Discount Rates PDF

DISCOUNT RATES © All Slides | Aswath Damodaran THE RISK-FREE RATE © All Slides | Aswath Damodaran  THE RISK-FREE RATE: LAYING THE FOUNDATIONS 3 q On a risk-free investment, the actual return is equal to the expected return. Therefore, there is no variance around the expect...

DISCOUNT RATES © All Slides | Aswath Damodaran THE RISK-FREE RATE © All Slides | Aswath Damodaran  THE RISK-FREE RATE: LAYING THE FOUNDATIONS 3 q On a risk-free investment, the actual return is equal to the expected return. Therefore, there is no variance around the expected return. q For an investment to be risk-free, then, it has to have q No default risk q No reinvestment risk q It follows then that if asked to estimate a risk free rate: 1. Time horizon matters: Thus, the risk-free rates in valuation will depend upon when the cash flow is expected to occur and will vary across time. 2. Currencies matter: A risk free rate is currency-specific and can be very different for different currencies. 3. Not all government securities are riskfree: Some governments face default risk and the rates on bonds issued by them will not be risk-free. © All Slides | Aswath Damodaran  TEST 1: A RISKFREE RATE IN US DOLLARS! 4 q 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 be a. A three-month Treasury bill rate (4.42%) b. A ten-year Treasury bond rate (3.88%) c. A thirty-year Treasury bond rate (3.97%) d. A TIPs (inflation-indexed treasury) rate (1.53%) e. The highest of these numbers f. The lowest of these numbers g. Other (Specify) q What are we implicitly assuming about the US treasury when we use any of the treasury numbers? © All Slides | Aswath Damodaran  TEST 2: A RISK-FREE RATE IN EUROS? 5 Government Bond Rates: 10-year Euro bonds 4,00% 3,50% 3,00% 2,50% 2,00% 1,50% 1,00% 0,50% 0,00% Germany Netherlands Ireland France Belgium Finland Austria Portugal Spain Italy Slovenia Greece © All Slides | Aswath Damodaran  TEST 3: A RISK-FREE RATE IN INDIAN RUPEES 6 q The Indian government had 10-year Rupee bonds outstanding, with a yield to maturity of about 7.18% on January 1, 2024. q In January 2024, 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 2024 was 2.39%. The risk-free rate in Indian Rupees is a. The yield to maturity on the 10-year bond (7.18%) b. The yield to maturity on the 10-year bond + Default spread (9.57%) c. The yield to maturity on the 10-year bond – Default spread (4.78%) d. None of the above © All Slides | Aswath Damodaran  SOVEREIGN DEFAULT SPREAD: THREE PATHS TO THE SAME DESTINATION… 7 q Sovereign dollar or euro denominated bonds: Find sovereign bonds denominated in US dollars, issued by an emerging sovereign. q Default spread = Emerging Govt Bond Rate (in US $) – US Treasury Bond rate with same maturity. q CDS spreads: Obtain the traded value for a sovereign Credit Default Swap (CDS) for the emerging government. q Default spread = Sovereign CDS spread (with perhaps an adjustment for CDS market frictions). q Sovereign-rating based spread: For countries which don’t issue dollar denominated bonds or have a CDS spread, you have to use the average spread for other countries with the same sovereign rating. © All Slides | Aswath Damodaran APPROACH 1: DEFAULT SPREAD FROM GOVERNMENT BONDS Country $ Bond Rate Risk-free Rate Default Spread $ Bonds Peru 5.36% 3.88% 1.48% Brazil 5.75% 3.88% 1.87% Colombia 5.25% 3.88% 1.37% Poland 4.39% 3.88% 0.51% Turkey 7.10% 3.88% 3.22% Mexico 4.75% 3.88% 0.87% Russia 11.55% 3.88% 7.67% Euro Bonds Bulgaria 3.50% 2.03% 1.47% © All Slides | Aswath Damodaran  APPROACH 2: CDS SPREADS – JANUARY 2024 9 © All Slides | Aswath Damodaran  APPROACH 3: TYPICAL DEFAULT SPREADS: JANUARY 2024 10 S&P Sovereign Rating Moody's Sovereign Rating Default Spread AAA Aaa 0.00% AA+ Aa1 0.44% AA Aa2 0.54% AA- Aa3 0.65% A+ A1 0.77% A A2 0.92% A- A3 1.31% BBB+ Baa1 1.74% BBB Baa2 2.07% BBB- Baa3 2.39% BB+ Ba1 2.73% BB Ba2 3.28% BB Ba3 3.92% B+ B1 4.90% B B2 5.99% B- B3 7.08% CCC+ Caa1 8.17% CCC Caa2 9.81% CCC- Caa3 10.90% CC+ Ca1 12.25% CC Ca2 14.00% CC- Ca3 15.00% C+ C1 15.75% C C2 16.75% C- C3 18.00% © All Slides | Aswath Damodaran  GETTING TO A RISK-FREE RATE IN BRAZILIAN REALS