chapter 11 cost of equity

8/12/2019 Chapter 11 Cost of Equity

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Chapter 11

The Opportunity Cost of Capital:

The Cost of Equity

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The Cost of Capital

To value a company using enterprise DCF, we discount free cash flow by the

weighted average cost of capital (WACC). The WACC represents theopportunity cost that investors face for investing their funds in one particular

business instead of others with similar risk.

In its simplest form, the weighted average cost of capital is the market-based

weighted average of the after-tax cost of debt and cost of equity:

To determine the weighted average cost of capital, we must calculate itsthree components: (1) the cost of equity, (2) the after-tax cost of debt, and

(3) the companys target capital structure.

emd kV

ETk

V

D )(1WACC


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Successful Implementation Requires Consistency

The most important principle underlying successful implementation

of the cost of capital is consistency between the components of

WACC and free cash flow. To ensure consistency,

It must include the opportunity costs of all investorsdebt, equity, and so on

since free cash flow is available to all investors, who expect compensation for

the risks they take.

It must weight each securitys required return by its target market-based weight,

not by its historical book value.

Any financing-related benefits or costs, such as interest tax shields, not included

in free cash flow must be incorporated into the cost of capital or valued

separately using adjusted present value.

It must be computed after corporate taxes (since free cash flow is calculated in

after-tax terms), based on the same expectations of inflation, and match the

duration of the cash flows.


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The Cost of Capital: An Example

The weighted average cost of capital at Home Depot equals 8.5 percent.

The majority of enterprise value is held by equity holders (68.5 percent),

whose CAPM-based required return equals 10.4 percent. The remaining

capital is provided by debt holders at 4.2 percent of an after-tax basis.

Lets examine the components of WACC

one by one, starting with the cost of equity

percent

After-tax Contribution to

Source of Proportion of Cost of Marginal opportunity weighted

capital total capital capital tax rate cost average

Debt 31.5 6.8 37.6 4.2 1.3

Equity 68.5 10.4 10.4 7.1

WACC 100.0 8.5

Home Depot: Weighted Average Cost of Capital


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1. The Cost of Equity

To estimate the cost of equity, we must determine the expected rate of return of the

companys stock. Since expected rates of return are unobservable, we rely on asset-pricing models that translate risk into expected return.

The three most common asset-pricing models differ primarily in how they define risk.

The capital asset pr ic ing model (CAPM)states that a stocks expected return is

driven by how sensitive its returns are to the market portfolio. This sensitivity is

measured using a term known as beta.

The Fama-French three-factor modeldefines risk as a stocks sensitivity to three

portfolios: the stock market, a portfolio based on firm size, and a portfolio based on

book-to-market ratios.

The arbi t rage pr ic in g theory (APT)is a generalized multifactor model, but

unfortunately provides no guidance on the appropriate factors that drive returns.

The CAPM is the most common method for estimating expected returns, so we begin

our analysis with that model.


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Capital Asset Pricing Model

A stocks expected return is driven by three components: the

risk-free rate, beta, and the expected market risk premium.

)][(][ fmifi RREBRRE

Expected

return

of stock i

Expected

market

risk premium

Risk-freerate

Stocksbeta

6

Estimating the Cost of Equity Using the CAPM

Data requirements Considerations

Risk-free rate Use a long-term government rate dominated

in the same currency as cash flows.

Market risk premium The market risk premium is difficult to

measure. Various models point to a risk

premium between 4.5 percent and 5.5 percent.

Company beta To estimate beta, lever the company's

industry beta to the company's target debt-to-

equity ratio.


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Risk-Free Rate: 10-Year Local Treasury

The cost of capital must be in the

same currency as the companys

financials. Thus, use a risk-free

rate posted by the local central

bank of the companys

country/region.

The cost of capital must match the

duration of the cash flows in

question. For long-term projectvaluation and company evaluation,

use no less than the 10-year rate.

7

Source: Bloomberg.

0

1

2

3

4

5

0 5 10 15 20

Yieldtomaturity(percent)

Years to maturity

German

Eurobond

zero coupon bonds

U.S.

Treasury

STRIPS

Government Zero Coupon Yields, May 2009


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2. The Market Risk Premium

Sizing the market risk premiumthe difference between the marketsexpected return and the risk-free rateis arguably the most debated

issue in finance.

Methods to estimate the market risk premium fall into three general

categories:

1. Estimating the future risk premium by measuring and extrapolating

historical returns.

2. Using regression analysis to link current market variables, such as the

aggregate dividend-to-price ratio, to project the expected market risk

premium.

