cost of capital equity capital 3335

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Cost of Capital

(Equity Capital)



Topics Covered 72 Years of Capital Market History

Measuring Risk, Beta and Unique Risk

CAPM and Cost of Capital

Introduction to WACC & Capital Structure



The Future Value of anInvestment of $1 in 1925

0.1

10

1000

1930 1940 1950 1960 1970 1980 1990 2000

Common Stocks

Long T-Bonds

T-Bills

$59.70

$17.48

Source: © Stocks, Bonds, Bills, and Inflation 2003 Yearbook™, Ibbotson Associates, Inc., Chicago (annually updates work by

Roger G. Ibbotson and Rex A. Sinquefield). All rights reserved.

$1,775.34



Historical Returns, 1926-2002



– 90% + 90%0%

Average StandardSeries Annual Return Deviation Distribution

Large Company Stocks 12.2% 20.5%

Small Company Stocks 16.9 33.2

Long-Term Corporate Bonds 6.2 8.7

Long-Term Government Bonds 5.8 9.4

U.S. Treasury Bills 3.8 3.2

Inflation 3.1 4.4



Average Stock Returns and RiskFree Returns The Risk Premium is the additional return (over and above

the risk-free rate) resulting from bearing risk. One of the most significant observations of stock market

data is this long-run excess of stock return over the risk-freereturn. The average excess return from large company common

stocks for the period 1926 through 1999 was 8.4% =12.2% – 3.8%

The average excess return from small company commonstocks for the period 1926 through 1999 was 13.2% =16.9% – 3.8%

The average excess return from long-term corporate

bonds for the period 1926 through 1999 was 2.4% =6.2% – 3.8%



The Risk-Return Tradeoff

2%

4%

6%

8%

10%

12%

14%

16%

18%

0% 5% 10% 15% 20% 25% 30% 35%

Annual Return Standard Deviation

A n

n u a l R e t u r n A v e r a

g e

T-Bonds

T-Bills

Large-Company Stocks

Small-Company Stocks



Rates of Return 1926-2002

-60

-40

-20

0

20

40

60

26 30 35 40 45 50 55 60 65 70 75 80 85 90 95 2000

Common Stocks

Long T-Bonds

T-Bills





Measuring Total Risk

There is no universally agreed-upon definition of risk.

The measures of risk that we discuss are varianceand standard deviation.

Variance - A measure of volatility. Average valueof squared deviations from mean.

Standard Deviation - The standard deviation isthe standard statistical measure of the spread of a sample (the square root of the variance). It isthe measure of total risk that we use most of thetime.



Stock Market Volatility 1926-2004

0

10

20

30

40

50

60

1 9 2 6

1 9 3 5

1 9 4 0

1 9 4 5

1 9 5 0

1 9 5 5

1 9 6 0

1 9 6 5

1 9 7 0

1 9 7 5

1 9 8 0

1 9 8 5

1 9 9 0

1 9 9 5

2 0 0 0

StdDe

v

2004



Country Risk Premia (%)

0

2

4

6

8

10

12Italy

Japan

France

Germany (ex 1 922/3)

Australia

South Africa

Sweden

USA

Average

UK

Ireland

Canada

Spain

Switzerland

Belgium

Denmark

Norway



Measuring Risk

Diversification - Strategy designed to reduce riskby spreading the portfolio across manyinvestments.

Unique Risk - Risk factors affecting only that firm.Also called “diversifiable risk.”

Market Risk - Economy-wide sources of risk thataffect the overall stock market. Also called “systematic risk.”



Measuring Risk

0

5 10 15

Number of Securities

P o r t f o l i o s

t a n d a r d d

e v i a t i o n

Market risk

Uniquerisk



Capital Asset Pricing Model

R = r f + B ( r m - r f )

CAPMSecurity Market Line (SML)

RP = Risk Premium



Security Market Line

Expected

Return

BETA

r f

Risk Free

Return =

Market Return = r m

1.0

Security Market

Line (SML)

)(β _

F M

i F ir r r r −×+=



The Formula for Beta

)(

)(2

,

M

M i

i

R

R RCov

σ β =

2m

im

i σ

σ

β =

Covariance with the

market

Variance of the market



Beta

Market Portfolio - Portfolio of all assets inthe economy. In practice a broad stockmarket index, such as the S&PComposite, is used to represent themarket.

Beta - Sensitivity of a stock’s return tothe return on the market portfolio.



Beta and CL

beta

Expected

return

Expected

market

return

10%10%- +

-10%+10%

stock

Copyright 1996 by The McGraw-Hill Companies, Inc

-10%

1. Market risk is

measured by beta,

the sensitivity to

market changes.

