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TRANSCRIPT
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Copyright 2011 Pearson Prentice Hall. All rights reserved.
Topic 10 (Ch12)
Estimating the Costof Capital
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Chapter Outline
12.1 The Equity Cost of Capital
12.2 The Market Portfolio
12.3 Beta Estimation
12.4 The Debt Cost of Capital
12.5 A Projects Cost of Capital
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12.1 The Equity Cost of Capital
The Capital Asset Pricing Model (CAPM) is a practical way toestimate.
Example 12.1
Suppose you estimate that Wal-Marts stock has avolatility of 16.1% and a beta of 0.20. A similar process forJohnson &Johnson yields a volatility of 13.7% and a beta of0.54. Which stock carries more total risk? Which has moremarket risk? If the risk-free interest rate is 4% and you
estimate the markets expected return to be 12%, calculatethe equity cost of capital for Wal-Mart and Johnson &Johnson. Which company has a higher cost of equitycapital?
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12.2 The Market Portfolio
Constructing the market portfolio
Value-Weighted Portfolio
A portfolio in which each security is held inproportion to its market capitalization
Market Value of
Total Market Value of All Securities
i
i
jj
MVix
MV
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Market Indexes
Report the value of a particular portfolio ofsecurities.
Examples:
S&P 500, Wilshire 5000, Dow JonesIndustrial Average (DJIA)
Index funds
Exchange-traded funds (ETFs)
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The Market Risk Premium
Determining the Risk-Free Rate
The yield on U.S. Treasury securities
10 to 30 year treasuries
The Historical Risk Premium
Estimate the risk premium (E[RMkt]-rf)
Table 12.1 Historical Excess Returns of the S&P 500 Compared to One-Year andTen-Year U.S. Treasury Securities
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The Market Risk Premium (contd)
A fundamental approach
Using historical data has two drawbacks:
One alternative is to solve for the discount rate
that is consistent with the current level of theindex.
1
0
DividendYield ExpectedDividendGrowthRateMkt
Divr g
P
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12.3 Beta Estimation
Estimating Beta from Historical Returns
Consider Cisco Systems stock and how it changes withthe market portfolio.
Figure 12.1 Monthly Returns for Cisco Stock and for the S&P 500, 1996
2009
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Figure 12.2 Scatterplot of Monthly ExcessReturns for Cisco Versus the S&P 500, 19962009
We can see that a
10% change in themarkets returncorresponds to about a20% change in Ciscosreturn.
So Ciscos beta isabout 2!
Beta corresponds to the
slope of the best-fitting line inthe plot of the securitys
excess returns versus the
market excess return.
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Using Linear Regression
Since E[i] = 0:
irepresents a risk-adjusted performance measure forthe historical returns.
Ifi is positive, the stock has performed better thanpredicted by the CAPM.
Ifiis negative, the stocks historical return is belowthe SML.
Distance above / below the SMLExpected return for from the SML
[ ] ( [ ] ) i f i Mkt f i
i
E R r E R r
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Example 12.2
Suppose the risk-free interest rate is 4%, andthe market risk premium is 6%. What range forApples equity cost of capital is consistent withthe 95% confidence interval for its beta?
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12.4 The Debt Cost of Capital
Debt Yields - Yield to maturity
Consider a one-year bond with YTM ofy. For each $1invested in the bond today, the issuer promises to pay
$(1+y) in one year.
Suppose the bond will default with probabilityp, in whichcase bond holders receive only $(1+y-L), where L is theexpected loss per $1 of debt in the event of default.
So the expected return of the bond is:
rd= (1-p)y + p(y-L) = y - pL
= Yield to Maturity Prob(default) X Expected Loss Rate
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Table 12.2 Annual Default Rates by Debt Rating (19832008)
The average loss rate for unsecured debt is 60%.
During average times the annual default rate for B-ratedbonds is 5.2%.
So the expected return to B-rated bondholders during
average times is 0.052X0.60=3.1% below the bondsquoted yield.
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12.4 The Debt Cost of Capital(contd)
Debt Betas
Alternatively, we can estimate the debt cost of capitalusing the CAPM.
One approximation is to use estimates of betas of bond
indices by rating category.
Table 12.3 Average Debt Betas by Rating and Maturity
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12.5 A Projects Cost ofCapital
Asset (unlevered) cost of capital
Expected return required by investors to hold the firmsunderlying assets.
Weighted average of the firms equity and debt costs of
capital
Asset (unlevered) beta
U E D
E Dr = r + r
E+D E+D
U E D
E D = +
E+D E+D