should be exposed to different degrees country risk. • •A % of revenues domestically % of revenues Firms might be able to actively manage their country risk exposures where it is located company’s risk exposure company’s λ ” measures the relative exposure of a firm to country risk. One λ = is determined by where it does business and not firm 35%/ 70 % = 0.5 / % of revenues domestically / % of revenues

avg firm 33 Aswath Damodaran Embraer is less exposed to country risk than the typical Brazilian firm since much E(Return)= 4.5% + E(Return) = 4.5% + 0.88 (5.51%+ 10.24%) 18.36% E(Return) =4.5% + 10.24% 0.88 (5.51%) = 19.59% I I I I of its business is overseas. their revenues come from non-domestic sales) have different exposures to country risk (perhaps based upon the proportion of Approach 3: Treat country risk as a separate factor and allow firms to its exposure to other market risk. exposure to country risk is similar Approach 2: Assume that a company’s country risk. In this case, Approach 1: Assume that every company in the country is equally exposed to 4.5%. (Real Riskfree Rate) Embraer is 0.88, and that the riskfree rate used Assume that the beta for Estimating E(Return) for Embraer 0 .88 (5.51%) + 0.50 (10.24 0.50

%) = 14.47% 34 Aswath Damodaran I I I greater than that of the economy, and then a stable growth period. initial period where the entire market will have earnings growth This model can be extended to allow for two stages of growth - an Gordon Growth Model: For instance, if stock prices are determined by a variation of the simple implied risk premium from the current level of stock prices. If we use a basic discounted cash flow model, can estimate the Plugging in the current level of index, dividends on index and • • • Subtracting out the riskfree rate will yield implied premium. expected return on stocks. “implied” expected growth rate will yield a high growth period. Dividends can be extended to included expected stock buybacks and a Expected Growth Rate) Value = Expected Dividends next year/ (Required Returns on Stocks -

Implied Equity Premiums 35 Aswath Damodaran Estimating Implied Premium for U.S. Market: 1148 = 34.72/(1+r) + 38.30/(1+r) Expected dividends + buybacks in year 6 = 51.39 (1.0505) $ 54.73 + Stock Buybacks $34.72 Expected Dividends = Implied risk premium = Solving for r, r = 8.67%. (Only way to do this is trial and error) I I I I I Dividends + stock buybacks = 2.74% of index (Current year) Expected growth rate after year 5 = 5.05% estimate for S&P 500) Expected Growth rate in earnings (next 5 years) = 10.3% (Consensus Treasury bond rate = 5.05% Level of the index = 1148 .0505))/(1+r) 5 er1Ya er3Ya Year 5 Year 4 Year 3 Year 2 Year 1 8.67% - 5.05% = - 5.05% 8.67% Jan 1, 2002 2 + 42.24/(1+r) 3.0$22 4.9$51.39 $46.59 $42.24 $38.30 3.62 % 3 + 46.59/(1+r) 4

+ (51.39+(54.73/(r- 36 Aswath Damodaran Implied Premiums: US- 1960 - 2001

Implied Premium

0.00% 1.00% 2.00% 3.00% 4.00% 5.00% 6.00% 7.00%

1960

1962

1964

1966

1968 1970

Implied Premium for US Equity Market

1972

1974

1976

1978

Year 1980

1982

1984

1986

1988

1990

1992

1994

1996

1998

2000 37 Aswath Damodaran Implied Premiums: US- 2000 - 2002

S&P 500 1000 1200 1400 1600 200 400 600 800

0

1/1/00

2/1/00

3/1/00

Apr-00

May-00 Jun-00

Implied Equity Risk Premiums: Monthly - Jan 2000 to July 2002

Jul-00

Aug-00

Sep-00

Oct-00

Nov-00

Dec-00

Jan-01 Feb-01

Index Mar-01

Month Apr-01 May-01

Dividends Jun-01

Jul-01

Aug-01

Sep-01

Oct-01

Nov-01

Dec-01

Jan-02

Feb-02

Mar-02

Apr-02

May-02

Jun-02

Jul-02 22-Jul-02 0.00% 0.50% 1.00% 1.50% 2.00% 2.50% 3.00% 3.50% 4.00% 4.50% 5.00%

Implied Equity risk premium 38 Aswath Damodaran Implied Premium for Brazilian Market: March 1, I I I I Solving for the expected return: Other parameters Dividends on the Index = 4.40% of (Used weighted yield) Level of the Index = 16417 • • • • Implied Equity premium = 11.16% -4. 5% 6.66% Expected return on Equity = 11.16% Expected Growth Riskfree Rate = 4.5% (real riskfree rate) – – After year 5 = 4.5% (real growth rate in long term) Next 5 years = 13.5% (Used expected real growth rate in Earnings)

2001 39 Aswath Damodaran The Effect of Using Implied Equity Premiums I I I Embraer’s stock price (at the time of valuation) = 15.25 BR Embraer’s 20.02 BR value per share (using implied equity premium of 6.66%) = Embraer’s adjustment) = 11.22 BR value per share (using historical premium + country risk Embraer’s

on Value 40 Aswath Damodaran I I I This beta has three problems: measures the riskiness of stock. The slope of the regression corresponds to beta stock, and (R The standard procedure for estimating betas is to regress stock returns • • • where a is the intercept and b slope of regression. • j ) against market returns (R the current leverage. It reflects the firm’s average financial leverage over period rather than the current mix It reflects the firm’s business mix over period of regression, not It has high standard error Estimating Beta R j = a + b R = a + b m ) -

m 41 Aswath Damodaran

Beta Estimation: The Noise Problem 42 Aswath Damodaran

Beta Estimation: The Index Effect 43 Aswath Damodaran I I I interest expenses, that increases exposure to market risk. beta will be of the equity in that business. Debt creates a fixed cost, Financial Leverage including market risk. This is because higher fixed costs increase your exposure to all risk, cost structure of a business, the higher beta will be that business. Operating Leverage to macroeconomic factors that affect the overall market. sensitivity of the demand for its products and services costs Product or Service • •C firms that sell less discretionary products Firms which sell more discretionary products will have higher betas than yclical companies have higher betas than non-cyclical firms Determinants of Betas : The beta value for a firm depends upon the : The more debt a firm takes on, the higher

: The greater the proportion of fixed costs in 44 Aswath Damodaran where I I market risk (and has a beta of zero), you can have modified version: While this beta is estimated on the assumption that debt carries no beta and the debt-equity ratio unlevered The beta of equity alone can be written as a function the β β E = Market Value of Equity D = Market Value of Debt t = Corporate marginal tax rate u L = Unlevered Beta (Asset Beta) = Unlevered = Levered or Equity Beta Equity Betas and Leverage β L = β u (1+ ((1-t)D/E)) - β L = β u (1+ ((1-t)D/E)) β debt

(1-t) (D/E) 45 Aswath Damodaran I I I I Solutions to the Regression Beta Problem Use an alternative measure of market risk that does not need a regression. regression technique. This will require Estimate the beta for firm from bottom up without employing Estimate the beta for firm using Modify the regression beta by • • • • • •

estimating the financial leverage of firm understanding the business mix of firm accounting earnings or revenues, which are less noisy than market prices. the standard deviation in stock prices instead of a regression against an index. fundamentals of the company adjusting the regression beta estimate, by bringing in information about changing the index used to estimate beta 46 Aswath Damodaran I I when The bottom up beta will give you a better estimate of the true The bottom up beta can be estimated by : • • • • It reflects the firm’s current business mix and financial leverage • It has lower standard error (SE debt/equity ratio Lever up using the firm’s betas of the different businesses a firm is in. unlevered Taking a weighted (by sales or operating income) average of the It can be estimated for divisions and private firms. (The unlevered beta of a business can be estimated by looking at other firms in unlevered (The

the same business) ββ eee unlevered levered =+− Bottom-up Betas ∑ jk j [] = = 1(1

1 β j

   Operating Income tax rate) (Current Debt/Equity Ratio) Operating Income average = SE Firm j firm    / √

n (n = number of firms) 47 Aswath Damodaran Bottom-up Beta: Firm in Multiple Businesses Levered Beta for Boeing = 0.88 (1 + - .35) (.2438)) 1.02 Tax Rate = 35% Market Debt/Equity Ratio = 24.38% Market Value of Debt = $8,143 Market Value of Equity = $ 33,401 Levered Beta Calculation 12,687.50 Beta of firm = 0.91 (.7039) + 0.80 (.2961) 0.88 Unlevered Defense Commercial Aircraft Segment Estimated Value = Revenues of division * Enterprise Value/Sales siae au neee ea Segment Weight Beta Unlevered Estimated Value 30,160.48 0.91 Boeing in 1998 0.80 70.39% 29.61%

Business 48 Aswath Damodaran te .859%0.71 5.97% 0.68 Siderar= 0.71 Levered Beta for Levered Proportion of operating income from steel = 100% D/E Ratio Unlevered Steel Business Siderar is an Argentine steel company. Siderar’s Bottom-up Beta Beta

Beta 49 Aswath Damodaran

beta estimated using U.S. steel companies be used to Can an unlevered estimate the beta for an Argentine steel company? No Yes

Comparable Firms? 50 Aswath Damodaran cash flows (real or nominal) as the and defined in same terms currency as cash flows, Has to be in the same Cost of Equity = The Cost of Equity: A Recap ikreRt + Riskfree Rate

leverage business, and firm’s own financial based upon other firms in the Preferably, a bottom-up beta, Country Default Spread* ( 2. Country risk premium = stocks over T.Bonds in U.S. Average premium earned by 1. Mature Equity Market Premium: Historical Premium ea*(R * Beta σ Equity isk Premium) / σ Country bond )

or

model and a simple valuation market is priced today Based on how equity Implied Premium 51 Aswath Damodaran I I I debt based upon that rating. for a firm), estimate synthetic rating your firm and the cost of When in trouble (either because you have no ratings or multiple The two most widely used approaches to estimating cost of debt are: in the market. will reflect not only your default risk but also the level of interest rates The cost of debt is the rate at which you can borrow currently, It • • for the firm the same firm can have different ratings. You to use a median rating upon the rating. While this approach is more robust, different bonds from Looking up the rating for firm and estimating a default spread based straight bonds that are liquid and widely traded firm. The limitation of this approach is that very few firms have long term Looking up the yield to maturity on a straight bond outstanding from

Estimating the Cost of Debt 52 Aswath Damodaran I I I EBIT from 2000. interest coverage ratio, we used the expenses and For Titan’s Siderar, in 1999, for instance For estimated from the interest coverage ratio characteristics of the firm. In its simplest form, rating can be The rating for a firm can be estimated using the financial • 1.25% (given the rating of A-) With a default spread of Siderar. we would estimate a rating of A- for Based upon the relationship between interest coverage ratios and ratings, Estimating Synthetic Ratings Interest Coverage Ratio = EBIT / Expenses Interest Coverage Ratio = 55,467/ 4028= 13.77

Interest Coverage Ratio = 161/48 3.33 53 Aswath Damodaran Interest Coverage Ratios, Ratings and Default > 8.50 fCvrg ai sEstimated Bond If Coverage Ratio is .0-65 A+ AA 5.50 - 6.50 6.50 - 8.50 .0-12 CCC – B B B+ 0.80 - 1.25 BB 1.25 - 1.50 BBB 1.50 - 1.75 A– 1.75 - 2.00 A 2.00 - 2.50 2.50 - 3.00 3.00 - 4.25 4.25 - 5.50 .0-06 C CC < 0.20 0.20 - 0.65 0.65 - 0.80 AAA D Spreads aigDefault Spread(1/99) Rating 0.80% 0.50% 4.25% 3.25% 2.50% 2.00% 1.50% 1.25% 1.00% 7.50% 6.00% 5.00% 0.20% 10.00%

Default Spread(1/01) 1.00% 8.00% 6.50% 4.75% 3.50% 2.25% 2.00% 1.80% 1.50% 12.70% 11.50% 10.00% 15.00% 0.75% 54 Aswath Damodaran I I 0.75%. The synthetic rating for Titan is AAA. default spread in 2001 might bear the burden of country default risk Companies in countries with low bond ratings and high default risk = 5.10% + 0.75% 0.95%= 6.80% = Riskfree Rate + Company Default Spread+ Country Spread Pre-tax Cost of Debt = 6% + 5.25% 1.25% 12.50% = US T.Bond rate + Country default spread Company Default Spread Pre-tax Cost of Debt in 1999 • For Siderar, the rating estimated of A- yields a cost debt as follows: For

Cost of Debt computations 55 Aswath Damodaran I I markets with higher interest rates than the US. They are more problematic when looking at smaller companies in close to the US interest rate analyzing large manufacturing firms in markets with interest rates developed using US companies, tends to travel well, as long we are The relationship between interest coverage ratios and ratings,

Synthetic Ratings: Some Caveats 56 Aswath Damodaran Weights for the Cost of Capital Computation I I I

compute the cost of capital. arrive at the value of equity should be same debt that you used to As a general rule, the debt that you should subtract from firm value to them at the beginning. equity at the end of analysis are different from values we gave valuation by doing this, since the values that we attach to firm and There is an element of circularity that introduced into every value weights for debt and equity. The weights used to compute the cost of capital should be market 57 Aswath Damodaran I I I Cost of Capital = 10.47 % (.787) + 6.80% (1- .2449) (0.213)) 9.33 Estimating Cost of Capital: Titan Cements Cost of Capital Debt Equity • • • • Market Value of Debt = 199,766 million GDr (21.3 %) Market Value of Debt = 199,766 million Cost of debt = 5.10% + 0.75% +0.95%= 6.80% Market Value of Equity = 739,217 million GDr (78.7%) Cost of Equity = 5.10% + 0.96 (4%+1.59%) 10.47% Company default spread premium market Mature Country default spread

Greek country premium 58 Aswath Damodaran I capital using book value weights instead of market weights. a book value of debt 200,000 million GDR. Estimate the cost Titan Cement has a book value of equity 135,857 million GDR and

Titan Cement: Book Value Weights 59 Aswath Damodaran I I I Cost of Capital = 16.32 % (.9437) + 12.50% (1-.3345) (.0563)) Estimating A U.S. Dollar Cost of Capital: Cost of Capital Debt Equity Siderar - An Argentine Steel Company Siderar • • • • Market Value of Debt = 59 Mil (5.63%) default) = 12.5% Cost of debt = 6.00% + 5.25% (Country default) +1.25% (Company Market Value of Equity = 3.20* 310.89 995 million (94.37%) Cost of Equity = 6.00% + 0.71 (4% +10.53%) 16.32% = 16.32 % (.9437) + 8.32% (.0563)) 15.87 Mature Market Premium

Country Risk Premium for Argentina 60 Aswath Damodaran Converting a Dollar Cost of Capital into Peso Cost of capital= I I U.S. is 3% For instance, if the inflation rate in pesos is 7% and Approach 2: Use the differential inflation rate to estimate cost of capital. computed as follows: instance, if the peso riskfree rate was 10%, cost of capital would be Approach 1: Use a peso riskfree rate in all of the calculations above. For (This assumes the peso riskfree rate has no country risk premium embedded in it.) • • 16.5% Cost of Debt = 10.00% + 5.25% (Country default) +1.25% (Company Cost of Equity = 10.00% + 0.71 (4% +10.53%) 20.32% = 1.1587 (1.07/1.03) 1.2037--> 20.37% () 1 + Cost of Capital cost of capital $    Inflation 1 Inflation 1 + + Peso $

   61 Aswath Damodaran I I Dealing with Hybrids and Preferred Stock

no significant impact on your valuation). outstanding market value of the firm, lumping it in with debt will make (As a rule of thumb, if the preferred stock is less than 5% component. The cost of preferred stock is the dividend yield. When dealing with preferred stock, it is better to keep as a separate option components. The conversion is equity. outstanding, break the $125 million into straight debt and conversion accordingly. Thus, if a firm has $ 125 million in convertible debt security down into debt and equity allocate the amounts When dealing with hybrids (convertible bonds, for instance), break the 62 Aswath Damodaran oto aia oto qiy(qiy(et+Eut) + Cost of Equity (Equity/(Debt + Equity)) Cost of Capital = beta based upon bottom-up Cost of equity Recapping the Cost of Capital Cost of Borrowing = Riskfree rate + Default spread (2) default spread (1) synthetic or actual bond rating Cost of borrowing should be based upon Weights should be market value weights oto orwn (1-t) Cost of Borrowing (Debt/(Debt + Equity))

tax benefits of debt Marginal tax rate, reflecting 63 Aswath Damodaran II. Estimating Cash Flows

DCF Valuation 64 Aswath Damodaran I I I debt issues (debt issued - repaid) If looking at cash flows to equity, consider the from net Consider how much the firm invested to create future growth Estimate the current earnings of firm • • If looking at cash flows to the firm, look operating earnings after taxes • • Increasing working capital needs are also investments for future growth cover some of these expenditures. expenditures. To the extent that depreciation provides a cash flow, it will If the investment is not expensed, it will be categorized as capital i.e. net income If looking at cash flows to equity, look earnings after interest expenses -

Steps in Cash Flow Estimation 65 Aswath Damodaran = Free Cash Flow to Firm (FCFF) - Change in non-cash working capital - ( Capital Expenditures Depreciation) EBIT (1- tax rate) All claimholders in the firm Measuring Cash Flows Cash flows can be measured to - Preferred Dividend - (Principal Repaid New Debt Issues) - Change in non-cash Working Capital - (Capital Expenditures Depreciation) Net Income Just Equity Investors

+ Stock Buybacks Dividends 66 Aswath Damodaran I EBIT ( 1 - tax rate) = Cash flow to the firm - Change in Working Capital - (Capital Expenditures Depreciation) Where are the tax savings from interest payments in this cash flow?