ON JANUARY 1, 2024 11 q The Brazilian government bond rate in nominal reais on January 1, 2024, was 10.35%. To get to a riskfree rate in nominal reais, we can use one of three approaches. q Approach 1: Government Bond spread q Default Spread = Brazil $ Bond Rate – US T.Bond Rate = 5.75% - 3.88% = 1.87% q Risk-free rate in $R = 10.35% - 1.87% = 8.48% q Approach 2: The CDS Spread q The CDS spread for Brazil, adjusted for the US CDS spread was 1.81%. q Riskfree rate in $R = 10.35% - 1.81% = 8.54% q Approach 3: The Rating based spread q Brazil has a Ba2 local currency rating from Moody’s. The default spread for that rating is 3.28% q Riskfree rate in $R = 10.35% - 3.28% = 7.07% © All Slides | Aswath Damodaran  TEST 4: A REAL RISK-FREE RATE 12 q In some cases, you may want a riskfree rate in real terms (in real terms) rather than nominal terms. q To get a real riskfree rate, you would like a security with no default risk and a guaranteed real return. Treasury indexed securities offer this combination. q In January 2024, the yield on a 10-year indexed treasury bond was 1.80%. Which of the following statements would you subscribe to? a. This (1.80%) is the real riskfree rate to use, if you are valuing US companies in real terms. b. This (1.80%) is the real riskfree rate to use, anywhere in the world q Explain. © All Slides | Aswath Damodaran  WHY DO RISK FREE-RATES VARY ACROSS CURRENCIES? 13 © All Slides | Aswath Damodaran OR ACROSS TIME… © All Slides | Aswath Damodaran RISK-FREE RATE: DON’T HAVE OR DON’T TRUST THE GOVERNMENT BOND RATE? q You can scale up the risk-free rate in a base currency ($, Euros) by the differential inflation between the base currency and the currency in question. In US $: /1 + 012*3-*4 56(7,-%86%&'()*+ ,-''(+./9 Risk-free rateCurrency= (1 + $%&'()** ),-*!" $) (1 + 012*3-*4 56(7,-%86!" $) −1 q Thus, if the US $ risk free rate is 2.00%, the inflation rate in Egyptian pounds is 15% and the inflation rate in US $ is 1.5%, the foreign currency risk free rate is as follows: ( "."$ ) Risk-free rate = (1.02) (".&"$) − 1 = 15.57% © All Slides | Aswath Damodaran  ONE MORE TEST ON RISKFREE RATES… 16 q On January 1, 2022, the 10-year treasury bond rate in the United States was 1.51%, low by historic standards. Assume that you are valuing a company in US dollars then but are wary about the riskfree rate being too low. Which of the following should you do? a. Replace the current 10-year bond rate with a more reasonable normalized risk-free rate (the average 10-year bond rate over the last 30 years has been about 5-6%) b. Use the current 10-year bond rate as your risk-free rate but make sure that your other assumptions (about growth and inflation) are consistent with the risk-free rate. c. Something else… © All Slides | Aswath Damodaran  SOME PERSPECTIVE ON RISK FREE RATES 17 © All Slides | Aswath Damodaran NEGATIVE INTEREST RATES? q In 2022, there were at least three currencies (Swiss Franc, Japanese Yen, Euro) with negative interest rates. Using the fundamentals (inflation and real growth) approach, how would you explain negative interest rates? q How negative can rates get? (Is there a bound?) q Would you use these negative interest rates as risk free rates? q If no, why not and what would you do instead? q If yes, what else would you have to do in your valuation to be internally consistent? © All Slides | Aswath Damodaran THE EQUITY RISK PREMIUM © All Slides | Aswath Damodaran  THE UBIQUITOUS HISTORICAL RISK PREMIUM 20 q The historical premium is the premium that stocks have historically earned over riskless securities. q While the users of historical risk premiums act as if it is a fact (rather than an estimate), it is sensitive to q How far back you go in history… q Whether you use T.bill rates or T.Bond rates q Whether you use geometric or arithmetic averages. q For instance, looking at the US: © All Slides | Aswath Damodaran  THE PERILS OF TRUSTING THE PAST……. 