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13-0
Risk Cost of Capital and
Valuation
Chapter 13
13-1
Key Concepts and Skills
bull Know how to determine a firmrsquos cost of equity capital
bull Understand the impact of beta in determining the firmrsquos cost of equity capital
bull Know how to determine a firmrsquos cost of debt
bull Know how to determine the firmrsquos overall cost of capital
bull Understand how to find the appropriate cost of capital for any given capital project
bull Understand the impact of flotation costs on capital budgeting
13-2
Chapter Outline
131 The Cost of Equity Capital
132 Estimating the Cost of Equity Capital with the CAPM
133 Estimation of Beta
134 Determinants of Beta
135 The Dividend Discount Model Approach
136 Cost of Capital for Divisions and Projects
137 Cost of Fixed Income Securities
138 The Weighted Average Cost of Capital
139 Valuation with RWACC
1310 Estimating Eastman Chemicalrsquos Cost of Capital
1311 Flotation Costs and the Weighted Average Cost of Capital
13-3
Where Do We Stand
bull Earlier chapters on capital budgeting focused on the identification of relevant (incremental) cash flows and their timing evaluating say NPV using a given discount rate
bull This chapter discusses how to find the appropriate discount rate or required rate of return or the cost of capital when cash flows are risky
13-4
4
Invest in project
131 The Cost of Equity Capital
Firm with
excess cash
Shareholderrsquos
Terminal
Value
Pay cash dividend
Shareholder
invests in
financial
asset
Because stockholders can reinvest the dividend in risky financial assets
the expected return on a capital-budgeting project should be at least as
great as the expected return on a financial asset of comparable risk
A firm with excess cash can either pay a dividend or make a capital investment
13-5
5
Cost of Equity Capital
bull Implication Discount rate needs to be
appropriate for projectrsquos risk (not necessarily the
same as the firmrsquos overall risk)
bull Letrsquos begin by considering how to estimate a
firmrsquos cost of equity capital
bull Two approaches for finding a firmrsquos equity cost
of capital
ndash From last time CAPM
ndash Dividend Discount Model (DDM)
13-6
The Cost of Equity Capitalbull The cost of equity capital is the required return on the
stockholdersrsquo investment in the firm CAPM can be
used to estimate the required return From the firmrsquos
perspective the expected return is the Cost of Equity
Capital )( FMiFi RRβRR
bull To estimate a firmrsquos cost of equity capital we need to know three things
1 The risk-free rate RF
FM RR 2 The market risk premium
2
)(
)(
M
Mi
M
Mii
σ
σ
RVar
RRCovβ 3 The company beta
13-7
Examplebull Suppose the stock of Stansfield Enterprises a
publisher of PowerPoint presentations has a
beta of 15 The firm is 100 equity financed
bull Assume a risk-free rate of 3 and a market
risk premium of 7
bull What is the appropriate discount rate for an
expansion of this firm
)( FMFs RRβRR
7513 sR
513sR
13-8
ExampleSuppose Stansfield Enterprises is evaluating the
following independent projects Each costs $100 and
lasts one year
Project Project b Projectrsquos
Estimated Cash
Flows Next
Year
IRR NPV at
135
A 15 $125 25 $1013
B 15 $1135 135 $0
C 15 $105 5 -$749
13-9
Using the SML
An all-equity firm should accept projects whose IRRs exceed the
cost of equity capital and reject projects whose IRRs fall short of
the cost of capital
Pro
ject
IRR
Firmrsquos risk (beta)
SML
5
Good
project
Bad project
30
25
A
B
C
13-10
The Risk-free Ratebull Treasury securities are close proxies for the risk-free
rate
bull Although the T-Bill rate is theoretically risk free it is
frequently distorted by Fed Policy
bull The CAPM is a period model However projects are
long-lived So average period (short-term) rates need to
be used
bull The historic premium of long-term (20-year) rates over short-term rates for government securities is 2
bull So the risk-free rate to be used in the CAPM could be estimated as 2 below the prevailing rate on 20-year treasury securities
bull Or use short term T-Note rates instead say 10 years
bull httpfinanceyahoocomqs=^TNX
13-11
The Market Risk Premium
bull Method 1 Use historical data
bull Method 2 Use the Dividend Discount Model
ndash Market data and analyst forecasts can be used to
implement the DDM approach on a market-wide
basis
ndash Will not be stable Also subject to growth assumption
bull Method 3 Use forecasts
gP
DR 1
13-12
Historical Market Risk Premium
bull From SBBI Data1926-2010
ndash Small Stocks 1222
ndash SampP 500 985
ndash US LT Gov Bonds 545
ndash US 30 Day T Bills 362
ndash US Inflation 304
bull Risk Premium
ndash SP500-LT Bonds = 985-545= 44
ndash SP500-T Bills = 985-362= 623
13-13
Implied Risk Premium using the
SampP 500bull httppagessternnyuedu~adamodar
bull D1P is the dividend yield Because firms also buyback shares we can use
in its place the dividend yield plus the buyback yieldndash 181+208 = 388
bull g is the growth rate of dividends For simplicity use the historic growth ratendash Dividend in 2001 = 1574 in 2010 = 2273 g=(22731574)(19)-1 = 42
0862088
088
24883
1
RFRERP
ERPRFR
R
R
gP
DR
13-14
Survey data on the risk premium
bull Most survey data is of academics and industry
professionals
ndash Average is about 55
ndash Has fallen in recent years from above 6
13-15
Estimation of Beta
Market Portfolio - Portfolio of all assets in the
economy In practice a broad stock market
index such as the SampP 500 is used to represent
the market
Beta - Sensitivity of a stockrsquos return to the return
on the market portfolio
13-16
Estimation of Beta
)(
)(
M
Mi
RVar
RRCovβ
bull Problems
1 Betas may vary over time
2 The sample size may be inadequate
3 Betas are influenced by changing financial leverage and business risk
(see Rolling Beta for TGTxlsx)
13-17
Stability of Beta
bull Most analysts argue that betas are generally
stable for firms remaining in the same industry
bull That is not to say that a firmrsquos beta cannot
change
ndash Changes in product line
ndash Changes in technology
ndash Deregulation
ndash Changes in financial leverage
13-18
Determinants of Beta
bull Business Risk
ndash Cyclicality of Revenues
ndash Operating Leverage
bull Financial Risk
ndash Financial Leverage
bull Highly cyclical stocks have higher betas
ndash Retailers auto makers
bull Less cyclical
ndash Utilities
13-19
Example
bull Suppose the stock of Stansfield Enterprises a
publisher of PowerPoint presentations has a beta of
25 The firm is 100 equity financed
bull Assume a risk-free rate of 5 and a market risk
premium of 10
bull What is the appropriate discount rate for an expansion
of this firm
13-20
Example
Suppose Stansfield Enterprises is evaluating the
following independent projects Each costs $100 and
lasts one year
Project Project b Projectrsquos
Estimated Cash
Flows Next Year
IRR NPV at
30
A 25 $150 50 $1538
B 25 $130 30 $0
C 25 $110 10 -$1538
13-21
Using the SML
An all-equity firm should accept projects whose IRRs
exceed the cost of equity capital and reject projects whose
IRRs fall short of the cost of capital
Pro
ject
IRR
Firmrsquos risk (beta)
SML
5
Good
project
Bad project
30
25
A
B
C
13-22
What if project betas vary
bull If the firm has a single cost of capital but
considers projects of varying risk adjustments
should be made
ndash Different risk adjusted costs of capital should be used
for each project
bull Otherwise the firm will over invest in risky
projects
ndash Why - See the following example
13-23
Suppose the Conglomerate Company has a cost of capital
based on the CAPM of 17 The risk-free rate is 4 the
market risk premium is 10 and the firmrsquos beta is 13
17 = 4 + 13 times 10
This is a breakdown of the companyrsquos investment projects
13 Automotive Retailer b = 20
13 Computer Hard Drive Manufacturer b = 13
13 Electric Utility b = 06
average b of assets = 13
When evaluating a new electrical generation investment
which cost of capital should be used
Capital Budgeting amp Project Risk
13-24
Capital Budgeting amp Project RiskP
roje
ct I
RR
Projectrsquos risk (b)
17
13 2006
R = 4 + 06times(14 ndash 4 ) = 10
10 reflects the opportunity cost of capital on an investment in electrical generation given the unique risk of the project
10
24 Investments in hard
drives or auto
retailing should have
higher discount rates
SML
13-25
Capital Budgeting amp Project Risk
A firm that uses one discount rate for all projects may over
time increase the risk of the firm while decreasing its value
Pro
ject
IR
R
Firmrsquos risk (beta)
SML
rf
bFIRM
Incorrectly rejected
positive NPV projects
Incorrectly accepted
negative NPV projects
Hurdle
rate)( FMFIRMF RRβR
The SML can tell us why
13-26
The Weighted Average Cost of
Capital
bull The Weighted Average Cost of Capital is given
by
bull Because interest expense is tax-deductible we multiply the last term by (1 ndash TC)
RWACC = Equity + Debt
Equitytimes REquity +
Equity + Debt
Debttimes RDebt times(1 ndash TC)
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-27
Cost of Debt
bull Interest rate required on new debt issuance (ie yield to
maturity on outstanding debt)
bull Adjust for the tax deductibility of interest expense
bull In practice finding new debt issuances is tricky
bull For companies with publicly traded debt we can rely on
the yield to maturity of the debt
ndash Note that the coupon rate is NOT a measure of the cost of debt
today
bull httpfinanceyahoocombonds
13-28
Example Target Corp
bull First we estimate the cost of equity and the cost
of debt
ndash We estimate an equity beta to estimate the cost of
equity
ndash We can often estimate the cost of debt by observing
the YTM of the firmrsquos debt
bull Second we determine the WACC by weighting
these two costs appropriately
13-29
Example International Paper
bull The industry average beta is 082 the risk free rate is
3 and the market risk premium is 84
bull Thus the cost of equity capital is
RS = RF + bi times (RM ndash RF)
= 3 +82times84
= 989
13-30
Example International Paper
bull The yield on the companyrsquos debt is 8 and
the firm has a 37 marginal tax rate The
debt to value ratio is 32
834 is Internationalrsquos cost of capital
= 068 times 989 + 032 times 8 times (1 ndash 037)
= 834
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-31
Financial Leverage and Beta
bull Operating leverage refers to the sensitivity to the firmrsquos
fixed costs of production
bull Financial leverage is the sensitivity to a firmrsquos fixed
costs of financing
bull The relationship between the betas of the firmrsquos debt
equity and assets is given by
bull Financial leverage always increases the equity beta relative to the asset beta
bAsset = Debt + Equity
Debttimes bDebt +
Debt + Equity
Equitytimes bEquity
13-32
Example
Consider Grand Sport Inc which is currently all-equity
financed and has a beta of 090
The firm has decided to lever up to a capital structure of 1
part debt to 1 part equity
Since the firm will remain in the same industry its asset
beta should remain 090
However assuming a zero beta for its debt its equity beta
would become twice as large
bAsset = 090 = 1 + 1
1times bEquity bEquity = 2 times 090 = 180
13-1
Key Concepts and Skills
bull Know how to determine a firmrsquos cost of equity capital
bull Understand the impact of beta in determining the firmrsquos cost of equity capital
bull Know how to determine a firmrsquos cost of debt
bull Know how to determine the firmrsquos overall cost of capital
bull Understand how to find the appropriate cost of capital for any given capital project
bull Understand the impact of flotation costs on capital budgeting
13-2
Chapter Outline
131 The Cost of Equity Capital
132 Estimating the Cost of Equity Capital with the CAPM
133 Estimation of Beta
134 Determinants of Beta
135 The Dividend Discount Model Approach
136 Cost of Capital for Divisions and Projects
137 Cost of Fixed Income Securities
138 The Weighted Average Cost of Capital
139 Valuation with RWACC
1310 Estimating Eastman Chemicalrsquos Cost of Capital
1311 Flotation Costs and the Weighted Average Cost of Capital
13-3
Where Do We Stand
bull Earlier chapters on capital budgeting focused on the identification of relevant (incremental) cash flows and their timing evaluating say NPV using a given discount rate
bull This chapter discusses how to find the appropriate discount rate or required rate of return or the cost of capital when cash flows are risky
13-4
4
Invest in project
131 The Cost of Equity Capital
Firm with
excess cash
Shareholderrsquos
Terminal
Value
Pay cash dividend
Shareholder
invests in
financial
asset
Because stockholders can reinvest the dividend in risky financial assets
the expected return on a capital-budgeting project should be at least as
great as the expected return on a financial asset of comparable risk
A firm with excess cash can either pay a dividend or make a capital investment
13-5
5
Cost of Equity Capital
bull Implication Discount rate needs to be
appropriate for projectrsquos risk (not necessarily the
same as the firmrsquos overall risk)
bull Letrsquos begin by considering how to estimate a
firmrsquos cost of equity capital
bull Two approaches for finding a firmrsquos equity cost
of capital
ndash From last time CAPM
ndash Dividend Discount Model (DDM)
13-6
The Cost of Equity Capitalbull The cost of equity capital is the required return on the
stockholdersrsquo investment in the firm CAPM can be
used to estimate the required return From the firmrsquos
perspective the expected return is the Cost of Equity
Capital )( FMiFi RRβRR
bull To estimate a firmrsquos cost of equity capital we need to know three things
1 The risk-free rate RF
FM RR 2 The market risk premium
2
)(
)(
M
Mi
M
Mii
σ
σ
RVar
RRCovβ 3 The company beta
13-7
Examplebull Suppose the stock of Stansfield Enterprises a
publisher of PowerPoint presentations has a
beta of 15 The firm is 100 equity financed
bull Assume a risk-free rate of 3 and a market
risk premium of 7
bull What is the appropriate discount rate for an
expansion of this firm
)( FMFs RRβRR
7513 sR
513sR
13-8
ExampleSuppose Stansfield Enterprises is evaluating the
following independent projects Each costs $100 and
lasts one year
Project Project b Projectrsquos
Estimated Cash
Flows Next
Year
IRR NPV at
135
A 15 $125 25 $1013
B 15 $1135 135 $0
C 15 $105 5 -$749
13-9
Using the SML
An all-equity firm should accept projects whose IRRs exceed the
cost of equity capital and reject projects whose IRRs fall short of
the cost of capital
Pro
ject
IRR
Firmrsquos risk (beta)
SML
5
Good
project
Bad project
30
25
A
B
C
13-10
The Risk-free Ratebull Treasury securities are close proxies for the risk-free
rate
bull Although the T-Bill rate is theoretically risk free it is