Measuring Cash Flow to the Firm 67 Aswath Damodaran history Firm’s From Reported to Actual Earnings Earnings Normalize Firms Comparable Measurin - Unofficial numbers - Trailing Earnings Update - Adjust operating income - Convert into debt Operating leases g Earnin g - Non-recurring expenses - Capital Expenses - Financial Expenses Cleanse s operating items of

- Adjust operating income - Convert into asset R&D Expenses 68 Aswath Damodaran I I restructuring. firms, as well for firms that have undergone significant Updating makes the most difference for smaller and more volatile and can be updated by using- for inputs on earnings and assets. Annual reports are often outdated When valuing companies, we often depend upon financial statements • • Informal and unofficial news reports, if quarterly reports are unavailable. Trailing 12-month data, constructed from quarterly earnings reports.

I. Update Earnings 69 Aswath Damodaran I I reflect its treatment. than an operating expense), the income has to be adjusted The R & D Adjustment equity earnings but does change the operating expenses and need to be reclassified as such. This has no effect on operating leases as expenses, they are really financial The Operating Lease Adjustment II. Correcting Accounting Earnings : Since R&D is a capital expenditure (rather

: While accounting convention treats 70 Aswath Damodaran The Magnitude of Operating Leases 10.00% 20.00% 30.00% 40.00% 50.00% 60.00% 0.00% aktA Market Operating Lease expenses as % of Income pparel Stores Furniture Stores

Restaurants 71 Aswath Damodaran I I I Dealing with Operating Lease Expenses Adjusted Operating Earnings the pre-tax cost of debt Debt Value of Operating Leases = PV Lease Expenses at adjustments to earnings and capital: should be treated as financing expenses, with the following computing operating income. In reality, lease expenses Operating Lease Expenses are treated as operating expenses in Adjusted Operating Earnings = + Pre-tax cost of Debt * • Adjusted Operating Earnings = + Lease

PV of Operating Leases. As an approximation, this works: Expenses - Depreciation on Leased Asset 72 Aswath Damodaran Operating Leases at The Home Depot in 1998 -5 20 $ 1,450 (PV of 10-yr annuity) I I $ 270 6-15 Present Value Operating Lease Expense Yr I 5$ 4$ 3$ 2$ 1$ Adjusted Operating Income = $2,016 + 2,571 (.0625) $2,177 mil Debt outstanding at the Home Depot = $1,205 + $2,571 $3,776 mil The pre-tax cost of debt at the Home Depot is 6.25% Present Value of Operating Leases =$ 2,571 (The Home Depot has other debt outstanding of $1,205 million)

3 $ 174 $ 192 $ 220 $ 258 $ 277 236 245 264 291 294 73 Aswath Damodaran The Effects of Capitalizing Operating Leases I I I I book capital invested operating income will be proportionately lower than the increase in Return on Capital financial expenses anyway Net income : will be unaffected since it is after both operating and before the imputed interest on operating lease expense Operating income cost of capital and levered beta calculation Debt : will increase, leading to an increase in debt ratios used the

: will increase, since operating leases now be

will generally decrease since the increase in 74 Aswath Damodaran The Magnitude of R&D Expenses 10.00% 20.00% 30.00% 40.00% 50.00% 60.00% 0.00% Market R&D as % of Operating Income Petroleum

Computers 75 Aswath Damodaran R&D Expenses: Operating or Capital Expenses I I To capitalize R&D, more logical to treat it as capital expenditures. expense even though it is designed to generate future growth. It Accounting standards require us to consider R&D as an operating Sum up the unamortized R&D over period. (Thus, if amortizable • • •S years ago...: R&D expense from five years ago, 2/5th of the four life is 5 years, the research asset can be obtained by adding up 1/5th of Collect past R&D expenses for as long the amortizable life

pecify an amortizable life for R&D (2 - 10 years) 76 Aswath Damodaran 99(urn)19.010 1594.00 1.00 1997 1594.00 1998 1999 (current) Year I 1996 1994 1995 mriaino eerhasti 98=$ 484.6 million Adjustment to Operating Income = $ 1,594 million - 484.6 1,109.4 Amortization of research asset in 1998 = Value of research asset = Total R & D was assumed to have a 5-year life. Capitalizing R&D Expenses: Cisco & xes nmrie oto Amortization this year Unamortized portion R&D Expense 698.00 399.00 89.00 060 0.80 1026.00 211.00 0.60 0.40 0.00 .042.20 0.20 820.80 418.80 159.60 0.00 $ 3,035.4 million $ 3,035.40

$205.20 $139.60 $79.80 $ 484.60 $17.80 $42.20 77 Aswath Damodaran I I I I after-tax operating income. For all firms, the net cap ex will increase by same amount as Depreciation will increase by the amortization of research asset; Capital expenditures will increase by the amount of R&D; Research asset Book value of equity (and capital) will increase by the capitalized fast R&D is growing Net income will increase proportionately, depending again upon how R&D is growing the more operating income will be affected. since the amortization will offset R&D added back. The faster whether R&D is growing or not. If it flat, there will be no effect Operating Income will generally increase, though it depends upon

The Effect of Capitalizing R&D 78 Aswath Damodaran J J J J I Would your answer be any different if the firm had reported one-time III. One-Time and Non-recurring Charges

No Yes losses like these once every five years? A profit of $ 500 million A loss of $ 500 million you would use in your valuation? million, due to a one-time charge of $ 1 billion. What is the earnings Assume that you are valuing a firm is reporting loss of $ 500 79 Aswath Damodaran I I warning signals in financial statements and correct for them: While you will not be able to catch outright fraud, should look for firms. aggressive firms will show higher earnings than more conservative the fidelity that they show to these standards can vary. More Though all firms may be governed by the same accounting standards, •S • •I R&D expenses, for instance. Income from asset sales or financial transactions (for a non-financial firm) not revealed or from special purpose entities. ncome from unspecified sources - holdings in other businesses that are udden changes in standard expense items - a big drop S,G &A or

IV. Accounting Malfeasance…. 80 Aswath Damodaran V. Dealing with Negative or Abnormally Low the firm over time Firm made by if Equity and EBIT Earnings (Net Income Average Dollar over time changed significantly If firm’s size has not Problems Temporary A Framework for Anal Normalize Earnings over time If firm’s size has changed in recession Eg. Auto firm Cyclicality: BV of capital (if ROC) BV of equity (if ROE) or current ROC (if valuing firm) on current valuing equity) or average Use firm’s average ROE (if y zin Earnings Why are the earnings negative or abnormally low? g Com p anies with Ne problems infrastructure firms and with reasons: Young Life Cycle related g ative or Abnormall

(b) sector. operating margins of stable firms in the (a) time.: reduce or eliminate the problem over flow forecasts starting with revenues and Value the firm by doing detailed cash industry-average operating margin. (c) own optimal or the industry average. with by end of period, which could be its debt ratio that the firm will be comfortable

If problem is structura

If problem is operating If problem is leverage too much debt. healthy firm with An otherwise Problems: Eg. Leverage y Low Earnin l: Target for : Target for an : Target for a problems. production or cost with significant Problems: Eg. A firm Operating Long-term g

s 81 Aswath Damodaran J J J J J I using the same tax rate Any of the above, as long you compute your after-tax cost debt None of the above The marginal tax rate The tax rate based upon taxes paid and EBIT (taxes paid/EBIT) income) The effective tax rate in the financial statements (taxes paid/Taxable income should be The tax rate that you should use in computing the after-tax operating

What tax rate? 82 Aswath Damodaran I I I the marginal tax rate over time. If you choose to use the effective tax rate, adjust rate towards income is more accurate in later years operating income in the earlier years, but after-tax tax By using the marginal tax rate, we tend to understate after-tax accounting and the tax books. effective tax rate is really a reflection of the difference between doing projections, it is far safer to use the marginal tax rate since The choice really is between the effective and marginal tax rate. In

The Right Tax Rate to Use 83 Aswath Damodaran I BT5050500 500 500 Tax rate EBIT (1-t) Taxes EBIT year for the next 3 years. that make money is 40%. Estimate the after-tax operating income each for the next 3 years, and marginal tax rate on income all firms firm is expected to have operating income of $ 500 million each year for a firm with $ 1 billion in net operating losses carried forward. This Assume that you are trying to estimate the after-tax operating income A Tax Rate for a Money Losing Firm

er1Ya Year 3 Year 2 Year 1 84 Aswath Damodaran I I I made independently of assumptions about growth in the future. Assumptions about net capital expenditures can therefore never be much higher net capital expenditures than low growth firms. firm is growing or expecting to grow. High growth firms will have In general, the net capital expenditures will be a function of how fast for some or a lot (or sometimes all of) the capital expenditures. expenditures and depreciation. Depreciation is a cash inflow that pays Net capital expenditures represent the difference between

Net Capital Expenditures 85 Aswath Damodaran I I categorized as capital expenses. The adjusted net cap ex will be Acquisitions of other firms Research and development expenses The adjusted net cap ex will be 1. Most firms do not do acquisitions every year. Hence, a normalized 1. Most firms do not acquisitions every year. Hence, a Two caveats: Adjusted Net Cap Ex = Capital Expenditures + Acquisitions of other Adjusted Net Capital Expenditures = + Current 2. The best place to find acquisitions is in the statement of cash flows, Capital expenditures should include firms - Amortization of such acquisitions year’s R&D expenses - Amortization of Research Asset measure of acquisitions usually categorized under other investment activities (looking at an average over time) should be used , since these are like capital expenditures.

, once they have been re- 86 Aswath Damodaran Acquired GeoTel Fibex Sentient Summa Four American Internent Clarity Wireless Selsius Systems ieik Purchase Amteva Tech PipeLinks Cisco’s Acquisitions: 1999 Method of Acquisition Pooling Pooling Pooling ucae$58 5 $ Purchase Purchase Purchase Purchase Purchase

Price Paid $1,344 $318 $103 $129 $153 $118 $134 $2,516 $159 87 Aswath Damodaran custos= $ 2,516 mil = $ 1,594 mil = $ 485 mil = $3,723 mil (Amortization was included in the depreciation number) Adjusted Net Capital Expenditures + Acquisitions = $ 98 mil - Amortization of R&D + R & D expense = $ 486 mil Net Cap Ex (from statement of CF) - Depreciation (from statement of CF) = $ 584 mil Cap Expenditures (from statement of CF)

Cisco’s Net Capital Expenditures in 1999 88 Aswath Damodaran I I I I receivable) and non-debt current liabilities receivable) and into the cash flows. of such growth on working capital needs, and building these effects When forecasting future growth, it is important to forecast the effects (increase) cash flows in that period. Therefore, any increases (decreases) in working capital will reduce Any investment in this measure of working capital ties up cash. the difference between non-cash current assets A cleaner definition of working capital from a cash flow perspective is next year) liabilities (accounts payables, short term debt and due within the current assets (inventory, cash and accounts receivable) In accounting terms, the working capital is difference between Working Capital Investments (accounts payable)

(inventory and accounts 89 Aswath Damodaran I I Some firms have negative non-cash working capital capital as a proportion of revenues looking forward, can be estimated by at non-cash working volatile Changes in non-cash working capital from year to tend be zero, when it is negative. forever. Thus, it is better that non-cash working capital needs be set to the firm. While this is indeed feasible for a period of time, it not this will continue into the future generate positive cash flows for Working Capital: General Propositions . A far better estimate of non-cash working capital needs,

. Assuming that 90 Aswath Damodaran Ca fRvne30%00%8.23% 7.04% 0.00% 8.91% -2.71% 3.00% WC as % of Revenue Assumption in Valuation 8.71% -3.16% Average: industry Average: last 3 years-15.16% o-ahW 49-0 2547 8.23% $30,931 -404 $12,154 -3.32% -25.53% $ 1,640 -419 $ Change from last year % of Revenues Non-cash WC Revenues Volatile Working Capital? mznCsoMotorola Cisco Amazon (309)

$0)(89 ($829) ($700) 91 Aswath Damodaran I I I will be paid on the stock. from an equity investment in a publicly traded firm is the dividend from an equity investment in a publicly traded firm is the that focuses only on dividends When actual dividends are less than potential dividends, using a model Actual dividends only cash flow In the strictest sense, may be much lower than the potential dividends ( may be much equity in a firm. paid out) • • Dividends and Cash Flows to Equity managers like to hold on cash managers are conservative managers are and investment opportunities , however, are set by the managers of firm and and try to smooth out dividends will under state the true value to meet unforeseen future contingencies that an investor will receive that could have been of the

that 92 Aswath Damodaran I I growth and net debt repayments (debt - new issues) any made has it needs to make create future “investments” firm The potential dividends of a firm are the cash flows left over after dividends. This cannot be true for several reasons: Some analysts assume that the earnings of a firm represent its potential • Valuation models, where earnings are discounted back to the present, will • • • valuation. non-discretionary loses its basis when there is future growth built into the The common categorization of capital expenditures into discretionary and over estimate the value of equity in firm dividends would not be investing in new assets and thus could grow Even if earnings were cash flows, a firm that paid its out as expenses in the earnings calculation Earnings are not cash flows, since there both non-cash revenues and

Measuring Potential Dividends 93 Aswath Damodaran I Cash flows to Equity for a Levered Firm •I dividends will also need to be netted out = Free Cash flow to Equity - (Principal Repayments New Debt Issues) - Changes in non-cash Working Capital - (Capital Expenditures Depreciation) Net Income have ignored preferred dividends. If stock exist,

Estimating Cash Flows: FCFE 94 Aswath Damodaran I For this firm, δ Net Income Estimating FCFE when Leverage is Stable = Debt/Capital Ratio = Free Cash flow to Equity - (1- - (1- value debt to capital ratio, looking forward. used when looking back in time but can be replaced with the market In computing FCFE, the book value debt to capital ratio should be • Expenditures - Depreciation + Working Capital Needs) Proceeds from new debt issues = Principal Repayments + d (Capital

δ ) Working Capital Needs δ ) (Capital Expenditures - Depreciation) 95 Aswath Damodaran I I I I I I Estimating FCFE (1997): Debt to Capital Ratio = 23.83% Increase in non-cash working capital = $ 477 Million Depreciation per Share = $ 1,134 Million Capital spending = $ 1,746 Million Net Income=$ 1533 Million =Fe Ft qiy$ 704 Million Dividends Paid [477(1-.2383)] [(1746-1134)(1-.2383)] = Free CF to Equity $363.33 $465.90 Chg. Working Capital*(1-DR) Depr)*(1-DR) - (Cap. Exp Net Income Estimating FCFE: Disney

$1,533 Mil $ 345 Million 96 Aswath Damodaran FCFE and Leverage: Is this a free lunch?

