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## Valuation

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**Valuation**Aswath Damodaran http://www.damodaran.com**Some Initial Thoughts**" One hundred thousand lemmings cannot be wrong" Graffiti**Misconceptions about Valuation**• Myth 1: A valuation is an objective search for “true” value • Truth 1.1: All valuations are biased. The only questions are how much and in which direction. • Truth 1.2: The direction and magnitude of the bias in your valuation is directly proportional to who pays you and how much you are paid. • Myth 2.: A good valuation provides a precise estimate of value • Truth 2.1: There are no precise valuations • Truth 2.2: The payoff to valuation is greatest when valuation is least precise. • Myth 3: . The more quantitative a model, the better the valuation • Truth 3.1: One’s understanding of a valuation model is inversely proportional to the number of inputs required for the model. • Truth 3.2: Simpler valuation models do much better than complex ones.**Approaches to Valuation**• Discounted cashflow valuation, relates the value of an asset to the present value of expected future cashflows on that asset. • Relative valuation, estimates the value of an asset by looking at the pricing of 'comparable' assets relative to a common variable like earnings, cashflows, book value or sales. • Contingent claim valuation, uses option pricing models to measure the value of assets that share option characteristics.**Discounted Cash Flow Valuation**• What is it: In discounted cash flow valuation, the value of an asset is the present value of the expected cash flows on the asset. • Philosophical Basis: Every asset has an intrinsic value that can be estimated, based upon its characteristics in terms of cash flows, growth and risk. • Information Needed: To use discounted cash flow valuation, you need • to estimate the life of the asset • to estimate the cash flows during the life of the asset • to estimate the discount rate to apply to these cash flows to get present value • Market Inefficiency: Markets are assumed to make mistakes in pricing assets across time, and are assumed to correct themselves over time, as new information comes out about assets.**Discounted Cashflow Valuation: Basis for Approach**where CFt is the expected cash flow in period t, r is the discount rate appropriate given the riskiness of the cash flow and n is the life of the asset. Proposition 1: For an asset to have value, the expected cash flows have to be positive some time over the life of the asset. Proposition 2: 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.**DCF Choices: Equity Valuation versus Firm Valuation**Firm Valuation: Value the entire business Equity valuation: Value just the equity claim in the business**Choosing a Currency for the Valuation**• Any company can be valued in any currency, as long as you maintain internal consistency by: • Using the same currency for cashflows, growth rate and discount rate estimates • Being consistent in inflation assumptions when estimating growth rates, discount rates and expected future exchange rates. • The currency you choose to value a company in is therefore driven by pragmatic concerns. In other words, in which currency will the estimates of the cashflows and discount rates be easiest to make. • For Embraer, which derives almost all of its cashflows from dollar sources and has almost all dollar denominated debt, both cashflows and discount rates are easier to estimate in US dollars.**A Simple Test**• You are valuing Embraer in U.S. dollars and are attempting to estimate a risk free rate to use in the analysis. The risk free rate that you should use is • The interest rate on a nominal real denominated Brazilian government bond • The interest rate on an inflation-indexed Brazilian government bond • The interest rate on a dollar denominated Brazilian government bond (10.18%) • The interest rate on a U.S. treasury bond (4.17%)**Everyone uses historical premiums, but..