frequently distorted by Fed Policy
bull The CAPM is a period model However projects are
long-lived So average period (short-term) rates need to
be used
bull The historic premium of long-term (20-year) rates over short-term rates for government securities is 2
bull So the risk-free rate to be used in the CAPM could be estimated as 2 below the prevailing rate on 20-year treasury securities
bull Or use short term T-Note rates instead say 10 years
bull httpfinanceyahoocomqs=^TNX
13-11
The Market Risk Premium
bull Method 1 Use historical data
bull Method 2 Use the Dividend Discount Model
ndash Market data and analyst forecasts can be used to
implement the DDM approach on a market-wide
basis
ndash Will not be stable Also subject to growth assumption
bull Method 3 Use forecasts
gP
DR 1
13-12
Historical Market Risk Premium
bull From SBBI Data1926-2010
ndash Small Stocks 1222
ndash SampP 500 985
ndash US LT Gov Bonds 545
ndash US 30 Day T Bills 362
ndash US Inflation 304
bull Risk Premium
ndash SP500-LT Bonds = 985-545= 44
ndash SP500-T Bills = 985-362= 623
13-13
Implied Risk Premium using the
SampP 500bull httppagessternnyuedu~adamodar
bull D1P is the dividend yield Because firms also buyback shares we can use
in its place the dividend yield plus the buyback yieldndash 181+208 = 388
bull g is the growth rate of dividends For simplicity use the historic growth ratendash Dividend in 2001 = 1574 in 2010 = 2273 g=(22731574)(19)-1 = 42
0862088
088
24883
1
RFRERP
ERPRFR
R
R
gP
DR
13-14
Survey data on the risk premium
bull Most survey data is of academics and industry
professionals
ndash Average is about 55
ndash Has fallen in recent years from above 6
13-15
Estimation of Beta
Market Portfolio - Portfolio of all assets in the
economy In practice a broad stock market
index such as the SampP 500 is used to represent
the market
Beta - Sensitivity of a stockrsquos return to the return
on the market portfolio
13-16
Estimation of Beta
)(
)(
M
Mi
RVar
RRCovβ
bull Problems
1 Betas may vary over time
2 The sample size may be inadequate
3 Betas are influenced by changing financial leverage and business risk
(see Rolling Beta for TGTxlsx)
13-17
Stability of Beta
bull Most analysts argue that betas are generally
stable for firms remaining in the same industry
bull That is not to say that a firmrsquos beta cannot
change
ndash Changes in product line
ndash Changes in technology
ndash Deregulation
ndash Changes in financial leverage
13-18
Determinants of Beta
bull Business Risk
ndash Cyclicality of Revenues
ndash Operating Leverage
bull Financial Risk
ndash Financial Leverage
bull Highly cyclical stocks have higher betas
ndash Retailers auto makers
bull Less cyclical
ndash Utilities
13-19
Example
bull Suppose the stock of Stansfield Enterprises a
publisher of PowerPoint presentations has a beta of
25 The firm is 100 equity financed
bull Assume a risk-free rate of 5 and a market risk
premium of 10
bull What is the appropriate discount rate for an expansion
of this firm
13-20
Example
Suppose Stansfield Enterprises is evaluating the
following independent projects Each costs $100 and
lasts one year
Project Project b Projectrsquos
Estimated Cash
Flows Next Year
IRR NPV at
30
A 25 $150 50 $1538
B 25 $130 30 $0
C 25 $110 10 -$1538
13-21
Using the SML
An all-equity firm should accept projects whose IRRs
exceed the cost of equity capital and reject projects whose
IRRs fall short of the cost of capital
Pro
ject
IRR
Firmrsquos risk (beta)
SML
5
Good
project
Bad project
30
25
A
B
C
13-22
What if project betas vary
bull If the firm has a single cost of capital but
considers projects of varying risk adjustments
should be made
ndash Different risk adjusted costs of capital should be used
for each project
bull Otherwise the firm will over invest in risky
projects
ndash Why - See the following example
13-23
Suppose the Conglomerate Company has a cost of capital
based on the CAPM of 17 The risk-free rate is 4 the
market risk premium is 10 and the firmrsquos beta is 13
17 = 4 + 13 times 10
This is a breakdown of the companyrsquos investment projects
13 Automotive Retailer b = 20
13 Computer Hard Drive Manufacturer b = 13
13 Electric Utility b = 06
average b of assets = 13
When evaluating a new electrical generation investment
which cost of capital should be used
Capital Budgeting amp Project Risk
13-24
Capital Budgeting amp Project RiskP
roje
ct I
RR
Projectrsquos risk (b)
17
13 2006
R = 4 + 06times(14 ndash 4 ) = 10
10 reflects the opportunity cost of capital on an investment in electrical generation given the unique risk of the project
10
24 Investments in hard
drives or auto
retailing should have
higher discount rates
SML
13-25
Capital Budgeting amp Project Risk
A firm that uses one discount rate for all projects may over
time increase the risk of the firm while decreasing its value
Pro
ject
IR
R
Firmrsquos risk (beta)
SML
rf
bFIRM
Incorrectly rejected
positive NPV projects
Incorrectly accepted
negative NPV projects
Hurdle
rate)( FMFIRMF RRβR
The SML can tell us why
13-26
The Weighted Average Cost of
Capital
bull The Weighted Average Cost of Capital is given
by
bull Because interest expense is tax-deductible we multiply the last term by (1 ndash TC)
RWACC = Equity + Debt
Equitytimes REquity +
Equity + Debt
Debttimes RDebt times(1 ndash TC)
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-27
Cost of Debt
bull Interest rate required on new debt issuance (ie yield to
maturity on outstanding debt)
bull Adjust for the tax deductibility of interest expense
bull In practice finding new debt issuances is tricky
bull For companies with publicly traded debt we can rely on
the yield to maturity of the debt
ndash Note that the coupon rate is NOT a measure of the cost of debt
today
bull httpfinanceyahoocombonds
13-28
Example Target Corp
bull First we estimate the cost of equity and the cost
of debt
ndash We estimate an equity beta to estimate the cost of
equity
ndash We can often estimate the cost of debt by observing
the YTM of the firmrsquos debt
bull Second we determine the WACC by weighting
these two costs appropriately
13-29
Example International Paper
bull The industry average beta is 082 the risk free rate is
3 and the market risk premium is 84
bull Thus the cost of equity capital is
RS = RF + bi times (RM ndash RF)
= 3 +82times84
= 989
13-30
Example International Paper
bull The yield on the companyrsquos debt is 8 and
the firm has a 37 marginal tax rate The
debt to value ratio is 32
834 is Internationalrsquos cost of capital
= 068 times 989 + 032 times 8 times (1 ndash 037)
= 834
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-31
Financial Leverage and Beta
bull Operating leverage refers to the sensitivity to the firmrsquos
fixed costs of production
bull Financial leverage is the sensitivity to a firmrsquos fixed
costs of financing
bull The relationship between the betas of the firmrsquos debt
equity and assets is given by
bull Financial leverage always increases the equity beta relative to the asset beta
bAsset = Debt + Equity
Debttimes bDebt +
Debt + Equity
Equitytimes bEquity
13-32
Example
Consider Grand Sport Inc which is currently all-equity
financed and has a beta of 090
The firm has decided to lever up to a capital structure of 1
part debt to 1 part equity
Since the firm will remain in the same industry its asset
beta should remain 090
However assuming a zero beta for its debt its equity beta
would become twice as large
bAsset = 090 = 1 + 1
1times bEquity bEquity = 2 times 090 = 180
13-2
Chapter Outline
131 The Cost of Equity Capital
132 Estimating the Cost of Equity Capital with the CAPM
133 Estimation of Beta
134 Determinants of Beta
135 The Dividend Discount Model Approach
136 Cost of Capital for Divisions and Projects
137 Cost of Fixed Income Securities
138 The Weighted Average Cost of Capital
139 Valuation with RWACC
1310 Estimating Eastman Chemicalrsquos Cost of Capital
1311 Flotation Costs and the Weighted Average Cost of Capital
13-3
Where Do We Stand
bull Earlier chapters on capital budgeting focused on the identification of relevant (incremental) cash flows and their timing evaluating say NPV using a given discount rate
bull This chapter discusses how to find the appropriate discount rate or required rate of return or the cost of capital when cash flows are risky
13-4
4
Invest in project
131 The Cost of Equity Capital
Firm with
excess cash
Shareholderrsquos
Terminal
Value
Pay cash dividend
Shareholder
invests in
financial
asset
Because stockholders can reinvest the dividend in risky financial assets
the expected return on a capital-budgeting project should be at least as
great as the expected return on a financial asset of comparable risk
A firm with excess cash can either pay a dividend or make a capital investment
13-5
5
Cost of Equity Capital
bull Implication Discount rate needs to be
appropriate for projectrsquos risk (not necessarily the
same as the firmrsquos overall risk)
bull Letrsquos begin by considering how to estimate a
firmrsquos cost of equity capital
bull Two approaches for finding a firmrsquos equity cost
of capital
ndash From last time CAPM
ndash Dividend Discount Model (DDM)
13-6
The Cost of Equity Capitalbull The cost of equity capital is the required return on the
stockholdersrsquo investment in the firm CAPM can be
used to estimate the required return From the firmrsquos
perspective the expected return is the Cost of Equity
Capital )( FMiFi RRβRR
bull To estimate a firmrsquos cost of equity capital we need to know three things
1 The risk-free rate RF
FM RR 2 The market risk premium
2
)(
)(
M
Mi
M
Mii
σ
σ
RVar
RRCovβ 3 The company beta
13-7
Examplebull Suppose the stock of Stansfield Enterprises a
publisher of PowerPoint presentations has a
beta of 15 The firm is 100 equity financed
bull Assume a risk-free rate of 3 and a market
risk premium of 7
bull What is the appropriate discount rate for an
expansion of this firm
)( FMFs RRβRR
7513 sR
513sR
13-8
ExampleSuppose Stansfield Enterprises is evaluating the
following independent projects Each costs $100 and
lasts one year
Project Project b Projectrsquos
Estimated Cash
Flows Next
Year
IRR NPV at
135
A 15 $125 25 $1013
B 15 $1135 135 $0
C 15 $105 5 -$749
13-9
Using the SML
An all-equity firm should accept projects whose IRRs exceed the
cost of equity capital and reject projects whose IRRs fall short of
the cost of capital
Pro
ject
IRR
Firmrsquos risk (beta)
SML
5
Good
project
Bad project
30
25
A
B
C
13-10
The Risk-free Ratebull Treasury securities are close proxies for the risk-free
rate
bull Although the T-Bill rate is theoretically risk free it is
frequently distorted by Fed Policy
bull The CAPM is a period model However projects are
long-lived So average period (short-term) rates need to
be used
bull The historic premium of long-term (20-year) rates over short-term rates for government securities is 2
bull So the risk-free rate to be used in the CAPM could be estimated as 2 below the prevailing rate on 20-year treasury securities
bull Or use short term T-Note rates instead say 10 years
bull httpfinanceyahoocomqs=^TNX
13-11
The Market Risk Premium
bull Method 1 Use historical data
bull Method 2 Use the Dividend Discount Model
ndash Market data and analyst forecasts can be used to
implement the DDM approach on a market-wide
basis
ndash Will not be stable Also subject to growth assumption
bull Method 3 Use forecasts
gP
DR 1
13-12
Historical Market Risk Premium
bull From SBBI Data1926-2010
ndash Small Stocks 1222
ndash SampP 500 985
ndash US LT Gov Bonds 545
ndash US 30 Day T Bills 362
ndash US Inflation 304
bull Risk Premium
ndash SP500-LT Bonds = 985-545= 44
ndash SP500-T Bills = 985-362= 623
13-13
Implied Risk Premium using the
SampP 500bull httppagessternnyuedu~adamodar
bull D1P is the dividend yield Because firms also buyback shares we can use
in its place the dividend yield plus the buyback yieldndash 181+208 = 388
bull g is the growth rate of dividends For simplicity use the historic growth ratendash Dividend in 2001 = 1574 in 2010 = 2273 g=(22731574)(19)-1 = 42
0862088
088
24883
1
RFRERP
ERPRFR
R
R
gP
DR
13-14
Survey data on the risk premium
bull Most survey data is of academics and industry
professionals
ndash Average is about 55
ndash Has fallen in recent years from above 6
13-15
Estimation of Beta
Market Portfolio - Portfolio of all assets in the
economy In practice a broad stock market
index such as the SampP 500 is used to represent
the market
Beta - Sensitivity of a stockrsquos return to the return
on the market portfolio
13-16
Estimation of Beta
)(
)(
M
Mi
RVar
RRCovβ
bull Problems
1 Betas may vary over time
2 The sample size may be inadequate
3 Betas are influenced by changing financial leverage and business risk
(see Rolling Beta for TGTxlsx)
13-17
Stability of Beta
bull Most analysts argue that betas are generally
stable for firms remaining in the same industry
bull That is not to say that a firmrsquos beta cannot
change
ndash Changes in product line
ndash Changes in technology
ndash Deregulation
ndash Changes in financial leverage
13-18
Determinants of Beta
bull Business Risk
ndash Cyclicality of Revenues
ndash Operating Leverage
bull Financial Risk
ndash Financial Leverage
bull Highly cyclical stocks have higher betas
ndash Retailers auto makers
bull Less cyclical
ndash Utilities
13-19
Example
bull Suppose the stock of Stansfield Enterprises a
publisher of PowerPoint presentations has a beta of
25 The firm is 100 equity financed
bull Assume a risk-free rate of 5 and a market risk
premium of 10
bull What is the appropriate discount rate for an expansion
of this firm
13-20
Example
Suppose Stansfield Enterprises is evaluating the
following independent projects Each costs $100 and
lasts one year
Project Project b Projectrsquos
Estimated Cash
Flows Next Year
IRR NPV at
30
A 25 $150 50 $1538
B 25 $130 30 $0
C 25 $110 10 -$1538
13-21
Using the SML
An all-equity firm should accept projects whose IRRs
exceed the cost of equity capital and reject projects whose
IRRs fall short of the cost of capital
Pro
ject
IRR
Firmrsquos risk (beta)
SML
5
Good
project
Bad project
30
25
A
B
C
13-22
What if project betas vary
bull If the firm has a single cost of capital but
considers projects of varying risk adjustments
should be made
ndash Different risk adjusted costs of capital should be used
for each project
bull Otherwise the firm will over invest in risky
projects
ndash Why - See the following example
13-23
Suppose the Conglomerate Company has a cost of capital
based on the CAPM of 17 The risk-free rate is 4 the
market risk premium is 10 and the firmrsquos beta is 13
17 = 4 + 13 times 10
This is a breakdown of the companyrsquos investment projects
13 Automotive Retailer b = 20
13 Computer Hard Drive Manufacturer b = 13