2. The slope of the

characteristic line

is beta



regression

Securit

yReturns

Securit

yRetu

rns

Return onReturn on

market %market %

R R ii == α ii ++ β iiR R

mm ++ eeii

Slope =Slope =β ii

C h a

r a c t e

r i s t i c

L i n

e

C h a

r a c t e

r i s t i c

L i n

e



Measuring Betas

The SML shows the relationshipbetween return and risk.

CAPM uses Beta as the measure for

risk. Beta is the slope of the Characteristic

Line (CL). Other methods - Regression Analysis -

can be employed to determine the slopeof the CL and thus Beta.



Measuring BetasHewlett Packard Beta

Slope determined from 60 months of

prices and plotting the line of best

fit.

Price data - Jan 78 - Dec 82

Market return (%)

Hewle

tt-Packardr e

turn (%

)

R 2 = .53

B = 1.35



Measuring BetasHewlett Packard Beta



fit.


Market return (%)

Hewle

tt-Packardr e

turn (%

)

R 2 = .35

B = 1.69



Measuring BetasA T & T Beta



fit.


Market return (%)

A

T&

T

(%)

R 2 = .28

B = 0.21



Measuring BetasA T & T Beta



fit.


Market return (%)

R 2 = ..17

B = .90

A

T&

T

(%)

s ng e o s ma e e



s ng e o s ma e eRisk-Adjusted Discount Ratefor Projects

An all-equity firm should accept a project whose IRRexceeds the cost of equity capital and reject projectswhose IRRs fall short of the cost of capital.

Projec

t

IRR

Firm’s risk (beta)

SML

5%

Good

project

Bad project

30%

2.5

A

B

C

E i f h B i



Extensions of the BasicModel

The Firm versus the Project

The Cost of Capital with Debt



The Firm versus the Project

Any project’s cost of capital dependson the use to which the capital isbeing put—not the source.

Therefore, it depends on the risk of the project and not the risk of thecompany .



Company Cost of Capital

A company’s cost of capital can becompared to the CAPM required return.

Requiredreturn

Project Beta1.26

Company Cost

of Capital

13

5.5

0

SML

Possible error

Possible error



Capital Budgeting & Risk

Modifying the CAPM

(account for proper risk)

•

Use COC unique to project, if possible,rather than Company COC

• Take into account Capital Structure (next

topic)



Capital Structure - the mix of debt & equity within acompany

Expand CAPM to include CS

R = rf + B ( rm - rf )becomes

Requity = rf + B ( rm - rf ) (because equity returns are observable)

Capital Structure

RP = market

risk premium



Capital Structure & COC

+

=

+

==

==

V

E

V

D

V

Er

V

Dr WACCr

r r COC

equitydebtassets

equitydebtassets

assets portfolio

β β β

r equity = r f + βequity ( r m - r f )

r debt = r f + βdebt ( r m - r f )

IMPORTANT

E, D, and V are

all market values



Using an Industry Beta

It is frequently argued that one can better estimate a firm’sbeta by involving the whole industry.

If you believe that the operations of the firm are similar to theoperations of the rest of the industry, you should use theindustry beta.

If you believe that the operations of the firm are fundamentallydifferent from the operations of the rest of the industry, youshould use the firm’s beta.

Don’t forget about adjustments for financial leverage (moredetails coming later in the course).

Utilit E l



Utility ExamplePinnacle West Corp.

Equity

Beta D/V if Beta Debt = 0 if Beta Debt = .25

Boston Electric 0.60 0.65 0.21 0.37

Consolidated Edison 0.65 0.46 0.35 0.47

DTE Energy 0.56 0.51 0.27 0.40

GPU Inc. 0.65 0.76 0.16 0.35

PP&L Resources 0.37 0.39 0.23 0.32

Average 0.57 0.24 0.38

Asset Beta



Example:Pinnacle West Corp

R asset = r f + β ( r m - r f )

= .045 + .24(.08) = .064 or 6.4%

(7.5% for Pinnacle’s beta = .38)

Assumes riskfree rate of 4.5% and market risk

premium of 8%

Oth M th d f E ti ti



Other Methods of EstimatingCost of Equity Capital

•The EP Method

r = EPS / Stock Price

•The Constant Growth (Gordon) Model

r = DIV1 / P 0 + g

compute g from earnings, dividend,or cash flow growth or use the

sustainable growth estimate



Conclusion

Now compute the cost of capital forAmeritrade Corporation

Use the CAPM – compute the beta for

comparable firms to Ameritrade Compute asset betas from equity betas

What is the cost of capital for Ameritrade?

cost of capital equity capital 3335

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