Valuation: Lecture Note Packet 1Intrinsic ValuationAswath DamodaranUpdated: September 2015Aswath Damodaran*

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The essence of intrinsic valueIn intrinsic valuation, you value an asset based upon its intrinsic characteristics. For cash flow generating assets, the intrinsic value will be a function of the magnitude of the expected cash flows on the asset over its lifetime and the uncertainty about receiving those cash flows.Discounted cash flow valuation is a tool for estimating intrinsic value, where the expected value of an asset is written as the present value of the expected cash flows on the asset, with either the cash flows or the discount rate adjusted to reflect the risk.Aswath Damodaran*

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The two faces of discounted cash flow valuationThe value of a risky asset can be estimated by discounting the expected cash flows on the asset over its life at a risk-adjusted discount rate: where the asset has a n-year life, E(CFt) is the expected cash flow in period t and r is a discount rate that reflects the risk of the cash flows.Alternatively, we can replace the expected cash flows with the guaranteed cash flows we would have accepted as an alternative (certainty equivalents) and discount these at the riskfree rate:

where CE(CFt) is the certainty equivalent of E(CFt) and rf is the riskfree rate.

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Risk Adjusted Value: Two Basic PropositionsIf the value of an asset is the risk-adjusted present value of the cash flows:

The IT proposition: If IT does not affect the expected cash flows or the riskiness of the cash flows, IT cannot affect value.The DUH proposition: For an asset to have value, the expected cash flows have to be positive some time over the life of the asset.The DONT FREAK OUT proposition: Assets that generate cash flows early in their life will be worth more than assets that generate cash flows later; the latter may however have greater growth and higher cash flows to compensate.Aswath Damodaran*

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DCF Choices: Equity Valuation versus Firm ValuationEquity valuation: Value just the equity claim in the businessFirm Valuation: Value the entire businessAswath Damodaran*

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Equity ValuationAswath Damodaran*

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Firm ValuationAswath Damodaran*

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Firm Value and Equity ValueTo get from firm value to equity value, which of the following would you need to do?Subtract out the value of long term debtSubtract out the value of all debtSubtract the value of any debt that was included in the cost of capital calculationSubtract out the value of all liabilities in the firmDoing so, will give you a value for the equity which isgreater than the value you would have got in an equity valuationlesser than the value you would have got in an equity valuationequal to the value you would have got in an equity valuationAswath Damodaran*

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Cash Flows and Discount RatesAssume that you are analyzing a company with the following cashflows for the next five years. YearCF to EquityInterest Exp (1-tax rate)CF to Firm1$ 50$ 40$ 902$ 60$ 40$ 1003$ 68$ 40$ 1084$ 76.2$ 40$ 116.25$ 83.49$ 40$ 123.49Terminal Value$ 1603.0$ 2363.008Assume also that the cost of equity is 13.625% and the firm can borrow long term at 10%. (The tax rate for the firm is 50%.) The current market value of equity is $1,073 and the value of debt outstanding is $800.Aswath Damodaran*

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Equity versus Firm ValuationMethod 1: Discount CF to Equity at Cost of Equity to get value of equityCost of Equity = 13.625%Value of Equity = 50/1.13625 + 60/1.136252 + 68/1.136253 + 76.2/1.136254 + (83.49+1603)/1.136255 = $1073Method 2: Discount CF to Firm at Cost of Capital to get value of firmCost of Debt = Pre-tax rate (1- tax rate) = 10% (1-.5) = 5%Cost of Capital = 13.625% (1073/1873) + 5% (800/1873) = 9.94%PV of Firm = 90/1.0994 + 100/1.09942 + 108/1.09943 + 116.2/1.09944 + (123.49+2363)/1.09945 = $1873Value of Equity = Value of Firm - Market Value of Debt = $ 1873 - $ 800 = $1073 Aswath Damodaran*

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First Principle of ValuationDiscounting Consistency Principle: Never mix and match cash flows and discount rates. Mismatching cash flows to discount rates is deadly.Discounting cashflows after debt cash flows (equity cash flows) at the weighted average cost of capital will lead to an upwardly biased estimate of the value of equityDiscounting pre-debt cashflows (cash flows to the firm) at the cost of equity will yield a downward biased estimate of the value of the firm.Aswath Damodaran*

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The Effects of Mismatching Cash Flows and Discount RatesError 1: Discount CF to Equity at Cost of Capital to get equity valuePV of Equity = 50/1.0994 + 60/1.09942 + 68/1.09943 + 76.2/1.09944 + (83.49+1603)/1.09945 = $1248Value of equity is overstated by $175.Error 2: Discount CF to Firm at Cost of Equity to get firm valuePV of Firm = 90/1.13625 + 100/1.136252 + 108/1.136253 + 116.2/1.136254 + (123.49+2363)/1.136255 = $1613PV of Equity = $1612.86 - $800 = $813Value of Equity is understated by $ 260.Error 3: Discount CF to Firm at Cost of Equity, forget to subtract out debt, and get too high a value for equityValue of Equity = $ 1613Value of Equity is overstated by $ 540

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

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Generic DCF Valuation ModelAswath Damodaran*

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Same ingredients, different approachesAswath Damodaran*

InputDividend Discount ModelFCFE (Potential dividend) discount modelFCFF (firm) valuation modelCash flow DividendPotential dividends = FCFE = Cash flows after taxes, reinvestment needs and debt cash flowsFCFF = Cash flows before debt payments but after reinvestment needs and taxes.Expected growthIn equity income and dividendsIn equity income and FCFEIn operating income and FCFFDiscount rateCost of equityCost of equityCost of capitalSteady stateWhen dividends grow at constant rate foreverWhen FCFE grow at constant rate foreverWhen FCFF grow at constant rate forever

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Start easy: The Dividend Discount ModelAswath Damodaran*

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Moving on up: The potential dividends or FCFE modelAswath Damodaran*

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To valuing the entire business: The FCFF modelAswath Damodaran*

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Discounted Cash Flow Valuation: The InputsAswath DamodaranAswath Damodaran*

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I. Estimating Discount RatesDiscount rates matter, but not as much as you think they do!Aswath Damodaran*

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Estimating Inputs: Discount RatesWhile discount rates obviously matter in DCF valuation, they dont matter as much as most analysts think they do.At an intuitive level, the discount rate used should be consistent with both the riskiness and the type of cashflow being discounted.Equity versus Firm: If the cash flows being discounted are cash flows to equity, the appropriate discount rate is a cost of equity. If the cash flows are cash flows to the firm, the appropriate discount rate is the cost of capital.Currency: The currency in which the cash flows are estimated should also be the currency in which the discount rate is estimated.Nominal versus Real: If the cash flows being discounted are nominal cash flows (i.e., reflect expected inflation), the discount rate should be nominalAswath Damodaran*

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Risk in the DCF ModelAswath Damodaran*

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Not all risk is created equalEstimation versus Economic uncertaintyEstimation uncertainty reflects the possibility that you could have the wrong model or estimated inputs incorrectly within this model.Economic uncertainty comes the fact that markets and economies can change over time and that even the best models will fail to capture these unexpected changes.Micro uncertainty versus Macro uncertaintyMicro uncertainty refers to uncertainty about the potential market for a firms products, the competition it will face and the quality of its management team.Macro uncertainty reflects the reality that your firms fortunes can be affected by changes in the macro economic environment.Discrete versus continuous uncertaintyDiscrete risk: Risks that lie dormant for periods but show up at points in time. (Examples: A drug working its way through the FDA pipeline may fail at some stage of the approval process or a company in Venezuela may be nationalized)Continuous risk: Risks changes in interest rates or economic growth occur continuously and affect value as they happen.

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Risk and Cost of Equity: The role of the marginal investorNot all risk counts: While the notion that the cost of equity should be higher for riskier investments and lower for safer investments is intuitive, what risk should be built into the cost of equity is the question.Risk through whose eyes? While risk is usually defined in terms of the variance of actual returns around an expected return, risk and return models in finance assume that the risk that should be rewarded (and thus built into the discount rate) in valuation should be the risk perceived by the marginal investor in the investmentThe diversification effect: Most risk and return models in finance also assume that the marginal investor is well diversified, and that the only risk that he or she perceives in an investment is risk that cannot be diversified away (i.e, market or non-diversifiable risk). In effect, it is primarily economic, macro, continuous risk that should be incorporated into the cost of equity. Aswath Damodaran*

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The Cost of Equity: Competing Market Risk ModelsModelExpected ReturnInputs NeededCAPME(R) = Rf + (Rm- Rf)Riskfree RateBeta relative to market portfolioMarket Risk PremiumAPME(R) = Rf + j (Rj- Rf)Riskfree Rate; # of Factors;Betas relative to each factorFactor risk premiumsMulti E(R) = Rf + j (Rj- Rf)Riskfree Rate; Macro factorsfactorBetas relative to macro factorsMacro economic risk premiumsProxyE(R) = a + bj YjProxiesRegression coefficientsAswath Damodaran*

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The CAPM: Cost of EquityConsider the standard approach to estimating cost of equity:Cost of Equity = Riskfree Rate + Equity Beta * (Equity Risk Premium)In practice,Government security rates are used as risk free ratesHistorical risk premiums are used for the risk premiumBetas are estimated by regressing stock returns against market returns

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I. A Riskfree RateOn a riskfree asset, the actual return is equal to the expected return. Therefore, there is no variance around the expected return.For an investment to be riskfree, then, it has to haveNo default riskNo reinvestment riskTime horizon matters: Thus, the riskfree rates in valuation will depend upon when the cash flow is expected to occur and will vary across time. Not all government securities are riskfree: Some governments face default risk and the rates on bonds issued by them will not be riskfree.Aswath Damodaran*

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Test 1: A riskfree rate in US dollars!In valuation, we estimate cash flows forever (or at least for very long time periods). The right risk free rate to use in valuing a company in US dollars would beA three-month Treasury bill rate (0.2%)A ten-year Treasury bond rate (2%)A thirty-year Treasury bond rate (3%)A TIPs (inflation-indexed treasury) rate (1%)None of the aboveAswath Damodaran*

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Test 2: A Riskfree Rate in EurosAswath Damodaran*

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Test 3: A Riskfree Rate in Indian RupeesThe Indian government had 10-year Rupee bonds outstanding, with a yield to maturity of about 7.87% on January 1, 2015. In January 2015, the Indian government had a local currency sovereign rating of Baa3. The typical default spread (over a default free rate) for Baa3 rated country bonds in early 2015 was 2.2%. The riskfree rate in Indian Rupees isThe yield to maturity on the 10-year bond (7.87%)The yield to maturity on the 10-year bond + Default spread (10.07%)The yield to maturity on the 10-year bond Default spread (5.67%)None of the above

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Sovereign Default Spread: Three paths to the same destinationSovereign dollar or euro denominated bonds: Find sovereign bonds denominated in US dollars, issued by emerging markets. The difference between the interest rate on the bond and the US treasury bond rate should be the default spread. CDS spreads: Obtain the default spreads for sovereigns in the CDS market. Average spread: For countries which dont issue dollar denominated bonds or have a CDS spread, you have to use the average spread for other countries in the same rating class.Aswath Damodaran*

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Local Currency Government Bond Rates January 2015Aswath Damodaran*