13 Electric Utility b = 06
average b of assets = 13
When evaluating a new electrical generation investment
which cost of capital should be used
Capital Budgeting amp Project Risk
13-24
Capital Budgeting amp Project RiskP
roje
ct I
RR
Projectrsquos risk (b)
17
13 2006
R = 4 + 06times(14 ndash 4 ) = 10
10 reflects the opportunity cost of capital on an investment in electrical generation given the unique risk of the project
10
24 Investments in hard
drives or auto
retailing should have
higher discount rates
SML
13-25
Capital Budgeting amp Project Risk
A firm that uses one discount rate for all projects may over
time increase the risk of the firm while decreasing its value
Pro
ject
IR
R
Firmrsquos risk (beta)
SML
rf
bFIRM
Incorrectly rejected
positive NPV projects
Incorrectly accepted
negative NPV projects
Hurdle
rate)( FMFIRMF RRβR
The SML can tell us why
13-26
The Weighted Average Cost of
Capital
bull The Weighted Average Cost of Capital is given
by
bull Because interest expense is tax-deductible we multiply the last term by (1 ndash TC)
RWACC = Equity + Debt
Equitytimes REquity +
Equity + Debt
Debttimes RDebt times(1 ndash TC)
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-27
Cost of Debt
bull Interest rate required on new debt issuance (ie yield to
maturity on outstanding debt)
bull Adjust for the tax deductibility of interest expense
bull In practice finding new debt issuances is tricky
bull For companies with publicly traded debt we can rely on
the yield to maturity of the debt
ndash Note that the coupon rate is NOT a measure of the cost of debt
today
bull httpfinanceyahoocombonds
13-28
Example Target Corp
bull First we estimate the cost of equity and the cost
of debt
ndash We estimate an equity beta to estimate the cost of
equity
ndash We can often estimate the cost of debt by observing
the YTM of the firmrsquos debt
bull Second we determine the WACC by weighting
these two costs appropriately
13-29
Example International Paper
bull The industry average beta is 082 the risk free rate is
3 and the market risk premium is 84
bull Thus the cost of equity capital is
RS = RF + bi times (RM ndash RF)
= 3 +82times84
= 989
13-30
Example International Paper
bull The yield on the companyrsquos debt is 8 and
the firm has a 37 marginal tax rate The
debt to value ratio is 32
834 is Internationalrsquos cost of capital
= 068 times 989 + 032 times 8 times (1 ndash 037)
= 834
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-31
Financial Leverage and Beta
bull Operating leverage refers to the sensitivity to the firmrsquos
fixed costs of production
bull Financial leverage is the sensitivity to a firmrsquos fixed
costs of financing
bull The relationship between the betas of the firmrsquos debt
equity and assets is given by
bull Financial leverage always increases the equity beta relative to the asset beta
bAsset = Debt + Equity
Debttimes bDebt +
Debt + Equity
Equitytimes bEquity
13-32
Example
Consider Grand Sport Inc which is currently all-equity
financed and has a beta of 090
The firm has decided to lever up to a capital structure of 1
part debt to 1 part equity
Since the firm will remain in the same industry its asset
beta should remain 090
However assuming a zero beta for its debt its equity beta
would become twice as large
bAsset = 090 = 1 + 1
1times bEquity bEquity = 2 times 090 = 180
13-3
Where Do We Stand
bull Earlier chapters on capital budgeting focused on the identification of relevant (incremental) cash flows and their timing evaluating say NPV using a given discount rate
bull This chapter discusses how to find the appropriate discount rate or required rate of return or the cost of capital when cash flows are risky
13-4
4
Invest in project
131 The Cost of Equity Capital
Firm with
excess cash
Shareholderrsquos
Terminal
Value
Pay cash dividend
Shareholder
invests in
financial
asset
Because stockholders can reinvest the dividend in risky financial assets
the expected return on a capital-budgeting project should be at least as
great as the expected return on a financial asset of comparable risk
A firm with excess cash can either pay a dividend or make a capital investment
13-5
5
Cost of Equity Capital
bull Implication Discount rate needs to be
appropriate for projectrsquos risk (not necessarily the
same as the firmrsquos overall risk)
bull Letrsquos begin by considering how to estimate a
firmrsquos cost of equity capital
bull Two approaches for finding a firmrsquos equity cost
of capital
ndash From last time CAPM
ndash Dividend Discount Model (DDM)
13-6
The Cost of Equity Capitalbull The cost of equity capital is the required return on the
stockholdersrsquo investment in the firm CAPM can be
used to estimate the required return From the firmrsquos
perspective the expected return is the Cost of Equity
Capital )( FMiFi RRβRR
bull To estimate a firmrsquos cost of equity capital we need to know three things
1 The risk-free rate RF
FM RR 2 The market risk premium
2
)(
)(
M
Mi
M
Mii
σ
σ
RVar
RRCovβ 3 The company beta
13-7
Examplebull Suppose the stock of Stansfield Enterprises a
publisher of PowerPoint presentations has a
beta of 15 The firm is 100 equity financed
bull Assume a risk-free rate of 3 and a market
risk premium of 7
bull What is the appropriate discount rate for an
expansion of this firm
)( FMFs RRβRR
7513 sR
513sR
13-8
ExampleSuppose Stansfield Enterprises is evaluating the
following independent projects Each costs $100 and
lasts one year
Project Project b Projectrsquos
Estimated Cash
Flows Next
Year
IRR NPV at
135
A 15 $125 25 $1013
B 15 $1135 135 $0
C 15 $105 5 -$749
13-9
Using the SML
An all-equity firm should accept projects whose IRRs exceed the
cost of equity capital and reject projects whose IRRs fall short of
the cost of capital
Pro
ject
IRR
Firmrsquos risk (beta)
SML
5
Good
project
Bad project
30
25
A
B
C
13-10
The Risk-free Ratebull Treasury securities are close proxies for the risk-free
rate
bull Although the T-Bill rate is theoretically risk free it is
frequently distorted by Fed Policy
bull The CAPM is a period model However projects are
long-lived So average period (short-term) rates need to
be used
bull The historic premium of long-term (20-year) rates over short-term rates for government securities is 2
bull So the risk-free rate to be used in the CAPM could be estimated as 2 below the prevailing rate on 20-year treasury securities
bull Or use short term T-Note rates instead say 10 years
bull httpfinanceyahoocomqs=^TNX
13-11
The Market Risk Premium
bull Method 1 Use historical data
bull Method 2 Use the Dividend Discount Model
ndash Market data and analyst forecasts can be used to
implement the DDM approach on a market-wide
basis
ndash Will not be stable Also subject to growth assumption
bull Method 3 Use forecasts
gP
DR 1
13-12
Historical Market Risk Premium
bull From SBBI Data1926-2010
ndash Small Stocks 1222
ndash SampP 500 985
ndash US LT Gov Bonds 545
ndash US 30 Day T Bills 362
ndash US Inflation 304
bull Risk Premium
ndash SP500-LT Bonds = 985-545= 44
ndash SP500-T Bills = 985-362= 623
13-13
Implied Risk Premium using the
SampP 500bull httppagessternnyuedu~adamodar
bull D1P is the dividend yield Because firms also buyback shares we can use
in its place the dividend yield plus the buyback yieldndash 181+208 = 388
bull g is the growth rate of dividends For simplicity use the historic growth ratendash Dividend in 2001 = 1574 in 2010 = 2273 g=(22731574)(19)-1 = 42
0862088
088
24883
1
RFRERP
ERPRFR
R
R
gP
DR
13-14
Survey data on the risk premium
bull Most survey data is of academics and industry
professionals
ndash Average is about 55
ndash Has fallen in recent years from above 6
13-15
Estimation of Beta
Market Portfolio - Portfolio of all assets in the
economy In practice a broad stock market
index such as the SampP 500 is used to represent
the market
Beta - Sensitivity of a stockrsquos return to the return
on the market portfolio
13-16
Estimation of Beta
)(
)(
M
Mi
RVar
RRCovβ
bull Problems
1 Betas may vary over time
2 The sample size may be inadequate
3 Betas are influenced by changing financial leverage and business risk
(see Rolling Beta for TGTxlsx)
13-17
Stability of Beta
bull Most analysts argue that betas are generally
stable for firms remaining in the same industry
bull That is not to say that a firmrsquos beta cannot
change
ndash Changes in product line
ndash Changes in technology
ndash Deregulation
ndash Changes in financial leverage
13-18
Determinants of Beta
bull Business Risk
ndash Cyclicality of Revenues
ndash Operating Leverage
bull Financial Risk
ndash Financial Leverage
bull Highly cyclical stocks have higher betas
ndash Retailers auto makers
bull Less cyclical
ndash Utilities
13-19
Example
bull Suppose the stock of Stansfield Enterprises a
publisher of PowerPoint presentations has a beta of
25 The firm is 100 equity financed
bull Assume a risk-free rate of 5 and a market risk
premium of 10
bull What is the appropriate discount rate for an expansion
of this firm
13-20
Example
Suppose Stansfield Enterprises is evaluating the
following independent projects Each costs $100 and
lasts one year
Project Project b Projectrsquos
Estimated Cash
Flows Next Year
IRR NPV at
30
A 25 $150 50 $1538
B 25 $130 30 $0
C 25 $110 10 -$1538
13-21
Using the SML
An all-equity firm should accept projects whose IRRs
exceed the cost of equity capital and reject projects whose
IRRs fall short of the cost of capital
Pro
ject
IRR
Firmrsquos risk (beta)
SML
5
Good
project
Bad project
30
25
A
B
C
13-22
What if project betas vary
bull If the firm has a single cost of capital but
considers projects of varying risk adjustments
should be made
ndash Different risk adjusted costs of capital should be used
for each project
bull Otherwise the firm will over invest in risky
projects
ndash Why - See the following example
13-23
Suppose the Conglomerate Company has a cost of capital
based on the CAPM of 17 The risk-free rate is 4 the
market risk premium is 10 and the firmrsquos beta is 13
17 = 4 + 13 times 10
This is a breakdown of the companyrsquos investment projects
13 Automotive Retailer b = 20
13 Computer Hard Drive Manufacturer b = 13
13 Electric Utility b = 06
average b of assets = 13
When evaluating a new electrical generation investment
which cost of capital should be used
Capital Budgeting amp Project Risk
13-24
Capital Budgeting amp Project RiskP
roje
ct I
RR
Projectrsquos risk (b)
17
13 2006
R = 4 + 06times(14 ndash 4 ) = 10
10 reflects the opportunity cost of capital on an investment in electrical generation given the unique risk of the project
10
24 Investments in hard
drives or auto
retailing should have
higher discount rates
SML
13-25
Capital Budgeting amp Project Risk
A firm that uses one discount rate for all projects may over
time increase the risk of the firm while decreasing its value
Pro
ject
IR
R
Firmrsquos risk (beta)
SML
rf
bFIRM
Incorrectly rejected
positive NPV projects
Incorrectly accepted
negative NPV projects
Hurdle
rate)( FMFIRMF RRβR
The SML can tell us why
13-26
The Weighted Average Cost of
Capital
bull The Weighted Average Cost of Capital is given
by
bull Because interest expense is tax-deductible we multiply the last term by (1 ndash TC)
RWACC = Equity + Debt
Equitytimes REquity +
Equity + Debt
Debttimes RDebt times(1 ndash TC)
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-27
Cost of Debt
bull Interest rate required on new debt issuance (ie yield to
maturity on outstanding debt)
bull Adjust for the tax deductibility of interest expense
bull In practice finding new debt issuances is tricky
bull For companies with publicly traded debt we can rely on
the yield to maturity of the debt
ndash Note that the coupon rate is NOT a measure of the cost of debt
today
bull httpfinanceyahoocombonds
13-28
Example Target Corp
bull First we estimate the cost of equity and the cost
of debt
ndash We estimate an equity beta to estimate the cost of
equity
ndash We can often estimate the cost of debt by observing
the YTM of the firmrsquos debt
bull Second we determine the WACC by weighting
these two costs appropriately
13-29
Example International Paper
bull The industry average beta is 082 the risk free rate is
3 and the market risk premium is 84
bull Thus the cost of equity capital is
RS = RF + bi times (RM ndash RF)
= 3 +82times84
= 989
13-30
Example International Paper
bull The yield on the companyrsquos debt is 8 and
the firm has a 37 marginal tax rate The
debt to value ratio is 32
834 is Internationalrsquos cost of capital
= 068 times 989 + 032 times 8 times (1 ndash 037)
= 834
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-31
Financial Leverage and Beta
bull Operating leverage refers to the sensitivity to the firmrsquos
fixed costs of production
bull Financial leverage is the sensitivity to a firmrsquos fixed
costs of financing
bull The relationship between the betas of the firmrsquos debt
equity and assets is given by
bull Financial leverage always increases the equity beta relative to the asset beta
bAsset = Debt + Equity
Debttimes bDebt +
Debt + Equity
Equitytimes bEquity
13-32
Example
Consider Grand Sport Inc which is currently all-equity
financed and has a beta of 090
The firm has decided to lever up to a capital structure of 1
part debt to 1 part equity
Since the firm will remain in the same industry its asset
beta should remain 090
However assuming a zero beta for its debt its equity beta
would become twice as large
bAsset = 090 = 1 + 1
1times bEquity bEquity = 2 times 090 = 180
13-4
4
Invest in project
131 The Cost of Equity Capital
Firm with
excess cash
Shareholderrsquos
Terminal
Value
Pay cash dividend
Shareholder
invests in
financial
asset
Because stockholders can reinvest the dividend in risky financial assets
the expected return on a capital-budgeting project should be at least as
great as the expected return on a financial asset of comparable risk
A firm with excess cash can either pay a dividend or make a capital investment
13-5
5
Cost of Equity Capital
bull Implication Discount rate needs to be
appropriate for projectrsquos risk (not necessarily the
same as the firmrsquos overall risk)
bull Letrsquos begin by considering how to estimate a
firmrsquos cost of equity capital
bull Two approaches for finding a firmrsquos equity cost
of capital
ndash From last time CAPM
ndash Dividend Discount Model (DDM)
13-6
The Cost of Equity Capitalbull The cost of equity capital is the required return on the
stockholdersrsquo investment in the firm CAPM can be
used to estimate the required return From the firmrsquos
perspective the expected return is the Cost of Equity
Capital )( FMiFi RRβRR
bull To estimate a firmrsquos cost of equity capital we need to know three things
1 The risk-free rate RF
