Equity Risk Premium Analysis for Brazil

Discount Rates

• Discount rates are crucial in valuation.
• A risk-free investment has an actual return equal to the expected return, with no variance.
• No default risk and no reinvestment risk are required for a risk-free investment.

Risk-Free Rate

• Time horizon influences risk-free rates in valuation.
• Risk-free rates differ by currency.
• Not all government securities are risk-free; some governments face default risk.

Risk-Free Rate in US Dollars

• For valuing a company in US dollars, the appropriate risk-free rate is dependent upon the cash flow timeframe.
• Options include three-month Treasury bill rate (4.42%), ten-year Treasury bond rate (3.88%), thirty-year Treasury bond rate (3.97%), and TIPS rate (1.53%).
• Implicit assumptions about US Treasury need to be considered when using treasury numbers.

Risk-Free Rate in Euros

• Graph showing government bond rates for 10-year Euro bonds across different European countries.

Risk-Free Rate in Indian Rupees

• The Indian government's 10-year Rupee bonds had a yield to maturity of ~7.18% on January 1, 2024.
• In early 2024, the typical default spread for Baa3-rated country bonds was 2.39%.
• The risk-free rate in Indian Rupees can be calculated using the yield to maturity of the 10-year bond and the default spread.

Sovereign Default Spread

• Three methods for determining sovereign default spread include analyzing sovereign dollar/Euro bonds, CDS spreads, and sovereign rating-based spread.

Approach 1: Default Spread from Government Bonds

• Tables showing default spreads for various countries using US bond rates as the risk-free rate.

Approach 2: CDS Spreads

• Tables providing CDS spreads for various countries as of January 2024.

Approach 3: Typical Default Spreads

• Tables of typical default spreads based on S&P and Moody's sovereign ratings.

Getting to a Risk-Free Rate in Brazilian Reais

• Three methods to determine the risk-free rate in Brazilian Reais for January 1, 2024 when the Brazilian government bond rate was 10.35%.

A Real Risk-Free Rate

• Sometimes, a real risk-free rate (in real terms) is preferred over a nominal risk-free rate.
• Treasury-indexed securities provide a guaranteed real return.
• A 10-year indexed Treasury bond yield of 1.80% in January 2024.

Why Do Risk-Free Rates Vary Across Currencies?

• Chart showing risk-free rate variations across different currencies (in January 2024) based on government bond rates.

US Treasuries Across Time

• Graph demonstrating US treasury changes over time (showing 3-month, 2-year, 10-year, and 30-year maturities) from February 14, 2020, to August 14, 2020.

Risk-Free Rate: Don't Have or Don't Trust the Government Bond Rate?

• Formula for deriving a risk-free rate by using the differential inflation rate.
• The formula considers inflation rates in the base currency (e.g., US dollars) and the currency of interest.

One More Test on Risk-Free Rates

• A 10-year treasury bond rate of 1.51% in January 2022.
• Options for adjusting the risk-free rate in a situation where it is considered too low.

Some Perspective on Risk-Free Rates

• Graph showing T. Bond rate, inflation rate, and Real GDP growth rate from 1954 to 2023.

Negative Interest Rates?

• Discussion regarding negative interest rates and how to handle them in valuations, as well as how low rates can go.

The Equity Risk Premium

• The historical premium is the premium that stocks have earned over risk-free securities.
• The historical equity risk premiums, are sensitive to timeframe.
• Different measures of risk premiums (arithmetic or geometric averages) can be used.
• Historical Premiums are noisy and subject to survivorship bias.

The Country Default Spread

• Calculation methods for country equity risk premium based on dollar-based bonds, sovereign CDS spreads and country rating-based spreads.
• Approach to add a country risk premium to a market premium.

An Equity Volatility-Based Approach to Estimating the Total ERP

• Estimate the total equity risk premium based on volatility.
• Calculation using the volatility of the US market as the base and the emerging market in question.

A Melded Approach Estimating Country Risk Premium

• Combining country ratings and volatility.
• A formula and example for the approach.

A Template for Estimating the ERP

• Procedures to estimate ERP.
• Check sovereign rating.
• Determine if there is no risk score.

ERP: January 2024

• Table presenting country ratings, calculated country risk premiums, and corresponding equity risk premiums for January 2024.

From Country Equity Risk Premiums to Corporate Equity Risk Premiums

• Three distinct approaches to determining the appropriate corporate equity risk premiums according to country risk exposures.

Estimating Country Risk Premium Exposure

• Chart showing the interaction between a company’s country of incorporation and its operations across different countries to estimate the country risk premium
• A formula for determining the overall risk, taking country and operation factors into consideration.

Operation Based CRP: Single Versus Multiple Emerging Markets

• Examples demonstrating the computation of country risk premium based on operation factors for companies like Embraer and Ambev.

Extending to a Multinational: Regional Breakdown

• Breakdown of Coca-Cola’s revenue by region and corresponding ERP in 2012.
• Highlights of considerations for international business operations.

Two Problems with These Approaches

• Cautionary note regarding solely relying on revenue figures for determining risk exposures.
• A note regarding issues with beta-based approaches in assessing country-specific risk premium exposure.

A Production-Based ERP: Royal Dutch Shell in 2015

• Detailed breakdown of Royal Dutch Shell’s oil and gas production by country for 2015, indicating the percentage of total production and ERP for each country.

Estimate a Lambda for Country Risk

• Considerations for estimating lambda to assess the impact of country risk on a company’s operations.
• Discusses informational components in the country credit risk estimate.

A Revenue-Based Lambda

• Computation of lambda using the percentage of domestic revenues relative to the average firm in the same sector.
• Firm-specific operational analysis to determine a company’s relative country risk exposure component.