CurrencyGovt Bond Rate (1/1/15CurrencyGovt Bond Rate (1/1/15)Australian $2.81%Mexican Peso5.83%British Pound1.73%Naira15.13%Bulgarian Lev3.15%Norwegian Krone1.51%Canadian $1.79%NZ $3.67%Chilean Peso4.30%Pakistani Rupee10.00%Chinese Yuan3.65%Peruvian Sol5.43%Colombian Peso7.17%Phillipine Peso4.37%Czech Koruna0.47%Polish Zloty2.53%Danish Krone0.79%Reai (Brazil)12.42%Euro0.54%Romanian Leu3.68%HK $1.97%Russian Ruble14.09%Hungarian Forint3.69%Singapore $2.33%Iceland Krona6.15%South African Rand7.80%Indian Rupee7.87%Swedish Krona0.90%Indonesian Rupiah7.81%Swiss Franc0.31%Israeli Shekel2.30%Taiwanese $1.61%Japanese Yen0.33%Thai Baht2.91%Kenyan Shilling12.35%Turkish Lira8.09%Korean Won2.60%US $2.12%Kuna3.78%Venezuelan Bolivar10.05%Malyasian Ringgit4.13%Vietnamese Dong7.15%

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Approach 1: Default spread from Government BondsThe Brazil Default SpreadBrazil 2020 Bond: 3.20%US 2020 T.Bond: 1.65%Spread: 1.55%

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Approach 2: CDS Spreads January 2015Aswath Damodaran*

CountryMoody's ratingCDS SpreadCDS Spread adj for USCountryMoody's ratingCDS SpreadCDS Spread adj for USCountryMoody's ratingCDS SpreadCDS Spread adj for USAbu DhabiAa21.43%1.12%HungaryBa12.64%2.33%PolandA21.46%1.15%ArgentinaCaa183.48%83.17%IcelandBaa32.27%1.96%PortugalBa13.09%2.78%AustraliaAaa0.97%0.66%IndiaBaa32.64%2.33%QatarAa21.57%1.26%AustriaAaa0.81%0.50%IndonesiaBaa32.82%2.51%RomaniaBaa32.23%1.92%BahrainBaa23.18%2.87%IrelandBaa11.26%0.95%RussiaBaa25.63%5.32%BelgiumAa31.20%0.89%IsraelA10.42%0.11%Saudi ArabiaAa31.39%1.08%BrazilBaa23.17%2.86%ItalyBaa22.34%2.03%SlovakiaA21.32%1.01%BulgariaBaa22.99%2.68%JapanA11.55%1.24%SloveniaBa12.14%1.83%ChileAa31.77%1.46%KazakhstanBaa24.16%3.85%South AfricaBaa22.96%2.65%ChinaAa31.78%1.47%KoreaAa31.17%0.86%SpainBaa21.79%1.48%ColombiaBaa22.57%2.26%LatviaBaa11.92%1.61%SwedenAaa0.65%0.34%Costa RicaBa13.58%3.27%LebanonB24.69%4.38%SwitzerlandAaa0.72%0.41%CroatiaBa13.65%3.34%LithuaniaBaa11.88%1.57%ThailandBaa11.91%1.60%CyprusB36.35%6.04%MalaysiaA32.15%1.84%TunisiaBa33.38%3.07%Czech RepublicA11.25%0.94%MexicoA32.05%1.74%TurkeyBaa32.77%2.46%EgyptCaa13.56%3.25%NetherlandsAaa0.78%0.47%UkraineCaa315.74%15.43%EstoniaA11.20%0.89%New ZealandAaa1.01%0.70%United Arab EmiratesAa21.54%1.23%FinlandAaa0.81%0.50%NorwayAaa0.61%0.30%United KingdomAa10.77%0.46%FranceAa11.22%0.91%PakistanCaa110.41%10.10%United States of AmericaAaa0.31%0.00%GermanyAaa0.74%0.43%PanamaBaa22.09%1.78%VenezuelaCaa118.06%17.75%GreeceCaa110.76%10.45%PeruA32.23%1.92%VietnamB13.15%2.84%Hong KongAa11.12%0.81%PhilippinesBaa21.98%1.67%

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Approach 3: Typical Default Spreads: January 2014Aswath Damodaran*

Sovereign RatingDefault Spread over riskfreeAaa0.00%Aa10.40%Aa20.50%Aa30.60%A10.70%A20.85%A31.20%Baa11.60%Baa21.90%Baa32.20%Ba12.50%Ba23.00%Ba33.60%B14.50%B25.50%B36.50%Caa17.50%Caa29.00%Caa310.00%

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Getting to a risk free rate in a currency: ExampleThe Brazilian government bond rate in nominal reais in January 2015 was 12.42%. To get to a riskfree rate in nominal reais, we can use one of three approaches.Approach 1: Government Bond spreadThe 2020 Brazil bond, denominated in US dollars, has a spread of 1.55% over the US treasury bond rate.Riskfree rate in $R = 12.42% - 1.55%% = 10.87%Approach 2: The CDS SpreadThe CDS spread for Brazil, adjusted for the US CDS spread, on January 1, 2015 was 2.86%. Riskfree rate in $R = 12.42% - 2.86% = 9.56%Approach 3: The Rating based spreadBrazil has a Baa2 local currency rating from Moodys. The default spread for that rating is 1.90%Riskfree rate in $R = 12.42% - 1.90% = 10.52%Aswath Damodaran*

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Test 4: A Real Riskfree RateIn some cases, you may want a riskfree rate in real terms (in real terms) rather than nominal terms. To get a real riskfree rate, you would like a security with no default risk and a guaranteed real return. Treasury indexed securities offer this combination. In January 2015, the yield on a 10-year indexed treasury bond was 1.00%. Which of the following statements would you subscribe to?This (1.00%) is the real riskfree rate to use, if you are valuing US companies in real terms.This (1.00%) is the real riskfree rate to use, anywhere in the worldExplain.

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No default free entity: Choices with riskfree rates.Estimate a range for the riskfree rate in local terms:Approach 1: Subtract default spread from local government bond rate:Government bond rate in local currency terms - Default spread for Government in local currencyApproach 2: Use forward rates and the riskless rate in an index currency (say Euros or dollars) to estimate the riskless rate in the local currency.Do the analysis in real terms (rather than nominal terms) using a real riskfree rate, which can be obtained in one of two ways from an inflation-indexed government bond, if one existsset equal, approximately, to the long term real growth rate of the economy in which the valuation is being done.Do the analysis in a currency where you can get a riskfree rate, say US dollars or Euros.Aswath Damodaran*

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Risk free Rate: Dont have or trust the government bond rate? Build up approach: The risk free rate in any currency can be written as the sum of two variables:Risk free rate = Expected Inflation in currency + Expected real interest rateThe expected real interest rate can be computed in one of two ways: from the US TIPs rate or set equal to real growth in the economy. Thus, if the expected inflation rate in a country is expected to be 15% and the TIPs rate is 1%, the risk free rate is 16%.US $ rate & Differential Inflation: Alternatively, you can scale up the US $ risk free rate by the differential inflation between the US $ and the currency in question:Risk free rateCurrency=

Thus, if the US $ risk free rate is 3.04%, the inflation rate in the foreign currency is 15% and the inflation rate in US $ is 2%, the foreign currency risk free rate is as follows:Risk free rate =

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Why do risk free rates vary across currencies?January 2015 Risk free ratesAswath Damodaran*

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One more test on riskfree ratesIn January 2015, the 10-year treasury bond rate in the United States was 2.17%, a historic low. Assume that you were valuing a company in US dollars then, but were wary about the risk free rate being too low. Which of the following should you do?Replace the current 10-year bond rate with a more reasonable normalized riskfree rate (the average 10-year bond rate over the last 30 years has been about 5-6%)Use the current 10-year bond rate as your riskfree rate but make sure that your other assumptions (about growth and inflation) are consistent with the riskfree rateSomething elseAswath Damodaran*

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Some perspective on risk free ratesAswath Damodaran*

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II. Equity Risk PremiumsThe ubiquitous historical risk premiumThe historical premium is the premium that stocks have historically earned over riskless securities.While the users of historical risk premiums act as if it is a fact (rather than an estimate), it is sensitive to How far back you go in historyWhether you use T.bill rates or T.Bond ratesWhether you use geometric or arithmetic averages.For instance, looking at the US:Aswath Damodaran*

Arithmetic AverageGeometric AverageStocks - T. BillsStocks - T. BondsStocks - T. BillsStocks - T. Bonds1928-20148.00%6.25%6.11%4.60%2.17%2.32%1965-20146.19%4.12%4.84%3.14%2.42%2.74%2005-20147.94%4.06%6.18%2.73%6.05%8.65%

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The perils of trusting the past.Noisy estimates: Even with long time periods of history, the risk premium that you derive will have substantial standard error. For instance, if you go back to 1928 (about 80 years of history) and you assume a standard deviation of 20% in annual stock returns, you arrive at a standard error of greater than 2%: Standard Error in Premium = 20%/80 = 2.26%Survivorship Bias: Using historical data from the U.S. equity markets over the twentieth century does create a sampling bias. After all, the US economy and equity markets were among the most successful of the global economies that you could have invested in early in the century.Aswath Damodaran*

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Risk Premium for a Mature Market? Broadening the sample to 1900-2013Aswath Damodaran*

CountryGeometric Average ERPArithmetic Average ERPStd ErrorAustralia 5.60%7.50%1.90%Austria2.50%21.50%14.40%Belgium 2.30%4.40%2.00%Canada 3.50%5.10%1.70%Denmark 2.00%3.60%1.70%Finland5.10%8.70%2.80%France 3.00%5.30%2.10%Germany 5.00%8.40%2.70%Ireland 2.60%4.50%1.80%Italy 3.10%6.50%2.70%Japan 5.10%9.10%3.00%Netherlands 3.20%5.60%2.10%New Zealand3.90%5.50%1.70%Norway 2.30%5.30%2.60%South Africa 5.40%7.10%1.80%Spain 1.90%3.90%1.90%Sweden 3.00%5.30%2.00%Switzerland 2.10%3.60%1.60%U.K. 3.70%5.00%1.60%U.S. 4.40%6.50%1.90%Europe3.10%4.40%1.50%World-ex U.S. 2.80%3.90%1.40%World 3.20%4.50%1.50%

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The simplest way of estimating an additional country risk premium: The country default spreadDefault spread for country: In this approach, the country equity risk premium is set equal to the default spread for the country, estimated in one of three ways:The default spread on a dollar denominated bond issued by the country. (In January 2015, that spread was 1.55% for the Brazilian $ bond)The sovereign CDS spread for the country. In January 2015, the ten year CDS spread for Brazil was 2.86%.The default spread based on the local currency rating for the country. Brazils sovereign local currency rating is Baa2 and the default spread for a Baa2 rated sovereign was about 1.90% in January 2015. Add the default spread to a mature market premium: This default spread is added on to the mature market premium to arrive at the total equity risk premium for Brazil, assuming a mature market premium of 5.75%.Country Risk Premium for Brazil = 1.90%Total ERP for Brazil = 5.75% + 1.90% = 7.65%Aswath Damodaran*

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An equity volatility based approach to estimating the country total ERPThis approach draws on the standard deviation of two equity markets, the emerging market in question and a base market (usually the US). The total equity risk premium for the emerging market is then written as:Total equity risk premium = Risk PremiumUS* Country Equity / US EquityThe country equity risk premium is based upon the volatility of the market in question relative to U.S market.Assume that the equity risk premium for the US is 5.75%.Assume that the standard deviation in the Bovespa (Brazilian equity) is 21% and that the standard deviation for the S&P 500 (US equity) is 18%.Total Equity Risk Premium for Brazil = 5.75% (21%/18%) = 6.71%Country equity risk premium for Brazil = 6.71% - 5.75% = 0.96%