FM RR 2 The market risk premium
2
)(
)(
M
Mi
M
Mii
σ
σ
RVar
RRCovβ 3 The company beta
13-7
Examplebull Suppose the stock of Stansfield Enterprises a
publisher of PowerPoint presentations has a
beta of 15 The firm is 100 equity financed
bull Assume a risk-free rate of 3 and a market
risk premium of 7
bull What is the appropriate discount rate for an
expansion of this firm
)( FMFs RRβRR
7513 sR
513sR
13-8
ExampleSuppose Stansfield Enterprises is evaluating the
following independent projects Each costs $100 and
lasts one year
Project Project b Projectrsquos
Estimated Cash
Flows Next
Year
IRR NPV at
135
A 15 $125 25 $1013
B 15 $1135 135 $0
C 15 $105 5 -$749
13-9
Using the SML
An all-equity firm should accept projects whose IRRs exceed the
cost of equity capital and reject projects whose IRRs fall short of
the cost of capital
Pro
ject
IRR
Firmrsquos risk (beta)
SML
5
Good
project
Bad project
30
25
A
B
C
13-10
The Risk-free Ratebull Treasury securities are close proxies for the risk-free
rate
bull Although the T-Bill rate is theoretically risk free it is
frequently distorted by Fed Policy
bull The CAPM is a period model However projects are
long-lived So average period (short-term) rates need to
be used
bull The historic premium of long-term (20-year) rates over short-term rates for government securities is 2
bull So the risk-free rate to be used in the CAPM could be estimated as 2 below the prevailing rate on 20-year treasury securities
bull Or use short term T-Note rates instead say 10 years
bull httpfinanceyahoocomqs=^TNX
13-11
The Market Risk Premium
bull Method 1 Use historical data
bull Method 2 Use the Dividend Discount Model
ndash Market data and analyst forecasts can be used to
implement the DDM approach on a market-wide
basis
ndash Will not be stable Also subject to growth assumption
bull Method 3 Use forecasts
gP
DR 1
13-12
Historical Market Risk Premium
bull From SBBI Data1926-2010
ndash Small Stocks 1222
ndash SampP 500 985
ndash US LT Gov Bonds 545
ndash US 30 Day T Bills 362
ndash US Inflation 304
bull Risk Premium
ndash SP500-LT Bonds = 985-545= 44
ndash SP500-T Bills = 985-362= 623
13-13
Implied Risk Premium using the
SampP 500bull httppagessternnyuedu~adamodar
bull D1P is the dividend yield Because firms also buyback shares we can use
in its place the dividend yield plus the buyback yieldndash 181+208 = 388
bull g is the growth rate of dividends For simplicity use the historic growth ratendash Dividend in 2001 = 1574 in 2010 = 2273 g=(22731574)(19)-1 = 42
0862088
088
24883
1
RFRERP
ERPRFR
R
R
gP
DR
13-14
Survey data on the risk premium
bull Most survey data is of academics and industry
professionals
ndash Average is about 55
ndash Has fallen in recent years from above 6
13-15
Estimation of Beta
Market Portfolio - Portfolio of all assets in the
economy In practice a broad stock market
index such as the SampP 500 is used to represent
the market
Beta - Sensitivity of a stockrsquos return to the return
on the market portfolio
13-16
Estimation of Beta
)(
)(
M
Mi
RVar
RRCovβ
bull Problems
1 Betas may vary over time
2 The sample size may be inadequate
3 Betas are influenced by changing financial leverage and business risk
(see Rolling Beta for TGTxlsx)
13-17
Stability of Beta
bull Most analysts argue that betas are generally
stable for firms remaining in the same industry
bull That is not to say that a firmrsquos beta cannot
change
ndash Changes in product line
ndash Changes in technology
ndash Deregulation
ndash Changes in financial leverage
13-18
Determinants of Beta
bull Business Risk
ndash Cyclicality of Revenues
ndash Operating Leverage
bull Financial Risk
ndash Financial Leverage
bull Highly cyclical stocks have higher betas
ndash Retailers auto makers
bull Less cyclical
ndash Utilities
13-19
Example
bull Suppose the stock of Stansfield Enterprises a
publisher of PowerPoint presentations has a beta of
25 The firm is 100 equity financed
bull Assume a risk-free rate of 5 and a market risk
premium of 10
bull What is the appropriate discount rate for an expansion
of this firm
13-20
Example
Suppose Stansfield Enterprises is evaluating the
following independent projects Each costs $100 and
lasts one year
Project Project b Projectrsquos
Estimated Cash
Flows Next Year
IRR NPV at
30
A 25 $150 50 $1538
B 25 $130 30 $0
C 25 $110 10 -$1538
13-21
Using the SML
An all-equity firm should accept projects whose IRRs
exceed the cost of equity capital and reject projects whose
IRRs fall short of the cost of capital
Pro
ject
IRR
Firmrsquos risk (beta)
SML
5
Good
project
Bad project
30
25
A
B
C
13-22
What if project betas vary
bull If the firm has a single cost of capital but
considers projects of varying risk adjustments
should be made
ndash Different risk adjusted costs of capital should be used
for each project
bull Otherwise the firm will over invest in risky
projects
ndash Why - See the following example
13-23
Suppose the Conglomerate Company has a cost of capital
based on the CAPM of 17 The risk-free rate is 4 the
market risk premium is 10 and the firmrsquos beta is 13
17 = 4 + 13 times 10
This is a breakdown of the companyrsquos investment projects
13 Automotive Retailer b = 20
13 Computer Hard Drive Manufacturer b = 13
13 Electric Utility b = 06
average b of assets = 13
When evaluating a new electrical generation investment
which cost of capital should be used
Capital Budgeting amp Project Risk
13-24
Capital Budgeting amp Project RiskP
roje
ct I
RR
Projectrsquos risk (b)
17
13 2006
R = 4 + 06times(14 ndash 4 ) = 10
10 reflects the opportunity cost of capital on an investment in electrical generation given the unique risk of the project
10
24 Investments in hard
drives or auto
retailing should have
higher discount rates
SML
13-25
Capital Budgeting amp Project Risk
A firm that uses one discount rate for all projects may over
time increase the risk of the firm while decreasing its value
Pro
ject
IR
R
Firmrsquos risk (beta)
SML
rf
bFIRM
Incorrectly rejected
positive NPV projects
Incorrectly accepted
negative NPV projects
Hurdle
rate)( FMFIRMF RRβR
The SML can tell us why
13-26
The Weighted Average Cost of
Capital
bull The Weighted Average Cost of Capital is given
by
bull Because interest expense is tax-deductible we multiply the last term by (1 ndash TC)
RWACC = Equity + Debt
Equitytimes REquity +
Equity + Debt
Debttimes RDebt times(1 ndash TC)
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-27
Cost of Debt
bull Interest rate required on new debt issuance (ie yield to
maturity on outstanding debt)
bull Adjust for the tax deductibility of interest expense
bull In practice finding new debt issuances is tricky
bull For companies with publicly traded debt we can rely on
the yield to maturity of the debt
ndash Note that the coupon rate is NOT a measure of the cost of debt
today
bull httpfinanceyahoocombonds
13-28
Example Target Corp
bull First we estimate the cost of equity and the cost
of debt
ndash We estimate an equity beta to estimate the cost of
equity
ndash We can often estimate the cost of debt by observing
the YTM of the firmrsquos debt
bull Second we determine the WACC by weighting
these two costs appropriately
13-29
Example International Paper
bull The industry average beta is 082 the risk free rate is
3 and the market risk premium is 84
bull Thus the cost of equity capital is
RS = RF + bi times (RM ndash RF)
= 3 +82times84
= 989
13-30
Example International Paper
bull The yield on the companyrsquos debt is 8 and
the firm has a 37 marginal tax rate The
debt to value ratio is 32
834 is Internationalrsquos cost of capital
= 068 times 989 + 032 times 8 times (1 ndash 037)
= 834
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-31
Financial Leverage and Beta
bull Operating leverage refers to the sensitivity to the firmrsquos
fixed costs of production
bull Financial leverage is the sensitivity to a firmrsquos fixed
costs of financing
bull The relationship between the betas of the firmrsquos debt
equity and assets is given by
bull Financial leverage always increases the equity beta relative to the asset beta
bAsset = Debt + Equity
Debttimes bDebt +
Debt + Equity
Equitytimes bEquity
13-32
Example
Consider Grand Sport Inc which is currently all-equity
financed and has a beta of 090
The firm has decided to lever up to a capital structure of 1
part debt to 1 part equity
Since the firm will remain in the same industry its asset
beta should remain 090
However assuming a zero beta for its debt its equity beta
would become twice as large
bAsset = 090 = 1 + 1
1times bEquity bEquity = 2 times 090 = 180
13-5
5
Cost of Equity Capital
bull Implication Discount rate needs to be
appropriate for projectrsquos risk (not necessarily the
same as the firmrsquos overall risk)
bull Letrsquos begin by considering how to estimate a
firmrsquos cost of equity capital
bull Two approaches for finding a firmrsquos equity cost
of capital
ndash From last time CAPM
ndash Dividend Discount Model (DDM)
13-6
The Cost of Equity Capitalbull The cost of equity capital is the required return on the
stockholdersrsquo investment in the firm CAPM can be
used to estimate the required return From the firmrsquos
perspective the expected return is the Cost of Equity
Capital )( FMiFi RRβRR
bull To estimate a firmrsquos cost of equity capital we need to know three things
1 The risk-free rate RF
FM RR 2 The market risk premium
2
)(
)(
M
Mi
M
Mii
σ
σ
RVar
RRCovβ 3 The company beta
13-7
Examplebull Suppose the stock of Stansfield Enterprises a
publisher of PowerPoint presentations has a
beta of 15 The firm is 100 equity financed
bull Assume a risk-free rate of 3 and a market
risk premium of 7
bull What is the appropriate discount rate for an
expansion of this firm
)( FMFs RRβRR
7513 sR
513sR
13-8
ExampleSuppose Stansfield Enterprises is evaluating the
following independent projects Each costs $100 and
lasts one year
Project Project b Projectrsquos
Estimated Cash
Flows Next
Year
IRR NPV at
135
A 15 $125 25 $1013
B 15 $1135 135 $0
C 15 $105 5 -$749
13-9
Using the SML
An all-equity firm should accept projects whose IRRs exceed the
cost of equity capital and reject projects whose IRRs fall short of
the cost of capital
Pro
ject
IRR
Firmrsquos risk (beta)
SML
5
Good
project
Bad project
30
25
A
B
C
13-10
The Risk-free Ratebull Treasury securities are close proxies for the risk-free
rate
bull Although the T-Bill rate is theoretically risk free it is
frequently distorted by Fed Policy
bull The CAPM is a period model However projects are
long-lived So average period (short-term) rates need to
be used
bull The historic premium of long-term (20-year) rates over short-term rates for government securities is 2
bull So the risk-free rate to be used in the CAPM could be estimated as 2 below the prevailing rate on 20-year treasury securities
bull Or use short term T-Note rates instead say 10 years
bull httpfinanceyahoocomqs=^TNX
13-11
The Market Risk Premium
bull Method 1 Use historical data
bull Method 2 Use the Dividend Discount Model
ndash Market data and analyst forecasts can be used to
implement the DDM approach on a market-wide
basis
ndash Will not be stable Also subject to growth assumption
bull Method 3 Use forecasts
gP
DR 1
13-12
Historical Market Risk Premium
bull From SBBI Data1926-2010
ndash Small Stocks 1222
ndash SampP 500 985
ndash US LT Gov Bonds 545
ndash US 30 Day T Bills 362
ndash US Inflation 304
bull Risk Premium
ndash SP500-LT Bonds = 985-545= 44
ndash SP500-T Bills = 985-362= 623
13-13
Implied Risk Premium using the
SampP 500bull httppagessternnyuedu~adamodar
bull D1P is the dividend yield Because firms also buyback shares we can use
in its place the dividend yield plus the buyback yieldndash 181+208 = 388
bull g is the growth rate of dividends For simplicity use the historic growth ratendash Dividend in 2001 = 1574 in 2010 = 2273 g=(22731574)(19)-1 = 42
0862088
088
24883
1
RFRERP
ERPRFR
R
R
gP
DR
13-14
Survey data on the risk premium
bull Most survey data is of academics and industry
professionals
ndash Average is about 55
ndash Has fallen in recent years from above 6
13-15
Estimation of Beta
Market Portfolio - Portfolio of all assets in the
economy In practice a broad stock market
index such as the SampP 500 is used to represent
the market
Beta - Sensitivity of a stockrsquos return to the return
on the market portfolio
13-16
Estimation of Beta
)(
)(
M
Mi
RVar
RRCovβ
bull Problems
1 Betas may vary over time
2 The sample size may be inadequate
3 Betas are influenced by changing financial leverage and business risk
(see Rolling Beta for TGTxlsx)
13-17
Stability of Beta
bull Most analysts argue that betas are generally
stable for firms remaining in the same industry
bull That is not to say that a firmrsquos beta cannot
change
ndash Changes in product line
ndash Changes in technology
ndash Deregulation
ndash Changes in financial leverage
13-18
Determinants of Beta
bull Business Risk
ndash Cyclicality of Revenues
ndash Operating Leverage
bull Financial Risk
ndash Financial Leverage
bull Highly cyclical stocks have higher betas
ndash Retailers auto makers
bull Less cyclical
ndash Utilities
13-19
Example
bull Suppose the stock of Stansfield Enterprises a
publisher of PowerPoint presentations has a beta of
25 The firm is 100 equity financed
bull Assume a risk-free rate of 5 and a market risk
premium of 10
bull What is the appropriate discount rate for an expansion
of this firm
13-20
Example
Suppose Stansfield Enterprises is evaluating the
following independent projects Each costs $100 and
lasts one year
Project Project b Projectrsquos
Estimated Cash
Flows Next Year
IRR NPV at
30
A 25 $150 50 $1538
B 25 $130 30 $0
C 25 $110 10 -$1538
13-21
Using the SML
An all-equity firm should accept projects whose IRRs
exceed the cost of equity capital and reject projects whose
IRRs fall short of the cost of capital
Pro
ject
IRR
Firmrsquos risk (beta)
SML
5
Good
project
Bad project
30
25
A
B
C
13-22
What if project betas vary
bull If the firm has a single cost of capital but
considers projects of varying risk adjustments
should be made
ndash Different risk adjusted costs of capital should be used
for each project
bull Otherwise the firm will over invest in risky
projects
ndash Why - See the following example
13-23
Suppose the Conglomerate Company has a cost of capital
based on the CAPM of 17 The risk-free rate is 4 the
market risk premium is 10 and the firmrsquos beta is 13
17 = 4 + 13 times 10
This is a breakdown of the companyrsquos investment projects
13 Automotive Retailer b = 20
13 Computer Hard Drive Manufacturer b = 13
13 Electric Utility b = 06
average b of assets = 13
When evaluating a new electrical generation investment
which cost of capital should be used
Capital Budgeting amp Project Risk
13-24