FCFE 1000 1200 1400 1600 200 400 600 800 0 0% 0 0 0 0 0 0 0 0 90% 80% 70% 60% 50% 40% 30% 20% 10% Debt Ratio and FCFE: Disney

Debt Ratio 97 Aswath Damodaran FCFE and Leverage: The Other Shoe Drops

Beta 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 0% 0 0 0 0 0 0 0 0 90% 80% 70% 60% 50% 40% 30% 20% 10% Debt Ratio and Beta

Debt Ratio 98 Aswath Damodaran J J J J I and where it is in terms of current leverage Any of the above, depending upon what company you are looking at exactly offset the cash flow effect Increasing leverage will not affect value because the risk effect greater than the cash flow effects Increasing leverage will decrease value because the risk effect be will dominate the discount rate effects Increasing leverage will increase value because the cash flow effects to value would you subscribe to? these cash flows. Which of the following statements relating leverage future time periods and also the cost of equity applied in discounting generally increase the expected free cash flows to equity investors over In a discounted cash flow model, increasing the debt/equity ratio will

Leverage, FCFE and Value 99 Aswath Damodaran I I I I I I Estimating FCFE (1996): Debt Ratio = 43.48% Increase in Non-cash Working capital Change (1996) = 12 Million BR Depreciation (1996) = 183 Million BR Capital spending (1996) = 396 Million Net Income (1996) = 325 Million BR Dividends Paid Free Cashflow to Equity 120.39 Million BR 6.78 Million BR - Change in Non-cash WC (1-DR) = 12 (1-.4348) (1-DR) = (396-183)(1-.4348) - (Cap Ex-Depr) Earnings per Share Estimating FCFE: Brahma

197.83 Million Br 325.00 Million BR 232.00 Million BR 100 Aswath Damodaran III. Estimating Growth

DCF Valuation 101 Aswath Damodaran I I I Ways of Estimating Growth in Earnings Look at fundamentals Look at what others are estimating Look at the past • • •

projects are making for the firm. how much the firm is investing in new projects, and what returns these Ultimately, all growth in earnings can be traced to two fundamentals - to know what their estimates are. Analysts estimate growth in earnings per share for many firms. It is useful for growth estimation The historical growth in earnings per share is usually a good starting point 102 Aswath Damodaran I I I considered In using historical growth rates, the following factors have to be Historical growth rates can be sensitive to Historical growth rates can be estimated in a number of different ways • • • • • the effect of changing size how to deal with negative earnings the period used in estimation Simple versus Regression Models Arithmetic versus Geometric Averages

I. Historical Growth in EPS 103 Aswath Damodaran Arithmetic Average Standard deviation Geometric Average Motorola: Arithmetic versus Geometric Growth 9930,931 29,398 1999 1998 9729,794 27,973 27,037 1997 22,245 1996 1995 1994 $ $ $ $ $ $ $ $ eeus% Revenues -1.33% 21.54% 7.08% 5.21% 8.61% 6.82% 6.51% 3.46% Change Rates $ $ $ $ $ $ $ $ BTA% EBITDA 5,398 3,019 4,276 4,268 4,850 4,151 -29.40% -12.00% 41.56% 10.89% 78.80% 16.84% 5.39% 0.19% hneEI % Change EBIT Change $ $ $ $ $ $ $ $ $ $ 3,216 1,947 1,960 2,931 2,604 822 141.78% 291.24% -57.78% -33.13% 42.45% -0.66% 12.56%

4.31% 104 Aswath Damodaran I $ $ I $ 1999 $ 1998 $ 1997 $ 1996 $ 1995 $ 1994 $ EPS 1993 1992 1991 Year Growth Rate = $0.0383/$0.13 30.5% ($0.13: Average EPS from 91-99) Cisco: Linear and Log-Linear Models for P .6 .33(t:EPS grows by $0.0383 a year ln(EPS) = -4.66 + 0.4212 (t): Growth rate approximately 42.12% EPS = -.066 + 0.0383 ( t): 0.32 0.25 0.18 0.16 0.08 0.07 0.04 0.02 0.01 Growth

ln(EPS) -1.1394 -1.3863 -1.7148 -1.8326 -2.5257 -2.6593 -3.2189 -3.9120 -4.6052 105 Aswath Damodaran J J J J I Cannot be estimated +120% +600% -600% What is the growth rate? deficit of $0.05. In 1997, the expected earnings per share is $ 0.25. Time Warner from 1996 to 1997. In 1996, the earnings per share was a You are trying to estimate the growth rate in earnings per share at

A Test 106 Aswath Damodaran I I I the future. while the growth rate can be estimated, it does not tell you much about When earnings are negative, the growth rate is meaningless. Thus, There are three solutions: cannot be estimated. (0.30/-0.05 = -600%) When the earnings in starting period are negative, growth rate • Use the absolute value of earnings in starting period as • • earnings. Use a linear regression model and divide the coefficient by average denominator (0.30/0.05=600%) Use the higher of two numbers as denominator (0.30/0.25 = 120%)

Dealing with Negative Earnings 107 Aswath Damodaran The Effect of Size on Growth: Callaway Golf

96123 25.18% 25.26% 89.32% 122.30 Geometric Average Growth Rate = 102% 113.47% 97.70 1996 201.56% 78.00 1995 255.56% 41.20 1994 19.30 1993 6.40 1992 Rate Growth 1.80 1991 Net Profit 1990 Year 108 Aswath Damodaran 01$ 4,113.23 I $ 2,036.25 2001 $ 1,008.05 2000 $ 499.03 1999 $ 247.05 1998 $ 122.30 1997 Net Profit 1996 Year years, the expected net income in 5 years will be $ 4.113 billion. If net profit continues to grow at the same rate as it has in past 6

Extrapolation and its Dangers 109 Aswath Damodaran I I U.S companies. Zacks and IBES, at least for widely disseminated by services such as Analyst forecasts of earnings per share and expected growth are time (outside of selling) is spent forecasting earnings per share. the sectors that they follow, a significant proportion of an analyst’s While the job of an analyst is to find under and over valued stocks in •M While many analysts forecast expected growth in earnings per share over • this estimate is far more limited. the next 5 years, analysis and information (generally) that goes into next earnings report

II. Analyst Forecasts of Growth ost of this time, in turn, is spent forecasting earnings per share the 110 Aswath Damodaran How good are analysts at forecasting growth? I Earnings I Value Givoly Fried & Rozeff Brown & Value Collins & Hopwood Study I simple time series models, but the differences tend to be small across analysts. Forecasts of growth (and revisions thereof) tend to be highly correlated The advantage that analysts have over time series models tend to be closer Analysts forecasts of EPS • • • tends to be greater at the industry level tends to be tends to decrease with the forecast period tends to tends to be greater for larger firms tends to be iePro nls oeatErrTime Series Model Analyst Forecast Error Time Period Line Forecasts Line Forecasts Forecaster 16.4% 28.4% 31.7% than for smaller firms than at the company level (next quarter versus 5 years) to the actual EPS than

19.8% 32.2% 34.1% 111 Aswath Damodaran Are some analysts more equal than others? I A study of All-America Analysts (chosen by Institutional Investor) found that • • • • Earnings revisions made by All-America analysts tend to have a much greater Earnings revisions made by All-America analysts forecast error for other analysts) (The median forecast error for All-America analysts is 2% lower than the these analysts become slightly better forecasters these analysts become However, in the calendar year following being chosen as All-America analysts, error of other analysts was 28%) forecast error in the quarter prior to being chosen was 30%; median stock prices impact There is no evidence There is buys; 13.8% for the sells). changes are sustained, and they continue to rise in the following period (2.4% for The recommendations made by the All America analysts have a greater impact on The recommendations made by the All America analysts have a team were chosen because they were better forecasters team were chosen on the stock price than revisions from other analysts (3% on buys; 4.7% sells). For these recommendations the price that analysts who are chosen for the All-America Analyst than their less fortunate brethren.

of earnings. (Their median 112 Aswath Damodaran I I I I I investment banking business to the firm. Dr. Jekyll/Mr.Hyde with a refusal to face the facts. story teller): Tendency to base a recommendation on coupled “story” Factophobia that they are supposed to follow. Refers to analysts who start identifying with the managers of firms Stockholm Syndrome earnings estimates when other analysts do the same. Lemmingitis within the sector that you lose sight of bigger picture. Tunnel Vision The Five Deadly Sins of an Analyst (generally is coupled with delusions of being a famous :Strong urge felt to change recommendations & revise : Becoming so focused on the sector and valuations : Analyst who thinks his primary job is to bring in

(shortly to be renamed the Bre-X syndrome): Bre-X (shortly to be renamed the 113 Aswath Damodaran I I I Propositions about Analyst Growth Rates case the information that they have is so noisy as to be useless). and when they agree to little (in which agree too much (lemmingitis) as earnings growth for a firm. There is, however, danger when they remains the company itself which might explain public information in most analyst forecasts than is generally claimed. Proposition 3 Proposition 2 Proposition 1 • • • after they are chosen to be part of the team. why All-America analysts become better forecasters than other why there is such a high correlation across analysts forecasts and revisions (information bias and the need to preserve sources) why there are more buy recommendations than sell

: There is value to knowing what analysts are forecasting : The biggest source of private information for analysts : There if far less private information and more 114 Aswath Damodaran $1000 Projects in Existing Investment $1000 Projects in Existing Investment $ 1000 Projects in Existing Investment III. Fundamental Growth Rates X X X 12% Projects Investment on Current Return on period: 0% current to next ROI from Change in 12% Investment Return on Next Period’s + + = $100 Projects in New Investment $100 Projects in New Investment $120 Earnings Current X X 12% New Projects Investment on Return on 12% New Projects Investment on Return on = = $ 12 Change in Earnings

132 Earnings Period’s Next 115 Aswath Damodaran In the special case where ROI on existing projects remains unchanged and is equal to new Current Earnings Investment in New Projects in the more general case where ROI can change from period to period, this be expanded as follows: For instance, if the ROI increases from 12% to 13%, expected growth rate can be written as follows: Reinvestment Rate Investment in Existing Projects*(Change ROI) + New Projects (ROI) $1,000 * (.13 - .12) + 100 (13%) 120 100 83.33% Growth Rate Derivations $ 1000 * .12 Investment in Existing Projects* Current ROI X X X X 12% Return on Investment 12% Return on Investment = = = = Current Earnings Change in Earnings $120 $12 10% Growth Rate in Earnings = = Current Earnings Change in Earnings $120 $23 =

19.17% 116 Aswath Damodaran I I I Reinvestment Rate = Retained Earnings/ Current Earnings Retention Ratio cannot exceed its r cannot P g the In where current case unchanged ROE to is expected the special remain follows: When looking at growth in earnings per share,these inputs can be cast as I. Expected Long Term Growth in EPS EPS roposition 1: The expected growth rate in earnings for a company Return on Investment = ROE Net Income/Book Value of Equity = b= * ROE = Retention Ratio * ROE

= Retained Earnings eturn on equityinlongterm. the t-1 / NI t-1

* ROE 117 Aswath Damodaran I I I Estimating Expected Growth in EPS: ABN expected growth in EPS will be: can maintain its current ROE and retention ratio, Amro If ABN Current Retention Ratio = 1 - DPS/EPS 1.13/2.45 53.88% Current Return on Equity = 15.79% Expected Growth Rate = 0.5388 (15.79%) 8.51%

Amro 118 Aswath Damodaran J J J I I equal to less than greater than greater than, less than or equal to this estimate? Will the expected growth rate in earnings per share next year be expected long term growth rate in earnings per share? to 17%, while its retention ratio remains at 53.88%. What is the new ROE next year is expected to increase Amro’s Assume now that ABN

Expected ROE changes and Growth 119 Aswath Damodaran I I I Changes in ROE and Expected Growth earnings per share from improvement in ROE. Proposition 3: No firm can, in the long term, sustain growth the expected growth rate. P Wh • •T roposition 2: Small changes in ROE translate into largechanges in en the is ROE expected to change, which it operates, the smaller scope for improvement in ROE. business in which it operates) and the more competitive Corollary: The higher the existing ROE of company (relative to the ROE. he he lo we r the current ROE, the greater the effect on growth of changesin growth of on effect the greater current ROE, the r the g EPS = b *ROE t+1 +(ROE t+1 – ROE t )/ ROE

t 120 Aswath Damodaran I I g EPS doubling of the growth rate from 8.51% to 16.83%. Note that 1.21% improvement in ROE translates into almost a growth rate in that year will be: 17%, while the retention ratio will remain 53.88%. The expected expansion into Asia will push up the ROE to ABN’s Assume now that = b *ROE = 16.83% =(.5388)(.17)+(.17-.1579)/(.1579) Changes in ROE: ABN Amro Changes in ROE: ABN t+1 + (ROE t+1 – ROE t )/ ROE t

121 Aswath Damodaran I I I where, BV: Book Value Note that BV of capital = Debt + Equity. t = Tax rate on ordinary income i = Interest Expense on Debt / BV of D/E = BV of Debt/ Equity EBIT ROC = ROE = ROC + D/E (ROC - i (1-t)) t (1 - tax rate)) / BV of Capital (1 - tax rate)) / BV of ROE and Leverage

t-1 122 Aswath Damodaran I I I I Return on Equity = ROC + D/E (ROC - i(1-t)) After-tax Cost of Debt = 8.25% (1-.32) 5.61% (Real BR) Debt/Equity Ratio = (542+478)/1326 0.77 Real Return on Capital = 687 (1-.32) / (1326+542+478) 19.91% 19.91% + 0.77 (19.91% - 5.61%) = 30.92% This is assumed to be real because both the book value and income are • inflation adjusted.

Decomposing ROE: Brahma 123 Aswath Damodaran I I I I Decomposing ROE: Titan Watches (India) Return on Equity = ROC + D/E (ROC - i(1-t)) After-tax Cost of Debt = 13.5% (1-.25) 10.125% Debt/Equity Ratio = (2378 + 1303)/1925 1.91 Return on Capital = 713 (1-.25)/(1925+2378+1303) 9.54%

9.54% + 1.91 (9.54% - 10.125%) = 8.42% 124 Aswath Damodaran I I investments (net capital expenditures and working capital): obtained by substituting in the equity reinvestment into real A more general version of expected growth in earnings can be invested in projects earning the return on equity. focuses on per share earnings and assumes that reinvested are The limitation of the EPS fundamental growth equation is that it Expected Growth Equity Reinvestment Rate = (Net Capital Expenditures + Change in Working II. Expected Growth in Net Income Capital) (1 - Debt Ratio)/ Net Income Net Income

= Equity Reinvestment Rate * ROE 125 Aswath Damodaran Fundamentals: Stable ROC and Reinvestment I I I of its investments. given growth rate, should be inversely proportional to the quality Proposition: The net capital expenditure needs of a firm, for g Reinvestment Rate and Return on Capital When looking at growth in operating income, the definitions are Return on Investment = ROC EBIT(1-t)/(BV of Debt + BV Equity) Reinvestment Rate = (Net Capital Expenditures + Change in WC)/EBIT(1-t) EBIT III. Expected Growth in EBIT And = (Net Capital Expenditures + Change in WC)/EBIT(1-t) * ROC = Reinvestment Rate * ROC

Rate 126 Aswath Damodaran No Net Capital Expenditures and Long Term I J J I Explain. No Yes return on capital over time. Is this a reasonable explanation? efficient with its existing assets and can be expected to increase that this is still feasible because the company becoming more after the terminal year. When you confront analyst, he contends there are no net cap ex or working capital investments being made the assumption that operating income will grow 3% a year forever, but You are looking at a valuation, where the terminal value is based upon

Growth 127 Aswath Damodaran I I I I I I Fundamentals Cisco’s Motorola’s Fundamentals Motorola’s Estimating Growth in EBIT: Cisco versus Expected Growth in EBIT = (.5299)(.1218) 6.45% Return on Capital = 12.18% Reinvestment Rate = 52.99% Expected Growth in EBIT =(1.0681)(.3407) = 36.39% Return on Capital =34.07% Reinvestment Rate = 106.81%

Motorola 128 Aswath Damodaran IV. Operating Income Growth when Return on I I I Expected Growth Rate = ROC Expected Growth Rate = spread out over each period. If the change is over multiple periods, second component should be If ROC negative if the return on capital is decreasing. component to growth, positive if the return on capital is increasing and When the return on capital is changing, there will be a second be: capital in period t+1, the expected growth rate operating income will t is the return on capital in period t and ROC is the return on capital in period t and Capital is Changing +( ROC t+1 * Reinvestment rate t+1 – ROC t )/ ROC t t+1

is the return on 129 Aswath Damodaran {Notethat I amthat assumingnew the investments makingstart17.22% Growth from more usingefficiently existing investments:17.40%-9.12%=8.28% G = Ex = I I One way to think about or = .174 rowth from new investments: .1722*5299= 9.12% ROC .1 pected Growthpected Rate immediately, while allowing for existing assets to improve gradually}returns (which is half way towards the industry average) return on capital to rise 17.22% over the next 5 years We expect Motorola’s 52.99%. current return on capital is 12.18% and its reinvestment rate Motorola’s 722* N ew Investments .5 17.40% 29 9 *Reinvestment Rate *Reinvestment +{ Motorola’s Growth Rate [1+(.1722-.1218)/.1218] th is is is curr to ent decomposeMotoro + {[1+(ROC 1/5 In 5 -1} years -ROC la’s expected g expected la’s Cur rent )/ROC Curr ent ] 1/5 rowth into

-1} 130 Aswath Damodaran V. Estimating Growth when Operating Income I over time, we use a three step process to estimate growth: When operating income is negative or margins are expected to change • • • is Negative or Margins are changing and expected margins Estimate the capital that needs to be invested generate revenue growth Estimate expected operating margins each year Estimate growth rates in revenues over time – – – –K – – needs each year. Estimate a sales to capital ratio that you will use generate reinvestment Adjust the current margin towards target Set a target margin that the firm will move towards Decrease the growth rate as firm becomes larger future Use historical revenue growth to get estimates of in the near

eep track of absolute revenues to make sure that the growth is feasible 131 Aswath Damodaran 10 9 urn 57-96%-$428 -79.62% 8 7 $537 6 5 4 3 Revenues 2 Growth Rate 1 Current Year Commerce One: Revenues and Revenue .0 1,0 13.08% $15,802 5.00% 10.00% 00%$,9 .0 $149 -$182 -$384 2.30% -$438 -$388 -3.91% -13.23% -27.21% -48.17% 20.00% $6,496 30.00% $4,640 35.00% $2,900 40.00% $1,611 60.00% $806 80.00% 100.00% 50.00% 1,4 12.27% $15,049 1,0 .0 $1,049 $565 11.04% 9.20% 6.44% $13,681 $11,401 $8,770 Growth prtn agnOperating Income Operating Margin