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A melded approach to estimating the additional country risk premiumCountry ratings measure default risk. While default risk premiums and equity risk premiums are highly correlated, one would expect equity spreads to be higher than debt spreads. Another is to multiply the bond default spread by the relative volatility of stock and bond prices in that market. Using this approach for Brazil in January 2015, you would get:Country Equity risk premium = Default spread on country bond* Country Equity / Country BondStandard Deviation in Bovespa (Equity) = 21%Standard Deviation in Brazil government bond = 14%Default spread on C-Bond = 1.90%Brazil Country Risk Premium = 1.90% (21%/14%) = 2.85%Brazil Total ERP = Mature Market Premium + CRP = 5.75% + 2.85% = 8.60%Aswath Damodaran*

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Black #: Total ERPRed #: Country risk premiumAVG: GDP weighted average

Angola10.25%4.50%Botswana7.03%1.28%Burkina Faso15.50%9.75%Cameroon14.00%8.25%Cape Verde14.00%8.25%Congo (DR)15.50%9.75%Congo (Republic)11.15%5.40%Cte d'Ivoire12.50%6.75%Egypt17.00%11.25%Ethiopia12.50%6.75%Gabon11.15%5.40%Ghana14.00%8.25%Kenya12.50%6.75%Morocco9.50%3.75%Mozambique12.50%6.75%Namibia9.05%3.30%Nigeria11.15%5.40%Rwanda14.00%8.25%Senegal12.50%6.75%South Africa8.60%2.85%Tunisia11.15%5.40%Uganda12.50%6.75%Zambia12.50%6.75%Africa11.73%5.98%

Bangladesh11.15%5.40%Cambodia14.00%8.25%China6.65%0.90%Fiji12.50%6.75%Hong Kong6.35%0.60%India9.05%3.30%Indonesia9.05%3.30%Japan6.80%1.05%Korea6.65%0.90%Macao6.50%0.75%Malaysia7.55%1.80%Mauritius8.15%2.40%Mongolia14.00%8.25%Pakistan17.00%11.25%Papua New Guinea12.50%6.75%Philippines8.60%2.85%Singapore5.75%0.00%Sri Lanka12.50%6.75%Taiwan6.65%0.90%Thailand8.15%2.40%Vietnam12.50%6.75%Asia7.26%1.51%

Australia5.75%0.00%Cook Islands12.50%6.75%New Zealand5.75%0.00%Australia & NZ5.75%0.00%

Abu Dhabi6.50%0.75%Bahrain8.60%2.85%Israel6.80%1.05%Jordan12.50%6.75%Kuwait6.50%0.75%Lebanon14.00%8.25%Oman6.80%1.05%Qatar6.50%0.75%Ras Al Khaimah7.03%1.28%Saudi Arabia6.65%0.90%Sharjah7.55%1.80%UAE6.50%0.75%Middle East6.85%1.10%

Albania12.50%6.75%Montenegro11.15%5.40%Armenia10.25%4.50%Poland7.03%1.28%Azerbaijan9.05%3.30%Romania9.05%3.30%Belarus15.50%9.75%Russia8.60%2.85%Bosnia15.50%.75%Serbia12.50%6.75%Bulgaria8.60%2.85%Slovakia7.03%1.28%Croatia9.50%3.75%Slovenia9.50%3.75%Czech Repub6.80%1.05%Ukraine20.75%15.00%Estonia6.80%1.05%E. Europe9.08%3.33%Georgia11.15%5.40%Hungary9.50%3.75%Kazakhstan8.60%2.85%Latvia8.15%2.40%Lithuania8.15%2.40%Macedonia11.15%5.40%Moldova15.50%9.75%

Andorra8.15%2.40%Italy8.60%2.85%Austria5.75%0.00%Jersey6.35%0.60%Belgium6.65%0.90%Liechtenstein5.75%0.00%Cyprus15.50%9.75%Luxembourg5.75%0.00%Denmark5.75%0.00%Malta7.55%1.80%Finland5.75%0.00%Netherlands5.75%0.00%France6.35%0.60%Norway5.75%0.00%Germany5.75%0.00%Portugal9.50%3.75%Greece17.00%11.25%Spain8.60%2.85%Guernsey6.35%0.60%Sweden5.75%0.00%Iceland9.05%3.30%Switzerland5.75%0.00%Ireland8.15%2.40%Turkey9.05%3.30%Isle of Man6.35%0.60%UK6.35%0.60%W. Europe6.88%1.13%

Argentina17.00%11.25%Belize19.25%13.50%Bolivia11.15%5.40%Brazil8.60%2.85%Chile6.65%0.90%Colombia8.60%2.85%Costa Rica9.50%3.75%Ecuador15.50%9.75%El Salvador11.15%5.40%Guatemala9.50%3.75%Honduras15.50%9.75%Mexico7.55%1.80%Nicaragua15.50%9.75%Panama8.60%2.85%Paraguay10.25%4.50%Peru7.55%1.80%Suriname11.15%5.40%Uruguay8.60%2.85%Venezuela17.00%11.25%Latin America9.95%4.20%

Canada5.75%0.00%US5.75%0.00%North America5.75%0.00%

Aswath Damodaran

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From Country Equity Risk Premiums to Corporate Equity Risk premiumsApproach 1: Assume that every company in the country is equally exposed to country risk. In this case, E(Return) = Riskfree Rate + CRP + Beta (Mature ERP)Implicitly, this is what you are assuming when you use the local Governments dollar borrowing rate as your riskfree rate.Approach 2: Assume that a companys exposure to country risk is similar to its exposure to other market risk.E(Return) = Riskfree Rate + Beta (Mature ERP+ CRP)Approach 3: Treat country risk as a separate risk factor and allow firms to have different exposures to country risk (perhaps based upon the proportion of their revenues come from non-domestic sales)E(Return)=Riskfree Rate+ (Mature ERP) + (CRP)Mature ERP = Mature market Equity Risk PremiumCRP = Additional country risk premiumAswath Damodaran*

Aswath Damodaran

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Approaches 1 & 2: Estimating country risk premium exposureLocation based CRP: The standard approach in valuation is to attach a country risk premium to a company based upon its country of incorporation. Thus, if you are an Indian company, you are assumed to be exposed to the Indian country risk premium. A developed market company is assumed to be unexposed to emerging market risk.Operation-based CRP: There is a more reasonable modified version. The country risk premium for a company can be computed as a weighted average of the country risk premiums of the countries that it does business in, with the weights based upon revenues or operating income. If a company is exposed to risk in dozens of countries, you can take a weighted average of the risk premiums by region.Aswath Damodaran*

Aswath Damodaran

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Operation based CRP: Single versus Multiple Emerging MarketsSingle emerging market: Embraer, in 2004, reported that it derived 3% of its revenues in Brazil and the balance from mature markets. The mature market ERP in 2004 was 5% and Brazils CRP was 7.89%.

Multiple emerging markets: Ambev, the Brazilian-based beverage company, reported revenues from the following countries during 2011. Aswath Damodaran*

Aswath Damodaran

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Extending to a multinational: Regional breakdownCoca Colas revenue breakdown and ERP in 2012Things to watch out forAggregation across regions. For instance, the Pacific region often includes Australia & NZ with AsiaObscure aggregations including Eurasia and Oceania*

Aswath Damodaran

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Two problems with these approaches..Focus just on revenues: To the extent that revenues are the only variable that you consider, when weighting risk exposure across markets, you may be missing other exposures to country risk. For instance, an emerging market company that gets the bulk of its revenues outside the country (in a developed market) may still have all of its production facilities in the emerging market.Exposure not adjusted or based upon beta: To the extent that the country risk premium is multiplied by a beta, we are assuming that beta in addition to measuring exposure to all other macro economic risk also measures exposure to country risk.

Aswath Damodaran*

Aswath Damodaran

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Approach 3: Estimate a lambda for country riskSource of revenues: Other things remaining equal, a company should be more exposed to risk in a country if it generates more of its revenues from that country. Manufacturing facilities: Other things remaining equal, a firm that has all of its production facilities in a risky country should be more exposed to country risk than one which has production facilities spread over multiple countries. The problem will be accented for companies that cannot move their production facilities (mining and petroleum companies, for instance).Use of risk management products: Companies can use both options/futures markets and insurance to hedge some or a significant portion of country risk.Government national interests: There are sectors that are viewed as vital to the national interests, and governments often play a key role in these companies, either officially or unofficially. These sectors are more exposed to country risk.Aswath Damodaran*

Aswath Damodaran

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Estimating Company Exposure to Country RiskThe factor l measures the relative exposure of a firm to country risk. One simplistic solution would be to do the following:l = % of revenues domesticallyfirm/ % of revenues domesticallyaverage firmConsider two firms Tata Motors and Tata Consulting Services, both Indian companies. In 2008-09, Tata Motors got about 91.37% of its revenues in India and TCS got 7.62%. The average Indian firm gets about 80% of its revenues in India:l Tata Motors= 91%/80% = 1.14l TCS= 7.62%/80% = 0.09There are two implicationsA companys risk exposure is determined by where it does business and not by where it is incorporated.Firms might be able to actively manage their country risk exposures

Aswath Damodaran

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A richer lambda estimate: Use stock returns and country bond returns: Estimating a lambda for Embraer in 2004ReturnEmbraer = 0.0195 + 0.2681 ReturnC BondReturnEmbratel = -0.0308 + 2.0030 ReturnC BondAswath Damodaran*

Aswath Damodaran

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Estimating a US Dollar Cost of Equity for Embraer - September 2004Assume that the beta for Embraer is 1.07, and that the US $ riskfree rate used is 4%. Also assume that the risk premium for the US is 5% and the country risk premium for Brazil is 7.89%. Finally, assume that Embraer gets 3% of its revenues in Brazil & the rest in the US.There are five estimates of $ cost of equity for Embraer:Approach 1: Constant exposure to CRP, Location CRPE(Return) = 4% + 1.07 (5%) + 7.89% = 17.24%Approach 2: Constant exposure to CRP, Operation CRPE(Return) = 4% + 1.07 (5%) + (0.03*7.89% +0.97*0%)= 9.59%Approach 3: Beta exposure to CRP, Location CRPE(Return) = 4% + 1.07 (5% + 7.89%)= 17.79%Approach 4: Beta exposure to CRP, Operation CRPE(Return) = 4% + 1.07 (5% +( 0.03*7.89%+0.97*0%)) = 9.60%Approach 5: Lambda exposure to CRPE(Return) = 4% + 1.07 (5%) + 0.27(7.89%) = 11.48%%Aswath Damodaran*

Aswath Damodaran

*

Valuing Emerging Market Companies with significant exposure in developed marketsThe conventional practice in investment banking is to add the country equity risk premium on to the cost of equity for every emerging market company, notwithstanding its exposure to emerging market risk. Thus, in 2004, Embraer would have been valued with a cost of equity of 17-18% even though it gets only 3% of its revenues in Brazil. As an investor, which of the following consequences do you see from this approach?Emerging market companies with substantial exposure in developed markets will be significantly over valued by equity research analysts.Emerging market companies with substantial exposure in developed markets will be significantly under valued by equity research analysts.Can you construct an investment strategy to take advantage of the misvaluation? What would need to happen for you to make money of this strategy?Aswath Damodaran*

Aswath Damodaran

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Implied Equity PremiumsLets start with a general proposition. If you know the price paid for an asset and have estimates of the expected cash flows on the asset, you can estimate the IRR of these cash flows. If you paid the price, this is what you have priced the asset to earn (as an expected return).If you assume that stocks are correctly priced in the aggregate and you can estimate the expected cashflows from buying stocks, you can estimate the expected rate of return on stocks by finding that discount rate that makes the present value equal to the price paid. Subtracting out the riskfree rate should yield an implied equity risk premium.This implied equity premium is a forward looking number and can be updated as often as you want (every minute of every day, if you are so inclined).