Capital Budgeting amp Project RiskP
roje
ct I
RR
Projectrsquos risk (b)
17
13 2006
R = 4 + 06times(14 ndash 4 ) = 10
10 reflects the opportunity cost of capital on an investment in electrical generation given the unique risk of the project
10
24 Investments in hard
drives or auto
retailing should have
higher discount rates
SML
13-25
Capital Budgeting amp Project Risk
A firm that uses one discount rate for all projects may over
time increase the risk of the firm while decreasing its value
Pro
ject
IR
R
Firmrsquos risk (beta)
SML
rf
bFIRM
Incorrectly rejected
positive NPV projects
Incorrectly accepted
negative NPV projects
Hurdle
rate)( FMFIRMF RRβR
The SML can tell us why
13-26
The Weighted Average Cost of
Capital
bull The Weighted Average Cost of Capital is given
by
bull Because interest expense is tax-deductible we multiply the last term by (1 ndash TC)
RWACC = Equity + Debt
Equitytimes REquity +
Equity + Debt
Debttimes RDebt times(1 ndash TC)
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-27
Cost of Debt
bull Interest rate required on new debt issuance (ie yield to
maturity on outstanding debt)
bull Adjust for the tax deductibility of interest expense
bull In practice finding new debt issuances is tricky
bull For companies with publicly traded debt we can rely on
the yield to maturity of the debt
ndash Note that the coupon rate is NOT a measure of the cost of debt
today
bull httpfinanceyahoocombonds
13-28
Example Target Corp
bull First we estimate the cost of equity and the cost
of debt
ndash We estimate an equity beta to estimate the cost of
equity
ndash We can often estimate the cost of debt by observing
the YTM of the firmrsquos debt
bull Second we determine the WACC by weighting
these two costs appropriately
13-29
Example International Paper
bull The industry average beta is 082 the risk free rate is
3 and the market risk premium is 84
bull Thus the cost of equity capital is
RS = RF + bi times (RM ndash RF)
= 3 +82times84
= 989
13-30
Example International Paper
bull The yield on the companyrsquos debt is 8 and
the firm has a 37 marginal tax rate The
debt to value ratio is 32
834 is Internationalrsquos cost of capital
= 068 times 989 + 032 times 8 times (1 ndash 037)
= 834
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-31
Financial Leverage and Beta
bull Operating leverage refers to the sensitivity to the firmrsquos
fixed costs of production
bull Financial leverage is the sensitivity to a firmrsquos fixed
costs of financing
bull The relationship between the betas of the firmrsquos debt
equity and assets is given by
bull Financial leverage always increases the equity beta relative to the asset beta
bAsset = Debt + Equity
Debttimes bDebt +
Debt + Equity
Equitytimes bEquity
13-32
Example
Consider Grand Sport Inc which is currently all-equity
financed and has a beta of 090
The firm has decided to lever up to a capital structure of 1
part debt to 1 part equity
Since the firm will remain in the same industry its asset
beta should remain 090
However assuming a zero beta for its debt its equity beta
would become twice as large
bAsset = 090 = 1 + 1
1times bEquity bEquity = 2 times 090 = 180
13-6
The Cost of Equity Capitalbull The cost of equity capital is the required return on the
stockholdersrsquo investment in the firm CAPM can be
used to estimate the required return From the firmrsquos
perspective the expected return is the Cost of Equity
Capital )( FMiFi RRβRR
bull To estimate a firmrsquos cost of equity capital we need to know three things
1 The risk-free rate RF
FM RR 2 The market risk premium
2
)(
)(
M
Mi
M
Mii
σ
σ
RVar
RRCovβ 3 The company beta
13-7
Examplebull Suppose the stock of Stansfield Enterprises a
publisher of PowerPoint presentations has a
beta of 15 The firm is 100 equity financed
bull Assume a risk-free rate of 3 and a market
risk premium of 7
bull What is the appropriate discount rate for an
expansion of this firm
)( FMFs RRβRR
7513 sR
513sR
13-8
ExampleSuppose Stansfield Enterprises is evaluating the
following independent projects Each costs $100 and
lasts one year
Project Project b Projectrsquos
Estimated Cash
Flows Next
Year
IRR NPV at
135
A 15 $125 25 $1013
B 15 $1135 135 $0
C 15 $105 5 -$749
13-9
Using the SML
An all-equity firm should accept projects whose IRRs exceed the
cost of equity capital and reject projects whose IRRs fall short of
the cost of capital
Pro
ject
IRR
Firmrsquos risk (beta)
SML
5
Good
project
Bad project
30
25
A
B
C
13-10
The Risk-free Ratebull Treasury securities are close proxies for the risk-free
rate
bull Although the T-Bill rate is theoretically risk free it is
frequently distorted by Fed Policy
bull The CAPM is a period model However projects are
long-lived So average period (short-term) rates need to
be used
bull The historic premium of long-term (20-year) rates over short-term rates for government securities is 2
bull So the risk-free rate to be used in the CAPM could be estimated as 2 below the prevailing rate on 20-year treasury securities
bull Or use short term T-Note rates instead say 10 years
bull httpfinanceyahoocomqs=^TNX
13-11
The Market Risk Premium
bull Method 1 Use historical data
bull Method 2 Use the Dividend Discount Model
ndash Market data and analyst forecasts can be used to
implement the DDM approach on a market-wide
basis
ndash Will not be stable Also subject to growth assumption
bull Method 3 Use forecasts
gP
DR 1
13-12
Historical Market Risk Premium
bull From SBBI Data1926-2010
ndash Small Stocks 1222
ndash SampP 500 985
ndash US LT Gov Bonds 545
ndash US 30 Day T Bills 362
ndash US Inflation 304
bull Risk Premium
ndash SP500-LT Bonds = 985-545= 44
ndash SP500-T Bills = 985-362= 623
13-13
Implied Risk Premium using the
SampP 500bull httppagessternnyuedu~adamodar
bull D1P is the dividend yield Because firms also buyback shares we can use
in its place the dividend yield plus the buyback yieldndash 181+208 = 388
bull g is the growth rate of dividends For simplicity use the historic growth ratendash Dividend in 2001 = 1574 in 2010 = 2273 g=(22731574)(19)-1 = 42
0862088
088
24883
1
RFRERP
ERPRFR
R
R
gP
DR
13-14
Survey data on the risk premium
bull Most survey data is of academics and industry
professionals
ndash Average is about 55
ndash Has fallen in recent years from above 6
13-15
Estimation of Beta
Market Portfolio - Portfolio of all assets in the
economy In practice a broad stock market
index such as the SampP 500 is used to represent
the market
Beta - Sensitivity of a stockrsquos return to the return
on the market portfolio
13-16
Estimation of Beta
)(
)(
M
Mi
RVar
RRCovβ
bull Problems
1 Betas may vary over time
2 The sample size may be inadequate
3 Betas are influenced by changing financial leverage and business risk
(see Rolling Beta for TGTxlsx)
13-17
Stability of Beta
bull Most analysts argue that betas are generally
stable for firms remaining in the same industry
bull That is not to say that a firmrsquos beta cannot
change
ndash Changes in product line
ndash Changes in technology
ndash Deregulation
ndash Changes in financial leverage
13-18
Determinants of Beta
bull Business Risk
ndash Cyclicality of Revenues
ndash Operating Leverage
bull Financial Risk
ndash Financial Leverage
bull Highly cyclical stocks have higher betas
ndash Retailers auto makers
bull Less cyclical
ndash Utilities
13-19
Example
bull Suppose the stock of Stansfield Enterprises a
publisher of PowerPoint presentations has a beta of
25 The firm is 100 equity financed
bull Assume a risk-free rate of 5 and a market risk
premium of 10
bull What is the appropriate discount rate for an expansion
of this firm
13-20
Example
Suppose Stansfield Enterprises is evaluating the
following independent projects Each costs $100 and
lasts one year
Project Project b Projectrsquos
Estimated Cash
Flows Next Year
IRR NPV at
30
A 25 $150 50 $1538
B 25 $130 30 $0
C 25 $110 10 -$1538
13-21
Using the SML
An all-equity firm should accept projects whose IRRs
exceed the cost of equity capital and reject projects whose
IRRs fall short of the cost of capital
Pro
ject
IRR
Firmrsquos risk (beta)
SML
5
Good
project
Bad project
30
25
A
B
C
13-22
What if project betas vary
bull If the firm has a single cost of capital but
considers projects of varying risk adjustments
should be made
ndash Different risk adjusted costs of capital should be used
for each project
bull Otherwise the firm will over invest in risky
projects
ndash Why - See the following example
13-23
Suppose the Conglomerate Company has a cost of capital
based on the CAPM of 17 The risk-free rate is 4 the
market risk premium is 10 and the firmrsquos beta is 13
17 = 4 + 13 times 10
This is a breakdown of the companyrsquos investment projects
13 Automotive Retailer b = 20
13 Computer Hard Drive Manufacturer b = 13
13 Electric Utility b = 06
average b of assets = 13
When evaluating a new electrical generation investment
which cost of capital should be used
Capital Budgeting amp Project Risk
13-24
Capital Budgeting amp Project RiskP
roje
ct I
RR
Projectrsquos risk (b)
17
13 2006
R = 4 + 06times(14 ndash 4 ) = 10
10 reflects the opportunity cost of capital on an investment in electrical generation given the unique risk of the project
10
24 Investments in hard
drives or auto
retailing should have
higher discount rates
SML
13-25
Capital Budgeting amp Project Risk
A firm that uses one discount rate for all projects may over
time increase the risk of the firm while decreasing its value
Pro
ject
IR
R
Firmrsquos risk (beta)
SML
rf
bFIRM
Incorrectly rejected
positive NPV projects
Incorrectly accepted
negative NPV projects
Hurdle
rate)( FMFIRMF RRβR
The SML can tell us why
13-26
The Weighted Average Cost of
Capital
bull The Weighted Average Cost of Capital is given
by
bull Because interest expense is tax-deductible we multiply the last term by (1 ndash TC)
RWACC = Equity + Debt
Equitytimes REquity +
Equity + Debt
Debttimes RDebt times(1 ndash TC)
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-27
Cost of Debt
bull Interest rate required on new debt issuance (ie yield to
maturity on outstanding debt)
bull Adjust for the tax deductibility of interest expense
bull In practice finding new debt issuances is tricky
bull For companies with publicly traded debt we can rely on
the yield to maturity of the debt
ndash Note that the coupon rate is NOT a measure of the cost of debt
today
bull httpfinanceyahoocombonds
13-28
Example Target Corp
bull First we estimate the cost of equity and the cost
of debt
ndash We estimate an equity beta to estimate the cost of
equity
ndash We can often estimate the cost of debt by observing
the YTM of the firmrsquos debt
bull Second we determine the WACC by weighting
these two costs appropriately
13-29
Example International Paper
bull The industry average beta is 082 the risk free rate is
3 and the market risk premium is 84
bull Thus the cost of equity capital is
RS = RF + bi times (RM ndash RF)
= 3 +82times84
= 989
13-30
Example International Paper
bull The yield on the companyrsquos debt is 8 and
the firm has a 37 marginal tax rate The
debt to value ratio is 32
834 is Internationalrsquos cost of capital
= 068 times 989 + 032 times 8 times (1 ndash 037)
= 834
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-31
Financial Leverage and Beta
bull Operating leverage refers to the sensitivity to the firmrsquos
fixed costs of production
bull Financial leverage is the sensitivity to a firmrsquos fixed
costs of financing
bull The relationship between the betas of the firmrsquos debt
equity and assets is given by
bull Financial leverage always increases the equity beta relative to the asset beta
bAsset = Debt + Equity
Debttimes bDebt +
Debt + Equity
Equitytimes bEquity
13-32
Example
Consider Grand Sport Inc which is currently all-equity
financed and has a beta of 090
The firm has decided to lever up to a capital structure of 1
part debt to 1 part equity
Since the firm will remain in the same industry its asset
beta should remain 090
However assuming a zero beta for its debt its equity beta
would become twice as large
bAsset = 090 = 1 + 1
1times bEquity bEquity = 2 times 090 = 180
13-7
Examplebull Suppose the stock of Stansfield Enterprises a
publisher of PowerPoint presentations has a
beta of 15 The firm is 100 equity financed
bull Assume a risk-free rate of 3 and a market
risk premium of 7
bull What is the appropriate discount rate for an
expansion of this firm
)( FMFs RRβRR
7513 sR
513sR
13-8
ExampleSuppose Stansfield Enterprises is evaluating the
following independent projects Each costs $100 and
lasts one year
Project Project b Projectrsquos
Estimated Cash
Flows Next
Year
IRR NPV at
135
A 15 $125 25 $1013
B 15 $1135 135 $0
C 15 $105 5 -$749
13-9
Using the SML
An all-equity firm should accept projects whose IRRs exceed the
cost of equity capital and reject projects whose IRRs fall short of
the cost of capital
Pro
ject
IRR
Firmrsquos risk (beta)
SML
5
Good
project
Bad project
30
25
A
B
C
13-10
The Risk-free Ratebull Treasury securities are close proxies for the risk-free
rate
bull Although the T-Bill rate is theoretically risk free it is
frequently distorted by Fed Policy
bull The CAPM is a period model However projects are
long-lived So average period (short-term) rates need to
be used
bull The historic premium of long-term (20-year) rates over short-term rates for government securities is 2
bull So the risk-free rate to be used in the CAPM could be estimated as 2 below the prevailing rate on 20-year treasury securities
bull Or use short term T-Note rates instead say 10 years
bull httpfinanceyahoocomqs=^TNX
13-11
The Market Risk Premium
bull Method 1 Use historical data
bull Method 2 Use the Dividend Discount Model
ndash Market data and analyst forecasts can be used to
implement the DDM approach on a market-wide
basis
ndash Will not be stable Also subject to growth assumption
bull Method 3 Use forecasts
gP
DR 1
13-12
Historical Market Risk Premium
bull From SBBI Data1926-2010
ndash Small Stocks 1222
ndash SampP 500 985
ndash US LT Gov Bonds 545
ndash US 30 Day T Bills 362
ndash US Inflation 304
bull Risk Premium
ndash SP500-LT Bonds = 985-545= 44
ndash SP500-T Bills = 985-362= 623
13-13
Implied Risk Premium using the
SampP 500bull httppagessternnyuedu~adamodar
bull D1P is the dividend yield Because firms also buyback shares we can use
in its place the dividend yield plus the buyback yieldndash 181+208 = 388
bull g is the growth rate of dividends For simplicity use the historic growth ratendash Dividend in 2001 = 1574 in 2010 = 2273 g=(22731574)(19)-1 = 42
0862088
088
24883
1
RFRERP
ERPRFR
R
R
gP
DR
13-14
Survey data on the risk premium
bull Most survey data is of academics and industry
professionals
ndash Average is about 55
ndash Has fallen in recent years from above 6