21 q 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 90 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%/√90 = 2.1% q 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. © All Slides | Aswath Damodaran  THE COUNTRY DEFAULT SPREAD 22 q Default 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: q The default spread on a dollar denominated bond issued by the country. (In January 2024, that spread was % for the Brazilian $ bond) was 1.817%. q The sovereign CDS spread for the country. In January 2024, the ten- year CDS spread for Brazil, adjusted for the US CDS, was 1.81%. q The default spread based on the local currency rating for the country. Brazil’s sovereign local currency rating is Ba2 and the default spread for a Ba2 rated sovereign was about 3.28% in January 2024. q 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 4.60%. q Country Risk Premium for Brazil = 3.28% q Total ERP for Brazil = 4.60% + 3.28% = 7.88% © All Slides | Aswath Damodaran  AN EQUITY VOLATILITY BASED APPROACH TO ESTIMATING THE COUNTRY TOTAL ERP 23 q This 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: q Total equity risk premium = Risk PremiumUS* sCountry Equity / sUS Equity q The country equity risk premium is based upon the volatility of the market in question relative to U.S market. q Assume that the equity risk premium for the US is 5.94%. q Assume that the standard deviation in the Bovespa (Brazilian equity) is 30% and that the standard deviation for the S&P 500 (US equity) is 18%. q Total Equity Risk Premium for Brazil = 4.60% (30%/18%) =7.67% q Country equity risk premium for Brazil = 7.67% - 4.60% = 3.07% © All Slides | Aswath Damodaran  A MELDED APPROACH TO ESTIMATING THE ADDITIONAL COUNTRY RISK PREMIUM 24 q 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. q 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 2024, you would get: q Country Equity risk premium = Default spread on country bond* sCountry Equity / sCountry Bond q Standard Deviation in Bovespa (Equity) = 30% q Standard Deviation in Brazil government bond = 20% q Default spread for Brazil= 3.28% q Brazil Country Risk Premium = 3.28% (30%/20%) = 4.92% q Brazil Total ERP = Mature Market Premium + CRP = 4.60% + 4.92% = 9.52% © All Slides | Aswath Damodaran A TEMPLATE FOR ESTIMATING THE ERP © All Slides | Aswath Damodaran ERP : Jan 2024 Blue: Moody’s Rating Red: Added Country Risk © All Slides | Aswath Damodaran Green #: Total ERP  FROM COUNTRY EQUITY RISK PREMIUMS TO CORPORATE EQUITY RISK PREMIUMS 27 q Approach 1: Assume that every company in the country is equally exposed to country risk. In this case, q E(Return) = Riskfree Rate + CRP + Beta (Mature ERP) q Approach 2: Assume that a company’s exposure to country risk is similar to its exposure to other market risk. q E(Return) = Riskfree Rate + Beta (Mature ERP+ CRP) q 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) q E(Return)=Riskfree Rate+ b (Mature ERP) + l (CRP) Mature ERP = Mature market Equity Risk Premium CRP = Additional country risk premium © All Slides | Aswath Damodaran  ESTIMATING COUNTRY RISK PREMIUM EXPOSURE 28 © All Slides | Aswath Damodaran  OPERATION BASED CRP: SINGLE VERSUS MULTIPLE EMERGING MARKETS 29 q Single 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 Brazil’s CRP was 7.89%. q Multiple emerging markets: Ambev, the Brazilian-based beverage company, reported revenues from the following countries during 2011. © All Slides | Aswath Damodaran  EXTENDING TO A MULTINATIONAL: REGIONAL BREAKDOWN 30 q Coca Cola’s revenue breakdown and ERP in 2012 q Things to watch out for q Aggregation across regions. For instance, the Pacific region often includes Australia & NZ with Asia q Obscure aggregations including Eurasia and Oceania © All Slides | Aswath Damodaran  TWO PROBLEMS WITH THESE APPROACHES.. 