Aswath Damodaran*

Aswath Damodaran

*

Implied Equity Premiums: January 2008We can use the information in stock prices to back out how risk averse the market is and how much of a risk premium it is demanding.

If you pay the current level of the index, you can expect to make a return of 8.39% on stocks (which is obtained by solving for r in the following equation)

Implied Equity risk premium = Expected return on stocks - Treasury bond rate = 8.39% - 4.02% = 4.37%

Aswath Damodaran*

Aswath Damodaran

*

Implied Risk Premium DynamicsAssume that the index jumps 10% on January 2 and that nothing else changes. What will happen to the implied equity risk premium?Implied equity risk premium will increase Implied equity risk premium will decreaseAssume that the earnings jump 10% on January 2 and that nothing else changes. What will happen to the implied equity risk premium?Implied equity risk premium will increase Implied equity risk premium will decreaseAssume that the riskfree rate increases to 5% on January 2 and that nothing else changes. What will happen to the implied equity risk premium?Implied equity risk premium will increase Implied equity risk premium will decreaseAswath Damodaran*

Aswath Damodaran

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A year that made a difference.. The implied premium in January 2009Aswath Damodaran*

YearMarket value of indexDividendsBuybacksCash to equityDividend yieldBuyback yieldTotal yield20011148.0915.7414.3430.081.37%1.25%2.62%2002879.8215.9613.8729.831.81%1.58%3.39%20031111.9117.8813.7031.581.61%1.23%2.84%20041211.9219.0121.5940.601.57%1.78%3.35%20051248.2922.3438.8261.171.79%3.11%4.90%20061418.3025.0448.1273.161.77%3.39%5.16%20071468.3628.1467.2295.361.92%4.58%6.49%2008903.2528.4740.2568.723.15%4.61%7.77%Normalized903.2528.4724.1152.5843.15%2.67%5.82%

Aswath Damodaran

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The Anatomy of a Crisis: Implied ERP from September 12, 2008 to January 1, 2009Aswath Damodaran*

Aswath Damodaran

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An Updated Equity Risk Premium: January 2015 Aswath Damodaran*

Aswath Damodaran

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Implied Premiums in the US: 1960-2014Aswath Damodaran*

Aswath Damodaran

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Implied Premium versus Risk Free RateAswath Damodaran*

Aswath Damodaran

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Equity Risk Premiums and Bond Default SpreadsAswath Damodaran*

Aswath Damodaran

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Equity Risk Premiums and Cap Rates (Real Estate)Aswath Damodaran*

Aswath Damodaran

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Why implied premiums matter?In many investment banks, it is common practice (especially in corporate finance departments) to use historical risk premiums (and arithmetic averages at that) as risk premiums to compute cost of equity. If all analysts in the department used the arithmetic average premium (for stocks over T.Bills) for 1928-2014 of 8% to value stocks in January 2014, given the implied premium of 5.75%, what are they likely to find?The values they obtain will be too low (most stocks will look overvalued)The values they obtain will be too high (most stocks will look under valued) There should be no systematic bias as long as they use the same premium to value all stocks.Aswath Damodaran*

Aswath Damodaran

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Which equity risk premium should you use?Aswath Damodaran*

If you assume thisPremium to usePremiums revert back to historical norms and your time period yields these normsHistorical risk premiumMarket is correct in the aggregate or that your valuation should be market neutralCurrent implied equity risk premiumMarker makes mistakes even in the aggregate but is correct over timeAverage implied equity risk premium over time.

Aswath Damodaran

*

And the approach can be extended to emerging marketsImplied premium for the Sensex (September 2007)Inputs for the computationSensex on 9/5/07 = 15446Dividend yield on index = 3.05%Expected growth rate - next 5 years = 14%Growth rate beyond year 5 = 6.76% (set equal to riskfree rate)Solving for the expected return:

Expected return on stocks = 11.18%Implied equity risk premium for India = 11.18% - 6.76% = 4.42%Aswath Damodaran*

Aswath Damodaran

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Can country risk premiums change? Brazil CRP & Total ERP from 2000 to 2013Aswath Damodaran*

Aswath Damodaran

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The evolution of Emerging Market RiskAswath Damodaran*

Aswath Damodaran

Aswath Damodaran*Measuring Relative Risk

Aswath Damodaran

*

The CAPM BetaThe standard procedure for estimating betas is to regress stock returns (Rj) against market returns (Rm) -Rj = a + b Rmwhere a is the intercept and b is the slope of the regression. The slope of the regression corresponds to the beta of the stock, and measures the riskiness of the stock. This beta has three problems:It has high standard errorIt reflects the firms business mix over the period of the regression, not the current mixIt reflects the firms average financial leverage over the period rather than the current leverage.Aswath Damodaran*

Aswath Damodaran

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Beta Estimation: The Noise ProblemAswath Damodaran*

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Beta Estimation: The Index EffectAswath Damodaran*

Aswath Damodaran

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Stock-priced based solutions to the Regression Beta ProblemModify the regression beta bychanging the index used to estimate the beta adjusting the regression beta estimate, by bringing in information about the fundamentals of the companyEstimate the beta for the firm using the standard deviation in stock prices instead of a regression against an indexRelative risk = Standard deviation in stock prices for investment/ Average standard deviation across all stocksEstimate the beta for the firm from the bottom up without employing the regression technique. This will requireunderstanding the business mix of the firmestimating the financial leverage of the firmImputed or implied beta (cost of equity) for the sector. Aswath Damodaran*

Aswath Damodaran

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Alternative measures of relative risk for equityAccounting risk measures: To the extent that you dont trust market-priced based measures of risk, you could compute relative risk measures based onAccounting earnings volatility: Compute an accounting beta or relative volatilityBalance sheet ratios: You could compute a risk score based upon accounting ratios like debt ratios or cash holdings (akin to default risk scores like the Z score)Proxies: In a simpler version of proxy models, you can categorize firms into risk classes based upon size, sectors or other characteristics.Qualitative Risk Models: In these models, risk assessments are based at least partially on qualitative factors (quality of management).Debt based measures: You can estimate a cost of equity, based upon an observable costs of debt for the company.Cost of equity = Cost of debt * Scaling factorAswath Damodaran*

Aswath Damodaran

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Determinants of Betas & Relative RiskAswath Damodaran*

Aswath Damodaran

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In a perfect world we would estimate the beta of a firm by doing the followingAswath Damodaran*

Aswath Damodaran

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Adjusting for operating leverageWithin any business, firms with lower fixed costs (as a percentage of total costs) should have lower unlevered betas. If you can compute fixed and variable costs for each firm in a sector, you can break down the unlevered beta into business and operating leverage components.Unlevered beta = Pure business beta * (1 + (Fixed costs/ Variable costs))The biggest problem with doing this is informational. It is difficult to get information on fixed and variable costs for individual firms. In practice, we tend to assume that the operating leverage of firms within a business are similar and use the same unlevered beta for every firm. Aswath Damodaran*

Aswath Damodaran

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Adjusting for financial leverageConventional approach: If we assume that debt carries no market risk (has a beta of zero), the beta of equity alone can be written as a function of the unlevered beta and the debt-equity ratioL = u (1+ ((1-t)D/E))In some versions, the tax effect is ignored and there is no (1-t) in the equation.Debt Adjusted Approach: If beta carries market risk and you can estimate the beta of debt, you can estimate the levered beta as follows:L = u (1+ ((1-t)D/E)) - debt (1-t) (D/E)While the latter is more realistic, estimating betas for debt can be difficult to do. Aswath Damodaran*

Aswath Damodaran

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Bottom-up BetasAswath Damodaran*

Aswath Damodaran

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Why bottom-up betas?The standard error in a bottom-up beta will be significantly lower than the standard error in a single regression beta. Roughly speaking, the standard error of a bottom-up beta estimate can be written as follows:Std error of bottom-up beta =

The bottom-up beta can be adjusted to reflect changes in the firms business mix and financial leverage. Regression betas reflect the past.You can estimate bottom-up betas even when you do not have historical stock prices. This is the case with initial public offerings, private businesses or divisions of companies.Aswath Damodaran*

Aswath Damodaran

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Estimating Bottom Up Betas & Costs of Equity: Vale

Aswath Damodaran

Aswath Damodaran

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Embraers Bottom-up BetaBusinessUnlevered BetaD/E RatioLevered betaAerospace0.9518.95%1.07

Levered Beta= Unlevered Beta ( 1 + (1- tax rate) (D/E Ratio)= 0.95 ( 1 + (1-.34) (.1895)) = 1.07

Can an unlevered beta estimated using U.S. and European aerospace companies be used to estimate the beta for a Brazilian aerospace company?YesNoWhat concerns would you have in making this assumption?

Aswath Damodaran*

Aswath Damodaran

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Gross Debt versus Net Debt ApproachesAnalysts in Europe and Latin America often take the difference between debt and cash (net debt) when computing debt ratios and arrive at very different values.For Embraer, using the gross debt ratioGross D/E Ratio for Embraer = 1953/11,042 = 18.95%Levered Beta using Gross Debt ratio = 1.07Using the net debt ratio, we getNet Debt Ratio for Embraer = (Debt - Cash)/ Market value of Equity= (1953-2320)/ 11,042 = -3.32%Levered Beta using Net Debt Ratio = 0.95 (1 + (1-.34) (-.0332)) = 0.93The cost of Equity using net debt levered beta for Embraer will be much lower than with the gross debt approach. The cost of capital for Embraer will even out since the debt ratio used in the cost of capital equation will now be a net debt ratio rather than a gross debt ratio.Aswath Damodaran*

Aswath Damodaran

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The Cost of Equity: A RecapAswath Damodaran*

Aswath Damodaran

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

Aswath Damodaran

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Estimating Synthetic RatingsThe rating for a firm can be estimated using the financial characteristics of the firm. In its simplest form, the rating can be estimated from the interest coverage ratioInterest Coverage Ratio = EBIT / Interest ExpensesFor Embraers interest coverage ratio, we used the interest expenses from 2003 and the average EBIT from 2001 to 2003. (The aircraft business was badly affected by 9/11 and its aftermath. In 2002 and 2003, Embraer reported significant drops in operating income)Interest Coverage Ratio = 462.1 /129.70 = 3.56

Aswath Damodaran*

Aswath Damodaran

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Interest Coverage Ratios, Ratings and Default Spreads: 2003 & 2004If Interest Coverage Ratio isEstimated Bond RatingDefault Spread(2003)Default Spread(2004)> 8.50(>12.50)AAA0.75%0.35%6.50 - 8.50(9.5-12.5)AA1.00%0.50%5.50 - 6.50(7.5-9.5)A+1.50%0.70%4.25 - 5.50(6-7.5)A1.80%0.85%3.00 - 4.25(4.5-6)A2.00%1.00%2.50 - 3.00(4-4.5)BBB2.25%1.50%2.25- 2.50(3.5-4)BB+2.75%2.00%2.00 - 2.25((3-3.5)BB3.50%2.50%1.75 - 2.00(2.5-3)B+4.75%3.25%1.50 - 1.75(2-2.5)B6.50%4.00%1.25 - 1.50(1.5-2)B 8.00%6.00%0.80 - 1.25(1.25-1.5)CCC10.00%8.00%0.65 - 0.80(0.8-1.25)CC11.50%10.00%0.20 - 0.65(0.5-0.8)C12.70%12.00%< 0.20(