13-15
Estimation of Beta
Market Portfolio - Portfolio of all assets in the
economy In practice a broad stock market
index such as the SampP 500 is used to represent
the market
Beta - Sensitivity of a stockrsquos return to the return
on the market portfolio
13-16
Estimation of Beta
)(
)(
M
Mi
RVar
RRCovβ
bull Problems
1 Betas may vary over time
2 The sample size may be inadequate
3 Betas are influenced by changing financial leverage and business risk
(see Rolling Beta for TGTxlsx)
13-17
Stability of Beta
bull Most analysts argue that betas are generally
stable for firms remaining in the same industry
bull That is not to say that a firmrsquos beta cannot
change
ndash Changes in product line
ndash Changes in technology
ndash Deregulation
ndash Changes in financial leverage
13-18
Determinants of Beta
bull Business Risk
ndash Cyclicality of Revenues
ndash Operating Leverage
bull Financial Risk
ndash Financial Leverage
bull Highly cyclical stocks have higher betas
ndash Retailers auto makers
bull Less cyclical
ndash Utilities
13-19
Example
bull Suppose the stock of Stansfield Enterprises a
publisher of PowerPoint presentations has a beta of
25 The firm is 100 equity financed
bull Assume a risk-free rate of 5 and a market risk
premium of 10
bull What is the appropriate discount rate for an expansion
of this firm
13-20
Example
Suppose Stansfield Enterprises is evaluating the
following independent projects Each costs $100 and
lasts one year
Project Project b Projectrsquos
Estimated Cash
Flows Next Year
IRR NPV at
30
A 25 $150 50 $1538
B 25 $130 30 $0
C 25 $110 10 -$1538
13-21
Using the SML
An all-equity firm should accept projects whose IRRs
exceed the cost of equity capital and reject projects whose
IRRs fall short of the cost of capital
Pro
ject
IRR
Firmrsquos risk (beta)
SML
5
Good
project
Bad project
30
25
A
B
C
13-22
What if project betas vary
bull If the firm has a single cost of capital but
considers projects of varying risk adjustments
should be made
ndash Different risk adjusted costs of capital should be used
for each project
bull Otherwise the firm will over invest in risky
projects
ndash Why - See the following example
13-23
Suppose the Conglomerate Company has a cost of capital
based on the CAPM of 17 The risk-free rate is 4 the
market risk premium is 10 and the firmrsquos beta is 13
17 = 4 + 13 times 10
This is a breakdown of the companyrsquos investment projects
13 Automotive Retailer b = 20
13 Computer Hard Drive Manufacturer b = 13
13 Electric Utility b = 06
average b of assets = 13
When evaluating a new electrical generation investment
which cost of capital should be used
Capital Budgeting amp Project Risk
13-24
Capital Budgeting amp Project RiskP
roje
ct I
RR
Projectrsquos risk (b)
17
13 2006
R = 4 + 06times(14 ndash 4 ) = 10
10 reflects the opportunity cost of capital on an investment in electrical generation given the unique risk of the project
10
24 Investments in hard
drives or auto
retailing should have
higher discount rates
SML
13-25
Capital Budgeting amp Project Risk
A firm that uses one discount rate for all projects may over
time increase the risk of the firm while decreasing its value
Pro
ject
IR
R
Firmrsquos risk (beta)
SML
rf
bFIRM
Incorrectly rejected
positive NPV projects
Incorrectly accepted
negative NPV projects
Hurdle
rate)( FMFIRMF RRβR
The SML can tell us why
13-26
The Weighted Average Cost of
Capital
bull The Weighted Average Cost of Capital is given
by
bull Because interest expense is tax-deductible we multiply the last term by (1 ndash TC)
RWACC = Equity + Debt
Equitytimes REquity +
Equity + Debt
Debttimes RDebt times(1 ndash TC)
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-27
Cost of Debt
bull Interest rate required on new debt issuance (ie yield to
maturity on outstanding debt)
bull Adjust for the tax deductibility of interest expense
bull In practice finding new debt issuances is tricky
bull For companies with publicly traded debt we can rely on
the yield to maturity of the debt
ndash Note that the coupon rate is NOT a measure of the cost of debt
today
bull httpfinanceyahoocombonds
13-28
Example Target Corp
bull First we estimate the cost of equity and the cost
of debt
ndash We estimate an equity beta to estimate the cost of
equity
ndash We can often estimate the cost of debt by observing
the YTM of the firmrsquos debt
bull Second we determine the WACC by weighting
these two costs appropriately
13-29
Example International Paper
bull The industry average beta is 082 the risk free rate is
3 and the market risk premium is 84
bull Thus the cost of equity capital is
RS = RF + bi times (RM ndash RF)
= 3 +82times84
= 989
13-30
Example International Paper
bull The yield on the companyrsquos debt is 8 and
the firm has a 37 marginal tax rate The
debt to value ratio is 32
834 is Internationalrsquos cost of capital
= 068 times 989 + 032 times 8 times (1 ndash 037)
= 834
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-31
Financial Leverage and Beta
bull Operating leverage refers to the sensitivity to the firmrsquos
fixed costs of production
bull Financial leverage is the sensitivity to a firmrsquos fixed
costs of financing
bull The relationship between the betas of the firmrsquos debt
equity and assets is given by
bull Financial leverage always increases the equity beta relative to the asset beta
bAsset = Debt + Equity
Debttimes bDebt +
Debt + Equity
Equitytimes bEquity
13-32
Example
Consider Grand Sport Inc which is currently all-equity
financed and has a beta of 090
The firm has decided to lever up to a capital structure of 1
part debt to 1 part equity
Since the firm will remain in the same industry its asset
beta should remain 090
However assuming a zero beta for its debt its equity beta
would become twice as large
bAsset = 090 = 1 + 1
1times bEquity bEquity = 2 times 090 = 180
13-8
ExampleSuppose Stansfield Enterprises is evaluating the
following independent projects Each costs $100 and
lasts one year
Project Project b Projectrsquos
Estimated Cash
Flows Next
Year
IRR NPV at
135
A 15 $125 25 $1013
B 15 $1135 135 $0
C 15 $105 5 -$749
13-9
Using the SML
An all-equity firm should accept projects whose IRRs exceed the
cost of equity capital and reject projects whose IRRs fall short of
the cost of capital
Pro
ject
IRR
Firmrsquos risk (beta)
SML
5
Good
project
Bad project
30
25
A
B
C
13-10
The Risk-free Ratebull Treasury securities are close proxies for the risk-free
rate
bull Although the T-Bill rate is theoretically risk free it is
frequently distorted by Fed Policy
bull The CAPM is a period model However projects are
long-lived So average period (short-term) rates need to
be used
bull The historic premium of long-term (20-year) rates over short-term rates for government securities is 2
bull So the risk-free rate to be used in the CAPM could be estimated as 2 below the prevailing rate on 20-year treasury securities
bull Or use short term T-Note rates instead say 10 years
bull httpfinanceyahoocomqs=^TNX
13-11
The Market Risk Premium
bull Method 1 Use historical data
bull Method 2 Use the Dividend Discount Model
ndash Market data and analyst forecasts can be used to
implement the DDM approach on a market-wide
basis
ndash Will not be stable Also subject to growth assumption
bull Method 3 Use forecasts
gP
DR 1
13-12
Historical Market Risk Premium
bull From SBBI Data1926-2010
ndash Small Stocks 1222
ndash SampP 500 985
ndash US LT Gov Bonds 545
ndash US 30 Day T Bills 362
ndash US Inflation 304
bull Risk Premium
ndash SP500-LT Bonds = 985-545= 44
ndash SP500-T Bills = 985-362= 623
13-13
Implied Risk Premium using the
SampP 500bull httppagessternnyuedu~adamodar
bull D1P is the dividend yield Because firms also buyback shares we can use
in its place the dividend yield plus the buyback yieldndash 181+208 = 388
bull g is the growth rate of dividends For simplicity use the historic growth ratendash Dividend in 2001 = 1574 in 2010 = 2273 g=(22731574)(19)-1 = 42
0862088
088
24883
1
RFRERP
ERPRFR
R
R
gP
DR
13-14
Survey data on the risk premium
bull Most survey data is of academics and industry
professionals
ndash Average is about 55
ndash Has fallen in recent years from above 6
13-15
Estimation of Beta
Market Portfolio - Portfolio of all assets in the
economy In practice a broad stock market
index such as the SampP 500 is used to represent
the market
Beta - Sensitivity of a stockrsquos return to the return
on the market portfolio
13-16
Estimation of Beta
)(
)(
M
Mi
RVar
RRCovβ
bull Problems
1 Betas may vary over time
2 The sample size may be inadequate
3 Betas are influenced by changing financial leverage and business risk
(see Rolling Beta for TGTxlsx)
13-17
Stability of Beta
bull Most analysts argue that betas are generally
stable for firms remaining in the same industry
bull That is not to say that a firmrsquos beta cannot
change
ndash Changes in product line
ndash Changes in technology
ndash Deregulation
ndash Changes in financial leverage
13-18
Determinants of Beta
bull Business Risk
ndash Cyclicality of Revenues
ndash Operating Leverage
bull Financial Risk
ndash Financial Leverage
bull Highly cyclical stocks have higher betas
ndash Retailers auto makers
bull Less cyclical
ndash Utilities
13-19
Example
bull Suppose the stock of Stansfield Enterprises a
publisher of PowerPoint presentations has a beta of
25 The firm is 100 equity financed
bull Assume a risk-free rate of 5 and a market risk
premium of 10
bull What is the appropriate discount rate for an expansion
of this firm
13-20
Example
Suppose Stansfield Enterprises is evaluating the
following independent projects Each costs $100 and
lasts one year
Project Project b Projectrsquos
Estimated Cash
Flows Next Year
IRR NPV at
30
A 25 $150 50 $1538
B 25 $130 30 $0
C 25 $110 10 -$1538
13-21
Using the SML
An all-equity firm should accept projects whose IRRs
exceed the cost of equity capital and reject projects whose
IRRs fall short of the cost of capital
Pro
ject
IRR
Firmrsquos risk (beta)
SML
5
Good
project
Bad project
30
25
A
B
C
13-22
What if project betas vary
bull If the firm has a single cost of capital but
considers projects of varying risk adjustments
should be made
ndash Different risk adjusted costs of capital should be used
for each project
bull Otherwise the firm will over invest in risky
projects
ndash Why - See the following example
13-23
Suppose the Conglomerate Company has a cost of capital
based on the CAPM of 17 The risk-free rate is 4 the
market risk premium is 10 and the firmrsquos beta is 13
17 = 4 + 13 times 10
This is a breakdown of the companyrsquos investment projects
13 Automotive Retailer b = 20
13 Computer Hard Drive Manufacturer b = 13
13 Electric Utility b = 06
average b of assets = 13
When evaluating a new electrical generation investment
which cost of capital should be used
Capital Budgeting amp Project Risk
13-24
Capital Budgeting amp Project RiskP
roje
ct I
RR
Projectrsquos risk (b)
17
13 2006
R = 4 + 06times(14 ndash 4 ) = 10
10 reflects the opportunity cost of capital on an investment in electrical generation given the unique risk of the project
10
24 Investments in hard
drives or auto
retailing should have
higher discount rates
SML
13-25
Capital Budgeting amp Project Risk
A firm that uses one discount rate for all projects may over
time increase the risk of the firm while decreasing its value
Pro
ject
IR
R
Firmrsquos risk (beta)
SML
rf
bFIRM
Incorrectly rejected
positive NPV projects
Incorrectly accepted
negative NPV projects
Hurdle
rate)( FMFIRMF RRβR
The SML can tell us why
13-26
The Weighted Average Cost of
Capital
bull The Weighted Average Cost of Capital is given
by
bull Because interest expense is tax-deductible we multiply the last term by (1 ndash TC)
RWACC = Equity + Debt
Equitytimes REquity +
Equity + Debt
Debttimes RDebt times(1 ndash TC)
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-27
Cost of Debt
bull Interest rate required on new debt issuance (ie yield to
maturity on outstanding debt)
bull Adjust for the tax deductibility of interest expense
bull In practice finding new debt issuances is tricky
bull For companies with publicly traded debt we can rely on
the yield to maturity of the debt
ndash Note that the coupon rate is NOT a measure of the cost of debt
today
bull httpfinanceyahoocombonds
13-28
Example Target Corp
bull First we estimate the cost of equity and the cost
of debt
ndash We estimate an equity beta to estimate the cost of
equity
ndash We can often estimate the cost of debt by observing
the YTM of the firmrsquos debt
bull Second we determine the WACC by weighting
these two costs appropriately
13-29
Example International Paper
bull The industry average beta is 082 the risk free rate is
3 and the market risk premium is 84
bull Thus the cost of equity capital is
RS = RF + bi times (RM ndash RF)
= 3 +82times84
= 989
13-30
Example International Paper
bull The yield on the companyrsquos debt is 8 and
the firm has a 37 marginal tax rate The
debt to value ratio is 32
834 is Internationalrsquos cost of capital
= 068 times 989 + 032 times 8 times (1 ndash 037)
= 834
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-31
Financial Leverage and Beta
bull Operating leverage refers to the sensitivity to the firmrsquos
fixed costs of production
bull Financial leverage is the sensitivity to a firmrsquos fixed
costs of financing
bull The relationship between the betas of the firmrsquos debt
equity and assets is given by
bull Financial leverage always increases the equity beta relative to the asset beta
bAsset = Debt + Equity
Debttimes bDebt +
Debt + Equity
Equitytimes bEquity
13-32
Example
Consider Grand Sport Inc which is currently all-equity
financed and has a beta of 090
The firm has decided to lever up to a capital structure of 1
part debt to 1 part equity
Since the firm will remain in the same industry its asset
beta should remain 090
However assuming a zero beta for its debt its equity beta
would become twice as large
bAsset = 090 = 1 + 1
1times bEquity bEquity = 2 times 090 = 180
13-9
Using the SML
An all-equity firm should accept projects whose IRRs exceed the
cost of equity capital and reject projects whose IRRs fall short of
the cost of capital
Pro
ject
IRR
Firmrsquos risk (beta)
SML
5
Good
project
Bad project
30
25
A
B
C
13-10
The Risk-free Ratebull Treasury securities are close proxies for the risk-free
rate
bull Although the T-Bill rate is theoretically risk free it is
frequently distorted by Fed Policy
bull The CAPM is a period model However projects are
long-lived So average period (short-term) rates need to
be used
bull The historic premium of long-term (20-year) rates over short-term rates for government securities is 2
bull So the risk-free rate to be used in the CAPM could be estimated as 2 below the prevailing rate on 20-year treasury securities