31 q 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. q 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. © All Slides | Aswath Damodaran  A PRODUCTION-BASED ERP: ROYAL DUTCH SHELL IN 2015 Country Oil & Gas Production % of Total ERP Denmark 17396 3.83% 6.20% Italy 11179 2.46% 9.14% Norway 14337 3.16% 6.20% UK 20762 4.57% 6.81% Rest of Europe 874 0.19% 7.40% Brunei 823 0.18% 9.04% Iraq 20009 4.40% 11.37% Malaysia 22980 5.06% 8.05% Oman 78404 17.26% 7.29% Russia 22016 4.85% 10.06% Rest of Asia & ME 24480 5.39% 7.74% Oceania 7858 1.73% 6.20% Gabon 12472 2.75% 11.76% Nigeria 67832 14.93% 11.76% Rest of Africa 6159 1.36% 12.17% USA 104263 22.95% 6.20% Canada 8599 1.89% 6.20% Brazil 13307 2.93% 9.60% Rest of Latin America 576 0.13% 10.78% Royal Dutch Shell 454326 100.00% 8.26% © All Slides | Aswath Damodaran  ESTIMATE A LAMBDA FOR COUNTRY RISK 33 q Country risk exposure is affected by where you get your revenues and where your production happens, but there are a host of other variables that also affect this exposure, including: q Use of risk management products: Companies can use both options/futures markets and insurance to hedge some or a significant portion of country risk. q 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. q It is conceivable that there is a richer measure of country risk that incorporates all of the variables that drive country risk in one measure. That way my rationale when I devised “lambda” as my measure of country risk exposure. © All Slides | Aswath Damodaran A REVENUE-BASED LAMBDA q The 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 firm q Consider 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% = 1.14 l TCS= 7.62%/80% = 0.09 q There are two implications q A company’s risk exposure is determined by where it does business and not by where it is incorporated. q Firms might be able to actively manage their country risk exposures © All Slides | Aswath Damodaran  A PRICE/RETURN BASED LAMBDA 35 ReturnEmbraer = 0.0195 + 0.2681 ReturnC Bond ReturnEmbratel = -0.0308 + 2.0030 ReturnC Bond Embraer versus C Bond: 2000-2003 Embratel versus C Bond: 2000-2003 40 100 80 20 60 40 Return on Embrat el Return on Embraer 0 20 0 -20 -20 -40 -40 -60 -60 -80 -30 -20 -10 0 10 20 -30 -20 -10 0 10 20 Return on C-Bond Return on C-Bond © All Slides | Aswath Damodaran  ESTIMATING A US DOLLAR COST OF EQUITY FOR EMBRAER - SEPTEMBER 2004 36 q Assume 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%. Assume that Embraer gets 3% of its revenues in Brazil & the rest in the US. q There are five estimates of $ cost of equity for Embraer: q Approach 1: Constant exposure to CRP, Location CRP q E(Return) = 4% + 1.07 (5%) + 7.89% = 17.24% q Approach 2: Constant exposure to CRP, Operation CRP q E(Return) = 4% + 1.07 (5%) + (0.03*7.89% +0.97*0%)= 9.59% q Approach 3: Beta exposure to CRP, Location CRP q E(Return) = 4% + 1.07 (5% + 7.89%)= 17.79% q Approach 4: Beta exposure to CRP, Operation CRP q E(Return) = 4% + 1.07 (5% +( 0.03*7.89%+0.97*0%)) = 9.60% q Approach 5: Lambda exposure to CRP q E(Return) = 4% + 1.07 (5%) + 0.27(7.89%) = 11.48% © All Slides | Aswath Damodaran  VALUING EMERGING MARKET COMPANIES WITH SIGNIFICANT EXPOSURE IN DEVELOPED MARKETS 37 q The 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. q 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? a. Emerging market companies with substantial exposure in developed markets will be significantly over valued by analysts b. Emerging market companies with substantial exposure in developed markets will be significantly under valued by analysts q 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? © All Slides | Aswath Damodaran  IMPLIED EQUITY PREMIUMS 38 q For a start: 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 your expected return. q Stock Price & Risk: 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. q Implied ERP: 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). © All Slides | Aswath Damodaran  EQUITY RISK PREMIUM: JANUARY 2020 39 © All Slides | Aswath Damodaran AND IN 2020...COVID EFFECTS © All Slides | Aswath Damodaran AN UPDATED ESTIMATE: ERP IN 2024 © All Slides | Aswath Damodaran IMPLIED PREMIUMS IN THE US: 1960-2023 © All Slides | Aswath Damodaran  IMPLIED PREMIUM VERSUS RISK FREE RATE 43 © All Slides | Aswath Damodaran  EQUITY RISK PREMIUMS AND BOND DEFAULT SPREADS 44 © All Slides | Aswath Damodaran  EQUITY RISK PREMIUMS AND CAP RATES (REAL ESTATE) 45 © All Slides | Aswath Damodaran  WHY IMPLIED PREMIUMS MATTER? 