II. Estimating Cash FlowsCash is kingAswath Damodaran*

Aswath Damodaran

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Steps in Cash Flow EstimationEstimate the current earnings of the firmIf looking at cash flows to equity, look at earnings after interest expenses - i.e. net incomeIf looking at cash flows to the firm, look at operating earnings after taxesConsider how much the firm invested to create future growthIf the investment is not expensed, it will be categorized as capital expenditures. To the extent that depreciation provides a cash flow, it will cover some of these expenditures.Increasing working capital needs are also investments for future growthIf looking at cash flows to equity, consider the cash flows from net debt issues (debt issued - debt repaid)Aswath Damodaran*

Aswath Damodaran

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Measuring Cash FlowsAswath Damodaran*

Aswath Damodaran

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Measuring Cash Flow to the FirmEBIT ( 1 - tax rate)- (Capital Expenditures - Depreciation)- Change in Working Capital= Cash flow to the firmWhere are the tax savings from interest payments in this cash flow?Aswath Damodaran*

Aswath Damodaran

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From Reported to Actual EarningsAswath Damodaran*

Aswath Damodaran

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I. Update EarningsWhen valuing companies, we often depend upon financial statements for inputs on earnings and assets. Annual reports are often outdated and can be updated by using-Trailing 12-month data, constructed from quarterly earnings reports.Informal and unofficial news reports, if quarterly reports are unavailable.Updating makes the most difference for smaller and more volatile firms, as well as for firms that have undergone significant restructuring.Time saver: To get a trailing 12-month number, all you need is one 10K and one 10Q (example third quarter). Use the Year to date numbers from the 10Q:Trailing 12-month Revenue = Revenues (in last 10K) - Revenues from first 3 quarters of last year + Revenues from first 3 quarters of this year.Aswath Damodaran*

Aswath Damodaran

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II. Correcting Accounting EarningsMake sure that there are no financial expenses mixed in with operating expensesFinancial expense: Any commitment that is tax deductible that you have to meet no matter what your operating results: Failure to meet it leads to loss of control of the business.Example: Operating Leases: While accounting convention treats operating leases as operating expenses, they are really financial expenses and need to be reclassified as such. This has no effect on equity earnings but does change the operating earningsMake sure that there are no capital expenses mixed in with the operating expensesCapital expense: Any expense that is expected to generate benefits over multiple periods.R & D Adjustment: Since R&D is a capital expenditure (rather than an operating expense), the operating income has to be adjusted to reflect its treatment.Aswath Damodaran*

Aswath Damodaran

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The Magnitude of Operating LeasesAswath Damodaran*

Aswath Damodaran

Chart1

0.1259

0.4384835372

0.5001598879

0.2658948631

Operating Lease expenses as % of Operating Income

Sheet1

SICNumber of firmsEBITDADAR&DLease ExpensesInterest ExpensesR&D as % of EBITLease Expenses as % of EBIT