**• The historical premium is the premium that stocks have historically earned over riskless securities. • Practitioners never seem to agree on the premium; it is sensitive to • How far back you go in history… • Whether you use T.bill rates or T.Bond rates • Whether you use geometric or arithmetic averages. • For instance, looking at the US: Arithmetic average Geometric Average Stocks - Stocks - Stocks - Stocks - Historical Period T.Bills T.Bonds T.Bills T.Bonds 1928-2004 7.92% 6.53% 6.02% 4.84% 1964-2004 5.82% 4.34% 4.59% 3.47% 1994-2004 8.60% 5.82% 6.85% 4.51%**Two Ways of Estimating Country Risk Premiums…**• Default spread on Country Bond: In this approach, the country risk premium is based upon the default spread of the bond issued by the country (but only if it is denominated in a currency where a default free entity exists. • Brazil was rated B2 by Moody’s and the default spread on the Brazilian dollar denominated C.Bond at the end of September 2003 was 6.01%. (10.18%-4.17%) • Relative Equity Market approach: The country risk premium is based upon the volatility of the market in question relative to U.S market. Country risk premium = Risk PremiumUS* Country Equity / US Equity Using a 4.53% premium for the US, this approach would yield: Total risk premium for Brazil = 4.53% (33.37%/18.59%) = 8.13% Country risk premium for Brazil = 8.13% - 4.53% = 3.60% (The standard deviation in weekly returns from 2001 to 2003 for the Bovespa was 33.37% whereas the standard deviation in the S&P 500 was 18.59%)**And a third approach**• Country 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. In this approach: • Country risk premium = Default spread on country bond* Country Equity / Country Bond • Standard Deviation in Bovespa (Equity) = 33.37% • Standard Deviation in Brazil C-Bond = 26.15% • Default spread on C-Bond = 6.01% • Country Risk Premium for Brazil = 6.01% (33.37%/26.15%) = 7.67%**Can country risk premiums change? Updating Brazil in January**2005 • Brazil’s financial standing and country rating improved dramatically towards the end of 2004. Its rating improved to B1. In January 2005, the interest rate on the Brazilian C-Bond dropped to 7.73%. The US treasury bond rate that day was 4.22%, yielding a default spread of 3.51% for Brazil. • Standard Deviation in Bovespa (Equity) = 25.09% • Standard Deviation in Brazil C-Bond = 15.12% • Default spread on C-Bond = 3.51% • Country Risk Premium for Brazil = 3.51% (25.09%/15.12%) = 5.82%**From Country Spreads to Corporate Risk premiums**• Approach 1: Assume that every company in the country is equally exposed to country risk. In this case, E(Return) = Riskfree Rate + Country Spread + Beta (US premium) Implicitly, this is what you are assuming when you use the local Government’s dollar borrowing rate as your riskfree rate. • Approach 2: Assume that a company’s exposure to country risk is similar to its exposure to other market risk. E(Return) = Riskfree Rate + Beta (US premium + Country Spread) • 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+ b (US premium) + l (Country Spread)**Estimating Company Exposure to Country Risk: Determinants**• Source 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. A Brazilian firm that generates the bulk of its revenues in Brazil should be more exposed to country risk than one that generates a smaller percent of its business within Brazil. • Manufacturing facilities: Other things remaining equal, a firm that has all of its production facilities in Brazil 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.**Estimating Lambdas: The Revenue Approach**• The easiest and most accessible data is on revenues. Most companies break their revenues down by region. One simplistic solution would be to do the following: l = % of revenues domesticallyfirm/ % of revenues domesticallyavg firm • Consider, for instance, Embraer and Embratel, both of which are incorporated and traded in Brazil. Embraer gets 3% of its revenues from Brazil whereas Embratel gets almost all of its revenues in Brazil. The average Brazilian company gets about 77% of its revenues in Brazil: • LambdaEmbraer = 3%/ 77% = .04 • LambdaEmbratel = 100%/77% = 1.30 • There are two implications • A company’s risk exposure is determined by where it does business and not by where it is located • Firms might be able to actively manage their country risk exposures**Estimating Lambdas: Stock Returns versus C-Bond Returns**ReturnEmbraer = 0.0195 + 0.2681 ReturnC Bond ReturnEmbratel = -0.0308 + 2.0030 ReturnC Bond**Estimating a US Dollar Cost of Equity