bull Or use short term T-Note rates instead say 10 years
bull httpfinanceyahoocomqs=^TNX
13-11
The Market Risk Premium
bull Method 1 Use historical data
bull Method 2 Use the Dividend Discount Model
ndash Market data and analyst forecasts can be used to
implement the DDM approach on a market-wide
basis
ndash Will not be stable Also subject to growth assumption
bull Method 3 Use forecasts
gP
DR 1
13-12
Historical Market Risk Premium
bull From SBBI Data1926-2010
ndash Small Stocks 1222
ndash SampP 500 985
ndash US LT Gov Bonds 545
ndash US 30 Day T Bills 362
ndash US Inflation 304
bull Risk Premium
ndash SP500-LT Bonds = 985-545= 44
ndash SP500-T Bills = 985-362= 623
13-13
Implied Risk Premium using the
SampP 500bull httppagessternnyuedu~adamodar
bull D1P is the dividend yield Because firms also buyback shares we can use
in its place the dividend yield plus the buyback yieldndash 181+208 = 388
bull g is the growth rate of dividends For simplicity use the historic growth ratendash Dividend in 2001 = 1574 in 2010 = 2273 g=(22731574)(19)-1 = 42
0862088
088
24883
1
RFRERP
ERPRFR
R
R
gP
DR
13-14
Survey data on the risk premium
bull Most survey data is of academics and industry
professionals
ndash Average is about 55
ndash Has fallen in recent years from above 6
13-15
Estimation of Beta
Market Portfolio - Portfolio of all assets in the
economy In practice a broad stock market
index such as the SampP 500 is used to represent
the market
Beta - Sensitivity of a stockrsquos return to the return
on the market portfolio
13-16
Estimation of Beta
)(
)(
M
Mi
RVar
RRCovβ
bull Problems
1 Betas may vary over time
2 The sample size may be inadequate
3 Betas are influenced by changing financial leverage and business risk
(see Rolling Beta for TGTxlsx)
13-17
Stability of Beta
bull Most analysts argue that betas are generally
stable for firms remaining in the same industry
bull That is not to say that a firmrsquos beta cannot
change
ndash Changes in product line
ndash Changes in technology
ndash Deregulation
ndash Changes in financial leverage
13-18
Determinants of Beta
bull Business Risk
ndash Cyclicality of Revenues
ndash Operating Leverage
bull Financial Risk
ndash Financial Leverage
bull Highly cyclical stocks have higher betas
ndash Retailers auto makers
bull Less cyclical
ndash Utilities
13-19
Example
bull Suppose the stock of Stansfield Enterprises a
publisher of PowerPoint presentations has a beta of
25 The firm is 100 equity financed
bull Assume a risk-free rate of 5 and a market risk
premium of 10
bull What is the appropriate discount rate for an expansion
of this firm
13-20
Example
Suppose Stansfield Enterprises is evaluating the
following independent projects Each costs $100 and
lasts one year
Project Project b Projectrsquos
Estimated Cash
Flows Next Year
IRR NPV at
30
A 25 $150 50 $1538
B 25 $130 30 $0
C 25 $110 10 -$1538
13-21
Using the SML
An all-equity firm should accept projects whose IRRs
exceed the cost of equity capital and reject projects whose
IRRs fall short of the cost of capital
Pro
ject
IRR
Firmrsquos risk (beta)
SML
5
Good
project
Bad project
30
25
A
B
C
13-22
What if project betas vary
bull If the firm has a single cost of capital but
considers projects of varying risk adjustments
should be made
ndash Different risk adjusted costs of capital should be used
for each project
bull Otherwise the firm will over invest in risky
projects
ndash Why - See the following example
13-23
Suppose the Conglomerate Company has a cost of capital
based on the CAPM of 17 The risk-free rate is 4 the
market risk premium is 10 and the firmrsquos beta is 13
17 = 4 + 13 times 10
This is a breakdown of the companyrsquos investment projects
13 Automotive Retailer b = 20
13 Computer Hard Drive Manufacturer b = 13
13 Electric Utility b = 06
average b of assets = 13
When evaluating a new electrical generation investment
which cost of capital should be used
Capital Budgeting amp Project Risk
13-24
Capital Budgeting amp Project RiskP
roje
ct I
RR
Projectrsquos risk (b)
17
13 2006
R = 4 + 06times(14 ndash 4 ) = 10
10 reflects the opportunity cost of capital on an investment in electrical generation given the unique risk of the project
10
24 Investments in hard
drives or auto
retailing should have
higher discount rates
SML
13-25
Capital Budgeting amp Project Risk
A firm that uses one discount rate for all projects may over
time increase the risk of the firm while decreasing its value
Pro
ject
IR
R
Firmrsquos risk (beta)
SML
rf
bFIRM
Incorrectly rejected
positive NPV projects
Incorrectly accepted
negative NPV projects
Hurdle
rate)( FMFIRMF RRβR
The SML can tell us why
13-26
The Weighted Average Cost of
Capital
bull The Weighted Average Cost of Capital is given
by
bull Because interest expense is tax-deductible we multiply the last term by (1 ndash TC)
RWACC = Equity + Debt
Equitytimes REquity +
Equity + Debt
Debttimes RDebt times(1 ndash TC)
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-27
Cost of Debt
bull Interest rate required on new debt issuance (ie yield to
maturity on outstanding debt)
bull Adjust for the tax deductibility of interest expense
bull In practice finding new debt issuances is tricky
bull For companies with publicly traded debt we can rely on
the yield to maturity of the debt
ndash Note that the coupon rate is NOT a measure of the cost of debt
today
bull httpfinanceyahoocombonds
13-28
Example Target Corp
bull First we estimate the cost of equity and the cost
of debt
ndash We estimate an equity beta to estimate the cost of
equity
ndash We can often estimate the cost of debt by observing
the YTM of the firmrsquos debt
bull Second we determine the WACC by weighting
these two costs appropriately
13-29
Example International Paper
bull The industry average beta is 082 the risk free rate is
3 and the market risk premium is 84
bull Thus the cost of equity capital is
RS = RF + bi times (RM ndash RF)
= 3 +82times84
= 989
13-30
Example International Paper
bull The yield on the companyrsquos debt is 8 and
the firm has a 37 marginal tax rate The
debt to value ratio is 32
834 is Internationalrsquos cost of capital
= 068 times 989 + 032 times 8 times (1 ndash 037)
= 834
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-31
Financial Leverage and Beta
bull Operating leverage refers to the sensitivity to the firmrsquos
fixed costs of production
bull Financial leverage is the sensitivity to a firmrsquos fixed
costs of financing
bull The relationship between the betas of the firmrsquos debt
equity and assets is given by
bull Financial leverage always increases the equity beta relative to the asset beta
bAsset = Debt + Equity
Debttimes bDebt +
Debt + Equity
Equitytimes bEquity
13-32
Example
Consider Grand Sport Inc which is currently all-equity
financed and has a beta of 090
The firm has decided to lever up to a capital structure of 1
part debt to 1 part equity
Since the firm will remain in the same industry its asset
beta should remain 090
However assuming a zero beta for its debt its equity beta
would become twice as large
bAsset = 090 = 1 + 1
1times bEquity bEquity = 2 times 090 = 180
13-10
The Risk-free Ratebull Treasury securities are close proxies for the risk-free
rate
bull Although the T-Bill rate is theoretically risk free it is
frequently distorted by Fed Policy
bull The CAPM is a period model However projects are
long-lived So average period (short-term) rates need to
be used
bull The historic premium of long-term (20-year) rates over short-term rates for government securities is 2
bull So the risk-free rate to be used in the CAPM could be estimated as 2 below the prevailing rate on 20-year treasury securities
bull Or use short term T-Note rates instead say 10 years
bull httpfinanceyahoocomqs=^TNX
13-11
The Market Risk Premium
bull Method 1 Use historical data
bull Method 2 Use the Dividend Discount Model
ndash Market data and analyst forecasts can be used to
implement the DDM approach on a market-wide
basis
ndash Will not be stable Also subject to growth assumption
bull Method 3 Use forecasts
gP
DR 1
13-12
Historical Market Risk Premium
bull From SBBI Data1926-2010
ndash Small Stocks 1222
ndash SampP 500 985
ndash US LT Gov Bonds 545
ndash US 30 Day T Bills 362
ndash US Inflation 304
bull Risk Premium
ndash SP500-LT Bonds = 985-545= 44
ndash SP500-T Bills = 985-362= 623
13-13
Implied Risk Premium using the
SampP 500bull httppagessternnyuedu~adamodar
bull D1P is the dividend yield Because firms also buyback shares we can use
in its place the dividend yield plus the buyback yieldndash 181+208 = 388
bull g is the growth rate of dividends For simplicity use the historic growth ratendash Dividend in 2001 = 1574 in 2010 = 2273 g=(22731574)(19)-1 = 42
0862088
088
24883
1
RFRERP
ERPRFR
R
R
gP
DR
13-14
Survey data on the risk premium
bull Most survey data is of academics and industry
professionals
ndash Average is about 55
ndash Has fallen in recent years from above 6
13-15
Estimation of Beta
Market Portfolio - Portfolio of all assets in the
economy In practice a broad stock market
index such as the SampP 500 is used to represent
the market
Beta - Sensitivity of a stockrsquos return to the return
on the market portfolio
13-16
Estimation of Beta
)(
)(
M
Mi
RVar
RRCovβ
bull Problems
1 Betas may vary over time
2 The sample size may be inadequate
3 Betas are influenced by changing financial leverage and business risk
(see Rolling Beta for TGTxlsx)
13-17
Stability of Beta
bull Most analysts argue that betas are generally
stable for firms remaining in the same industry
bull That is not to say that a firmrsquos beta cannot
change
ndash Changes in product line
ndash Changes in technology
ndash Deregulation
ndash Changes in financial leverage
13-18
Determinants of Beta
bull Business Risk
ndash Cyclicality of Revenues
ndash Operating Leverage
bull Financial Risk
ndash Financial Leverage
bull Highly cyclical stocks have higher betas
ndash Retailers auto makers
bull Less cyclical
ndash Utilities
13-19
Example
bull Suppose the stock of Stansfield Enterprises a
publisher of PowerPoint presentations has a beta of
25 The firm is 100 equity financed
bull Assume a risk-free rate of 5 and a market risk
premium of 10
bull What is the appropriate discount rate for an expansion
of this firm
13-20
Example
Suppose Stansfield Enterprises is evaluating the
following independent projects Each costs $100 and
lasts one year
Project Project b Projectrsquos
Estimated Cash
Flows Next Year
IRR NPV at
30
A 25 $150 50 $1538
B 25 $130 30 $0
C 25 $110 10 -$1538
13-21
Using the SML
An all-equity firm should accept projects whose IRRs
exceed the cost of equity capital and reject projects whose
IRRs fall short of the cost of capital
Pro
ject
IRR
Firmrsquos risk (beta)
SML
5
Good
project
Bad project
30
25
A
B
C
13-22
What if project betas vary
bull If the firm has a single cost of capital but
considers projects of varying risk adjustments
should be made
ndash Different risk adjusted costs of capital should be used
for each project
bull Otherwise the firm will over invest in risky
projects
ndash Why - See the following example
13-23
Suppose the Conglomerate Company has a cost of capital
based on the CAPM of 17 The risk-free rate is 4 the
market risk premium is 10 and the firmrsquos beta is 13
17 = 4 + 13 times 10
This is a breakdown of the companyrsquos investment projects
13 Automotive Retailer b = 20
13 Computer Hard Drive Manufacturer b = 13
13 Electric Utility b = 06
average b of assets = 13
When evaluating a new electrical generation investment
which cost of capital should be used
Capital Budgeting amp Project Risk
13-24
Capital Budgeting amp Project RiskP
roje
ct I
RR
Projectrsquos risk (b)
17
13 2006
R = 4 + 06times(14 ndash 4 ) = 10
10 reflects the opportunity cost of capital on an investment in electrical generation given the unique risk of the project
10
24 Investments in hard
drives or auto
retailing should have
higher discount rates
SML
13-25
Capital Budgeting amp Project Risk
A firm that uses one discount rate for all projects may over
time increase the risk of the firm while decreasing its value
Pro
ject
IR
R
Firmrsquos risk (beta)
SML
rf
bFIRM
Incorrectly rejected
positive NPV projects
Incorrectly accepted
negative NPV projects
Hurdle
rate)( FMFIRMF RRβR
The SML can tell us why
13-26
The Weighted Average Cost of
Capital
bull The Weighted Average Cost of Capital is given
by
bull Because interest expense is tax-deductible we multiply the last term by (1 ndash TC)
RWACC = Equity + Debt
Equitytimes REquity +
Equity + Debt
Debttimes RDebt times(1 ndash TC)
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-27
Cost of Debt
bull Interest rate required on new debt issuance (ie yield to
maturity on outstanding debt)
bull Adjust for the tax deductibility of interest expense
bull In practice finding new debt issuances is tricky
bull For companies with publicly traded debt we can rely on
the yield to maturity of the debt
ndash Note that the coupon rate is NOT a measure of the cost of debt
today
bull httpfinanceyahoocombonds
13-28
Example Target Corp
bull First we estimate the cost of equity and the cost
of debt
ndash We estimate an equity beta to estimate the cost of
equity
ndash We can often estimate the cost of debt by observing
the YTM of the firmrsquos debt
bull Second we determine the WACC by weighting
these two costs appropriately
13-29
Example International Paper
bull The industry average beta is 082 the risk free rate is
3 and the market risk premium is 84
bull Thus the cost of equity capital is
RS = RF + bi times (RM ndash RF)
= 3 +82times84
= 989
13-30
Example International Paper
bull The yield on the companyrsquos debt is 8 and
the firm has a 37 marginal tax rate The
debt to value ratio is 32
834 is Internationalrsquos cost of capital
= 068 times 989 + 032 times 8 times (1 ndash 037)
= 834
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-31
Financial Leverage and Beta
bull Operating leverage refers to the sensitivity to the firmrsquos
fixed costs of production
bull Financial leverage is the sensitivity to a firmrsquos fixed
costs of financing
bull The relationship between the betas of the firmrsquos debt
equity and assets is given by
bull Financial leverage always increases the equity beta relative to the asset beta
bAsset = Debt + Equity
Debttimes bDebt +
Debt + Equity
Equitytimes bEquity
13-32
Example
Consider Grand Sport Inc which is currently all-equity
financed and has a beta of 090
The firm has decided to lever up to a capital structure of 1
part debt to 1 part equity
Since the firm will remain in the same industry its asset
beta should remain 090
However assuming a zero beta for its debt its equity beta
