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  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 $R = 10.35% - 3.28% = 7.07% © All Slides | Aswath Damodaran  WHY DO RISK FREE-RATES VARY ACROSS CURRENCIES? 13 © All Slides | Aswath Damodaran OR ACROSS TIME… © All Slides | Aswath Damodaran RISK-FREE RATE: DON’T HAVE OR DON’T TRUST THE GOVERNMENT BOND RATE? q You can scale up the risk-free rate in a base currency ($, 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  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