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 + β ( R − R ) i f i m f w here E ( R ) is the ret u rn on stock i i R is the risk - free rate of ret u rn f R is the market ret u rn m − R is the eq u it y risk premi u m ( ERP ) R m f β is the sensiti v it y of stock i ' s ret u rn to the market ret u rn i EQUITY VALUATION IN R

Beta Don ' t p u t y o u r eggs in one basket Yo u sho u ld al w a y s tr y to red u ce � rm - speci � c risk In v estors are onl y compensated from taking on s y stematic risk ( a / k / a market or u ndi v ersi � able risk ) Beta is a meas u re of s y stematic risk EQUITY VALUATION IN R

Using Regression Anal y sis to Estimate Beta Beta is t y picall y estimated u sing a market model regression of the form : R = α + β × R i m (u nlike the CAPM , no risk - free rate in the market model !!!) w here α and β are coe � cients generated b y the regression R is the ret u rn on stock i i R is the market ret u rn m EQUITY VALUATION IN R

Using Regression Anal y sis to Estimate Beta The regression is t y picall y performed u sing 2 to 5 y ear estimation period Weekl y or monthl y ret u rns EQUITY VALUATION IN R

Estimating Beta # 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] EQUITY VALUATION IN R

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Unle v ering Betas E QU ITY VAL U ATION IN R Cli � Ang Senior Vice President , Compass Le x econ

Unle v ering Beta u sing the Hamada Form u la = β /(1 + (1 − T ) × D / E ) β U L c w here β is the Unle v ered Beta ( beta w itho u t e � ects of le v erage ) U β is the Le v ered or Eq u it y Beta ( beta from regression ) L T is the corporate ta x rate c D / E is the debt - to - eq u it y ratio Rele v ering Beta Using Hamada Form u la : = β × (1 + (1 − T ) × D / E ) β L U c EQUITY VALUATION IN R

Unle v ering Beta u sing Fernande z Form u la = [ β + β (1 − T ) D / E ]/[1 + (1 − T ) D / E ] β U L D c c Same v ariable de � nitions as Hamada Form u la , e x cept for the addition of β D for the debt beta . Rele v ering Beta Using Fernande z Form u la : = β + ( β − β )(1 − T ) D / E β L U U D c = 0 Hamada Form u la = Fernande z Form u la if β D EQUITY VALUATION IN R

Betas Used in Val u ation Which betas do y o u u se in the CAPM ? Use the beta obtained form regressing the stock ' s ret u rn on the market ' s ret u rn Use the rele v ered beta based on the median or a v erage peer compan y' s u nle v ered beta EQUITY VALUATION IN R

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Risk - Free Rate and Eq u it y Risk Premi u m E QU ITY VAL U ATION IN R Cli � Ang Senior Vice President , Compass Le x econ

Risk - Free Rate A risk - free sec u rit y is an asset w ith a beta of z ero ( i . e ., no s y stematic risk ) If β = 0 , then R = R + β ( R − R ) ⇒ R = R i i f i m f i f Yield on US Treas u r y sec u rities is o � en u sed as pro xy for risk - free rate Use a long - term US Treas u r y sec u rit y ( i . e ., 10, 20, or 30 y ears ) We can obtain the data from the Federal Reser v e Electronic Database or the Federal Reser v e H .15 Selected Interest Rates Database EQUITY VALUATION IN R

Eq u it y Risk Premi u m Eq u it y Risk Premi u m ( ERP ) is the e x tra ret u rn that in v estors demand for p u � ing their mone y in stocks , as pro x ied b y the S & P 500, instead of Treas u ries Mathematicall y, ERP = R − R m f The ERP can be di � erent depending on the term of the risk - free rate u sed b u t consistenc y is ke y For e x ample , if R in the CAPM is based on 10-y ear Treas u ries , then ERP sho u ld be f calc u lated u sing 10-y ear Treas u ries − R o v er a period of at least 35 y ears ERP is the a v erage ann u al R m f The t y pical range for the ERP is 5% to 8% EQUITY VALUATION IN R

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