10061210.894328.935171.656353.273224.24116.29%28.60%

2002360.50118.90800161.0630.00%0.00%

80013933522645.45%25.00%

100051595.006707.086030.961413.1090.00%3.37%

104023439.1581400.873013.994345.2550.00%-1.48%

10442-19.11855.538006.9790.00%0.00%

1090134.82811.64200.14.90.00%0.43%

12203245.741231.872020.94972.030.00%60.17%

13117110622.62615467.953258.3621055.8853496.821-5.63%-27.86%

1381194790.9461216.6750343.799487.4670.00%8.77%

13823726.701399.816.19658.23316.5671.86%15.12%

138954942.6941757.602908.783609.845335.35422.20%16.07%

14005864.255306.86919.51765.0342.4163.38%10.45%

1531192263.249180.865073.969674.3030.00%3.43%

1540264.96412.30509.6589.6180.00%15.50%

160071218.951472.78715.1181.075158.3811.98%19.53%

16235343.967118.993024.1833.7860.00%9.70%

17006286.80768.8630.8644.45932.3260.39%16.94%

1731277.1115.9603.5525.3630.00%5.49%

200028331.3771661.915921.297686.19651.50812.14%9.33%

20112743.739186.499921.969.3451.59%3.78%

201310.9090.45300.40500.00%47.04%

20154902.25335.7740120.772197.9220.00%17.57%

20201334.23591.77904882.2950.00%16.53%

2024116.7964.3101.6570.5450.00%11.72%

203063610.82556.909148.703110.336506.2294.64%3.49%

20332147.70640.1765.81535.74680.1795.13%24.95%

204073136.524687.625242.6147.291415.49.01%5.67%

20502218.085109.0501.82620.4270.00%1.65%

205245570.1321826.89309.63621274.9887.64%8.82%

206051491.188276.53728.647.909142.7362.30%3.79%

207041394.848570.23717.184.908343.7992.03%9.34%

208039569.71621.900.2676.40.00%0.00%

208233122.565859.44715.211.922304.6650.67%0.52%

2084112.3054.15100.3593.9470.00%4.22%

208523781.419594.34900504.1890.00%0.00%

208663607.5091962.5840160.2991041.6430.00%8.88%

20905454.76110.88816.919.631115.3994.68%5.40%

21003909.2447.8541.24414.09717.4440.14%1.61%

2111420562.5382693.436580.826570.0472240.7593.15%3.09%

22005729.237220.66331.13936.593173.7345.77%6.71%

22116504.304219.844029.119143.0530.00%9.29%

22213199.50769.28323.73234.11247.16215.41%20.76%

22505460.398174.5528.87147.34112.5169.17%14.21%

22534220.369109.29038.15565.5770.00%25.57%

22733819.602208.126080.533179.2330.00%11.64%

230091190.814228.1780185.431132.0950.00%16.15%

23206421.05191.69805.747.8380.00%1.71%

23305691.064111.3810166.38733.7970.00%22.30%

23402243.14147.082036.29866.4130.00%15.62%

23902203.27554.591025.17976.9970.00%14.48%

240052883.4961333.763125.6668.407649.7387.50%0.54%

242161054.705409.68021.3236.6050.00%3.20%

243031068.73195.741015187.2850.00%1.69%

24514615.60570.20905.79322.6230.00%1.05%

25105855.745196.162126789.7351.79%9.22%

25115263.59351.4240.922.95919.5010.42%9.76%

252241044.372231.193104.65482.02356.04911.40%9.16%

253141779.552615.679365.983187.569261.86323.92%13.88%

25903734.789153.757060.62161.6710.00%9.45%

260024045245995.52039695.68%11.35%

26111158.97336.56210.732036.8088.06%0.00%

2621159026.8283605.288331.148424.6811724.7825.76%7.26%

263151355.283632.685016.5432.9950.00%2.23%

26506898.521421.6418.166.465241.5083.66%12.23%

2670155191.2751386.8071182.961230.73426.28623.72%5.72%

267314.6940.96500.2580.4160.00%6.47%

2711167831.6831953.69660.988356.177876.7081.03%5.71%

272183474.961630.6730378.2981217.1210.00%17.02%

273141035.476276.8920157.54891.6690.00%17.20%

2750113421.1511301.39510.7148.924491.8160.50%6.56%

276171156.145367.266129.395193.127106.1814.09%19.67%

27712390.56467.349059.01329.340.00%15.44%

27803567.478130.15512.873.925.4372.84%14.46%

2790136.0497.74101.3893.5980.00%4.68%

280032386.1841.11436.9193.8451.748.19%11.15%

2810184768.9372575.062401.068280.535920.88815.46%11.34%

282036250.8111573.4022819.975238.082750.61637.61%4.84%

2821126675.7242295.5861911.357657.7959.95130.38%13.06%

28344052184.698052.6521833.5511290.9172474.03433.10%2.84%

28353428.356134.664486.60434.746104.42462.36%10.58%

2836141650.229250.477783.68421.97748.99935.89%1.55%

284058040.171692.7161589.07618.642576.00720.02%0.29%

28423989.284223.19888.8256.64996.3710.39%6.89%

2844103417.203617.033307.211402.907449.6349.89%12.58%

285152715.371584.854380.952192.762234.48115.17%8.30%

2860113007.1671115.734580.814162.176728.95223.49%7.90%

287082167.138612.06619.012194.946382.481.21%11.14%

289092471.697747.522320.078151.531236.29215.66%8.08%

29112975408.65547151.8013286.92910215.1958859.00610.42%26.55%

2950141.64511.05601.5052.7370.00%4.69%

2990229.0025.53810.2610.1152.28330.43%0.49%

301142048.976653.552468.707240.847234.8725.14%14.72%

30212176.29648.5247.65952.04478.1965.66%28.94%

30504548.378109.14583.2633.55726.44315.94%7.10%

30604292.07972.38630.67814.90632.12712.25%6.35%

30803158.39237.5610.3526.38318.3057.89%5.02%

3081370.41623.933.2651.86713.8676.56%3.86%

3089101164.881338.69886.78681.581139.1559.51%8.99%

310021.931.04401.6511.1860.00%65.08%

31409381.08674.9544.472150.96843.0181.44%33.03%

3220182.91419.50605.68412.6740.00%8.23%

322111341.8456.536.468.53803.95%7.18%

3231146.44222.636.4184.38.34760.43%15.28%

32412482.76692.937027.45421.980.00%6.58%

32501105.78927.873033.26945.1730.00%29.92%

32603259.69317.93027.57349.0290.00%10.24%

327061421.044307.23732.55588.681128.2142.84%7.37%

329051148.141370.397119.723159.637231.13613.34%17.03%

3310221.86417.4331.5673.4357.56126.13%43.67%

3312214623.7451937.651144.264433.144672.0355.10%13.89%

3317215.42219.71705.956.2960.00%359.52%

3320137.60411.76401.0063.8960.00%3.75%

333073217.6711653.456127.46555.5518.8037.53%3.43%

33342975.3349.744.775.63386.67%10.78%

3341156.88919.074009.5360.00%0.00%

3350134965.3861653.782245.388317.316519.5486.90%8.74%

335751374.399392.515341.22268.1141.30625.79%6.49%

336019.5014.93302.292.2990.00%33.39%

3390262.76116.2221.9823.1553.4674.08%6.35%

341141865.031736.50476.795.7538.3566.36%7.82%

342093977.205623.603374.39206.556175.1510.04%5.80%

34301870.7251.15449.8102.78.02%7.44%

3440142.1112.28904.23311.7030.00%12.43%

34423124.19728.03911.929.4757.90311.01%23.46%

34434455.843130.37114.353102.04579.4774.22%23.87%

34483183.24828.0162.916.42227.4851.83%9.57%

34524204.78958.9278.93114.56357.2435.77%9.08%

34603335.207106.972024.11560.5770.00%9.56%

34703100.88854.6037.0696.93425.95813.25%13.03%

34804267.91857.04330.3649.62619.87512.59%4.37%

3490101676.079446.298161.03191.83171.81411.58%6.95%

351041335.899451.911429.35136.7164.85232.69%13.39%

352375065.8571033.8641172.411139.083986.66322.53%3.33%

35241-68.95120.58835.816.331-3.47%-6.93%

35302893.151222.579131.26522.64860.74616.37%3.27%

353143821.002898.304665.099228.25767.99518.54%7.24%

35321-175.52766.76949.13124.46889.849-25.43%-11.23%

353382260.4531051.885163.183243.937254.46511.90%16.79%

35373478.735120.3556.814.194.8413.68%3.79%

354072246.672447.134173.363132.707219.0548.79%6.87%

3541166.84620.94810.55802.12918.70%0.00%

35502300.45477.4529.98624.52431.42811.85%9.91%

3555216.2564.9195.554.8864.37232.87%30.12%

355951256.933393.416687.60293.48195.23444.33%9.77%

356071588.631335.627278.02888.525256.63118.16%6.60%

35614744.456210.501292.11357.307153.66635.36%9.69%

35622491.24153.8774818.59331.34712.46%5.22%

35642124.9627.3624.2620.1545.06919.91%0.16%

3567246.0498.1134.5771.87711.13110.77%4.71%

356952637.776510.814167.619227.867264.6917.30%9.68%

357026051.7241964.3453473.731493.9249.43945.94%10.78%

357166549.1531967.0263344.97597.513280.23642.20%11.54%

357291995.7161053.7461684.37197.037108.164.13%17.30%

3575213.4853.8015.2020.732.9434.95%7.01%

357642923.216515.4552459.334119.570.04350.53%4.73%

357774852.263993.9441308.783501.666616.46625.33%11.51%

35785753.547415.002493.481123.75931.24659.31%26.77%

357911374.743361.333100.806112.2168.5589.05%9.97%

35804379.413102.64772.69950.44639.60920.80%15.42%

3585111721.939397.312169.817136.749370.47211.36%9.36%

35907414.767110.562122.77334.869.01728.75%10.27%

3600231062815230742025176611.83%8.12%

36121116.09537.66422.215.9316.55922.06%16.88%

362062238.255678.793854.109222.584253.64535.39%12.49%

36217405.372105.90183.68930.56637.59321.84%9.26%

363042190.16674.909294.035141.502393.30316.25%8.54%

36343101.70626.77706.15221.9660.00%7.59%

3640142185.162499.565290.82117.301246.87814.71%6.51%

36511162.83962.51465.92633.28824.88539.65%24.91%

366199357.1543325.489060.598879.818608.79260.03%12.73%

3663178171.1463644.9315072.78584.346868.56552.85%11.43%

36697360.566135.04273.72542.75884.31924.64%15.94%

36703634.403232.46280.93124.17880.11716.76%5.67%

36725650.426193.76331.22444.48940.9566.40%8.88%

36742016165.6746531.6996404.204440.747463.01439.93%4.37%

36782260.82655.96931.18918.22391.34513.21%8.17%

36797-11.86666.454137.31737.36815.055232.75%-91.25%

36906260.43367.3729.32828.17474.01613.19%12.73%

37111187139.50441482.26426739.8782159.79517925.09636.94%4.52%

3713120.4132.93501.0271.6480.00%5.55%

3714219571.1313734.7893153.44780.2541679.11435.08%11.79%

3715175.10418.4051.84.214.8433.08%6.90%

37163131.917.8996.0513.7662.4125.04%3.20%

37202371995739412037312.48%4.16%

372135023.4582008.5662124.03446.5886.95941.33%12.90%

372474385.9851024.4051477.053313.579363.76530.53%8.53%

372831802.663461.868295121.483268.12518.03%8.31%

373051018.892232.911131.46722.68181.114.33%2.80%

37433261.54547.71631.90620.65358.05712.98%8.81%

37512492.128105.50258.79.30833.13313.18%2.35%

376034068.81120.9872.4313.6891.222.84%9.62%

37902136.46436.83128.3872.53.0722.17%2.45%

381273954.646962.118718.674369.742809.90619.36%11.00%

382221296.113334.973498.198145.879117.33734.14%13.18%

382362900.345597.396537.436176.827160.6418.92%7.13%

3824322.6445.2947.8591.860.6331.18%9.68%

38255279.66898.428239.97828.5174.76356.97%13.60%

382691145.391374.921635.735173.709195.60445.21%18.40%

38272230.38440.485186.13618.9430.52149.50%9.07%

38291546.584162.277213.17183.8104.03535.68%17.90%

3841103927.602866.0522121.745224.818407.40340.93%6.84%

38423203.57151.89843.19223.72126.91922.17%13.52%

38432256.75430.15516.848.00957.4196.92%3.41%

38443202.98662.717159.88430.47218.56153.27%17.85%

38457500.223103.539308.60353.40740.39643.76%11.87%

38514239.78457.26234.61213.46732.21215.94%6.87%

386153241.881088.8371193.685209.137264.78935.67%8.85%

39111124.1623.171007.0260.00%0.00%

3931153.59810.6303.63812.9820.00%7.81%

39423911.465239.067182.49966.012120.41421.35%8.94%

39442515.563173.601186.34252.47440.19935.27%13.30%

39496151.76560.1752.71828.30539.42936.53%23.61%

3950332.19419.5796.8615.2359.39235.23%29.33%

39904326.39768.2674.51216.39945.5522.40%5.97%

4011910356.5893927.02023902475.2250.00%27.10%

41002908.183360.4140100.2213.9060.00%15.46%

4210326.44712.422020.5585.5140.00%59.45%

42136319.189189.579016.30645.9890.00%11.17%

42203209.56190.295078.826101.2510.00%39.79%

440072447.53650.060285.059413.9030.00%13.69%

44126648.297295.496052.789184.9030.00%13.02%