$2,068 $1,846 $1,510 132 Aswath Damodaran Industry average = 10 9 8 7 6 5 4 3 2 1 $537 Revenues Current Year Commerce One: Reinvestment Needs 1,4 13822 $622 2.20 $844 $752 $791 $1,368 $15,802 $586 $2,280 2.20 $15,049 $2,631 2.20 $13,681 $2,274 2.20 $11,401 $1,856 $8,770 $1,740 $6,496 $1,289 $4,640 $806 $2,900 $1,611 $806 $269 ∆ eeusSlsCptlRivsmn aia ROC Reinvestment Revenues Sales/Capital Capital .0$1,036 2.20 $1,196 $1,033 2.20 2.20 2.20 2.20 2.20 $342 $366 $122 87814.17% 16.17% $8,718 10.36% $7,682 $6,486 96214.39% 13.76% $9,682 $9,340 $5,452 $4,609 $3,818 $3,232 $2,866 $2,744

15% 3.24% -4.76% -11.87% -15.30% -14.14% 133 ROE * Retention Rati

tbeREChanging RO Stable ROE Aswath Damodaran Analysts Earnings per shar Equity Earnings o Fundamentals + (ROE ROE e t+1 t+1 *Retention Ratio -ROE E t Ex )/ROE p ected Growth Rate Historica t l Reinvestment Ratio ROE * Equity Stable ROE Reinvestment Rate ROC * Stable RO C Net Income Fundamentals Changing RO + (ROC ROC Changing RO + (ROE ROE t+1 t+1 t+1 *Reinvestment Rate t+1 *Eq. Reinv Ratio -ROC -ROE E Operating Incom C t t )/ROC )/ROE t t 3. Reinvestment Needs 2. Operating Margins 1. Revenue Growth e Historical

Negative Earnings 134 Aswath Damodaran IV. Closure in Valuation

Discounted Cashflow Valuation 135 Aswath Damodaran I I value at the end of period: and then estimate a terminal value, to capture the “growth period” for a Since we cannot estimate cash flows forever, therefore the present value of cash flows forever. A publicly traded firm potentially has an infinite life. The value is Getting Closure in Valuation au Value = t=N t=1 ∑ au Value = 1+r) + (1 CF t t t= t=1 + ∑ ∞ Terminal Value 1 r) (1+ CF 1+r) + (1 t t

N 136 Aswath Damodaran marketable and are separable when assets Most useful Value Liquidation Ways of Estimating Terminal Value a relative valuation makes the valuation Easiest approach but utpeApoc Stable Growth Multiple Approach Terminal Value during the period. (if any) that it will earn and the excess returns can sustain forever, at a stable rate which it when the firm will grow make judgments about but requires that you Technically soundest,

Model 137 Aswath Damodaran I I I I can be used to estimate the “terminal value” of all cash flows beyond. “terminal value” can be used to estimate the When they do approach stable growth, the valuation formula above at some point in time. “stable growth” they will all approach While companies can maintain high growth rates for extended periods, be higher than the growth rate of economy rate growth stable growth rate is called a This “constant” value of those cash flows can be written as: rate forever, the present “constant” cash flows grow at a When a firm’s operates. where, Value = Expected Cash Flow Next Period / (r - g) Stable Growth and Terminal Value g = Expected growth rate r = Discount rate (Cost of Equity or Cost Capital) in which the firm

and cannot 138 Aswath Damodaran I but it can be set lower. The stable growth rate cannot exceed the of economy The stable growth rate can be negative. terminal value will lower • • and you are assuming that your firm will disappear over time. growth rate of the economy. growth firms, the rate of latter will probably be lower than If you assume that the economy is composed of high growth and stable

Limits on Stable Growth 139 Aswath Damodaran I we can make one of three assumptions: high growth, and the pattern of growth during that period. In general, A key assumption in all discounted cash flow models is the period of • • • • Each year will have different margins and growth rates (n stage) will decline gradually to a stable growth rate(3-stage) there will be high growth for a period, at the end of which rate will drop to the stable growth rate (2-stage) there will be high growth for a period, at the end of which rate there is no high growth, in which case the firm already stable growth

Growth Patterns 140 Aswath Damodaran I I I Barriers to entry and differential advantages Current growth rate Size of the firm • • • • therefore be framed as a question about what the barriers to entry are, how therefore be framed as a question about The question of how long growth will last and high it be can comes from barriers to entry Ultimately, high growth comes from project returns, which, in turn, there is a correlation between current growth and future While past growth is not always a reliable indicator of future growth, become larger Success usually makes a firm larger. As firms long they will stay up and how strong remain. expected growth period than one growing 10% a year now. firm growing at 30% currently probably has higher growth and a longer much more difficult for them to maintain high growth rates Determinants of Growth Patterns and differential advantages . , it becomes

. Thus, a 141 Aswath Damodaran CF2 aehg ik2. Have average risk 1. Have lower net cap ex 2. Have high risk 1. Have high net cap ex 1. Pay high dividends FCFF FCFE/ Stable growth firms usually 1. Pay no or low dividends High Growth Firms usually DDM Model I firm should be given the characteristics of a stable growth firm. the “stability”, and how high project returns are. As growth rates approach The growth rate of a firm is driven by its fundamentals - how much it reinvests Stable Growth and Fundamentals .Hv o eeae4. Have leverage closer to 3. Earn ROC closer to WACC 3. Earn ROC closer to WACC 4. Have low leverage 2. Have average risk 3. Earn high ROC 3. Earn high ROC 2. Have high risk

industry average 142 Aswath Damodaran I I I The Dividend Discount Model: Estimating follows: The expected payout ratio in stable growth can then be estimated as rate of 5% (Real Growth + Inflation Rate in NV) average for European banks of 15%, and that it will grow at a nominal that point, let us assume its return on equity will be closer to the will be in stable growth 5 years. At Let us assume that ABN Amro growth in earnings per share of 8.51%. equity of 15.79% and its retention ratio 53.88%, we estimated a Based upon its current return on Amro. Consider the example of ABN Payout = 1- b b = g/ROE g = b (ROE) Stable Growth Payout Ratio = 1 - g/ ROE .05/.15 66.67%

Stable Growth Inputs 143 Aswath Damodaran The FCFE/FCFF Models: Estimating Stable I I I assumption. your terminal value will be unaffected by stable growth excess returns. If your return on capital is equal to cost of capital, that it is not the stable growth rate drives your value but If you are consistent about estimating reinvestment rates, will find be estimated as follows: (which is the industry average). The reinvestment rate in year 13 can now, growing at 5% a year and earning return on capital of 16.52% For instance, Cisco is expected to be in stable growth 13 years from to relate them expected growth and returns on capital: The soundest way of estimating reinvestment rates in stable growth is Reinvestment Rate = Growth in Operating Income/ROC Reinvestment Rate = 5%/16.52% 30.27%

Growth Inputs 144 Aswath Damodaran V. Beyond Inputs: Choosing and Using the Right Model

Discounted Cashflow Valuation 145 Aswath Damodaran I I The next step in the process is deciding the In summary, at this stage in the process, we should have an estimate of • • •w • • •t what pattern we will assume growth to follow which discount rate needs to be estimated and analysts forecasts and/or fundamentals the expected growth rate in earnings, based upon historical growth, the current cost of equity and/or capital on investment firm) (dividends or free cash flows to equity) the firm (cash flow he current cash flows on the investment, either to equity investors hich cash flow to discount, which should indicate

Summarizing the Inputs 146 Aswath Damodaran I I Use Firm Valuation Use Equity Valuation (b) if equity (stock) is being valued (a) for firms which have leverage which is too high or low (a) for firms which have (a) for firms which have stable leverage (b) for firms for which you have partial information on leverage (b) for firms which you have (c) in all other cases, where you are more interested in valuing the firm (c) in all other cases, where you are more interested Which cash flow should I discount? the equity. (Value Consulting?) does not change dramatically over time. have to be factored in the cash flows and discount rate (cost of capital) change the leverage over time, because debt payments and issues do not expenses are missing..) , whether high or not, and , and expect to (eg: interest

than 147 Aswath Damodaran Given cash flows to equity, should I discount I I Use the FCFE Model Use the Dividend Discount Model • • • • Companies, IPOs) (b) For firms where dividends are not available (Example: Private than 110% of FCFE over a 5-year period, use the model) thumb, if dividends are less than 80% of FCFE or greater than the Free Cash Flow to Equity. (What is significant? ... As a rule of (a) For firms which pay dividends are significantly higher or lower Financial Service companies) (b)For firms where FCFE are difficult to estimate (Example: Banks and to the Free Cash Flow Equity (over a extended period) (a) For firms which pay dividends (and repurchase stock) are close

dividends or FCFE? 148 Aswath Damodaran I I I Should I use real or nominal cash flows? What currency should the discount rate (risk free rate) be in? Cost of Equity versus Capital • • • • • • • If inflation is high (>10%) switch to real cash flows -> nominal cost of capital -> real cost of capital based upon nominal income If inflation is low (<10%), stick with nominal cash flows since taxes are If nominal cash flows If discounting real cash flows of your cash flows Match the currency in which you estimate risk free rate to -> Cost of Capital -> Cost of Equity If discounting cash flows to the firm If discounting cash flows to equity

What discount rate should I use? 149 Aswath Damodaran I I I If your firm If your firm If your firm is • • • •h • •h • • Which Growth Pattern Should I use? has firm characteristics that are very different from the norm has significant barriers to entry into the business is small and growing at a very high rate (> Overall growth + 10%) or is large & growing at a moderate rate ( constrained by regulation from growing at rate faster than the economy large and growing at a rate close to or less than growth of the economy as a single product & barriers to entry with finite life (e.g. patents) as the characteristics of a stable firm (average risk & reinvestment rates) Use a 3-Stage or n-stage Model Use a 2-Stage Growth Model Use a Stable Growth Model ≤ Overall growth rate + 10%) or

, or 150 Aswath Damodaran & a growth pa & a growth & A Discou Choose a Choose Cash Flow Cash The Building Blocks of Valuation nt Rate

ttern

• • Stockh Expect g Models: Basis ed Dividends to Dividends ed olders APM: Ri APM: CAPM: Riskfree Rate + Beta : The risk : The Stable Growth Divi sk de free Rate + equity. of the cost is the greater the investment, ier nds Cost of Equ Cost of Σ t Beta g j (Risk Premium)(Risk

(Risk Premium(Risk [ δ = Free Cash flow (FCFE) Equity to - (1- δ - (1- δ Net Income

= Debt Hi ity g h Growt ) Change Capital in Work. ) (Capital - Deprec’n) Exp. Two-Sta Cashflows Cashflows Ratio] h g j ): e Growt | n factors to Equity to Stabl h e g Hi E, D: Mkt Mkt D: E, = Free flow Cash to Firm (FCFF) - Changein - (CapitalDeprec’n)- Exp. EBIT WACC = k = WACC k g d k +

h Growt Three-Stage Growth = Cu (1- tax rate) rrent Borrowing Rate (1-t) Cashflows to FirmCashflows h Val of Equ of Val Cost of of Cost e d | Work. Capital Work.

( E/ (D+E)) Transition ( D/(D+E)) Cap ity anity ital

Stable d Debt 151 Aswath Damodaran

6. Tying up Loose Ends 152 Aswath Damodaran Dealing with Cash and Marketable Securities I I marketable securities. Once the firm has been valued, add back value of cash and operating assets alone to estimate the cost of equity). should not be contaminated by the inclusion of cash. (Use betas before interest income from cash and securities, the discount rate securities is to keep it out of the valuation - cash flows should be The simplest and most direct way of dealing with cash marketable •

overpaying on acquisitions, markets may discount the value of this cash. If you have a particularly incompetent management, with history of 153 Aswath Damodaran How much cash is too cash? 1000 1200 200 400 600 800 0 -%12 -%51%1-5 52%2-5 25-30% 20-25% 15-20% 10-15% 5-10% 2-5% 1-2% 0-1% Cash as % of Firm Value: July 2000

>30% 154 Aswath Damodaran I J J I What is or are the scenario(s)? No Yes firm? scenario where you would not be willing to pay $ 100 million for this marketable securities worth $ 100 million. Can you ever consider a face value. Assume now that you are buying a firm whose only asset is Implicitly, we are assuming here that the market will value cash at

The Value of Cash 155 Aswath Damodaran I I asset value (of between 10 and 20%) in the United States. The average closed end fund has always traded at a discount on net the net asset value. funds shares can and often do trade at prices which are different from asset value (which is the of securities in fund), closed end Unlike regular mutual funds, where the shares have to trade at net Closed end funds are mutual funds, with a fixed number of shares.

The Case of Closed End Funds 156 Aswath Damodaran Closed End Funds: Price and NAV Number of Funds 10 15 20 25 30 35 0 5

Discount > 25%

Discount: 20-25 % Closed End Equity Funds: December 31, 1997 Discount: 15- 20%

Discount: 10- 15%

Discount: 5-10% Premium or Discount on NAV

Discount: 0 -5%

Premium:0-5%

Premium: 5-10%

Premium:10- 15%

Premium: 15- 20%

Premium 20- 25%

Premium 25- 30%

Premium > 30% 157 Aswath Damodaran I A Simple Explanation for the Closed End the fund. end fund underperforms the market by 0.50%, estimate discount on investments) to make 11.5% annually over the long term. If closed stocks. Assume also that you expect the market (average risk ‘average risk” Assume that you have a closed-end fund invests in

Discount 158 Aswath Damodaran I the fund? willing to pay a premium over the value of marketable securities in of 80%+ on NAV December 31, 1997. Why might an investor be roughly 40% on net asset value and the Indonesian fund at a premium instance, the Thai closed end funds were trading at a premium of Some closed end funds trade at a premium on net asset value. For

A Premium for Marketable Securities 159 Aswath Damodaran

Value Per Share 10000 15000 20000 25000 30000 35000 40000 45000 5000 0

1987

1988 Berkshire Hathaway

1989

1990

1991 Year 1992 Berkshire Hathaway

1993

1994

1995

1996

1997 0.00% 20.00% 40.00% 60.00% 80.00% 100.00% 120.00% 140.00%

Premium over Book Value

Premium over Book Value Book Value/Share Market Value/Share 160 Aswath Damodaran I Holdings in other firms can be categorized into Majority active holdings, in which case the financial statements are • • • Dealing with Holdings in Other firms

consolidated. shown in the income statements Minority active holdings, in which case the share of equity income is holdings is shown in the balance sheet Minority passive holdings, in which case only the dividend from 161 Aswath Damodaran osldtdFr Strip operating income of subsidiary Firm Value subsidiary as a firm and add Consolidated Value equity in subsidiary and take What to do… Firm Not consolidated Equity Valuing Not consolidated Fin Statement How to value holdings in other firms

parent firm. portion of this value to and value subsidiary separately. Add estimating equity value. subsidiary to the debt in debt in portion of firm value. Add share of holding. 162 Aswath Damodaran I firm. What is wrong with this approach? interests from the firm value to arrive at of equity in firm with the consolidated operating income and then subtract minority When financial statements are consolidated, some analysts value the

How some deal with subsidiaries... 163 Aswath Damodaran I Equity Value and Per Share Value: A Test

shares outstanding. What is the value per share? value for equity is estimated to be $ 400 billion and there are 5 Assume that you have done an equity valuation of Microsoft. The total 164 Aswath Damodaran I 20 (the current stock price is $ 80). Estimate the value per share. employees over time. These options had an average exercise price of $ In 1999, Microsoft had 500 million options outstanding, granted to

An added fact 165 Aswath Damodaran I I I outstanding. the value of equity before dividing by number shares The value of these non-stock equity claims has to be subtracted from In many firms, there are other equity claims as well including: claim on the firm. approach assumes, however, that common stock is the only equity is to divide the equity value by number of shares outstanding. This The conventional way of getting from equity value to per share • • management and employee options, that have been granted, but do not • • Equity Value and Per Share

contingent value rights, that are also publicly traded. conversion options in convertible bonds trade warrants, that are publicly traded 166 Aswath Damodaran I I I for: equity of the firm and have to be treated as equity, which has relevance Warrants and other equity options issued by the firm are claims on and can be valued using option pricing models. A warrant is therefore a long term call option on the equity of firm during the life of warrant. with the right to buy a share of stock in company at fixed price A warrant is a security issued by company that provides the holder estimating per share value from total equity • • estimating debt and equity for the leverage calculation

Warrants 167 Aswath Damodaran I I I I rate paid on the bonds. Firms generally add conversions options to bonds lower the interest a straight bond and conversion option. A convertible bond can be considered to made up of two securities - increase. issue, conversion becomes a more attractive option as stock prices While it generally does not pay to convert at the time of bond determined number of shares, at the option bond holder. A convertible bond is a that can be converted into pre-

