Cost of Capital (Equity Capital)

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 an Investment of $1 in 1925

0.1

10

1000

1930 1940 1950 1960 1970 1980 1990 2000

Common StocksLong T-BondsT-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 Standard Series 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 Risk-Free 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-free return. 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 common stocks 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

Ann

ual R

etur

n A

vera

ge

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 variance

and standard deviation.Variance - A measure of volatility. Average value of

squared deviations from mean. Standard Deviation - The standard deviation is

the standard statistical measure of the spread of a sample (the square root of the variance). It is the measure of total risk that we use most of the time.

Stock Market Volatility 1926-2004

0

10

20

30

40

50

60

1926

1935

1940

1945

1950

1955

1960

1965

1970

1975

1980

1985

1990

1995

2000

Std

Dev

2004

Country Risk Premia (%)

0

2

4

6

8

10

12Italy

Japan

France

Germany (ex 1922/3)

Australia

South Africa

Sweden

USA

Average

UK

Ireland

Canada

Spain

Switzerland

Belgium

Denmark

Norway

Measuring Risk

Diversification - Strategy designed to reduce risk by spreading the portfolio across many investments.

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

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

Measuring Risk

05 10 15

Number of Securities

Po

rtfo

lio

sta

nd

ard

dev

iati

on

Market risk

Uniquerisk

Capital Asset Pricing Model

R = rf + B ( rm - rf )

CAPMSecurity Market Line (SML)

RP = Risk Premium

Security Market Line

Expected Return

BETA

rf

Risk Free

Return =

Market Return = rm

1.0

Security Market Line (SML)

)(β_

FMiFi rrrr

The Formula for Beta

)(

)(2

,

M

Mii R

RRCov

2m

imi

Covariance with the market

Variance of the market

Beta

Market Portfolio - Portfolio of all assets in the economy. In practice a broad stock market index, such as the S&P Composite, is used to represent the market.

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

Beta and CL

beta

Expected

return

Expectedmarketreturn

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

Estimating with regression

Sec

uri

ty R

etu

rns

Sec

uri

ty R

etu

rns

Return on Return on market %market %

RRii = = ii + + iiRRmm + + eeii

Slope = Slope = iiCharacte

ristic

Line

Characteris

tic Line

Measuring Betas The SML shows the relationship

between 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 slope of 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 (%)

Hew

lett-Packard return (%

)

R2 = .53

B = 1.35

Measuring BetasHewlett Packard Beta



Market return (%)

Hew

lett-Packard return (%

)

R2 = .35

B = 1.69

Measuring BetasA T & T Beta



Market return (%)

A T

& T

(%)

R2 = .28

B = 0.21

Measuring BetasA T & T Beta



Market return (%)

R2 = ..17

B = .90

A T

& T

(%)

Using the SML to Estimate the Risk-Adjusted Discount Rate for Projects

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

Pro

ject

IRR

Firm’s risk (beta)

SML

5%

Good project

Bad project

30%

2.5

A

B

C

Extensions of the Basic Model The Firm versus the Project The Cost of Capital with Debt

The Firm versus the Project Any project’s cost of capital depends

on the use to which the capital is being put—not the source.

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

Company Cost of Capital A company’s cost of capital can be

compared to the CAPM required return.

Required

return

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 a company

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 WACC r

r r COC

equitydebt assets

equitydebtassets

assetsportfolio

requity = rf + βequity ( rm - rf )

rdebt = rf + βdebt ( rm - rf )

IMPORTANT

E, D, and V are all market values

Using an Industry Beta It is frequently argued that one can better estimate

a firm’s beta by involving the whole industry. If you believe that the operations of the firm are

similar to the operations of the rest of the industry, you should use the industry beta.

If you believe that the operations of the firm are fundamentally different from the operations of the rest of the industry, you should use the firm’s beta.

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

Utility Example Pinnacle West Corp.

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

Boston Electric 0.60 0.65 0.21 0.37Consolidated Edison 0.65 0.46 0.35 0.47DTE Energy 0.56 0.51 0.27 0.40GPU Inc. 0.65 0.76 0.16 0.35PP&L Resources 0.37 0.39 0.23 0.32

Average 0.57 0.24 0.38

Asset Beta

Example:Pinnacle West Corp

Rasset = rf + β ( rm - rf )

= .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%

Other Methods of Estimating Cost of Equity Capital

•The EP Method r = EPS / Stock Price

•The Constant Growth (Gordon) Modelr = DIV1 / P 0 + gcompute g from earnings, dividend, or cash flow growth or use the

sustainable growth estimate

Conclusion Now compute the cost of capital for

Ameritrade 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?

Business

Cost of Capital (Equity Capital)