46 q 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. q If all analysts in a group used the arithmetic average premium (for stocks over T.Bills) for 1928-2023 of 8.32% to value stocks in January 2022, given the implied premium of 4.60%, what are they likely to find? a. The values they obtain will be too low (most stocks will look overvalued) b. The values they obtain will be too high (most stocks will look under valued) c. There should be no systematic bias as long as they use the same premium to value all stocks. © All Slides | Aswath Damodaran  WHICH EQUITY RISK PREMIUM SHOULD YOU USE? 47 If you assume this Premium to use Premiums revert back to historical Historical risk premium norms and your time period yields these norms Market is correct in the aggregate or Current implied equity risk premium that your valuation should be market neutral Marker makes mistakes even in the Average implied equity risk premium aggregate but is correct over time over time. Predictor Correlation with implied Correlation with actual Correlation with actual premium next year return- next 5 years return – next 10 years Current implied premium 0.763 0.427 0.500 Average implied premium: Last 0.718 0.326 0.450 5 years Historical Premium -0.497 -0.437 -0.454 Default Spread based premium 0.047 0.143 0.160 © All Slides | Aswath Damodaran  AN ERP FOR THE SENSEX 48 q Inputs for the computation q Sensex on 9/5/07 = 15446 q Dividend yield on index = 3.05% q Expected growth rate - next 5 years = 14% q Growth rate beyond year 5 = 6.76% (set equal to risk-free rate) q Solving for the expected return: 537.06 612.25 697.86 795.67 907.07 907.07(1.0676) 15446 = + + + + + (1+ r) (1+ r) 2 (1+ r) 3 (1+ r) 4 (1+ r) 5 (r −.0676)(1+ r) 5 q Expected return on stocks = 11.18% € q Implied equity risk premium for India = 11.18% - 6.76% = 4.42% © All Slides | Aswath Damodaran  THE EVOLUTION OF EMERGING MARKET RISK 49 © All Slides | Aswath Damodaran RELATIVE RISK MEASURES © All Slides | Aswath Damodaran  THE CAPM BETA: THE MOST USED (AND MISUSED) RISK MEASURE 51 q 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. q The slope of the regression corresponds to the beta of the stock, and measures the riskiness of the stock. q This beta has three problems: q It has high standard error q It reflects the firm’s business mix over the period of the regression, not the current mix q It reflects the firm’s average financial leverage over the period rather than the current leverage. © All Slides | Aswath Damodaran  UNRELIABLE, WHEN IT LOOKS BAD.. 52 © All Slides | Aswath Damodaran  OR WHEN IT LOOKS GOOD.. 53 © All Slides | Aswath Damodaran  ONE SLICE OF HISTORY.. 54 During 2019 and 2020, GME was an extraordinarily volatile stock, as short sellers and long only investors fought out a battle. © All Slides | Aswath Damodaran  AND SUBJECT TO GAME PLAYING 55 © All Slides | Aswath Damodaran MEASURING RELATIVE RISK: YOU DON’T LIKE BETAS OR MODERN PORTFOLIO THEORY? NO PROBLEM. © All Slides | Aswath Damodaran DON’T LIKE THE DIVERSIFIED INVESTOR FOCUS, BUT OKAY WITH PRICE-BASED MEASURES q Relative Standard Deviation a. Relative Volatility = Std dev of Stock/ Average Std dev across all stocks b. Captures all risk, rather than just market risk q Proxy Models a. Look at historical returns on all stocks and look for variables that explain differences in returns. b. You are, in effect, running multiple regressions with returns on individual stocks as the dependent variable and fundamentals about these stocks as independent variables. c. This approach started with market cap (the small cap effect) and over the last two decades has added other variables (momentum, liquidity etc.) q CAPM Plus Models a. Start with the traditional CAPM (Rf + Beta (ERP)) and then add other premiums for proxies. © All Slides | Aswath Damodaran  DON’T LIKE THE PRICE-BASED APPROACH.. 