Convertible Bonds 168 Aswath Damodaran I I I The straight bond component is clearly debt. accomplished as follows: conversion option does not exist and value the bond. This can be The easiest way to value the straight bond component is act as if Embedded in every convertible bond is a straight component. Value of Bond = PV coupons at market interest rate + face value • • • bond at market interest rate the market interest rate, estimate value of bond as: Step 3: Using the maturity of convertible bond, coupon rate and bonds that the company has outstanding or from its bond rating. if it had issued a straight bond. This can be obtained either from other Step 2: Estimate the interest rate that company would have had to pay generally be low because of the conversion option) Step 1: Obtain the coupon rate on convertible bond (which will

The Straight Bond Component 169 Aswath Damodaran I I Factors in Using Option Pricing Models to factoring in the dilution effect pricing model, allowing for shifts in variance and early exercise, These problems can be partially alleviated by using a binomial option – three caveats Option pricing models can be used to value the conversion option with • • •

dangerous to use European option pricing models. conversion options are often exercised before expiration, making it conversion options result in stock dilution, and variance and constant dividend yields much shakier, conversion options are long term, making the assumptions about constant

Value Convertibles and Warrants 170 Aswath Damodaran I I I I outstanding to get value per share. Step 4:Divide the remaining value of equity by number shares other equity claims: Step 3:Subtract out the market value (or estimated value) of directly. value of equity. Alternatively, skip step 1 and estimate the equity Step 2:Subtract out the value of outstanding debt to arrive at models. Step 1: Value the firm, using discounted cash flow or other valuation • • Steps in Getting to Value Per Share

Value of Straight Debt Portion Convertible Bonds Value of Conversion Option = Market Convertible Bonds - Alternatively estimate the value using option pricing model : Value of Warrants = Market Price per Warrant * Number 171 Aswath Damodaran I I upon projected cash flows The firm has two equity options outstanding: The equity in Sterling Software was valued at $2,036 million, based An Example: Valuing Sterling Software • •T per share; these are trading at $ 30 share The firm has 1.8 million warrants outstanding, with a strike price of $ 55 years; Bond Rating is A-; Interest rate on comparable debt = 7.50%; $1,522 and the face value is $ 1000; coupon rate of 5.75%; expires in 8 into 20 shares of stock. The market price each convertible bond is

he firm has 115,000 bonds outstanding, each of which can be converted 172 Aswath Damodaran I I million warrants * $ 30 = 54 = 1.8 Value of Warrants = Number warrants * Warrant Price 115 million; coupon rate of 5.75%; expires in 8 years; Convertible Debt has market value of $ 175 million; face • • • • tagtDb oto 7 0 2mlin:Equity - Straight Debt Portion = $ 175 103 72 million Value of Conversion Option in Debt = Market Convertible Annuity,7.5%,8 years) + $ 115 million/1.075 Value of Straight Debt Portion Convertible = $ 6.6125 (PV Coupon on Convertible Debt = .0575 * 115 million $ 6.6125 Bond Rating is A-; Interest rate on comparable debt = 7.50%; Estimating the Value of Options 8

= $ 103.21 million 173 Aswath Damodaran Value per Share / Number of Shares outstanding Value of Equity in Common Stock - Value of Equity in Warrants - Value of Equity in Convertible Debt Value of Equity Value Per Share: Sterling Software

= $ 72 million = $ 54 million = $ 1,910 million = $2,036 million = 25.50 million = $ 74.90 174 Aswath Damodaran I I Value of Equity per share = (Value + Proceeds from Exercise)/ Value of Equity per share = Equity/Fully diluted # shares Fully diluted number of shares outstanding: exercise to the numerator before dividing by number of shares The Treasury Stock Approach: Add the expected proceeds from outstanding, including those in the options. The Conservative Approach: Estimate the total number of shares A Comparison to Other Approaches = (2036 + 115 1.8*55)/(25.5 2.3 1.8) $ 76.01

= $ 2,036/ (25.50 + 2.3 1.8) 68.78 175 Aswath Damodaran Valuations

Aswath Damodaran 176 Aswath Damodaran mzncmnsaeFF Varying margins over time n-stage FCFF Dealing with Distress Amazon.com Dividends 2-stage FCFF Capitalizing Operating Leases Understated Earnings? Normalized Earnings; Stable Sector Global Crossing 2-Stage FCFE 2-stage FCFF The Home Depot Stable FCFE Stable FCFF DaimlerChrysler Collectively, market is an investment Tsingtao 3-Stage Dividends=FCFE, Stable D/E, Low g DDM 2-Stage FCFE=?, Regulated D/E, g>Stable Nestle Dividends Remarks Stable DDM Sony 2-Stage DDM FCFE 500 S&P Model Used ABN Amro Ed Con Company Companies Valued ≠ ≠

FCFE, Stable D/E,High g FCFE, Stable D/E, High g 177 Aswath Damodaran I I 5.5%. For the valuations from 1998 and earlier, I use a risk premium of premium from 1960 to 2001. mature equity markets is 4%. This the average implied risk The risk premium that I will be using in the latest valuations for

General Information 178 Aswath Damodaran I I Firm Characteristics are consistent with stable, DDM model firm allow profits to grow at extraordinary rates. serves. Its rates are also regulated; It is unlikely that the regulators will The firm is in stable growth; based upon size and the area that it • • • The firm pays out dividends that are roughly equal to FCFE. The firm is in stable leverage. The beta is 0.80 and has been stable over time. – – –

Con Ed: Rationale for Model Dividends as % of FCFE = 101% Average Annual Dividends between 1996 and 2001 = $ 567 million Average Annual FCFE between 1996 and 2001 = $563 million 179 Aswath Damodaran Con Ed: A Stable Growth DDM: December 31, I I I I I I The stock was trading at $ 37 on December 31, 2001 and had dropped Cost of Equity = 5.05% + 0.80*4% 8.25% Con Ed Beta = 0.80 (Bottom-up beta estimate) Expected Growth Rate in Earnings and Dividends =3% Dividends per share for 2001 = $2.22 Dividend Payout Ratio over 2001 = 70.93% Earnings per share for 2001 = $ 3.13 Value of Equity per Share = $2.22 *1.03 / (.0825 -.03) $ 43.55 to $ 35.25 on July 22, 2002

2001 180 Aswath Damodaran Con Ed: Break Even Growth Rates

Value per share $10.00 $20.00 $30.00 $40.00 $50.00 $60.00 $70.00 $80.00 $0.00 .0 .0 .0 .0 .0 .0 10%-.0 -3.00% -2.00% -1.00% 0.00% 1.00% 2.00% 3.00% 4.00% 5.00% Con Ed: Value versus Growth Rate Expected Growth rate

Break even point: Value = Price 181 Aswath Damodaran I I I equity. You could also frame the question in terms of a break-even return on 12%, the fundamental growth rate for Con Ed is: Given its retention ratio of 29.17% and return on equity in 2001 rate: we set the market price equal to value, and solve for growth current stock price, To estimate the implied growth rate in Con Ed’s • • • Break even Return on equity = g/ Retention ratio .0212/.2917 7.27% Implied growth rate = 2.12 Price per share = $ 37 $2.22*(1+g) / (.0825 -g) Estimating Implied Growth Rate Fundamental growth rate = (.2917*.12) 3.50%

% 182 Aswath Damodaran J J I I No Yes the market is wrong. Will you definitely profit from your investment? firm, and that you are right misvalued Assume that you invest in a wrong that you are right and the market is wrong When you do any valuation, there are three possibilities. The first is market is right and that you are wrong Implied Growth Rates and Valuation . In an efficient market, which is the most likely scenario? Judgments . The third is that you are both . The third is that you are

. The second is that the 183 Aswath Damodaran $10.00 $20.00 $30.00 $40.00 $50.00 $60.00 $- :Dcme 972 eebr19 3: June 1999 2: December 1998 1: December 1997 Con Ed: A Look Back Con Ed: Valuations over time 4: December 2000

Price per Share Estimated Value 184 Aswath Damodaran I I ABN Amro: Rationale for 2-Stage DDM ABN

what would be a stable growth rate (roughly 5% in Euros) 15.56% and a retention ratio of 62.5% is 9.73%. This higher than The expected growth rate based upon the current return on equity of difficult. As a financial service institution, estimating FCFE or FCFF is very 185 Aswath Damodaran ea09 1.00 4.95%+1.00(4%) 44.69% (b=g/ROE=4/8.95) Forever after yr 5 0.95 4% (Assumed) 8.95% (Set = Cost of equity) 4.95%+0.95(4%) Cost of Equity .16*.4156=.0665 Stable Growth Phase 41.56% 58.44% Beta years 5 Expected growth High Growth Phase Retention Ratio 16.00% Payout Ratio Return on Equity Length Variable I I Current Earnings Per Share = 1.54 Eur; Current DPS = 0.90 Eur; Current DPS = 0.90 Current Earnings Per Share = 1.54 Eur; Market Inputs • • ABN Amro: Summarizing the Inputs Risk Premium = 4% (U.S. premium : Netherlands is AAA rated) Long Term Riskfree Rate (in Euros) = 4.95% 87%= 8.95% =8.75%

55.31% (1 - 4/8.95) 186 Aswath Damodaran PV of Terminal Price = 24.69/(1.0875) EurTerminal Price (in year 5) = 1.22/(.0895-.04) 24.69 Expected DPS in year 6 = 2.21*0.5531=1.22 Eur PV at 8.75% Eur Expected EPS in year 6 = 2.12(1.04) 2.21 5 DPS 4 3 2 EPS 1 Year Value Per Share = 0.88 + 0.87+0.85+0.83+0.82+16.23 = 20.48 Eur Value Per Share = 0.88 + 0.87+0.85+0.83+0.82+16.23 20.48 The stock was trading at 18.09 Euros on December 31, 2002 .212 0.82 0.83 0.85 1.24 0.87 1.16 1.09 2.12 1.02 1.99 1.87 1.75 1.64 It had dropped to 13.50 Euros on July 22, 2002 ABN Amro: Valuation .60.88 0.96 5

= 16.23 Eur = 16.23 187

share = 20.48 Eur Value of Equit Aswath Damodaran y pe r 4.95% Euros Lon Riskfree Rate P 1.54 Eur 0.90 Eur DPS = * Payout Ratio 58.44% EPS = Dividends g term bond rate in Fi g 0.96 Eu ure 1: VALUING ABN AMRO : r 1.02 Eu 1.02 + Avera 0.95 r Discount at 0.95 Beta 1.09 Eu g e beta for Euro 4.95% + 0.95 (4%) = 8.75% Cost of Equit 41.56% Ratio = Retention Cost of Equit r 1.16 Eu 1.16 p y ean banks = 16% = 6.65% * 41.56% Expected Growth X r y 1.24 Eu 1.24 4% Risk Premium ...... r Terminal Value= EPS 4% Mature Market ROE = 16% = (2.21*.5531)/(.0895-.04) 24.69 Payout = (1- 5/15) .667 Beta = 1.00 g =4%: ROE = 8.95% (Cost of equity) 6 0% Countr *Payout/(r-g) Foreve y Risk

r 188 Aswath Damodaran P 0 = I DPS P r = Cost of Equity g accomplished as follows: to to attributable portion that and the portion attributable “high growth” that can be attributed to growth, and break this down further into In any valuation model, it is possible to extract the portion of value t n n t=1 ∑ t=n = Expected dividends per share in year t

“stable growth”. In the case of 2-stage DDM, this can be “stable growth”. = Growth rate forever after year n = Price at the end of year n (1+r) DPS au fHg rwhVleo tbe Assets in Value of Stable Value of High Growth t t + (1+r) P n The Value of Growth n - DPS (r-g 0 *(1+g n ) n ) + DPS (r-g 0 *(1+g rwhPlace Growth n ) n ) - DPS r 0 + DPS r

0 189 Aswath Damodaran (A more precise estimate would have required us to use the stable growth I I I payout ratio to re-estimate dividends) Value of High Growth = Total - (10.06+8.85) Value of Stable Growth = 0.90 (1.04)/(.0895-.04) - 10.06 Euros Value of Assets in Place = Current DPS/Cost Equity ABN Amro: Decomposing Value = 20.48 - (10.06+8.85) 1.57 Euros

= 8.85 Euros = 10.06 Euros = 0.90 Euros/..0895 190 Aswath Damodaran I I

buying the index. conservative) estimate of the cash flows to equity investors from dividends during the year should provide a reasonable (albeit S&P 500, it is not feasible for several (financial service firms). The Though it is possible to estimate FCFE for many of the firms in bottom-up estimates) and 8% (with top-down Zacks) is roughly 10% (with estimate of growth in earnings (from last 5 years) will continue to do so in the next years. The consensus U.S. companies (which have outpaced nominal GNP growth over the in which they operate, there is reason to believe that the earnings at While markets overall generally do not grow faster than the economies

S & P 500: Rationale for Use of Model 191 Aswath Damodaran I I egh5yasForever after year 5 4.7% (Nominal US g) 1.94% 1.00 5 years 8% 1.94% Beta Expected Growth Dividend Yield Length S &P 500: Inputs to the Model (08/22/02) Inputs for the Valuation General Inputs • • • Current level of the Index = 820 Risk Premium for U.S. Equities = 4% Long Term Government Bond Rate = 4.7% High Growth Phase Stable Growth Phase Growth Stable High Growth Phase

1.00 192

Intrinsic Value of Index = Present Value = Expected Terminal Value = Expected Dividends = Aswath Damodaran Terminal Value = 23.37*1.047/(.087 -.04) Cost of Equity = 4.7% + 1(4%) 8.7% S & P 500: 2-Stage DDM Valuation $481.17 1.1$57 1.0$55 $418.56 $23.37 $15.50 $21.64 $15.60 $20.04 $15.70 $18.56 $15.81 $17.18 12345 = 611.82

$611.82 193 Aswath Damodaran I indicates that one or more of the following has to be true. The index is at 820, while the model valuation comes in 481. This • • • • The market is overvalued. The risk premium used in the valuation (4%) is too high higher than 8%. The expected growth in earnings over the next 5 years will be much less than FCFE. The dividend discount model understates the value because dividends are

Explaining the Difference 194 Aswath Damodaran I I I nrni au fIdx=$899.94 At a level of 820, the market is undervalued by about 10%. Intrinsic Value of Index = xetdTria au $1,182.63 $24.44 $36.15 $33.47 $30.99 $28.69 $26.57 Present Value = Expected Terminal Value = Expected Dividends = in the valuation. average FCFE yield for the index was about 3% in 2001. to equity as a percent of market cap. The cashflow averaged the free With these inputs in the model: The average implied risk premium between 1960 and 2001 of 4% is used cashflows to equity for each firm in the index and We estimated the free A More Realistic Valuation of the Index 2 5 4 123 $24.28 $24.13

$23.97 $803.11 195 Aswath Damodaran I several reasons: Japanese firms have proved to be among the most difficult value for Sony: Background on Japanese firms • • • The earnings in 2001 for most Japanese firms was depressed relative to •

transparency in these holdings, makes it difficult to value holdings. The cross holdings that Japanese firms have in other firms, and the lack of influenced by exchange rate movements The earnings of many export oriented Japanese firms tends to be heavily unspecified expenses book value of equity, as firms are allowed to set aside provisions for Japanese accounting standards tend to understate earnings and overstate economy. earnings earlier in the decade and 1980s, reflecting Japanese 196 Aswath Damodaran I I I I this valuation. The long term government bond rate in Japan was 2% at the time of revenue ratio of 8.48%. revenues of 2593 billion yet, yielding a non-cash working capital to Non-cash working capital at Sony in 1999 was 220 billion JPY on depreciation is 76 billion JPY. Capital expenditures in 1999 amounted to 103 billion JPY, whereas dividends of 21 billion JPY in 1999. dropped from 5.25% in 1997 to 2.13% 1999. The firm paid out JPY in 1997 and 38 billion 1998. The return on equity at Sony Sony had net income of 31 billion JPY in 1999, down from 76

Valuing Sony: August 2000 197 Aswath Damodaran I I I I I the Japanese economy due to global exposure) (globally) and Sony’s market value debt to equity ratio (16%) (globally) and Sony’s beta of electronic firms unlevered We will use a beta of 1.10, to reflect the will finance reinvestment with this ratio (rather than the market value) current book debt to capital ratio Sony’s and that non-cash working capital will stay at 8.48% of revenues We will assume that the net capital expenditures grow at same rate We will assume a long term stable growth rate of 3% been 3.5%. posting high growth. Over the last 5 years, growth rate in revenues has dominant market share will keep it from We will assume that the firm’s equity it used to earn in the early 1990s. which is the return on equity that Sony had last year and close to depressed. To normalize earnings, we will use the return on equity of 5.25%, We will normalize earnings to reflect the fact that current are Sony: Rationale for Model is 25.8%; we will assume that they

(higher than 198 Aswath Damodaran I I I I Cost of Equity = 2% + 1.10 (4%) 6.40% Book Value Debt Ratio = 25.8% Reinvestment Needs Normalized Earnings: • • • • • • • • Expected Change in non-cash Working Capital = (2671 - 2593)*.0848 Expected Revenues next year = 2593(1.03) 2671 billion Current Revenues = 2593 billion Expected Net Capital Expenditures = 27 billion (1.03) 27.81 Current Net Capital Expenditures = (103 - 76) 27 billion JPY Normalized Net Income next year = 1795 billion * .0525 94.24 Estimated Return on Equity = 5.25% Book Value of Equity (3/1999) = 1795 billion JPY Estimating the Inputs

