Topic 10- FIN Slide

8/2/2019 Topic 10- FIN Slide

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Copyright 2011 Pearson Prentice Hall. All rights reserved.

Topic 10 (Ch12)

Estimating the Costof Capital


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Copyright 2011 Pearson Prentice Hall. All rights reserved. 12-2

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

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