58 q Accounting risk measures: To the extent that you don’t trust market- priced based measures of risk, you could compute relative risk measures based on a. Accounting earnings volatility: Compute an accounting beta or relative volatility b. Balance 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) q Qualitative Risk Models: In these models, risk assessments are based at least partially on qualitative factors (quality of management). q Debt based measures: You can estimate a cost of equity, based upon an observable costs of debt for the company. a. Cost of equity = Cost of debt * Scaling factor b. The scaling factor can be computed from implied volatilities. © All Slides | Aswath Damodaran  DETERMINANTS OF BETAS & RELATIVE RISK 59 Beta of Equity (Levered Beta) Beta of Firm (Unlevered Beta) Financial Leverage: Other things remaining equal, the greater the proportion of capital that a firm raises from debt,the higher its Nature of product or Operating Leverage (Fixed equity beta will be service offered by Costs as percent of total company: costs): Other things remaining equal, Other things remaining equal the more discretionary the the greater the proportion of Implciations product or service, the higher the costs that are fixed, the Highly levered firms should have highe betas the beta. higher the beta of the than firms with less debt. company. Equity Beta (Levered beta) = Unlev Beta (1 + (1- t) (Debt/Equity Ratio)) Implications Implications 1. Cyclical companies should 1. Firms with high infrastructure have higher betas than non- needs and rigid cost structures cyclical companies. should have higher betas than 2. Luxury goods firms should firms with flexible cost structures. have higher betas than basic 2. Smaller firms should have higher goods. betas than larger firms. 3. High priced goods/service 3. Young firms should have higher firms should have higher betas betas than more mature firms. than low prices goods/services firms. 4. Growth firms should have higher betas. © All Slides | Aswath Damodaran  IN A PERFECT WORLD… WE WOULD ESTIMATE THE BETA OF A FIRM BY DOING THE FOLLOWING 60 Start with the beta of the business that the firm is in Adjust the business beta for the operating leverage of the firm to arrive at the unlevered beta for the firm. Use the financial leverage of the firm to estimate the equity beta for the firm Levered Beta = Unlevered Beta ( 1 + (1- tax rate) (Debt/Equity)) © All Slides | Aswath Damodaran  ADJUSTING FOR OPERATING LEVERAGE… 61 q Within 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)) q The biggest problem with doing this is informational. It is difficult to get information on fixed and variable costs for individual firms. q 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. © All Slides | Aswath Damodaran  ADJUSTING FOR FINANCIAL LEVERAGE… 62 q Conventional 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 ratio q bL = bu (1+ ((1-t)D/E)) q In some versions, the tax effect is ignored and there is no (1-t) in the equation. q Debt Adjusted Approach: If beta carries market risk and you can estimate the beta of debt, you can estimate the levered beta as follows: q bL = bu (1+ ((1-t)D/E)) - bdebt (1-t) (D/E) q While the latter is more realistic, estimating betas for debt can be difficult to do. © All Slides | Aswath Damodaran  BOTTOM-UP BETAS 63 Step 1: Find the business or businesses that your firm operates in. Possible Refinements Step 2: Find publicly traded firms in each of these businesses and obtain their regression betas. Compute the simple average across these regression betas to arrive at an average beta for these publicly If you can, adjust this beta for differences traded firms. Unlever this average beta using the average debt to between your firm and the comparable equity ratio across the publicly traded firms in the sample. firms on operating leverage and product Unlevered beta for business = Average beta across publicly traded characteristics. firms/ (1 + (1- t) (Average D/E ratio across firms)) While revenues or operating income Step 3: Estimate how much value your firm derives from each of are often used as weights, it is better the different businesses it is in. to try to estimate the value of each business. Step 4: Compute a weighted average of the unlevered betas of the If you expect the business mix of your different businesses (from step 2) using the weights from step 3. firm to change over time, you can Bottom-up Unlevered beta for your firm = Weighted average of the change the weights on a year-to-year unlevered betas of the individual business basis. If you expect your debt to equity ratio to Step 5: Compute a levered beta (equity beta) for your firm, using change over time, the levered beta will the market debt to equity ratio for your firm. change over time. Levered bottom-up beta = Unlevered beta (1+ (1-t) (Debt/Equity)) © All Slides | Aswath Damodaran  WHY BOTTOM-UP BETAS? 