= 6.60 billion JPY 199 Aswath Damodaran I I I Sony was trading at a market value of equity 7146 billion JPY Value of Equity = 68.71 billion / (.064 - .03) 2021 JPY Cost of Equity = 6.4%; Stable growth rate 3%; Valuation Expected FCFE next year Nncs C 1Db ai)=66(-28 = 4.89 = 20.64 FCFE - ( ∆ Non-cash WC) (1-Debt ratio) = 6.6 (1-.258) - (Net Cap Ex) (1- Debt Ratio)= 27.81 (1-.258) Expected Net Income The Valuation

=68.71 billion JPY = 94.24 billion 200 Aswath Damodaran I I I these firms owned by the firm you are valuing. which these holdings are, and then take the percentage of value To value them right, we have to estimate the of companies in in valuations. Consequently, we tend to understate the value of these crossholdings net income. report only the dividends they receive from these holdings as part of When firms have minority passive holdings in other companies, they

The Effect of Cross-holdings 201 Aswath Damodaran Nestle: Rationale for Using Model - January I I I it has available in FCFE. Like many large European firms, Nestle has paid less in dividends than making an assumption.) change that leverage materially. (How do I know? not. am just Nestle has a debt to capital ratio of about 37.6% and is unlikely next 5 years) 11%. (Analysts are also forecasting a growth rate of 12% year for the years, but the fundamentals at firm suggest growth in EPS of about Earnings per share at the firm has grown about 5% a year for last 5

2001 202 Aswath Damodaran a xDpenCretRto150% 5.00% Forever after yr 5 9.30% (Grow with earnings) 16% Current Ratio NA 9.30% (Existing) Cap Ex/Deprecn 0.85 Debt Ratio 15.38% WC/Revenues 65.10% (Current) years 5 Expected Growth 23.63% Retention Ratio Return on Equity Beta Length I General Inputs • Current EPS = 108.88 Sfr; Revenue/share =1,820 Sfr • • Capital Expenditures/Share=114.2 Sfr; Depreciation/Share=73.8 Sfr Long Term Government Bond Rate (Sfr) = 4% Nestle: Summarizing the Inputs 37.60% Stable Growth High Growth

0.85 37.60% 203 Aswath Damodaran sa5.8 I 4 I Total 6.4 3 1 Eastern Europe Rest of W. Europe 1.1 Asia Italy/Spain 4.3 Germany/France/UK Switzerland South America North America Estimating the Risk Premium for Nestle

Cost of Equity = 4% + 0.85 (5.26%) 8.47% The risk premium that we will use in the valuation is 5.26%

70.5 18.4 17.5 Revenues

0.0 5.26% 100.00% 4.00% 26.10% 4.00% 24.82% Weight .7 8.00% 4.00% 5.67% 9.00% 18.44% 5.50% 8.23% 9.08% 4.00% 12.00% 1.56% 6.10%

Risk Premium 204 Aswath Damodaran Present Value anns$125.63 $80.31 Free Cashflow to Equity $33.54 $38.70 $44.65 $51.52 $29.07 - ∆ - (Net Earnings CpEX)*(1-DR) The stock was trading 2906 Sfr on December 31, 1999 WC*(1-DR) Value=$74.04 +$78.76 +$83.78 +$89.12 +$94.7 +3890/(1.0847) +$78.76 +$83.78 +$89.12 +$94.7 Value=$74.04 Terminal Value per Share = 173.93/(.0847-.05) 3890.16 Sfr Chg in WC FCFE Net Capital Ex Earnings per Share in year 6 = 222.66(1.05) 231.57 6 = 231.57 - 78.5(1-.376) 13.85(1-.376)= 173.93 Sfr 6 =( Rev 6 = Deprecn’n Nestle: Valuation 6 - Rev 5 )(.093) = 1820(1.1538) 6 $74.04 $78.76 $83.78 1 1.5 $18.75 $21.63 $24.96 $28.79 $16.25 * 0.50 =73.8(1.1538) $92.67 $106.92 $144.95 $167.25 $192.98 $222.66 2345 5 (.05)(.093)=13.85 Sfr 5 (1.05)(.5)= 78.5 Sfr $89.12 $123.37 5 =3011Sf

$94.7 $142.35 205 Aswath Damodaran Value= =$74.04 +$78.76 +$83.78 +$89.12 +$94.7 + Value= =$74.04 +$78.76 +$83.78 +$89.12 +$94.7 4986/(1.0847) Terminal Value per Share = 222.93/(.0847 -.05) 4986 Sfr I FCFE was zero, as many analysts do, the terminal value would have been: depreciation in steady state. If, instead, we had assumed that net cap ex In our valuation of Nestle, we assumed that cap ex would be 150% 3740.91 Sfr Nestle: The Net Cap Ex Assumption 6 = 231.57 - 13.85(1-.376) 222.93 Sfr 5

= 206 Aswath Damodaran 3011 Sfr per Share = Value of Equity Debt Ratio = 37.6% Financing Weights Swiss franc rate = 4% Riskfree Rate CE79.28 = FCFE - Change in WC (!- 25.19 - (Cap Ex Depr) (1- DR) Net Income Cashflow to Equity 03 f 26 f 0.2Sr 2.7Sr142.35 Sfr 123.37 Sfr 106.92 Sfr 92.67 Sfr 80.31 Sfr : R 4.41 DR) + A VALUATION OF NESTLE

for food= 0.79 Bottom-up beta 108.88 Discount at 4%+0.85(5.26%)=8.47% Cost of Equity 0.85 Beta Cost of Equit =.651*.2363=15.38% Return on Equity Retention Ratio * Expected Growth D/E=11% Market y X 4% + 1.26% Risk Premium ...... Premium: 4% Base Equity ( PER SHARE Terminal Value= 173.93/(.0847-.05) Debt ratio stays 37.6% Cap Ex/Deprec=150% g=5%; Beta=0.85; Firm is in stable growth: Premium:1.26% Country Risk Forever

= 3890 207 Aswath Damodaran I The Effects of New Information on Value competitors and the overall economy. susceptible to change as new information comes out about the firm, its No valuation is timeless. Each of the inputs to model are • • • Firm Specific Information Industry Wide Information Market Wide Information – – – – – – –

Changes in the Fundamentals (Risk and Return characteristics) New Earnings Reports Changes in technology Changes in laws and regulations Economic Growth Risk Premiums Interest Rates 208 Aswath Damodaran Nestle: Effects of an Earnings Announcement I I There are two effects on value: two pieces of news: Assume that Nestle makes an earnings announcement which includes • • • •

turnover ratios remain unchanged). This will reduce expected growth. The drop in net margin will make the return on equity lower (assuming lower, even if the growth rate remains same The drop in earnings will make the projected and cash flows analysis, is expected to shrink 5.79%. net profit margin. The after-tax margin, which was 5.98% in the previous Increased competition in its markets is putting downward pressure on the earnings per share will be 105.5 Sfr instead of 108.8 Sfr. The earnings per share come in lower than expected. base year 209 Aswath Damodaran 2854 Sfr per Share = Value of Equity Debt Ratio = 37.6% Financing Weights Swiss franc rate = 4% Riskfree Rate CE75.90 = FCFE - Change in WC (!- 25.19 - (Cap Ex Depr) (1- DR) Net Income Cashflow to Equity 64 f 80 f 0.5Sr 1.8Sr134.32 Sfr 116.68 Sfr 101.35 Sfr 88.04 Sfr 76.48 Sfr : R 4.41 DR) + A RE-VALUATION OF NESTLE

for food= 0.79 Bottom-up beta 105.50 Discount at 4%+0.85(5.26%)=8.47% Cost of Equity 0.85 Beta Cost of Equit = .651*.2323 Return on Equity Retention Ratio * Expected Growth D/E=11% Market y X 4% + 1.26% Risk Premium =15.12% ...... Premium: 4% Base Equity Terminal Value= 164.84/(.0847-.05) ( PER SHARE Debt ratio stays 37.6% Cap Ex/Deprec=150% g=5%; Beta=0.85; Firm is in stable growth: Premium:1.26% Country Risk Forever

= 3687 210 Aswath Damodaran Tsingtao Breweries: Rationale for Using Model: Tsingtao I I n the firm consistentlya portion fundsof its reinvestment with needs dividends are unlikely to reflect free flowcash to equity. Inaddition, Why FCFE? push improve over the next 5 years. As it increases, earnings growth will be firm’s currentreturn anticipatewe thatequitywill and on it is low, market – China, in particular, and the rest ofin Asia, general. The Why three stage? ew debt issues. ed up.

Corporate governance in China tends to beweak and

Tsingtao is a small firm servinggrowing a huge and

June 2001 211 Aswath Damodaran I I I I estimate the normalized reinvestment theequity normalized in estimate 1999. firm’s book debt to capital ratio of 40.94% at the end of 1999 and use itto As in 19 no Th m Th 2.80%. of equity income on a book value of equity of 2,588 million CY, giving it return a on In 2000, Tsingtao Breweries 72.36earned million CY(Chinese Yuan) in net = 335 - = Capital expenditures – Depreciation+ Normalized Changenon-cash in working Normalized Reinvestment No illion during CY the year. rma e e rm with working capital, debt issues have been volatile. We estimate the capital CY million Revenues Revenues firm had capital expenditures of 335 millionCY and depreciationof 204 working capital changes over lasthave and 4 years the been volatile, we 99: lize the change using non-cash working capital as a percent of revenues of percent a as workingcapital usinglizenon-cashchange the al ized change in non-cash working capital = (Non-cash working capital 204 + 52.3= + 52.3= 204 Background Information 1999 ) (Revenuess 183.3 million CY 1999

– Reve nues 1998 ) = (180/225) = 53-1598) = 52.3 53-1598) 22 3)*(

1999 212 / Aswath Damodaran ea07 oe o08 0.80 Forever after yr 10 4+0.95% 10% 50% Moves to 0.80 Moves to 10% Moves to 50% 20% 5 years 149.97% 44.91% 0.75 --> Expected Growth 12%->20% Reinv. Equity 5 years 4%+2.28% ROE 2.8%->12% Risk Premium Beta Length I We wil asssume that = Equity reinvestment rate * ROE Expected growth rate- next 5 years = 183.3 (1-4094) / 72.36 149.97% Equity Reinvestment Ratio= (1- Debt Ratio) / Net Income = 1.4997*. 12 + [((.12-.028)/.028) Inputs for the 3 Stages ihGot rniinPaeStable Growth Transition Phase High Growth New 1/5 - 1] = 44.91% +[(ROE 5 - ROE today )/ROE today ] 1/5

-1 213 Aswath Damodaran C erEpce rwhNet Income Expected Growth Year urr 01.0 Y,3.15.0 Y6.11.6 CY172.16 13.96% CY665.91 50.00% CY1,331.81 10.00% 10 9 8 7 6 5 4 3 2 1 n Y23 149.97% CY72.36 ent Tsingtao: Projected Cash Flows Tsingtao: 69%C1207 99%C332 41%CY107.04 CY34.83 14.11% 14.26% CY363.29 CY103.61 69.99% 89.99% CY1,210.74 109.98% CY1,034.98 129.98% 16.98% CY834.92 149.97% 23.96% CY637.61 149.97% 30.94% CY462.29 149.97% 37.93% CY319.03 149.97% 44.91% CY220.16 149.97% 44.91% CY151.93 44.91% CY104.85 44.91% 44.91% Sum of the present values of FCFE during high growth = high growth FCFE during of values present the Sum of Rei nvestment Rate FCFE Cost of Equity Present Value Present Equity of Cost FCFE Rate nvestment Equity (CY191.14) (CY231.02) (CY159.43) (CY110.02) (CY83.35) (CY75.92) (CY52.40) 14.41% 14.56% 14.71% 14.71% 14.71% 14.71% 14.71% (CY116.32) (CY32.02) (CY84.01) (CY92.08) (CY72.89) (CY57.70) (CY45.68)

($186.65) 214 Aswath Damodaran = 732.5/(.1396-.10) = CY 18,497 million = CY 1331.81 (1.10)(1-.5)million 1331.81732.50 = CY CY = I I I I I = FCFE Income= Net TerminalValueequity of in Tsingtao Breweries in FCFE Expected year 11 Cost of equity in stable growth = 13.96% Equity reinvestment rate in stable growth = 50% stableExpected rate =10% growth 11 / (Stable period cost of equity – Stable growth rate) 11 Tsingtao: Terminal Value Tsingtao:

*(1- Stable period equity reinvestment rate) 215 Aswath Damodaran = I I = I = -CY186.65+CY18,497/(1.1471 CY 4 ,596CY million PV overvalued,valuation.upon this based The stock tradingwas at 10.10 perYuan share, makewhich would it Value of Equity per share = Value of Equity/ Number of Shares Value of Equity of F of CFE during the high growth period + PV of terminal value = CY 4,596/653.15 =CY7.04 pershare Tsingtao: Valuation Tsingtao: 5

*1.1456*1.1441*1.1426*1.1411*1.1396) 216 Aswath Damodaran I I probably change over time. Hence, we will use the FCFF model. and bank-oriented in its use of debt than Chrysler), the ratio will on the use of debt (Daimler has traditionally been more conservative Since this is a relatively new organization, with two different cultures therefore assume that the firm is in stable growth. DaimlerChrysler is a mature firm in industry. We will DaimlerChrysler: Rationale for Model

June 2000 217 Aswath Damodaran I I I I I I 3%. We will assume that the firm maintain a long term growth rate of market premium of 4% is used. The long term German bond rate is 4.87% (in DM) and the mature Daimler is AAA rated. beta for automobile firms is 0.61, and unlevered The bottom-up market value of debt is 64.5 billion The market value of equity is 62.3 billion DM, while the estimated of 7.15%. equity as of 1998, DaimlerChrysler had an after-tax return on capital Based upon this operating income and the book values of debt 9,324 million DM and had an effective tax rate of 46.94%. In 1999, Daimler Chrysler had earnings before interest and taxes of

Daimler Chrysler: Inputs to the Model 218 Aswath Damodaran I I Cost of Capital Expected Reinvestment Rate = g/ ROC 3%/7.15% 41.98% Daimler/Chrysler: Analyzing the Inputs • • • •

5.62% Cost of Capital = 8.65%(62.3/(62.3+64.5))+ 2.69% (64.5/(62.3+64.5)) After-tax Cost of Debt = (4.87% + 0.20%) (1-.4694)= 2.69% Cost of Equity = 4.87% + 0.945 (4%) 8.65% Bottom-up Levered Beta = 0.61 (1+(1-.4694)(64.5/62.3)) 0.945 219 Aswath Damodaran I I Valuation of Firm Estimating FCFF au fEut 66,427 mil DM 130,915 mil DM 64,488 mil DM Stock was trading at 62.2 DM per share on August 14, 2000 Value per Share = 72.7 DM share 18,068 mil DM 2,957 mil DM Value of Equity = - Debt Outstanding = Value of Firm = + Cash Marketable Securities = 112,847 mil DM Value of operating assets = 2957 / (.056-.03) 2,139 mil DM Expected FCFF next year = 5,096 mil DM Expected Reinvestment needs = 5,096(.42) Expected EBIT (1-t) = 9324 (1.03) (1-.4694)

Daimler Chrysler Valuation 220 Aswath Damodaran I J J I If there is, can you think of a way around this problem? No Yes value for equity. Is there circular reasoning here? value of the FCFF as our for firm and derive an estimated using the market values of equity and debt. We then use present In discounting FCFF, we use the cost of capital, which is calculated

Circular Reasoning in FCFF Valuation 221 Aswath Damodaran Tube Investment: Rationale for Using 2-Stage I I running the firm reassesses its policy of funding firm. financing policy is also in a state of flux as the family The firm’s the next 5 years. its growth rate has been anemic, there is potential for high over Tube Investments is a diversified manufacturing firm in India. While

FCFF Model - June 2000 222 Aswath Damodaran Otos0 Value/Share 18,073 -Options 13,653 =Equity 15,158 - Debt: + Cash: Firm Value: 19,578 elrsfe rate riskfree Real Riskfree Rate 22.80% Cost of Equity Reinvestment Rate =112.82% = FCFF - 568 - Chg WC 4,150 - Nt CpX 843 EBIT(1-t) : 4,425 Current Cashflow to Firm 61.57 : = 12%

Tube Investments: Status Quo Discount at CF$1,868 $1,971 $2,080 $2,195 $2,316 $4,670 $4,928 $5,200 $5,487 $5,790 FCFF - Reinvestment EBIT(1-t) + etr:0.75 Sectors: Unlevered Beta for Cost of Ca = 9.45% (12%+1.50%)(1-.30) Cost of Debt 60% Reinvestment Rate 1.17 Beta $2,802 $2,957 $3,120 $3,292 $3,474 p ital ( WACC ai:79% Ratio: Firm’s D/E ) = 22.8% .2% 5.52 .60*.092-= .0552 in EBIT (1-t) Expected Growth X 9.23% Risk Premium ( ( in Rs .558 ) Weights 4% premium Mature risk E + 9.45% = ) 58 D 55.8%