for Embraer -**September 2003 • Assume that the beta for Embraer is 1.07, and that the riskfree rate used is 4.17%. The historical risk premium from 1928-2002 for the US is 4.53% and the country risk premium for Brazil is 7.67%. • Approach 1: Assume that every company in the country is equally exposed to country risk. In this case, E(Return) = 4.17% + 1.07 (4.53%) + 7.67% = 16.69% • Approach 2: Assume that a company’s exposure to country risk is similar to its exposure to other market risk. E(Return) = 4.17 % + 1.07 (4.53%+ 7.67%) = 17.22% • 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)= 4.17% + 1.07(4.53%) + 0.27 (7.67%) = 11.09%**Implied Equity Premiums**• We 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 7.87% on stocks (which is obtained by solving for r in the following equation) • Implied Equity risk premium = Expected return on stocks - Treasury bond rate = 7.87% - 4.22% = 3.65%**An Intermediate Solution**• The historical risk premium of 4.53% for the United States is too high a premium to use in valuation. It is much higher than the actual implied equity risk premium in the market • The current implied equity risk premium requires us to assume that the market is correctly priced today. (If I were required to be market neutral, this is the premium I would use) • The average implied equity risk premium between 1960-2001 in the United States is about 4%. We will use this as the premium for a mature equity market.**Implied Premium for Brazil: September 2003**• Level of the Index = 16889 • Dividends on the Index = 4.55% of 16889 • Other parameters (all in US dollars) • Riskfree Rate = 4.17% • Expected Growth (in dollars) • Next 5 years = 15% (Used expected growth rate in Earnings) • After year 5 = 5% • Solving for the expected return: • Expected return on Equity = 12.17% • Implied Equity premium = 12.17% - 4.17% = 8.00% • Implied Equity premium for US on same day = 3.79% • Implied country premium for Brazil = 4.21%**Implied Premium for Brazil: June 2005**• Level of the Index = 26196 • Dividends on the Index = 6.19% of 16889 • Other parameters (all in US dollars) • Riskfree Rate = 4.08% • Expected Growth (in dollars) • Next 5 years = 8% (Used expected growth rate in Earnings) • After year 5 = 4.08% • Solving for the expected return: • Expected return on Equity = 11.66% • Implied Equity premium = 11.66% - 4.08% = 7.58% • Implied Equity premium for US on same day = 3.70% • Implied country premium for Brazil = 7.58% - 3.70% = 3.88%**Estimating Beta**• The standard procedure for estimating betas is to regress stock returns (Rj) against market returns (Rm) - Rj = a + b Rm • where 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 error • It reflects the firm’s business mix over the period of the regression, not the current mix • It reflects the firm’s average financial leverage over the period rather than the current leverage.**Gross Debt versus Net Debt Approaches**• Net Debt Ratio for Embraer = (Debt - Cash)/ Market value of Equity = (1953-2320)/ 11,042 = -3.32% • Levered Beta for Embraer = 0.95 (1 + (1-.34) (-.0332)) = 0.93 • The 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, though, 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.**Total Risk versus Market Risk**• Adjust the beta to reflect total risk rather than market risk. This adjustment is a relatively simple one, since the R squared of the regression measures the proportion of the risk that is market risk. Total Beta = Market Beta / Correlation of the sector with the market • To estimate the beta for Kristin Kandy, we begin with the bottom-up unlevered beta of food processing companies: • Unlevered beta for publicly traded food processing companies = 0.78 • Average correlation of food processing companies with market = 0.333 • Unlevered total beta for Kristin Kandy = 0.78/0.333 = 2.34 • Debt to equity ratio for Kristin Kandy = 0.3/0.7 (assumed industry average) • Total Beta = 2.34 ( 1- (1-.40)(30/70)) = 2.94 • Total Cost of Equity = 4.50% + 2.94 (4%) = 16.26%**Estimating Synthetic Ratings**• The 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 ratio Interest Coverage Ratio = EBIT / Interest Expenses • For Embraer’s interest coverage ratio, we used the interest expenses and EBIT from 2002. Interest Coverage Ratio = 2166/ 222 = 9.74 • Amazon.com has negative operating income; this yields a negative interest coverage ratio, which should suggest a low rating. We computed an average interest coverage ratio of 2.82 over the next 5 years.