A Price/Return Based Lambda

• Charts demonstrating the correlations between realized returns of Embraer stocks, and those of comparable publicly traded companies, providing a price/return based method for determining a lambda.

Estimating a US Dollar Cost of Equity for Embraer - September 2004

• Five different approaches to estimate the cost of equity for Embraer in September 2004.
• These approaches account for factors like beta, location risk premium, operational risk premium.

Valuing Emerging Market Companies with Significant Exposure in Developed Markets

• A conventional practice in investment banking for estimating cost of equity for emerging markets is assessing exposure to country risk.
• Consequences of overlooking emerging market exposures are explored.
• Opportunity to generate profit from such misvaluation is discussed.

Implied Equity Premiums

• Explaining how to calculate implied equity premiums using stock price and expected cash flows.

Equity Risk Premium: January 2020

• Step-by-step calculation for implied equity premium based on actual cash flows and expected growth.

And In 2020…COVID Effects

• Graph illustrating the impact of the COVID-19 pandemic on the implied equity risk premium of the S&P 500 during 2019-2020.

An Updated Estimate: ERP in 2024

• Calculation of implied equity risk premium (ERP) for 2024, providing details on expected earnings/cash flow growth over 5 years.

Implied Premiums in the US: 1960-2023

• Implied equity risk premium for the US equity market from 1960-2023.

Implied Premium Versus Risk-Free Rate

• Graph comparing implied ERP and risk-free rate for the years 1960-2023.

Equity Risk Premiums and Bond Default Spreads

• Graph depicting the interplay between equity risk premiums and bond default spreads since 1960.

Equity Risk Premiums and Cap Rates (Real Estate)

• Graph showcasing equity risk premiums, bond spreads, and real estate risk premiums from 1980 to 2023.

Why Implied Premiums Matter?

• Importance of implied premiums, especially in corporate finance departments and for valuing stocks.
• Illustrative examples showcasing consequences of using incorrect premiums while evaluating stocks.

Which Equity Risk Premium Should You Use?

• Table summarizing correlations between various predictors of implied equity risk premium & actual stock returns.

An ERP for the Sensex

• Procedure for calculating the ERP based on market parameters, particularly the Sensex index.

The Evolution of Emerging Market Risk

• Comprehensive table highlighting the evolution of emerging market risk factors from 2004 to 2023, showing various metrics like PBV, PBV/ROE, US T-bond rate, Growth, Cost of Equity, etc. for developed and emerging markets.

Relative Risk Measures

• Discussion regarding relative risk measures.

The CAPM Beta: The Most Used (And Misused) Risk Measure

• Procedures and limitations in the commonly used market regression approach for estimating beta.

Unreliable, When It Looks Bad..

• Illustration of a method where beta estimates are inaccurate.

Or When It Looks Good..

• Graphs demonstrating a more accurate risk estimation methodology.

One Slice of History…

• Detailed information on the volatility of GME stock throughout 2019-2020, highlighting an exceptionally volatile stock from the period.

And Subject to Game Playing

• Graphs presenting a summary of data points for a firm (Bombardier Inc.) and an associated index (S&P 500 index).

Measuring Relative Risk: You Don't Like Betas or Modern Portfolio Theory? No Problem.

• Provides various approaches to estimating the relative risk of stocks in addition to the standard beta and their advantages.

Don't Like the Price-Based Approach…

• Detailed analysis on various methods for calculating relative risk other than using market prices.

Determinants of Betas & Relative Risk

• Factors determining equity beta, such as the nature of a company's products, operating, and financial leverage.

In a Perfect World... We Would Estimate the Beta of a Firm by Doing the Following

• Step-by-step outline of the process to determine accurate beta for companies in an ideal scenario.

Adjusting for Operating Leverage...

• Explanation of how to adjust for operating leverage when calculating beta, and the potential issues with securing appropriate data.

Adjusting for Financial Leverage...

• Different methods for adjusting equity beta based on the financial leverage (debt-equity ratio) of the firm and a consideration of the tax benefits of debt.

Bottom-Up Betas

• Step-by-step process for deriving bottom-up betas.

Why Bottom-Up Betas?

• Demonstrating the advantages of bottom-up betas, such as reduced standard error, ability to incorporate more current data, and overcoming reliance on historical price data.

Estimating Bottom Up Betas & Costs of Equity

• Tables containing data points pertaining to the bottom-up method for deriving betas across various businesses.

Embraer's Bottom-Up Beta

• Calculation details for Embraer's beta as derived by the bottom-up method.

Gross Debt Versus Net Debt Approaches

• Comparison of using gross debt to net debt in calculating debt ratios, and the consequence on cost of equity.

The Cost of Equity: A Recap

• Summary of the different methods for calculating a company's cost of equity.

Cost of Debt

• Explanation of how to calculate the cost of debt for a company.

Estimating Synthetic Ratings

• Simple methods for estimating synthetic ratings based on interest coverage ratios.

Interest Coverage Ratios, Ratings and Default Spreads: 2004

• Table displaying interest coverage ratios, corresponding ratings for corporate bonds, and calculated default spreads for 2004.

Cost of Debt Computations

• Example computation of the cost of debt for Embraer in 2004.
• Description of how to estimate the cost of equity and debt for a firm.

If You Had To Do It…Converting a Dollar Cost of Capital to a Nominal Real Cost of Capital

• Two different approaches to convert a dollar-based cost of capital to a nominal real cost of capital.

Dealing with Hybrids and Preferred Stock

• Explanation on how to treat hybrid securities (like convertible bonds) and preferred stock when evaluating a company's cost of capital.

Decomposing a Convertible Bond...

• Step-by-step demonstration of how to analyze a convertible bond by separating it into its components of debt and equity.

Recaping the Cost of Capital

• Summary of important elements to consider in determining the cost of capital for a firm.