Cost of Capital (Equity Capital)
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Cost of Capital
(Equity Capital)
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Topics Covered 72 Years of Capital Market History
Measuring Risk, Beta and Unique Risk
CAPM and Cost of Capital
Introduction to WACC & Capital Structure
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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
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Historical Returns, 1926-2002
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.
– 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
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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%
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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
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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
Source: © Stocks, Bonds, Bills, and Inflation 2000 Yearbook™, Ibbotson Associates, Inc., Chicago (annually updates work by
Roger G. Ibbotson and Rex A. Sinquefield). All rights reserved.
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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.
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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
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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
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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.”
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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
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Capital Asset Pricing Model
R = r f + B ( r m - r f )
CAPMSecurity Market Line (SML)
RP = Risk Premium
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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 −×+=
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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
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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.
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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
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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
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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.
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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
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Measuring BetasHewlett Packard Beta
Slope determined from 60 months of
prices and plotting the line of best
fit.
Price data - Jan 93 - Dec 97
Market return (%)
Hewle
tt-Packardr e
turn (%
)
R 2 = .35
B = 1.69
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Measuring BetasA T & T Beta
Slope determined from 60 months of
prices and plotting the line of best
fit.
Price data - Jan 78 - Dec 82
Market return (%)
A
T&
T
(%)
R 2 = .28
B = 0.21
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Measuring BetasA T & T Beta
Slope determined from 60 months of
prices and plotting the line of best
fit.
Price data - Jan 93 - Dec 97
Market return (%)
R 2 = ..17
B = .90
A
T&
T
(%)
s ng e o s ma e e
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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
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Extensions of the BasicModel
The Firm versus the Project
The Cost of Capital with Debt
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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 .
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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
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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)
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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
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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
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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
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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
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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
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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
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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?