**Interest Coverage Ratios, Ratings and Default Spreads**If Interest Coverage Ratio is Estimated Bond Rating Default Spread(1/00) Default Spread(9/03) > 8.50 (>12.50) AAA 0.20% 0.75% 6.50 - 8.50 (9.5-12.5) AA 0.50% 1.00% 5.50 - 6.50 (7.5-9.5) A+ 0.80% 1.50% 4.25 - 5.50 (6-7.5) A 1.00% 1.80% 3.00 - 4.25 (4.5-6) A– 1.25% 2.00% 2.50 - 3.00 (3.5-4.5) BBB 1.50% 2.25% 2.00 - 2.50 ((3-3.5) BB 2.00% 3.50% 1.75 - 2.00 (2.5-3) B+ 2.50% 4.75% 1.50 - 1.75 (2-2.5) B 3.25% 6.50% 1.25 - 1.50 (1.5-2) B – 4.25% 8.00% 0.80 - 1.25 (1.25-1.5) CCC 5.00% 10.00% 0.65 - 0.80 (0.8-1.25) CC 6.00% 11.50% 0.20 - 0.65 (0.5-0.8) C 7.50% 12.70% < 0.20 (<0.5) D 10.00% 15.00% For Embraer and Kristin Kandy, I used the interest coverage ratio table for smaller/riskier firms (the numbers in brackets) which yields a lower rating for the same interest coverage ratio.**Estimating the cost of debt for a firm**• The synthetic rating for Embraer is AA. Using the 2003 default spread of 1.00%, we estimate a cost of debt of 9.17% (using a riskfree rate of 4.17% and adding in two thirds of the country default spread of 6.01%): Cost of debt = Riskfree rate + 2/3(Brazil country default spread) + Company default spread =4.17% + 4.00%+ 1.00% = 9.17% • The synthetic rating for Kristin Kandy is A-. Using the 2004 default spread of 1.00% and a riskfree rate of 4.50%, we estimate a cost of debt of 5.50%. Cost of debt = Riskfree rate + Default spread =4.50% + 1.00% = 5.50% • The synthetic rating for Amazon.com in 2000 was BBB. The default spread for BBB rated bond was 1.50% in 2000 and the treasury bond rate was 6.5%. Cost of debt = Riskfree Rate + Default spread = 6.50% + 1.50% = 8.00%**Weights for the Cost of Capital Computation**• The weights used to compute the cost of capital should be the market value weights for debt and equity. • There is an element of circularity that is introduced into every valuation by doing this, since the values that we attach to the firm and equity at the end of the analysis are different from the values we gave them at the beginning. • For private companies, neither the market value of equity nor the market value of debt is observable. Rather than use book value weights, you should try • Industry average debt ratios for publicly traded firms in the business • Target debt ratio (if management has such a target) • Estimated value of equity and debt from valuation (through an iterative process)**Estimating Cost of Capital: Amazon.com**• Equity • Cost of Equity = 6.50% + 1.60 (4.00%) = 12.90% • Market Value of Equity = $ 84/share* 340.79 mil shs = $ 28,626 mil (98.8%) • Debt • Cost of debt = 6.50% + 1.50% (default spread) = 8.00% • Market Value of Debt = $ 349 mil (1.2%) • Cost of Capital Cost of Capital = 12.9 % (.988) + 8.00% (1- 0) (.012)) = 12.84%**Estimating Cost of Capital: Embraer**• Equity • Cost of Equity = 4.17% + 1.07 (4%) + 0.27 (7.67%) = 10.52% • Market Value of Equity =11,042 million BR ($ 3,781 million) • Debt • Cost of debt = 4.17% + 4.00% +1.00%= 9.17% • Market Value of Debt = 2,093 million BR ($717 million) • Cost of Capital Cost of Capital = 10.52 % (.84) + 9.17% (1- .34) (0.16)) = 9.81% The book value of equity at Embraer is 3,350 million BR. The book value of debt at Embraer is 1,953 million BR; Interest expense is 222 mil; Average maturity of debt = 4 years Estimated market value of debt = 222 million (PV of annuity, 4 years, 9.17%) + $1,953 million/1.09174 = 2,093 million BR**If you had to do it….Converting a Dollar Cost of Capital**to a Nominal Real Cost of Capital • Approach 1: Use a BR riskfree rate in all of the calculations above. For instance, if the BR riskfree rate was 12%, the cost of capital would be computed as follows: • Cost of Equity = 12% + 1.07(4%) + 27 (7.67%) = 18.35% • Cost of Debt = 12% + 1% = 13% • (This assumes the riskfree rate has no country risk premium embedded in it.) • Approach 2: Use the differential inflation rate to estimate the cost of capital. For instance, if the inflation rate in BR is 8% and the inflation rate in the U.S. is 2% Cost of capital= = 1.0981 (1.08/1.02)-1 = 1627. or 16.27%