3. Using DCF valuation, along with estimates of return on investment and

growth, to reverse engineer the markets cost of capital.

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Using Historical Excess Returns: Best Practices

To best measure the risk premium using historical data, you should:

Calculate the premium over long-term government bonds.

Use long-term government bonds, because they match the duration of a companys cash

flows better than do short-term rates.

Use the longest period possible.

If the market risk premium is stable, a longer history will reduce estimation error. Since no

statistically significant trend is observable, we recommend the longest period possible.

Use an arithmetic average of longer-dated intervals (such as five years).

Although the arithmetic average of annual returns is the best predictor of future one-year

returns, compounded averages will be upward biased (too high). Therefore, use longer-

dated intervals to build discount rates.

Adjust the result for econometric issues, such as survivorship bias.

Predictions based on U.S. data (a successful economy) are probably too high.


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The Market Risk Premium for Holding Stocks

Over the past 82 years, the

S&P 500 index has earned

on average a 11.1 percent

annual return.

The S&P 500 has earned

5.2 percent more than

long-term government

Treasuries (known as the

market risk premium).

10

11.1%

15.1%

5.8%

5.9%

3.6%

3.0%

Large Stocks

Small Stocks

Corporate Bonds

Government Bonds

Treasury Bills

Inflation

Average Annual Returns

19262008


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When Possible, Use Long-Dated Holding Periods

To correct for the bias caused by misestimation and/or negative autocorrelation in returns, we

have two choices. First, we can calculate multiperiod holding returns directly from the data,

rather than compound single-period averages.

Alternatively, we can use an estimator proposed by Marshall Blume, one that blends the

arithmetic and geometric averages.

Cumulative Returns for Various Intervals, 1900

2009

percent

U.S. U.S. U.S.

U.S. government excess excess Blume

Arithmetic mean of stocks bonds returns returns estimator

1-year holding periods 11.2 5.4 6.1 6.1 6.1





Source: Morningstar SBBI data, Morningstar Dimson, Marsh, Staunton Global Returns data.

Annualized returnsAverage cumulative returns


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Embedded Market Risk Premium

Using the key value driver formula, we

can reverse engineer the cost of equity.

After inflation is stripped out, the

expected market return (not excess

return) is remarkably constant in the

United States, averaging 7 percent. For

the United Kingdom, the real market

return is slightly more volatile, averaging

6 percent.

e

gNet Income 1-

ROEPrice =

k -g

To determine the market risk premium,

subtract the real interest rate from the

real cost of equity using Treasury

inflation-protected securities (TIPS).

12

0

4

8

12

16

20

1962 1972 1982 1992 2002

Real and Nominal Expected Market Returns

Implied keinreal terms

Implied keinnominal terms


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3. Estimating Beta

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According to the CAPM, a stocks

expected return is driven by beta,

which measures how much the

stock and market move together.

Since beta cannot be observed

directly, we must estimateits

value.

The most common regression

used to estimate a companys raw

beta is the market model:

mi

RaR

Based on data from 1998 to 2003,

Home Depots beta is estimated

at 1.37.

percent

-25

-20

-15

-10

-5

0

5

10

15

20

-20 -15 -10 -5 0 5 10 15 20

HomeDepotmonthlystockre

turns

Morgan Stanley Capital Index (MSCI) global monthly returns

Regression beta= 1.28

Home Depot: Stock Returns, 20012006

Even though Home Depot matched the market in aggregate losses during 2007 and 2008 (37 percent for

Home Depot versus 35 percent for the MSCI World Index), a slight difference in timing caused the two

measures to be uncorrelated. Prior to 2007, Home Depots market beta was relatively stable. For this

reason, we measure unlevered beta as of 2006.


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Beta Varies over Time

Between 1985 and 2008, IBMs

beta hovered near 0.7 in the

1980s but rose dramatically in

the mid-1990s to a peak above

1.7 before falling back down. It

now measures near 0.8.

This rise in beta occurred

during a period of great change

for IBM, as the company

moved from hardware (such as

mainframes) to services (such

as consulting).

14

0.0

0.4

0.8

1.2

1.6

2.0

1986 1991 1996 2001 2006

Marketbeta

IBM: Market Beta, 1985-2010

hardware

services


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Estimating Beta: Best Practices

As can be seen on the previous slide, estimating beta is a noisy process. Based on

certain market characteristics and a variety of empirical tests, we reach several

conclusions about the regression process:

Raw regressions should use at least 60 data points (e.g., five years of monthly

returns). Rolling betas should be graphed to examine any systematic changes in a

stocks risk.