64 q Less Noisy: 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: Average Std Error across Betas Std error of bottom-up beta = Number of firms in sample q Updated: The bottom-up beta can be adjusted to reflect changes in the firm’s business mix and financial leverage. Regression betas reflect the past. € q Don’t need prices: 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. © All Slides | Aswath Damodaran ESTIMATING BOTTOM UP BETAS & COSTS OF EQUITY: VALE Sample' Unlevered'beta' Peer'Group' Value'of' Proportion'of' Business' Sample' size' of'business' Revenues' EV/Sales' Business' Vale' Global'firms'in'metals'&' Metals'&' mining,'Market'cap>$1' Mining' billion' 48' 0.86' $9,013' 1.97' $17,739' 16.65%' Iron'Ore' Global'firms'in'iron'ore' 78' 0.83' $32,717' 2.48' $81,188' 76.20%' Global'specialty' Fertilizers' chemical'firms' 693' 0.99' $3,777' 1.52' $5,741' 5.39%' Global'transportation' Logistics' firms' 223' 0.75' $1,644' 1.14' $1,874' 1.76%' Vale' Operations' '' '' 0.8440' $47,151' '' $106,543' 100.00%' © All Slides | Aswath Damodaran  EMBRAER’S BOTTOM-UP BETA 66 Business Unlevered Beta D/E Ratio Levered beta Aerospace 0.95 18.95% 1.07 q Levered Beta = Unlevered Beta ( 1 + (1- tax rate) (D/E Ratio) = 0.95 ( 1 + (1-.34) (.1895)) = 1.07 q Can an unlevered beta estimated using U.S. and European aerospace companies be used to estimate the beta for a Brazilian aerospace company? a. Yes b. No q What concerns would you have in making this assumption? © All Slides | Aswath Damodaran  GROSS DEBT VERSUS NET DEBT APPROACHES 67 q Analysts 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. q For Embraer, using the gross debt ratio q Gross D/E Ratio for Embraer = 1953/11,042 = 18.95% q Levered Beta using Gross Debt ratio = 1.07 q Using the net debt ratio, we get q Net Debt Ratio for Embraer = (Debt - Cash)/ Market value of Equity = (1953-2320)/ 11,042 = -3.32% q Levered Beta using Net Debt Ratio = 0.95 (1 + (1-.34) (-.0332)) = 0.93 q 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 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. © All Slides | Aswath Damodaran  THE COST OF EQUITY: A RECAP 68 Preferably, a bottom-up beta, based upon other firms in the business, and firmʼs own financial leverage Cost of Equity = Riskfree Rate + Beta * (Risk Premium) Has to be in the same Historical Premium Implied Premium currency as cash flows, 1. Mature Equity Market Premium: Based on how equity and defined in same terms Average premium earned by or market is priced today (real or nominal) as the stocks over T.Bonds in U.S. and a simple valuation cash flows 2. Country risk premium = model Country Default Spread* ( σEquity/σCountry bond) © All Slides | Aswath Damodaran COST OF DEBT © All Slides | Aswath Damodaran  ESTIMATING THE COST OF DEBT 70 q The 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. q The two most widely used approaches to estimating cost of debt are: q 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 traded q Looking 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 firm q When 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. © All Slides | Aswath Damodaran  ESTIMATING SYNTHETIC RATINGS 71 q 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 q For Embraer’s 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 © All Slides | Aswath Damodaran  INTEREST COVERAGE RATIOS, RATINGS AND DEFAULT SPREADS: 2004 72 If Interest Coverage Ratio is Estimated Bond Rating Default Spread(2004) > 8.50 (>12.50) AAA 0.35% 6.50 - 8.50 (9.5-12.5) AA 0.50% 5.50 - 6.50 (7.5-9.5) A+ 0.70% 4.25 - 5.50 (6-7.5) A 0.85% 3.00 - 4.25 (4.5-6) A– 1.00% 2.50 - 3.00 (4-4.5) BBB 1.50% 2.25- 2.50 (3.5-4) BB+ 2.00% 2.00 - 2.25 ((3-3.5) BB 2.50% 1.75 - 2.00 (2.5-3) B+ 3.25% 1.50 - 1.75 (2-2.5) B 4.00% 1.25 - 1.50 (1.5-2) B– 6.00% 0.80 - 1.25 (1.25-1.5) CCC 8.00% 0.65 - 0.80 (0.8-1.25) CC 10.00% 0.20 - 0.65 (0.5-0.8) C 12.00% < 0.20 (