45121212838.8994284.09607893.9251583.9550.00%47.99%

45133881.627340.3890350.96261.2870.00%39.34%

45222192.77860.549014.616113.4440.00%9.95%

46105554.984120.754015.792131.160.00%3.51%

47002676.887264.2790204.759239.7040.00%33.17%

47312321.091178.5740199.93747.2650.00%58.38%

4812113988.2994683.8020706.122541.0210.00%6650.84%

48132392626.70237413.9362721.7558351.8948931.6054.70%13.14%

4822116.9816.6935.5651.9571.20535.10%15.98%

48327243.945318.587017.233233.8850.00%-30.02%

4833112145.23437.1150.714225.119662.3960.04%11.64%

484143345.8662837.6780223.8931700.4280.00%30.58%

48993352.236283.5077.91418.596115.310.33%21.30%

49115956061.33220921.59201476.98312958.7990.00%4.03%

4922106267.912413.830345.1542175.0420.00%8.22%

4923164016.5111711.8170140.4091199.5320.00%5.74%

4924357332.0362781.8950106.2471774.1920.00%2.28%

49314629145.52611535.3140685.0638046.5670.00%3.74%

493242011.0461193.50145.274418.7350.00%15.09%

49418963.233239.174018.648280.3360.00%2.51%

495356057.352263.0780310.0771059.6310.00%7.55%

49558216.968110.2552.95784.503137.2452.70%44.19%

4961147.12819.7804.20123.7420.00%13.32%

499152337.435741.6479.563157.8381209.1130.60%9.00%

50001482.20274.22016.3368.9750.00%3.85%

501019.2011.90702.51.9130.00%25.53%

50132683.40170.881079.73322.7580.00%11.52%

5030144.15310.07108.6428.0190.00%20.23%

50312305.49363.61556.621.330.24618.96%8.09%

50403603.335195.0020107.072285.3390.00%20.77%

50454914.679182.0440113.587205.7590.00%13.42%

5047291.54614.421027.51626.2150.00%26.30%

50515489.798130.214053.063106.5820.00%12.86%

50635384.99866.273069.016102.6980.00%17.80%

50656820.639127.531067.832137.8640.00%8.91%

5070160.2878.441021.11411.1070.00%28.94%

5072114.2151.798002.4480.00%0.00%

50807295.97545.648050.40361.70.00%16.76%

50844336.201101.93048.09265.5660.00%17.03%

5090263.98410.34206.9613.6220.00%11.49%

5093136.4337.901010.73125.6680.00%115.89%

51103847.941391.80611.769172.726233.6842.52%27.47%

512271287.505152.966096.489124.9360.00%7.84%

51404855.496206.453058.4774.5850.00%8.26%

514131288.751478.720275.169366.2710.00%25.36%

51502512.69994.54700147.7430.00%0.00%

51602299240.73528148.53163.91532.46%71.82%

51713151.2563.816072.70740.8580.00%45.40%

517293562.6351990.8760358.1521024.5860.00%18.56%

51902193.735136.653064.44867.2240.00%53.03%

521134206.176671.9790477.1184.6980.00%11.89%

53111013448.8733368.44201904.9993182.3870.00%15.89%

53311315974.1984094.4102724.7471812.9610.00%18.66%

5399145.18457.072072.49983.2550.00%119.61%

5411137882.8372610.040.4051391.8011116.9740.01%20.88%

5412228.80316.64019.48514.8480.00%61.57%

55008911.995194.290390.147116.80.00%35.22%

55313761.445214.1690190.344101.1640.00%25.81%

56001134.15821.878091.28900.00%44.84%

562141275.081398.1810958.427104.9780.00%52.22%

565173415.348691.31301031.5116.6890.00%27.47%

56615787.519338.01201169.419109.2170.00%72.23%

57003374.21385.4590258.01112.0920.00%47.19%

57123200.39383.4550225.90888.8590.00%65.89%

57314893.09239.9050545.68982.2250.00%45.52%

57341162.00848.96707912.3310.00%41.14%

57351124.28239.4710148.92530.4780.00%63.72%

58102336.08698.059062.80241.9990.00%20.88%

5812266922.7981943.484211826.9331034.3470.42%26.84%

59008512.16205.425091.605215.0080.00%23.00%

591273574.038798.89901504.844328.4580.00%35.16%

5940102070.062559.38601521.1798.4620.00%50.17%

59445381.24860.4820154.32451.9870.00%32.48%

594515952550334960.00%49.55%

596019.71510.21201.9267.4460.00%134.78%

59618221.86660.3891.35238.71820.5060.83%19.34%

59905861.413139.5560350.82359.1910.00%32.71%

6021183105243.66413864.77408425.47500.00%8.44%

602215812595.8192055.06601202.07900.00%10.24%

60291424578.5174290.88905927.16900.00%22.61%

60351679484.6681421.859062.54900.00%0.77%

6036661656.033211.6670000.00%0.00%

6099149.53126.76707.600.00%25.03%

61112597.2360.26100.2455.7310.00%0.03%

6141510954.771760.7230288.7955943.950.00%2.75%

61534163.2328.428014.99691.2590.00%8.83%

615961990.449176.51801.8021178.1770.00%0.10%

616242416.857630.288059.21062.0990.00%3.21%

617242027.377247.945027.6141156.8190.00%1.53%

6199239140.7951474.49801062.20627750.1350.00%2.74%

62001-3.4691.2310.6353.1881.765-15.62%-210.85%

621127103983.8652666.732111944.44584862.3840.01%1.88%

6282132820.722447.5910213.784243.6510.00%8.26%

63113010414.5821051.3040266.0411856.2150.00%2.76%

632164292.525913.154060.06642.8330.00%1.75%

6324104978.818889.6450442.311307.7170.00%9.76%

63316634093.4523186.9601580.5614137.7790.00%4.87%

6351183719.407131.046060.079235.4870.00%1.65%

636151160.323162.4250278.34351.8210.00%21.81%

6399144.2762.94400.46800.00%1.12%

6411123284.105478.6630653.839287.5370.00%18.90%

65002110.52713.20100.34855.2510.00%0.36%

6510241.0516.68102.778.3460.00%9.97%

6512121419.094269.517013.825735.9910.00%1.19%

65132128.54655.7640091.4290.00%0.00%

6519222.2569.76500.0512.7260.00%0.41%

65318344.98272.5120137.49661.2390.00%33.54%

65325158.02712.34200.51963.3360.00%0.35%

65527128.10830.54400.29434.8740.00%0.30%

679491810.637347.07218.902203.727146.3621.28%12.22%

679519.8630.20100.04500.00%0.46%

679892450.21681.880394.4521195.2860.00%18.24%

679940.23537.85604.602114.5230.00%-13.94%

700018.0782.538004.5990.00%0.00%

7011152517.078573.2710627.517497.2120.00%24.40%

720081232.81346.4120151.783390.4620.00%14.62%

731061221.013502.4390374.8357.3310.00%34.28%

731151814.747420.470697.476187.3360.00%33.34%

732041124.562219.7160121.18761.4330.00%11.81%

73312224.150.008035.214.2360.00%16.82%

7340285.64328.5270124.4983.4650.00%68.55%

73504671.812345.333033.912155.6740.00%9.41%

7359131178.881575.507091.684253.570.00%13.19%

736127.9990.88303.15200.00%30.70%

7363151495.833316.02215.328299.559158.381.28%20.25%

73701416035.965364.0734732.6641957.728900.68530.72%15.50%

73711191.62413.3173.516.10.1631.93%8.28%

73722312457.8971363.3744471.375500.879218.14328.73%4.32%

7373123843.0391435.081509.6961415.697352.98117.47%37.02%

737463543.768871.232489.025563.927150.67115.47%17.42%

73802160.7123.9408.0558.860.00%17.96%

73814340.25106.6060.73866.06240.4140.31%22.04%

738912962.007248.864166.374220.09194.75918.92%23.58%

7500159.45112.570172.67410.5330.00%78.65%

751065492.3023402.38401025.811077.0290.00%32.92%

7812914332.8666412.81201039.7822881.130.00%11.60%

7819114.657.95803.7193.6190.00%35.72%

78221178.1741.90704.07800.00%2.26%

7830394.05359.2520142.93432.8150.00%80.42%

79005251.62195.3950.12151.687185.2170.21%47.90%

79483110.21622.55202.10429.9950.00%2.34%

7990172953.4011101.0360231.4621128.8740.00%11.11%

79963416.387152.088012.218179.3180.00%4.42%

79971101.05748.255092.81641.4940.00%63.74%

8000368.8413.664019.6941.760.00%26.30%

80111156.30818.4016.978.7960.00%10.92%

8051102005.469648.9770706.744809.0710.00%34.25%

8060284.92112.63903.3754.3940.00%4.46%

806243224.3631283.579096.646647.3350.00%4.74%

80717424.983167.915.637131.829110.0752.15%33.90%

80823106.493150.483071.5985.9360.00%259.38%

80904298.46648.2945.27247.06774.7662.06%15.83%

809341363.92355.1080249.186155.270.00%19.81%

82004173.63355.777083.91617.9910.00%41.59%

83009152.02678.8630425.37105.7580.00%85.32%

87009981.475297.78332.8183.09929.4224.58%21.12%

87119421.139146.3348.381157.2158.85514.97%36.39%

87212268.40754.55377.838.7264.326.68%15.33%

87313126.37841.9630.34127.6778.790.40%24.69%

8734223.283.5791.6030.4070.1687.52%2.02%

87415883.46182.0970141.347208.5050.00%16.77%

874218.5793.17707.4291.8660.00%57.90%

8744126.0683.56704.700.00%17.28%

99952-5.460.19900.4933.7910.00%-9.54%

Grand Total28921422342.376418434.637144477.937120114.142288689.675

0.125809595210.69%22.33%

Operating Lease expenses as % of Operating Income

Market12.59%

Apparel Stores43.85%

Furniture Stores50.02%

Restaurants26.59%

Sheet2

Sheet3

*

Dealing with Operating Lease ExpensesOperating Lease Expenses are treated as operating expenses in computing operating income. In reality, operating lease expenses should be treated as financing expenses, with the following adjustments to earnings and capital:Debt Value of Operating Leases = Present value of Operating Lease Commitments at the pre-tax cost of debtWhen you convert operating leases into debt, you also create an asset to counter it of exactly the same value.Adjusted Operating EarningsAdjusted Operating Earnings = Operating Earnings + Operating Lease Expenses - Depreciation on Leased AssetAs an approximation, this works:Adjusted Operating Earnings = Operating Earnings + Pre-tax cost of Debt * PV of Operating Leases.Aswath Damodaran*

Aswath Damodaran

*

Operating Leases at The Gap in 2003The Gap has conventional debt of about $ 1.97 billion on its balance sheet and its pre-tax cost of debt is about 6%. Its operating lease payments in the 2003 were $978 million and its commitments for the future are below:YearCommitment (millions)Present Value (at 6%)1 $899.00 $848.11 2 $846.00 $752.94 3 $738.00 $619.64 4 $598.00 $473.67 5 $477.00 $356.44 6&7 $982.50 each year $1,346.04 Debt Value of leases = $4,396.85 (Also value of leased asset)Debt outstanding at The Gap = $1,970 m + $4,397 m = $6,367 mAdjusted Operating Income = Stated OI + OL exp this year - Deprecn= $1,012 m + 978 m - 4397 m /7 = $1,362 million (7 year life for assets)Approximate OI = $1,012 m + $ 4397 m (.06) = $1,276 mAswath Damodaran*

Aswath Damodaran

*

The Collateral Effects of Treating Operating Leases as DebtAswath Damodaran*

Aswath Damodaran

Conventional Accounting

Operating Leases Treated as Debt

Income Statement

EBIT& Leases = 1,990

- Op Leases = 978

EBIT = 1,012

Income Statement

EBIT& Leases = 1,990

- Deprecn: OL= 628

EBIT = 1,362

Interest expense will rise to reflect the conversion of operating leases as debt. Net income should not change.

Balance Sheet

Off balance sheet (Not shown as debt or as an asset). Only the conventional debt of $1,970 million shows up on balance sheet

Balance Sheet

Asset Liability

OL Asset 4397 OL Debt 4397

Total debt = 4397 + 1970 = $6,367 million

Cost of capital = 8.20%(7350/9320) + 4% (1970/9320) = 7.31%

Cost of equity for The Gap = 8.20%

After-tax cost of debt = 4%

Market value of equity = 7350

Cost of capital = 8.20%(7350/13717) + 4% (6367/13717) = 6.25%

Return on capital = 1012 (1-.35)/(3130+1970)

= 12.90%

Return on capital = 1362 (1-.35)/(3130+6367)

= 9.30%

*

The Magnitude of R&D ExpensesAswath Damodaran*

Aswath Damodaran

Chart1

0.1259

0.4384835372

0.5001598879

0.2658948631

Operating Lease expenses as % of Operating Income

Chart2

0.1069

0.3043

0.5035

R&D as % of Operating Income

Sheet1

SICNumber of firmsEBITDADAR&DLease ExpensesInterest ExpensesR&D as % of EBITLease Expenses as % of EBIT