Raw regressions should be based on monthly returns. Using shorter return periods,

such as daily and weekly returns, leads to systematic biases.

Company stock returns should be regressed against a value-weighted, well-

diversified portfolio, such as the S&P 500 or MSCI World Index.

Next, recalling that raw regressions provide only estimates of a companys true beta, we

improve estimates of a companys beta by deriving an unlevered industry betaand then

relevering the industry beta to the companys target capital structure.


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Measuring Beta Using Peer Groups

The Ibbotson Beta Book provides raw regression betas and peergroup betas.

To determine peer group betas, Ibbotson examines pure plays and

conglomerates, using a methodology pioneered by Kaplan and

Peterson....

Sales

Sales

Sales

Sales

Sales

SalesbetaRaw 3

32

21

1 xxxiii

i

...Sales

Sales

Sales

Sales

Sales

SalesbetaRaw 3

32

21

1 xxxjjj

j

such thatx1is the pure play

beta for industry 1,x2is the

beta for industry 2

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Operating Risk across Industries

A companys beta

represents the companys

exposure to changes in

the overall stock market. Since the stock market is

closely tied to the

economy, a companys

beta represents its

revenue and cash flow

exposure to the

economys strength.

17

2.13

1.75

1.55

1.38

1.18

1.12

1.16

1.06

1.00

0.98

0.83

0.63

0.51

Semiconductor Equipment

Life Insurance

Integrated Steel

Specialty Retail

Commodity Chemicals

Information Services

Retail Automotive

Hotel/Gaming

Aggregate Market

Homebuilding

Packaging & Container

Property Management

Water Utility

Unlevered Beta by Sector

Source: Aswath Damodaran,New York University.


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Cost of Equity Using CAPM

Base ReturnLong-Term

Treasuries

4.0%

Below

Average

Risk

Above

Average

Risk

9.2%

14.4%

Raytheon

(7.8%)

Cisco

(10.4%)

When the beta is high, the

stock is considered more

risky than the market.

For instance, Cisco Systems

moves more than the market,and has a beta of 1.86.

Thus, the companys cost of

equity is 10.4 percent.

With a beta of 0.73,

Raytheons cost of equity is

estimated at 7.8 percent.

Risk-free

rate

Expected

marketreturn

18


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An Alternative Model: Fama & French

In 1992, Eugene Fama and Kenneth French published a paper in the

Journal of Financethat received a great deal of attention because theyconcluded,

In short, our tests do not support the most basic prediction of the SLB [Sharpe-Lintner-Black]

Capital Asset Pricing Model that average stock returns are positively related to market betas.

Based on prior research and their own comprehensive regressions, Fama and French

concluded that:

Equity returns are inversely related to the size of a company (as measured by

market capitalization).

Equity returns are positively related to the ratio of the book value to market value of

the companys equity.

With this model, a stocks excess returns are regressed on three factors: excess market

returns, the excess returns of small stocks over big stocks (SMB), and the excess

returns of high book-to-market stocks over low book-to-market stocks (HML).


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An Alternative Model: Fama & French

Lets use the Fama-French three-factor model to continue our Home Depot

example. To determine the companys three betas, Home Depot stock returnsare regressed against the excess market portfolio, SMB, and HML (available

from professional service providers).

Home Depot: Fama-French Expected Returns

For Home Depot, the

Fama-French model

leads to a slightly

smaller cost of equity

than the market model.

Average Average Contribution

monthly annual to expected

premium1 premium Regression return

Factor (percent) (percent) coefficient2

(percent)

Market portfolio 5.4 1.39 7.5

SMB portfolio 0.23 2.8 (0.09) (0.3)

HML portfolio 0.40 5.0 (0.14) (0.7)

Premium over risk-free rate3 6.6

Risk-free rate

3.9

Cost of equity 10.5

1SMB and HML premiums based on average monthly returns data, 19262009.

2Based on monthly returns data, 20022006.

3Summation rounded to one decimal point.


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An Alternative Model: The Arbitrage Pricing Theory

The arbitrage pricing theory (APT) can be thought of as a generalized

version of the Fama-French three-factor model. In the APT, a securitysreturns are fullyspecified by kfactors and random noise:

eFbFbFbaR kki~~...

~~~2211

By creating well-diversified factor portfolios, it can be shown that a securitysexpected return must equal the risk-free rate plus its exposure to each factor

times the factors excess return (denoted by lambda):

kkfi bbbrRE ...][ 2211

Implementation of the APT, however, has been elusive, as there is little

agreement on either the number of factors, what the factors represent, or

how to measure the factors.

chapter 11 cost of equity

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