Terminal Value ( 0.442 = 9.20% Return on Capital 44.2% ) 23% 5 Premium Country Risk = 16.90% 5 = 2775/(.1478-.05) 28,378 Reinvestment Rate=54.35% ROC= 9.22% Country Premium= 3% Debt ratio = 44.2% g = 5%; Beta 1.00; Stable Growth

2,775 3,304 6,079 Term Yr 223 Aswath Damodaran I return on capital remain unchanged.) would my terminal value be? (Assume that the cost of capital and growth rate of 5%. If I used a 7% stable instead, what In estimating terminal value for Tube Investments, I used a stable

Stable Growth Rate and Value 224 Aswath Damodaran The Effects of Return Improvements on Value I I

growth. The value of the firm will be higher, because higher expected years. just new investments (and not on existing investments) over the next 5 management believes will increase the return on capital to 12.20% The firm is considering changes in the way which it invests, 225 Aswath Damodaran Otos0 Value/Share 18,073 -Options 13,653 =Equity 20,765 - Debt: + Cash: Firm Value: 25,185 elrsfe rate riskfree Real Tube Investments: Hi Riskfree Rate 22.80% Cost of Equity Reinvestment Rate =112.82% = FCFF - 568 - Chg WC 4,150 - Nt CpX 843 EBIT(1-t) : 4,425 Current Cashflow to Firm 84.34 : =

12% Discount at CF$1,900 $2,039 $2,188 $2,348 $2,520 $4,749 $5,097 $5,470 $5,871 $6,300 FCFF - Reinvestment EBIT(1-t) + etr:0.75 Sectors: Unlevered Beta for g Cost of Ca her Mar = 9.45% (12%+1.50%)(1-.30) Cost of Debt 60% Reinvestment Rate 1.17 Beta $2,850 $3,058 $3,282 $3,522 $3,780 p g ital inal Return ( WACC ai:79% Ratio: Firm’s D/E ) = 22.8% .2% 7.32 .60*.122-= .0732 in EBIT (1-t) Expected Growth X ( 9.23% Risk Premium in Rs ( .558 ) ) Weights 4% premium Mature risk E + 9.45%

= 58 D 55.8% Terminal Value ( 0.442 = 12.20% Return on Capital 44.2% ) 23% 5 Premium Country Risk = 16.90% 5 = 3904/(.1478-.05) 39.921 Reinvestment Rate= 40.98% ROC=12.22% Country Premium= 3% Debt ratio = 44.2% g = 5%; Beta 1.00; Stable Growth

3,904 2,711 6,615 Term Yr 226 Aswath Damodaran I I I Return Improvements on Existing Assets Expected Growth Rate = .122*.60 +{ (1+(.122-.092)/.092) component arising from improving returns on existing assets: The expected growth rate over the next 5 years will then have a second more. existing assets to 12.20% from 9.20%, its value will increase even If Tube Investments is also able to increase the return on capital =.1313 or 13.13% 1/5

-1} 227 Aswath Damodaran Otos0 Value/Share 18,073 -Options 13,653 =Equity 27,409 - Debt: + Cash: Firm Value: 31,829 elrsfe rate riskfree Real Tube Investments: Hi Riskfree Rate 22.80% Cost of Equity Reinvestment Rate =112.82% = FCFF - 568 - Chg WC 4,150 - Nt CpX 843 EBIT(1-t) : 4,425 Current Cashflow to Firm 111.3 : =

12% Discount at CF$2,003 $2,265 $2,563 $2,899 $3,280 $5,006 $5,664 $6,407 $7,248 $8,200 FCFF - Reinvestment EBIT(1-t) + etr:0.75 Sectors: Unlevered Beta for g Cost of Ca her Avera = 9.45% (12%+1.50%)(1-.30) Cost of Debt 60% Reinvestment Rate 1.17 Beta $3,004 $3,398 $3,844 $4,349 $4,920 p ital g ( WACC e Return ai:79% Ratio: Firm’s D/E ) = 22.8% 31 % 13.13 .0581 = .1313 60*.122 + Expected Growth X ( 9.23% Risk Premium in Rs ( .558 ) ) Weights 4% premium Mature risk E

+ 9.45% = 58 D 55.8% 12.20% Return on Capital Terminal Value ( 0.442 = 44.2% ) 23% 5 Premium Country Risk = 16.90% 5 = 5081/(.1478-.05) 51,956 { (1+(.122-.092)/.092) Improvement on existing assets Reinvestment Rate= 40.98% ROC=12.22% Country Premium= 3% Debt ratio = 44.2% g = 5%; Beta 1.00; Stable Growth 5,081 3,529 8,610 Term Yr 1/5

-1} 228 Aswath Damodaran Tube Investments and Tsingtao: Should there Tube Investments and Tsingtao:

I No. Yes estimated to allow for this absence of stockholder power? conflict of interests is huge. Would you discount the value that insiders own voting shares and control the firm potential for have little or no power over the managers of firm. In many cases, Stockholders in Asian, Latin American and many European companies

be a corporate governance discount? 229 Aswath Damodaran Dealing with Operating Leases: A Valuation of I I debt. This, in turn, will mean that operating income has to get restated. When doing firm valuation, these operating leases have to be treated as its balance sheet. However, it does have significant operating leases. The Home Depot does not carry much in terms of traditional debt on

the Home Depot 230 Aswath Damodaran Operating Leases at The Home Depot in 1998 I I n eod$ 7.0 $1,513.37 6 and beyond $ 270.00 Present Value 5 4 3 2 Commitment 1 Year etVleo ess=$ 2,647.70 Debt Value of leases = The pre-tax cost of debt at the Home Depot is 5.80%

260 $178.03 $195.53 $222.92 $259.97 $ 236.00 $277.88 $ 245.00 $ 264.00 $ 291.00 $ 294.00 231 Aswath Damodaran et$,3 i $ 4,081 mil $ 2,815 mil $1,433 mil $1,829 mil $ 2,661mil $1,730 mil Debt EBIT (1-t) EBIT Other Adjustments from Operating Leases

xesdconverted to Debt Expensed Lease Operating Operating Lease 232 Aswath Damodaran Otos2,021 64,930 Value/Share $42.55 4,081 -Options 62 =Equity - Debt: Cash: + Firm Value: Rate = 5% Government Bond Riskfree Rate 9.79% Cost of Equity Reinvestment Rate =108.75% = FCFF <160> - Chg WC 190 - Nt CpX 1,799 EBIT(1-t) : 1,829 Current Cashflow to Firm 68,949 :

FCFF - Reinv EBIT(1-t Discount at ) + Sectors: 0.86 Unlevered Beta for 238 1857 2095 Cost of Capital (WACC) = 9.79% (0.9555) + 3.77% (0.0445) 9.52% The Home De = 3.77% (5%+ 0.80%)(1-.35) Cost of Debt 88.62% Reinvestment Rate 273 2126 2399 0.87 Beta 313 2434 2747 p Ratio: 4.76% Firm’s D/E 358 2788 3146 ot: A Valuatio X 45 % 14.51 .8862*.1637= .1451 in EBIT (1-t) Expected Growth 5.5% Risk Premium 410 3192 3602 E = 95.55% D 4.45% Weights 5.5% Premium Historical US 469 3655 4125 n 538 4186 4723 Terminal Value 16.37% Return on Capital 0% Premium Country Risk 616 4793 5409 705 5489 6194 10 = 4806/(.0792-.05) 164,486 Reinvestment Rate=35.46% D/(D+E) = 30%;ROC=14.1% g = 5%; Beta 0.87; Stable Growth

807 6285 7092 233 Aswath Damodaran I I I I other firms in the same business also distress). value (and this will be lower if the economy is doing badly and there are The distress sale value of equity is usually best estimated as a percent book There are three ways in which we can estimate the probability of distress: sale value of equity (Probability distress) Value of Equity= DCF value equity (1 - Probability distress) + Distress the firm. cashflows (a distress sale value), DCF valuations will understate the value of will then be sold for a value less than the present of expected likelihood of the firm failing before it reaches stable growth and if assets A DCF valuation values a firm as going concern. If there is significant • • • Estimate the probability of distress by looking at market value bonds.. probit Estimate the probability of distress with a Use the bond rating to estimate cumulative probability of distress over 10 years

Dealing with Distress 234

Value per share $ $ $ 14 Value per share $ $ 4,923 Options Equity - $ = Value of Equity - Value of Debt $ 2,260 = Value of Firm + Cash & Non-op Value of Op Assets $ 5,530 Aswath Damodaran 2,076m NOL: T. Bond rate = 4.8% Riskfree Rate $ 3,804 Revenue Current : 2867 7,790 3.22 -1895m EBIT 16.80% Cost of Equity -49.82% Margin: Current oto aia 38%1.0 38%1.0 38%1.2 19%1.8 .2 7.98% 40.00% 46.98% 6.76% 9.72% 53.96% 10.88% 60.95% 8.96% 11.94% 67.93% 12.92% 74.91% 9.92% 13.80% 74.91% 10.88% 13.80% 74.91% 8.80% 11.84% 13.80% 74.91% 10.40% 12.80% 13.80% 74.91% 12.00% 12.80% 13.80% 13.60% 12.80% 15.20% 12.80% Cost of Capital 16.80% 12.80% 16.80% 16.80% Debt Ratio 16.80% 16.80% Cost of Debt Cost of Equity Beta EBITDA Revenues -CgW 4 $8 4 $5 2 $0 2 $1 $19 $21 $27 $30 $27 $25 $42 $48 ($1,761) ($3,526) $46 $ 0 FCFF $3,431 $1,716 $1,201 $1,261 $1,324 $1,390 $1,460 $1,533 $894 $1,609 $1,690 - Chg WC $852 $811 - $773 Cap $1,580 $1,738 $1,911 $2,102 $1,051 $736 + Ex EBIT (1-t) Depreciation EBIT + Retail Internet/ 3.00> 1.10 Beta .030 .030 .026 .018 .01.00 1.40 1.80 2.20 2.60 3.00 3.00 3.00 3.00 3.00 $10,053 $11,058 $11,942 $12,659 $13,292 0 $ $9,139 $8,308 $6,923 ($95) $5,326 $3,804 $,7)(178 $,6)(122 30 $1,074 $1,550 $1,697 $2,186 $2,276 $320 ($1,272) ($1,565) $1,074 $1,550 $1,697 $2,186 $2,694 ($1,738) ($1,675) $320 ($1,272) ($1,565) ($1,738) ($1,675) 13.33% Growth: Revenue 1568910 Leverage Operating decreases and net cap ex Cap ex growth slows 24 Tax rate = 0% -> 35% 4.8%+8.0%=12.8% Cost of Debt $346 $831 $1,371 $1,809 $2,322 $2,508 $3,038 $3,589 $2,508 $3,038 $2,322 $1,371 $1,809 $831 $346 $0)($472) ($903) 3 D/E: 441% Current X -> 30% EBITDA/Sales 4% Risk Premium $22 $392 $832 $949 $1,407 $1,461 Premium Base Equity 7 Debt= 74.91% -> 40% Weights Growth: 5% Revenue Stable =$ 28,683 Terminal Value= 677(.0736-.05)

Premium Country Risk Stable Growth 30% Sales EBITDA/ Stable Stock 2001 November Global Crossing $ 677 $ 20 $ 2,353 $ 939 $ 2,111 $ 3,248 $ 4,187 $13,902 Term. Yea 67.93% Reinvest ROC=7.36% Stable Forever p rice = $1.86

r 235 Aswath Damodaran I I I Distress adjusted value of equity Distress sale value of equity Probability of distress Valuing Global Crossing with Distress • • • • • • • • Value of Global Crossing = $3.22 (.2337) + $0.00 (.7663) $0.75 Distress sale value of equity = $ 0 Book value of debt = $7,647 million Distress sale value = 15% of book .15*14531 $2,180 million Book value of capital = $14,531 million survival over 10 years = (1- .1353) probabilityof Cumulative Probability of distress = 13.53% a year Price of 8 year, 12% bond issued by Global Crossing = $ 653 653 = ∑ t t = = 1 8 120(1 (. 0 105 105

− ππ Distress ) t8 ) t + 1000(1 ( − .) Distress ) 8 10

= 23.37% 236 Aswath Damodaran I I ripple effect on the following: When R&D expenses are reclassified as capital expenditures, there is a capital expenditures. though treated as operating expenditures, by accountants, are really amount of research and development expenses. These expenses, Bristol Myers, like most pharmaceutical firms, has a significant • • • • • Return on Capital Reinvestment Rates Depreciation and Amortization Capital Expendiutures Operating income

Dealing with R&D: Bristol Myers 237 Aswath Damodaran Converting R&D Expenses to Capital mriainti er=$1,237.90 $8,214.80 881.00 Amortization this year = Value of Research Asset = -10 -9 -8 -7 -6 Amortization this year -5 -4 -3 Unamortized portion -2 -1 R&D Expense Current Year 030 0.20 0.30 1261.60 0.40 983.00 1583.10 0.50 1083.00 1939.00 0.60 1128.00 0.70 1108.00 0.80 1199.00 0.90 1276.00 1.00 1385.00 1577.00 1759.00 1939.00 .000 $88.10 0.00 0.00 0.10 83 $98.30 98.30 216.60 338.40 443.20 599.50 765.60 969.50

$108.30 $112.80 $110.80 $119.90 $127.60 $138.50 $157.70 $175.90 238 Aswath Damodaran I I I The Consequences of a Research Asset Tax Effect of R&D Expensing Adjustment to Operating Income : $ 1,238 million Amortization of asset for current year = Additional tax benefit of expensing = (1939-1238) (.35) $ 245 million • The entire R&D expense of $1,939 million is tax-deductible, rather than • • • •

This creates a tax benefit that can be computed as follows: $ 701 million (Increase) just the amortization of $1,238 million $1,238 million $1,939 million Increase in Operating Income Subtract out the amortization Add back the R& D Expenses 239 Aswath Damodaran Vo qiy$1,0 i 830mlIncrease 38.65% Increase $ 701 mil 18,320 $ Unchanged Increase $ 1238 $ 10,105 mil Increase $ 701 Increase $ 701 $1,405 mil $ 79 mil Increase $1939 ROC $ 2,039 mil $ 704mil 20.04% BV of Equity $4,607 mil $6,710 mil Reinvestment Rate $ 79 mil $ 801 mil $ 3,444 mil Non-cash WC Chg = $ 3,906 mil $ 6,009 mil Net Cap Ex $1,505 mil Depreciation = Capital spending = EBIT (1-t) EBIT = Capitalizing R& D: The Effects & xesdRDcptlzdEffect R&D capitalized R&D expensed 25.21% 32.21%

Decrease Increase 240 Aswath Damodaran Otos2,300 Value/Share $ 52.97 -Options =Equity 105,241 - Debt: + Cash Oper. Assets: 103,742 (10-year T.Bond rate) Riskfree rate = 5.1% Riskfree Rate 8.42% Cost of Equity Reinvestment Rate =32.21% = FCFF 3,123 - Chg WC 79 - Nt CpX 1,405 EBIT(1-t) : 4,607 Current Cashflow to Firm 1,885 3,385 : Discount at CF$3,376 $3,649 $3,945 $4,264 $4,610 FCFF - Reinvestment EBIT (1-t) + Sectors: 0.82 Unlevered Beta for Cost of Capital (WACC) = 8.42% (.9834) + 3.80% (0.0166) 8.34% = 3.80% (5.1%+0.75%)(1-.35) Cost of Debt Synthetic rating = AA 32.21% Reinvestment Rate 0.83 Beta Bristol M $1,604 $1,734 $1,874 $2,026 $2,190 $4,980 $5,383 $5,819 $6,290 $6,800 Ratio: 1.69% Firm’s D/E A y ers: Status Quo X .0% 8.10 .3221*.2515= .081 in EBIT (1-t) Expected Growth 4.00% Risk Premium 4% premium Mature risk E =98.34% D = 1.66% Weights Terminal Value 25.15% Return on Capital 0% Premium Country Risk 5 = 4760/(.0861-.05) 131,716 Reinvestment Rate=33.33% ROC= 15% g = 5%; Beta 0.90; Stable Growth

4760 2380 7140 Term Yr 241 Aswath Damodaran The Dark Side of http://www.stern.nyu.edu/~adamodar Valuation

Aswath Damodaran 242 Aswath Damodaran I I I I much historical data but we have lots of comparable firms. comparable firms; in valuing a software firm, we might not have too in valuing Ford, we have 70 years+ of historical data, but not too many We often substitute one type of information for another; instance, The industry and comparable firm data statements. financial history, usually summarized in its The firm’s current financial statement The firm’s What happens to firms as they mature? (Margins.. Revenue growth… • • • • • To make our estimates, we draw Reinvestment needs… Risk) Susceptibility to macro-economic factors (recessions and cyclical firms) can we learn about cost structure and profitability from these trends? revenues and earnings grown over time? What How fast have the firm’s How much did it earn? How much did the firm sell?

