What is a disco u nt rate ? E QU ITY VAL U ATION IN R Cli Ang - - PowerPoint PPT Presentation
What is a disco u nt rate ? E QU ITY VAL U ATION IN R Cli Ang Senior Vice President , Compass Le x econ Capital Asset Pricing Model ( CAPM ) Mathematicall y, the CAPM is as follo w s : E ( R ) = R + ( R R ) i f i m f w here E ( R
E QU ITY VAL U ATION IN R
Cli Ang
Senior Vice President, Compass Lexecon
EQUITY VALUATION IN R
Mathematically, the CAPM is as follows:
E(R ) = R + β (R − R )
where
E(R ) is the return on stock i R is the risk-free rate of return R is the market return R − R is the equity risk premium (ERP) β is the sensitivity of stock i's return to the market return
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EQUITY VALUATION IN R
Don't put your eggs in one basket You should always try to reduce rm-specic risk Investors are only compensated from taking on systematic risk (a/k/a market or undiversiable risk) Beta is a measure of systematic risk
EQUITY VALUATION IN R
Beta is typically estimated using a market model regression of the form:
R = α + β × R
(unlike the CAPM, no risk-free rate in the market model!!!) where
α and β are coecients generated by the regression R is the return on stock i R is the market return
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EQUITY VALUATION IN R
The regression is typically performed using 2 to 5 year estimation period Weekly or monthly returns
EQUITY VALUATION IN R
# Calculate stock return rets <- Delt(prices$firm_ret) # Calculate market return rets$spy <- Delt(prices$spy) # Rename first variable names(rets)[1] <- "firm_ret" # Remove first observation - NA rets <- rets[-1, ] # Run regression reg <- lm(myl ~ spy, data = rets) # Extract beta beta <- summary(reg)$coeff[2]
E QU ITY VAL U ATION IN R
E QU ITY VAL U ATION IN R
Cli Ang
Senior Vice President, Compass Lexecon
EQUITY VALUATION IN R
β = β /(1 + (1 − T ) × D/E)
where
β is the Unlevered Beta (beta without eects of leverage) β is the Levered or Equity Beta (beta from regression) T is the corporate tax rate D/E is the debt-to-equity ratio
Relevering Beta Using Hamada Formula:
β = β × (1 + (1 − T ) × D/E)
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EQUITY VALUATION IN R
β = [β + β (1 − T )D/E]/[1 + (1 − T )D/E]
Same variable denitions as Hamada Formula, except for the addition of β for the debt beta. Relevering Beta Using Fernandez Formula:
β = β + (β − β )(1 − T )D/E
Hamada Formula = Fernandez Formula if β
= 0
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EQUITY VALUATION IN R
Which betas do you use in the CAPM? Use the beta obtained form regressing the stock's return on the market's return Use the relevered beta based on the median or average peer company's unlevered beta
E QU ITY VAL U ATION IN R
E QU ITY VAL U ATION IN R
Cli Ang
Senior Vice President, Compass Lexecon
EQUITY VALUATION IN R
A risk-free security is an asset with a beta of zero (i.e., no systematic risk) If β = 0, then R = R + β (R
− R ) ⇒ R = R
Yield on US Treasury securities is oen used as proxy for risk-free rate Use a long-term US Treasury security (i.e., 10, 20, or 30 years) We can obtain the data from the Federal Reserve Electronic Database or the Federal Reserve H.15 Selected Interest Rates Database
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EQUITY VALUATION IN R
Equity Risk Premium (ERP) is the extra return that investors demand for puing their money in stocks, as proxied by the S&P 500, instead of Treasuries Mathematically, ERP = R
− R
The ERP can be dierent depending on the term of the risk-free rate used but consistency is key For example, if R in the CAPM is based on 10-year Treasuries, then ERP should be calculated using 10-year Treasuries ERP is the average annual R
− R over a period of at least 35 years
The typical range for the ERP is 5% to 8%
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E QU ITY VAL U ATION IN R