10061210.894328.935171.656353.273224.24116.29%28.60%

2002360.50118.90800161.0630.00%0.00%

80013933522645.45%25.00%

100051595.006707.086030.961413.1090.00%3.37%

104023439.1581400.873013.994345.2550.00%-1.48%

10442-19.11855.538006.9790.00%0.00%

1090134.82811.64200.14.90.00%0.43%

12203245.741231.872020.94972.030.00%60.17%

13117110622.62615467.953258.3621055.8853496.821-5.63%-27.86%

1381194790.9461216.6750343.799487.4670.00%8.77%

13823726.701399.816.19658.23316.5671.86%15.12%

138954942.6941757.602908.783609.845335.35422.20%16.07%

14005864.255306.86919.51765.0342.4163.38%10.45%

1531192263.249180.865073.969674.3030.00%3.43%

1540264.96412.30509.6589.6180.00%15.50%

160071218.951472.78715.1181.075158.3811.98%19.53%

16235343.967118.993024.1833.7860.00%9.70%

17006286.80768.8630.8644.45932.3260.39%16.94%

1731277.1115.9603.5525.3630.00%5.49%

200028331.3771661.915921.297686.19651.50812.14%9.33%

20112743.739186.499921.969.3451.59%3.78%

201310.9090.45300.40500.00%47.04%

20154902.25335.7740120.772197.9220.00%17.57%

20201334.23591.77904882.2950.00%16.53%

2024116.7964.3101.6570.5450.00%11.72%

203063610.82556.909148.703110.336506.2294.64%3.49%

20332147.70640.1765.81535.74680.1795.13%24.95%

204073136.524687.625242.6147.291415.49.01%5.67%

20502218.085109.0501.82620.4270.00%1.65%

205245570.1321826.89309.63621274.9887.64%8.82%

206051491.188276.53728.647.909142.7362.30%3.79%

207041394.848570.23717.184.908343.7992.03%9.34%

208039569.71621.900.2676.40.00%0.00%

208233122.565859.44715.211.922304.6650.67%0.52%

2084112.3054.15100.3593.9470.00%4.22%

208523781.419594.34900504.1890.00%0.00%

208663607.5091962.5840160.2991041.6430.00%8.88%

20905454.76110.88816.919.631115.3994.68%5.40%

21003909.2447.8541.24414.09717.4440.14%1.61%

2111420562.5382693.436580.826570.0472240.7593.15%3.09%

22005729.237220.66331.13936.593173.7345.77%6.71%

22116504.304219.844029.119143.0530.00%9.29%

22213199.50769.28323.73234.11247.16215.41%20.76%

22505460.398174.5528.87147.34112.5169.17%14.21%

22534220.369109.29038.15565.5770.00%25.57%

22733819.602208.126080.533179.2330.00%11.64%

230091190.814228.1780185.431132.0950.00%16.15%

23206421.05191.69805.747.8380.00%1.71%

23305691.064111.3810166.38733.7970.00%22.30%

23402243.14147.082036.29866.4130.00%15.62%

23902203.27554.591025.17976.9970.00%14.48%

240052883.4961333.763125.6668.407649.7387.50%0.54%

242161054.705409.68021.3236.6050.00%3.20%

243031068.73195.741015187.2850.00%1.69%

24514615.60570.20905.79322.6230.00%1.05%

25105855.745196.162126789.7351.79%9.22%

25115263.59351.4240.922.95919.5010.42%9.76%

252241044.372231.193104.65482.02356.04911.40%9.16%

253141779.552615.679365.983187.569261.86323.92%13.88%

25903734.789153.757060.62161.6710.00%9.45%

260024045245995.52039695.68%11.35%

26111158.97336.56210.732036.8088.06%0.00%

2621159026.8283605.288331.148424.6811724.7825.76%7.26%

263151355.283632.685016.5432.9950.00%2.23%

26506898.521421.6418.166.465241.5083.66%12.23%

2670155191.2751386.8071182.961230.73426.28623.72%5.72%

267314.6940.96500.2580.4160.00%6.47%

2711167831.6831953.69660.988356.177876.7081.03%5.71%

272183474.961630.6730378.2981217.1210.00%17.02%

273141035.476276.8920157.54891.6690.00%17.20%

2750113421.1511301.39510.7148.924491.8160.50%6.56%

276171156.145367.266129.395193.127106.1814.09%19.67%

27712390.56467.349059.01329.340.00%15.44%

27803567.478130.15512.873.925.4372.84%14.46%

2790136.0497.74101.3893.5980.00%4.68%

280032386.1841.11436.9193.8451.748.19%11.15%

2810184768.9372575.062401.068280.535920.88815.46%11.34%

282036250.8111573.4022819.975238.082750.61637.61%4.84%

2821126675.7242295.5861911.357657.7959.95130.38%13.06%

28344052184.698052.6521833.5511290.9172474.03433.10%2.84%

28353428.356134.664486.60434.746104.42462.36%10.58%

2836141650.229250.477783.68421.97748.99935.89%1.55%

284058040.171692.7161589.07618.642576.00720.02%0.29%

28423989.284223.19888.8256.64996.3710.39%6.89%

2844103417.203617.033307.211402.907449.6349.89%12.58%

285152715.371584.854380.952192.762234.48115.17%8.30%

2860113007.1671115.734580.814162.176728.95223.49%7.90%

287082167.138612.06619.012194.946382.481.21%11.14%

289092471.697747.522320.078151.531236.29215.66%8.08%

29112975408.65547151.8013286.92910215.1958859.00610.42%26.55%

2950141.64511.05601.5052.7370.00%4.69%

2990229.0025.53810.2610.1152.28330.43%0.49%

301142048.976653.552468.707240.847234.8725.14%14.72%

30212176.29648.5247.65952.04478.1965.66%28.94%

30504548.378109.14583.2633.55726.44315.94%7.10%

30604292.07972.38630.67814.90632.12712.25%6.35%

30803158.39237.5610.3526.38318.3057.89%5.02%

3081370.41623.933.2651.86713.8676.56%3.86%

3089101164.881338.69886.78681.581139.1559.51%8.99%

310021.931.04401.6511.1860.00%65.08%

31409381.08674.9544.472150.96843.0181.44%33.03%

3220182.91419.50605.68412.6740.00%8.23%

322111341.8456.536.468.53803.95%7.18%

3231146.44222.636.4184.38.34760.43%15.28%

32412482.76692.937027.45421.980.00%6.58%

32501105.78927.873033.26945.1730.00%29.92%

32603259.69317.93027.57349.0290.00%10.24%

327061421.044307.23732.55588.681128.2142.84%7.37%

329051148.141370.397119.723159.637231.13613.34%17.03%

3310221.86417.4331.5673.4357.56126.13%43.67%

3312214623.7451937.651144.264433.144672.0355.10%13.89%

3317215.42219.71705.956.2960.00%359.52%

3320137.60411.76401.0063.8960.00%3.75%

333073217.6711653.456127.46555.5518.8037.53%3.43%

33342975.3349.744.775.63386.67%10.78%

3341156.88919.074009.5360.00%0.00%

3350134965.3861653.782245.388317.316519.5486.90%8.74%

335751374.399392.515341.22268.1141.30625.79%6.49%

336019.5014.93302.292.2990.00%33.39%

3390262.76116.2221.9823.1553.4674.08%6.35%

341141865.031736.50476.795.7538.3566.36%7.82%

342093977.205623.603374.39206.556175.1510.04%5.80%

34301870.7251.15449.8102.78.02%7.44%

3440142.1112.28904.23311.7030.00%12.43%

34423124.19728.03911.929.4757.90311.01%23.46%

34434455.843130.37114.353102.04579.4774.22%23.87%

34483183.24828.0162.916.42227.4851.83%9.57%

34524204.78958.9278.93114.56357.2435.77%9.08%

34603335.207106.972024.11560.5770.00%9.56%

34703100.88854.6037.0696.93425.95813.25%13.03%

34804267.91857.04330.3649.62619.87512.59%4.37%

3490101676.079446.298161.03191.83171.81411.58%6.95%

351041335.899451.911429.35136.7164.85232.69%13.39%

352375065.8571033.8641172.411139.083986.66322.53%3.33%

35241-68.95120.58835.816.331-3.47%-6.93%

35302893.151222.579131.26522.64860.74616.37%3.27%

353143821.002898.304665.099228.25767.99518.54%7.24%

35321-175.52766.76949.13124.46889.849-25.43%-11.23%

353382260.4531051.885163.183243.937254.46511.90%16.79%

35373478.735120.3556.814.194.8413.68%3.79%

354072246.672447.134173.363132.707219.0548.79%6.87%

3541166.84620.94810.55802.12918.70%0.00%

35502300.45477.4529.98624.52431.42811.85%9.91%

3555216.2564.9195.554.8864.37232.87%30.12%

355951256.933393.416687.60293.48195.23444.33%9.77%

356071588.631335.627278.02888.525256.63118.16%6.60%

35614744.456210.501292.11357.307153.66635.36%9.69%

35622491.24153.8774818.59331.34712.46%5.22%

35642124.9627.3624.2620.1545.06919.91%0.16%

3567246.0498.1134.5771.87711.13110.77%4.71%

356952637.776510.814167.619227.867264.6917.30%9.68%

357026051.7241964.3453473.731493.9249.43945.94%10.78%

357166549.1531967.0263344.97597.513280.23642.20%11.54%

357291995.7161053.7461684.37197.037108.164.13%17.30%

3575213.4853.8015.2020.732.9434.95%7.01%

357642923.216515.4552459.334119.570.04350.53%4.73%

357774852.263993.9441308.783501.666616.46625.33%11.51%

35785753.547415.002493.481123.75931.24659.31%26.77%

357911374.743361.333100.806112.2168.5589.05%9.97%

35804379.413102.64772.69950.44639.60920.80%15.42%

3585111721.939397.312169.817136.749370.47211.36%9.36%

35907414.767110.562122.77334.869.01728.75%10.27%

3600231062815230742025176611.83%8.12%

36121116.09537.66422.215.9316.55922.06%16.88%

362062238.255678.793854.109222.584253.64535.39%12.49%

36217405.372105.90183.68930.56637.59321.84%9.26%

363042190.16674.909294.035141.502393.30316.25%8.54%

36343101.70626.77706.15221.9660.00%7.59%

3640142185.162499.565290.82117.301246.87814.71%6.51%

36511162.83962.51465.92633.28824.88539.65%24.91%

366199357.1543325.489060.598879.818608.79260.03%12.73%

3663178171.1463644.9315072.78584.346868.56552.85%11.43%

36697360.566135.04273.72542.75884.31924.64%15.94%

36703634.403232.46280.93124.17880.11716.76%5.67%

36725650.426193.76331.22444.48940.9566.40%8.88%

36742016165.6746531.6996404.204440.747463.01439.93%4.37%

36782260.82655.96931.18918.22391.34513.21%8.17%

36797-11.86666.454137.31737.36815.055232.75%-91.25%

36906260.43367.3729.32828.17474.01613.19%12.73%

37111187139.50441482.26426739.8782159.79517925.09636.94%4.52%

3713120.4132.93501.0271.6480.00%5.55%

3714219571.1313734.7893153.44780.2541679.11435.08%11.79%

3715175.10418.4051.84.214.8433.08%6.90%

37163131.917.8996.0513.7662.4125.04%3.20%

37202371995739412037312.48%4.16%

372135023.4582008.5662124.03446.5886.95941.33%12.90%

372474385.9851024.4051477.053313.579363.76530.53%8.53%

372831802.663461.868295121.483268.12518.03%8.31%

373051018.892232.911131.46722.68181.114.33%2.80%

37433261.54547.71631.90620.65358.05712.98%8.81%

37512492.128105.50258.79.30833.13313.18%2.35%

376034068.81120.9872.4313.6891.222.84%9.62%

37902136.46436.83128.3872.53.0722.17%2.45%

381273954.646962.118718.674369.742809.90619.36%11.00%

382221296.113334.973498.198145.879117.33734.14%13.18%

382362900.345597.396537.436176.827160.6418.92%7.13%

3824322.6445.2947.8591.860.6331.18%9.68%

38255279.66898.428239.97828.5174.76356.97%13.60%

382691145.391374.921635.735173.709195.60445.21%18.40%

38272230.38440.485186.13618.9430.52149.50%9.07%

38291546.584162.277213.17183.8104.03535.68%17.90%

3841103927.602866.0522121.745224.818407.40340.93%6.84%

38423203.57151.89843.19223.72126.91922.17%13.52%

38432256.75430.15516.848.00957.4196.92%3.41%

38443202.98662.717159.88430.47218.56153.27%17.85%

38457500.223103.539308.60353.40740.39643.76%11.87%

38514239.78457.26234.61213.46732.21215.94%6.87%

386153241.881088.8371193.685209.137264.78935.67%8.85%

39111124.1623.171007.0260.00%0.00%

3931153.59810.6303.63812.9820.00%7.81%

39423911.465239.067182.49966.012120.41421.35%8.94%

39442515.563173.601186.34252.47440.19935.27%13.30%

39496151.76560.1752.71828.30539.42936.53%23.61%

3950332.19419.5796.8615.2359.39235.23%29.33%

39904326.39768.2674.51216.39945.5522.40%5.97%

4011910356.5893927.02023902475.2250.00%27.10%

41002908.183360.4140100.2213.9060.00%15.46%

4210326.44712.422020.5585.5140.00%59.45%

42136319.189189.579016.30645.9890.00%11.17%

42203209.56190.295078.826101.2510.00%39.79%

440072447.53650.060285.059413.9030.00%13.69%

44126648.297295.496052.789184.9030.00%13.02%

45121212838.8994284.09607893.9251583.9550.00%47.99%

45133881.627340.3890350.96261.2870.00%39.34%

45222192.77860.549014.616113.4440.00%9.95%

46105554.984120.754015.792131.160.00%3.51%

47002676.887264.2790204.759239.7040.00%33.17%

47312321.091178.5740199.93747.2650.00%58.38%

4812113988.2994683.8020706.122541.0210.00%6650.84%

48132392626.70237413.9362721.7558351.8948931.6054.70%13.14%

4822116.9816.6935.5651.9571.20535.10%15.98%

48327243.945318.587017.233233.8850.00%-30.02%

4833112145.23437.1150.714225.119662.3960.04%11.64%

484143345.8662837.6780223.8931700.4280.00%30.58%

48993352.236283.5077.91418.596115.310.33%21.30%

49115956061.33220921.59201476.98312958.7990.00%4.03%

4922106267.912413.830345.1542175.0420.00%8.22%

4923164016.5111711.8170140.4091199.5320.00%5.74%

4924357332.0362781.8950106.2471774.1920.00%2.28%

49314629145.52611535.3140685.0638046.5670.00%3.74%

493242011.0461193.50145.274418.7350.00%15.09%

49418963.233239.174018.648280.3360.00%2.51%

495356057.352263.0780310.0771059.6310.00%7.55%

49558216.968110.2552.95784.503137.2452.70%44.19%

4961147.12819.7804.20123.7420.00%13.32%

499152337.435741.6479.563157.8381209.1130.60%9.00%

50001482.20274.22016.3368.9750.00%3.85%

501019.2011.90702.51.9130.00%25.53%

50132683.40170.881079.73322.7580.00%11.52%

5030144.15310.07108.6428.0190.00%20.23%

50312305.49363.61556.621.330.24618.96%8.09%

50403603.335195.0020107.072285.3390.00%20.77%

50454914.679182.0440113.587205.7590.00%13.42%