information from.. 243 Aswath Damodaran I Valuation is most difficult when a company • • Has negative earnings and low revenues in its current financial statements • life cycle as the firm being valued) No comparables ( or even if they exist, are all at the same stage of No history

The Dark Side... 244

= Value of Equity in Stock - Equity Options = Value of Equity - Value of Debt = Value of Firm + Cash & Non-op Assets Value of Operating Assets Aswath Damodaran nominal as cash flows in same terms (real or - In same currency and - No reinvestment risk - No default risk Riskfree Rate - NOLs Tax Rate Revenue Current : Cost of Equity EBI T Margin Operating Current FCFF = Revenue* Op Margin (1-t) - Reinvestment Discounted Cash Flow Valuation: High Growth with Negative Earnings

+ Business Type of Discount at FCFF - Measures market risk Beta 1 Ratio Sales Turnover WACC= Cost of Equity (Equity/(Debt + Equity)) Debt (Debt/(Debt+ Leverage Operating Growth Revenue FCFF 2 + Default Spread) (1-t) (Riskfree Rate Cost of Debt FCFF Leverage Financial X 3 risk investment - Premium for average Risk Premium Margin Operating Expected Advantages Competitive Reinvestment FCFF Premium Base Equity 4 FCFF Terminal Value= FCFF Based on Market Value Weights 5 ...... Premium Country Risk Growth Revenue Stable FCFF

n Stable Growth Margin Operating Stable n+1 /(r-g Forever n

Reinvestment Stable

) 245 Aswath Damodaran I 1.00 beta for firms in specialty retailing = Unlevered beta for firms in Unlevered towards the beta of retailing business. companies to begin the valuation but move beta, after first five years, the fact that it is an online retailer. Hence we will use beta of internet Amazon is a specialty retailer, but its risk currently seems to be determined by Amazon’s Bottom-up Beta

nentrtiig=1.60 internet retailing = 246 Aswath Damodaran Estimating Synthetic Ratings and cost of debt I I higher in the later years than BBB) first 5 years. (In effect, the rating will be lower in earlier years and years. This yields an average rating of BBB for Amazon.com the computed an average interest coverage ratio of 2.82 over the next 5 interest coverage ratio, which should suggest a low rating. We Amazon.com has negative operating income; this yields a estimated from the interest coverage ratio characteristics of the firm. In its simplest form, rating can be The rating for a firm can be estimated using the financial

Interest Coverage Ratio = EBIT / Expenses 247 Aswath Damodaran a ae0 %0 61 5 3% 3% 5 3%35% 35% 35% 35% 35% 35% 16.1% 0% 0% 8.00% 8.00% After-tax 0% Tax rate I I I r-a .0 8.00% 8.00% Pre-tax debt changes, the after tax cost of will change as well. tax rate changes and its cost of paying no taxes currently. As the firm’s After-tax cost of debt right now = 8.00% (1- 0) 8.00%: The firm is Pre-tax cost of debt = Riskfree Rate + Default spread BBB rated bonds is 1.50% The synthetic rating for Amazon.com is BBB. default spread 123456 Estimating the cost of debt 8.00% = 6.50% + 1.50% 8.00% 8.00% 6.71% 8.00% 5.20% 8.00% 5.07% 7.80% 5.04% 7.75% 78910

.8 .8 4.55% 4.88% 4.98% .7 7.50% 7.00% 7.67% 248 Aswath Damodaran I I I I Cost of Capital = 12.9 % (.988) + 8.00% (1- 0) (.012)) 12.84% Estimating Cost of Capital: Amazon.com is in this process. value of debt $ 349 million. Shows you how irrelevant book Amazon.com has a book value of equity $ 138 million and Cost of Capital Debt Equity • • • • Market Value of Debt = $ 349 mil (1.2%) Cost of debt = 6.50% + 1.50% (default spread) 8.00% (98.8%) Market Value of Equity = $ 84/share* 340.79 mil Cost of Equity = 6.50% + 1.60 (4.00%) 12.90%

shs = $ 28,626 mil shs 249 Aswath Damodaran Calendar Years, Financial Years and Updated I I BT-$2 ilo - $ 410 million $1,117 million - $125 million $ 610 million EBIT Revenues evolving and growing rapidly. This rule becomes even more critical when valuing companies that are earnings and revenues than numbers for the most recent financial year. As a general rule, it is better to use 12-month trailing estimates for is that they are dated. updated numbers. One of the problems with using financial statements The operating income and revenue that we use in valuation should be Information

at1- Trailing 12-month Last 10-K 250 Aswath Damodaran Are S, G & A expenses capital expenditures? I I I

Should Amazon.com’s selling expenses be treated as cap ex? Should Amazon.com’s will, however, make not their cash flows less negative. also mean that they are reinvesting far more than we think are. It these expenses, which will make many of firms profitable. It If we adopt this rationale, should be computing earnings before should be treated as capital expenditures. are the equivalent of R&D expenses for a high-technology firms and Many internet companies are arguing that selling and G&A expenses 251 Aswath Damodaran er12345 $570 35% 16.13% $167 4 0% $0 0% After year 5, the tax rate becomes 35%. 3 $1,038 $407 $0 $407 0% NOL -$94 2 -$94 Tax rate $0 -$373 EBIT(1-t) -$373 1 Taxes EBIT Year $500 Amazon.com’s Tax Rate Amazon.com’s 83$967 $873 $871 50$0 $560

$1,058 $1,628 252 Aswath Damodaran I I I I I I Estimating FCFF (1999) Non-cash Working capital Change (1999) = - 80 million Depreciation (Trailing 1999) = $ 31 million acquisitions) Capital spending (Trailing 1999) = $ 243 million (includes Tax rate used = 0% (Assumed Effective Marginal) EBIT (Trailing 1999) = -$ 410 million urn CF= - $542 million = -$ 80 million = $212 million Current FCFF - Change in Working Capital - (Capital Spending Depreciation) = - $410 million Current EBIT * (1 - tax rate) = 410 (1-0)

Estimating FCFF: Amazon.com 253 Aswath Damodaran The sales/capital ratio of 3.00 was based on what Amazon accomplished last year 10 9 8 7 6 5 4 3 2 1 Revenue Chg in Year .0 $2,208 and the averages for industry. 6.00% 10.80% 15.60% 20.40% 25.20% 30.00% $4,189 50.00% $2,793 75.00% $1,676 100.00% 150.00% Growth in Revenues, Earnings and rwhRevenue Investment Growth Reinvestment: Amazon $3,587 $4,482 $4,868 $4,803 $4,398 $4,887 763.00 3.00 $736 3.00 $1,196 3.00 $1,494 3.00 $1,623 3.00 $1,601 3.00 $1,466 3.00 3.00 $1,629 3.00 $1,396 $931 Sales/Capital ROC $559 New

20.39% 21.19% 21.87% 22.30% 22.23% 21.16% 25.82% 20.59% -8.96% -76.62% 254 Aswath Damodaran

• • • • • Amazon.com: Stable Growth Inputs ea16 1.00 6%/20% = 30% 15% 6% 20% >100% 1.60 1.20% Negative NMF Reinvestment Rate Expected Growth Rate Return on Capital Debt Ratio Beta

ihGot Stable Growth High Growth 255 Aswath Damodaran I I Estimating the Value of Equity Options model) Value of options outstanding (using dilution-adjusted Black-Scholes Details of options outstanding • • • • • • • •

rauybn ae=6.50% 340.79 million 38 million Value of equity options = $ 2,892 million 0.00% Number of shares outstanding = 50.00% Number of options outstanding = Treasury bond rate = 8.4 years Annualized dividend yield on stock = ln(stock price) = Standard deviation in $ 13.375 Average maturity of options outstanding = Average strike price of options outstanding = 256

Value per share $ $ $ 2,892 Value per share $ 26 $ 349 - Equity Options = Value of Equity - Value of Debt = Value of Firm Cash + Value of Op Assets $ 14,910 Aswath Damodaran 500 m NOL: T. Bond rate = 6.5% Riskfree Rate $ 1,117 Revenue Current $14,587 $14,936 34.32 : -410m EBIT 12.90% Cost of Equity -36.71% Margin: Current Tcs fdb .0 .0 .0 .1 .0 .7 .4 .8 .8 4.55% 7.00% 4.88% 7.50% 4.98% 7.67% 5.04% 7.75% 9.61% 11.15% 5.07% 7.80% 11.69% 11.96% 5.20% 8.00% 12.13% 12.81% 6.71% 8.00% 12.83% 10.50% 12.84% 11.70% 8.00% 8.00% 12.84% 12.10% $736 12.84% 12.30% 8.00% 8.00% 12.42% $1,196 Cost of Capital 12.90% 8.00% 8.00% 12.90% $1,494 AT cost of debt 12.90% $1,623 12.90% 12.90% $1,601 Cost of Debt -$931 $1,466 Cost of Equity $1,629 $1,396 $931 FCFF $559 - Reinvestment EBIT (1-t) EBIT Revenues + Retail Internet/ 1.60 -> 1.00 Beta Ratio: 3.00 Sales Turnover $7 -$94 -$94 -$373 -$373 42% Growth: Revenue 273 555 974 1,6 1,5 2,6 879 3213,9 3,0 39,006 36,798 33,211 28,729 23,862 19,059 14,661 9,774 5,585 $2,793 Leverage Operating 1568910 -$1,024 24 Tax rate = 0% -> 35% 6.5%+1.5%=8.0% Cost of Debt Reinvestment: Working capital is 3% of revenues Cap ex includes acquisitions 47$7 108$,3 179$,1 230$2,524 $2,370 -$163 $2,119 $3,883 -$408 $1,799 $3,646 $1,438 $3,261 -$758 $1,058 $2,768 -$989 $2,212 $871 $1,628 $1,038 $407 $407 3 D/E: 1.21% Current X Advantages Competitive -> 10.00% Margin: Expected 4% Risk Premium Premium Base Equity 17$2 114$1,788 $1,174 $625 $177 7 Growth: 6% Revenue Stable Debt= 1.2% -> 15% Weights =52,148 Terminal Value= 1881/(.0961-.06)

Premium Country Risk Stable Growth 10.00% Margin: Operating Stable Stock Price = $ 84 January 2000 Amazon.com of EBIT(1-t) Reinvest 30% ROC=20% Stable Forever Term. Yea $1,881 $ 807 $2,688 35.00% 10.00% $41,346

r 257 Aswath Damodaran What do you need to break-even at $ 84? 35% 30% 40% 45% 50% 55% 60% $ $ $ $ $ $ $ $ $ $ $ $ 6% 12.59 21.47 33.47 49.53 (1.94) 1.41 6.10 $ $ $ $ $ $ $ $ $ $ $ $ $ %10% 8% 15.93 26.34 40.50 59.60 85.10 2.95 8.37 $ $ $ $ $ $ $ $ $ $ $ $ $ $ 120.66 15.33 25.74 40.05 59.52 85.72 7.84 $ $ $ $ $ $ $ $ $ $ $ $ $ $ 2 14% 12% 111.84 156.22 12.71 22.27 35.54 53.77 78.53 $ $ $ $ $ $ $ 137.95 191.77

17.57 29.21 45.34 67.48 97.54 258

Value per share $ $ $ 748 Value per share $ $ 1,890 - Equity Options $ = Value of Equity - Value of Debt = Value of Firm $ 1,263 + Cash & Non-op Value of Op Assets $ 7,967 Aswath Damodaran 1,289 m NOL: T. Bond rate = 5.1% Riskfree Rate $ 2,465 Revenue Current 18.74 9,230 : 7,340 -853m EBIT 13.81% Cost of Equity -Rivsmn 62$1 87$0 70$9 76$8 54$7 $445 $374 $1,509 $1,406 $554 $1,318 $687 $1,187 $1,018 $766 $1,133 $796 $898 $780 $499 -$1 $900 $54 $24,912 $23,726 $22,596 $857 $20,922 -$364 $18,849 $16,534 $14,132 $714 -$703 $11,777 $9,059 FCFF $612 $6,471 - Reinvestment $4,314 EBIT(1-t) EB IT Revenues -34.60% Margin: Current Tcs fdb 00%1.0 00%1.0 .6 .1 .1 .5 .3 4.55% 8.76% 5.53% 9.34% 5.85% 9.98% 10.62% 6.01% 9.50% 11.25% 10.36% 12.52% 6.11% 15.00% 11.22% 12.77% 21.13% 12.09% 12.77% 9.06% 23.18% 12.95% 12.77% 10.00% 24.20% 13.81% 12.77% 10.00% 24.81% 13.81% 10.00% 27.27% Cost of Capital 13.81% 10.00% 27.27% 13.81% 27.27% 13.81% AT cost of debt 27.27% 27.27% Cost of Equity B Debt Ratio eta + Retail Internet/ 2.18-> 1.10 Beta $0 $6 5 49$9 125$,6 187$,2 214$2,322 $2,164 $2,028 $1,827 $1,566 $1,255 $898 $499 $54 -$364 -$703 Ratio: 3.02 Sales Turnover .821 .821 .8 .6 17 .3 13 1.10 1.32 1.53 1.75 1.96 2.18 2.18 2.18 2.18 2.18 35-108-83-41$1 37$5 51$6 102$1,064 $1,032 $764 $501 $252 $337 $118 -$401 -$803 -$1,078 ,315 25.41% Growth: Revenue Leverage Operating 15 24 Tax rate = 0% -> 35% 5.1%+4.75%= 9.85% Cost of Debt Reinvestment: Working capital is 3% of revenues Cap ex includes acquisitions 3 D/E: 37.5% Current X Advantages Competitive -> 9.32% Margin: Expected 4% Risk Premium Premium Base Equity 6 7 Growth: 5% Revenue Stable Debt= 27.38% -> 15% Weights =$ 28,310 Terminal Value= 1064/(.0876-.05) Premium Country Risk 8

9 Stable Growth 9.32% Margin: Operating Stable 1 0 Stock January 2001 Amazon.com Term. Yea Forever $1,064 $ 445 $1,509 $2,322 $24,912 of EBIT(1-t) Reinvest 29.5% ROC=16.94% Stable p rice = $14

r 259

Value per share $ $ $ 827 $ 1007 Value per share $ $ 2,220 - Equity Options = Value of Equity - Value of Debt = Value of Firm + Cash Value of Op Assets $ 10,669 Aswath Damodaran 2183 m NOL: T. Bond rate = 4.70% Riskfree Rate $ 3,122 Revenue Current $11,676 : 23.01 9,456 13.30% Cost of Equity -202m EBIT -6.48% Mar Current Tcs fdb .5 .5 .5 .5 .2 .2 .4 .1 .5 4.55% 7.00% 5.35% 8.23% 5.61% 8.63% 8.42% 5.74% 8.84% 8.95% $393 5.82% 8.96% 9.56% 10.17% 7.22% 9.45% 10.78% $582 11.60% 9.10% 9.45% 9.45% 12.22% 12.22% 9.94% $720 9.45% 9.45% 12.22% 10.78% 12.22% 11.62% 9.45% 9.45% 12.46% $804 Cost of Capital 13.30% 9.45% 9.45% 13.30% 13.30% AT cost of debt $835 13.30% 13.30% Cost of Debt $818 Cost of Equity -$512 $944 Beta $899 $698 $5 FCFF $517 - Reinvestment EBIT(1-t) EBIT $5 Revenues + g in: Retail Internet/ 2.15 -> 1.00 Beta .521 .521 .5 .4 17 .2 13 1.10 1.31 1.52 1.73 1.94 2.15 2.15 2.15 2.15 2.15 $24,898 $23,713 $21,956 $19,780 $17,351 $14,830 $12,358 $9,506 $6,790 $4,683 Ratio: 3.02 Sales Turnover 23.08% Growth: Revenue 1568910 Levera Operatin 28$8 96$3 91$,5 130$,1 $1,497 $1,417 $1,300 $1,152 $2,303 $2,181 $981 $2,000 $1,772 $935 $1,509 -$312 $1,224 $926 -$430 $926 $588 $588 $268 $268 24 g e Tax rate = 0% -> 35% 4.7%+4.75%=9.45% Cost of Debt g

Reinvestment: Working capital is 3% of revenues Cap ex includes acquisitions 3 D/E: 33.5% Current -$19 X -> 9.32% Advanta Com Ex Mar 4% Risk Premium p 16$4 37$7 86$1,104 $836 $579 $347 $146 $116 g ected p in: etitive g es Premium Base Equity 7 Wei Debt= 28% -> 15% 4.7% Growth: Revenue Stable = 29,170 Terminal Value= 1084/ Premium Country Risk g

hts Stable Growt 9.32% Operatin Stable Mar g in: Stock price =15.50 July 2002 Amazon g

( .0842-.045 h Reinvest 31.33 ROC=15% Stable Foreve of EBIT(1-t) Term. Yea $1,084 $495 $1,579 $2,430 $26,069 r r

) 260 %