would become twice as large
bAsset = 090 = 1 + 1
1times bEquity bEquity = 2 times 090 = 180
13-11
The Market Risk Premium
bull Method 1 Use historical data
bull Method 2 Use the Dividend Discount Model
ndash Market data and analyst forecasts can be used to
implement the DDM approach on a market-wide
basis
ndash Will not be stable Also subject to growth assumption
bull Method 3 Use forecasts
gP
DR 1
13-12
Historical Market Risk Premium
bull From SBBI Data1926-2010
ndash Small Stocks 1222
ndash SampP 500 985
ndash US LT Gov Bonds 545
ndash US 30 Day T Bills 362
ndash US Inflation 304
bull Risk Premium
ndash SP500-LT Bonds = 985-545= 44
ndash SP500-T Bills = 985-362= 623
13-13
Implied Risk Premium using the
SampP 500bull httppagessternnyuedu~adamodar
bull D1P is the dividend yield Because firms also buyback shares we can use
in its place the dividend yield plus the buyback yieldndash 181+208 = 388
bull g is the growth rate of dividends For simplicity use the historic growth ratendash Dividend in 2001 = 1574 in 2010 = 2273 g=(22731574)(19)-1 = 42
0862088
088
24883
1
RFRERP
ERPRFR
R
R
gP
DR
13-14
Survey data on the risk premium
bull Most survey data is of academics and industry
professionals
ndash Average is about 55
ndash Has fallen in recent years from above 6
13-15
Estimation of Beta
Market Portfolio - Portfolio of all assets in the
economy In practice a broad stock market
index such as the SampP 500 is used to represent
the market
Beta - Sensitivity of a stockrsquos return to the return
on the market portfolio
13-16
Estimation of Beta
)(
)(
M
Mi
RVar
RRCovβ
bull Problems
1 Betas may vary over time
2 The sample size may be inadequate
3 Betas are influenced by changing financial leverage and business risk
(see Rolling Beta for TGTxlsx)
13-17
Stability of Beta
bull Most analysts argue that betas are generally
stable for firms remaining in the same industry
bull That is not to say that a firmrsquos beta cannot
change
ndash Changes in product line
ndash Changes in technology
ndash Deregulation
ndash Changes in financial leverage
13-18
Determinants of Beta
bull Business Risk
ndash Cyclicality of Revenues
ndash Operating Leverage
bull Financial Risk
ndash Financial Leverage
bull Highly cyclical stocks have higher betas
ndash Retailers auto makers
bull Less cyclical
ndash Utilities
13-19
Example
bull Suppose the stock of Stansfield Enterprises a
publisher of PowerPoint presentations has a beta of
25 The firm is 100 equity financed
bull Assume a risk-free rate of 5 and a market risk
premium of 10
bull What is the appropriate discount rate for an expansion
of this firm
13-20
Example
Suppose Stansfield Enterprises is evaluating the
following independent projects Each costs $100 and
lasts one year
Project Project b Projectrsquos
Estimated Cash
Flows Next Year
IRR NPV at
30
A 25 $150 50 $1538
B 25 $130 30 $0
C 25 $110 10 -$1538
13-21
Using the SML
An all-equity firm should accept projects whose IRRs
exceed the cost of equity capital and reject projects whose
IRRs fall short of the cost of capital
Pro
ject
IRR
Firmrsquos risk (beta)
SML
5
Good
project
Bad project
30
25
A
B
C
13-22
What if project betas vary
bull If the firm has a single cost of capital but
considers projects of varying risk adjustments
should be made
ndash Different risk adjusted costs of capital should be used
for each project
bull Otherwise the firm will over invest in risky
projects
ndash Why - See the following example
13-23
Suppose the Conglomerate Company has a cost of capital
based on the CAPM of 17 The risk-free rate is 4 the
market risk premium is 10 and the firmrsquos beta is 13
17 = 4 + 13 times 10
This is a breakdown of the companyrsquos investment projects
13 Automotive Retailer b = 20
13 Computer Hard Drive Manufacturer b = 13
13 Electric Utility b = 06
average b of assets = 13
When evaluating a new electrical generation investment
which cost of capital should be used
Capital Budgeting amp Project Risk
13-24
Capital Budgeting amp Project RiskP
roje
ct I
RR
Projectrsquos risk (b)
17
13 2006
R = 4 + 06times(14 ndash 4 ) = 10
10 reflects the opportunity cost of capital on an investment in electrical generation given the unique risk of the project
10
24 Investments in hard
drives or auto
retailing should have
higher discount rates
SML
13-25
Capital Budgeting amp Project Risk
A firm that uses one discount rate for all projects may over
time increase the risk of the firm while decreasing its value
Pro
ject
IR
R
Firmrsquos risk (beta)
SML
rf
bFIRM
Incorrectly rejected
positive NPV projects
Incorrectly accepted
negative NPV projects
Hurdle
rate)( FMFIRMF RRβR
The SML can tell us why
13-26
The Weighted Average Cost of
Capital
bull The Weighted Average Cost of Capital is given
by
bull Because interest expense is tax-deductible we multiply the last term by (1 ndash TC)
RWACC = Equity + Debt
Equitytimes REquity +
Equity + Debt
Debttimes RDebt times(1 ndash TC)
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-27
Cost of Debt
bull Interest rate required on new debt issuance (ie yield to
maturity on outstanding debt)
bull Adjust for the tax deductibility of interest expense
bull In practice finding new debt issuances is tricky
bull For companies with publicly traded debt we can rely on
the yield to maturity of the debt
ndash Note that the coupon rate is NOT a measure of the cost of debt
today
bull httpfinanceyahoocombonds
13-28
Example Target Corp
bull First we estimate the cost of equity and the cost
of debt
ndash We estimate an equity beta to estimate the cost of
equity
ndash We can often estimate the cost of debt by observing
the YTM of the firmrsquos debt
bull Second we determine the WACC by weighting
these two costs appropriately
13-29
Example International Paper
bull The industry average beta is 082 the risk free rate is
3 and the market risk premium is 84
bull Thus the cost of equity capital is
RS = RF + bi times (RM ndash RF)
= 3 +82times84
= 989
13-30
Example International Paper
bull The yield on the companyrsquos debt is 8 and
the firm has a 37 marginal tax rate The
debt to value ratio is 32
834 is Internationalrsquos cost of capital
= 068 times 989 + 032 times 8 times (1 ndash 037)
= 834
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-31
Financial Leverage and Beta
bull Operating leverage refers to the sensitivity to the firmrsquos
fixed costs of production
bull Financial leverage is the sensitivity to a firmrsquos fixed
costs of financing
bull The relationship between the betas of the firmrsquos debt
equity and assets is given by
bull Financial leverage always increases the equity beta relative to the asset beta
bAsset = Debt + Equity
Debttimes bDebt +
Debt + Equity
Equitytimes bEquity
13-32
Example
Consider Grand Sport Inc which is currently all-equity
financed and has a beta of 090
The firm has decided to lever up to a capital structure of 1
part debt to 1 part equity
Since the firm will remain in the same industry its asset
beta should remain 090
However assuming a zero beta for its debt its equity beta
would become twice as large
bAsset = 090 = 1 + 1
1times bEquity bEquity = 2 times 090 = 180
13-12
Historical Market Risk Premium
bull From SBBI Data1926-2010
ndash Small Stocks 1222
ndash SampP 500 985
ndash US LT Gov Bonds 545
ndash US 30 Day T Bills 362
ndash US Inflation 304
bull Risk Premium
ndash SP500-LT Bonds = 985-545= 44
ndash SP500-T Bills = 985-362= 623
13-13
Implied Risk Premium using the
SampP 500bull httppagessternnyuedu~adamodar
bull D1P is the dividend yield Because firms also buyback shares we can use
in its place the dividend yield plus the buyback yieldndash 181+208 = 388
bull g is the growth rate of dividends For simplicity use the historic growth ratendash Dividend in 2001 = 1574 in 2010 = 2273 g=(22731574)(19)-1 = 42
0862088
088
24883
1
RFRERP
ERPRFR
R
R
gP
DR
13-14
Survey data on the risk premium
bull Most survey data is of academics and industry
professionals
ndash Average is about 55
ndash Has fallen in recent years from above 6
13-15
Estimation of Beta
Market Portfolio - Portfolio of all assets in the
economy In practice a broad stock market
index such as the SampP 500 is used to represent
the market
Beta - Sensitivity of a stockrsquos return to the return
on the market portfolio
13-16
Estimation of Beta
)(
)(
M
Mi
RVar
RRCovβ
bull Problems
1 Betas may vary over time
2 The sample size may be inadequate
3 Betas are influenced by changing financial leverage and business risk
(see Rolling Beta for TGTxlsx)
13-17
Stability of Beta
bull Most analysts argue that betas are generally
stable for firms remaining in the same industry
bull That is not to say that a firmrsquos beta cannot
change
ndash Changes in product line
ndash Changes in technology
ndash Deregulation
ndash Changes in financial leverage
13-18
Determinants of Beta
bull Business Risk
ndash Cyclicality of Revenues
ndash Operating Leverage
bull Financial Risk
ndash Financial Leverage
bull Highly cyclical stocks have higher betas
ndash Retailers auto makers
bull Less cyclical
ndash Utilities
13-19
Example
bull Suppose the stock of Stansfield Enterprises a
publisher of PowerPoint presentations has a beta of
25 The firm is 100 equity financed
bull Assume a risk-free rate of 5 and a market risk
premium of 10
bull What is the appropriate discount rate for an expansion
of this firm
13-20
Example
Suppose Stansfield Enterprises is evaluating the
following independent projects Each costs $100 and
lasts one year
Project Project b Projectrsquos
Estimated Cash
Flows Next Year
IRR NPV at
30
A 25 $150 50 $1538
B 25 $130 30 $0
C 25 $110 10 -$1538
13-21
Using the SML
An all-equity firm should accept projects whose IRRs
exceed the cost of equity capital and reject projects whose
IRRs fall short of the cost of capital
Pro
ject
IRR
Firmrsquos risk (beta)
SML
5
Good
project
Bad project
30
25
A
B
C
13-22
What if project betas vary
bull If the firm has a single cost of capital but
considers projects of varying risk adjustments
should be made
ndash Different risk adjusted costs of capital should be used
for each project
bull Otherwise the firm will over invest in risky
projects
ndash Why - See the following example
13-23
Suppose the Conglomerate Company has a cost of capital
based on the CAPM of 17 The risk-free rate is 4 the
market risk premium is 10 and the firmrsquos beta is 13
17 = 4 + 13 times 10
This is a breakdown of the companyrsquos investment projects
13 Automotive Retailer b = 20
13 Computer Hard Drive Manufacturer b = 13
13 Electric Utility b = 06
average b of assets = 13
When evaluating a new electrical generation investment
which cost of capital should be used
Capital Budgeting amp Project Risk
13-24
Capital Budgeting amp Project RiskP
roje
ct I
RR
Projectrsquos risk (b)
17
13 2006
R = 4 + 06times(14 ndash 4 ) = 10
10 reflects the opportunity cost of capital on an investment in electrical generation given the unique risk of the project
10
24 Investments in hard
drives or auto
retailing should have
higher discount rates
SML
13-25
Capital Budgeting amp Project Risk
A firm that uses one discount rate for all projects may over
time increase the risk of the firm while decreasing its value
Pro
ject
IR
R
Firmrsquos risk (beta)
SML
rf
bFIRM
Incorrectly rejected
positive NPV projects
Incorrectly accepted
negative NPV projects
Hurdle
rate)( FMFIRMF RRβR
The SML can tell us why
13-26
The Weighted Average Cost of
Capital
bull The Weighted Average Cost of Capital is given
by
bull Because interest expense is tax-deductible we multiply the last term by (1 ndash TC)
RWACC = Equity + Debt
Equitytimes REquity +
Equity + Debt
Debttimes RDebt times(1 ndash TC)
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-27
Cost of Debt
bull Interest rate required on new debt issuance (ie yield to
maturity on outstanding debt)
bull Adjust for the tax deductibility of interest expense
bull In practice finding new debt issuances is tricky
bull For companies with publicly traded debt we can rely on
the yield to maturity of the debt
ndash Note that the coupon rate is NOT a measure of the cost of debt
today
bull httpfinanceyahoocombonds
13-28
Example Target Corp
bull First we estimate the cost of equity and the cost
of debt
ndash We estimate an equity beta to estimate the cost of
equity
ndash We can often estimate the cost of debt by observing
the YTM of the firmrsquos debt
bull Second we determine the WACC by weighting
these two costs appropriately
13-29
Example International Paper
bull The industry average beta is 082 the risk free rate is
3 and the market risk premium is 84
bull Thus the cost of equity capital is
RS = RF + bi times (RM ndash RF)
= 3 +82times84
= 989
13-30
Example International Paper
bull The yield on the companyrsquos debt is 8 and
the firm has a 37 marginal tax rate The
debt to value ratio is 32
834 is Internationalrsquos cost of capital
= 068 times 989 + 032 times 8 times (1 ndash 037)
= 834
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-31
Financial Leverage and Beta
bull Operating leverage refers to the sensitivity to the firmrsquos
fixed costs of production
bull Financial leverage is the sensitivity to a firmrsquos fixed
costs of financing
bull The relationship between the betas of the firmrsquos debt
equity and assets is given by
bull Financial leverage always increases the equity beta relative to the asset beta
bAsset = Debt + Equity
Debttimes bDebt +
Debt + Equity
Equitytimes bEquity
13-32
Example
Consider Grand Sport Inc which is currently all-equity
financed and has a beta of 090
The firm has decided to lever up to a capital structure of 1
part debt to 1 part equity
Since the firm will remain in the same industry its asset
beta should remain 090
However assuming a zero beta for its debt its equity beta
would become twice as large
bAsset = 090 = 1 + 1
1times bEquity bEquity = 2 times 090 = 180
13-13
Implied Risk Premium using the
SampP 500bull httppagessternnyuedu~adamodar
bull D1P is the dividend yield Because firms also buyback shares we can use
in its place the dividend yield plus the buyback yieldndash 181+208 = 388
bull g is the growth rate of dividends For simplicity use the historic growth ratendash Dividend in 2001 = 1574 in 2010 = 2273 g=(22731574)(19)-1 = 42
0862088
088
24883
1
RFRERP
ERPRFR
R
R
gP
DR
13-14
Survey data on the risk premium
bull Most survey data is of academics and industry
professionals
ndash Average is about 55
ndash Has fallen in recent years from above 6
13-15
Estimation of Beta
Market Portfolio - Portfolio of all assets in the
economy In practice a broad stock market
index such as the SampP 500 is used to represent
the market
Beta - Sensitivity of a stockrsquos return to the return
on the market portfolio
13-16
Estimation of Beta
)(
)(
M
Mi
RVar
RRCovβ
bull Problems
1 Betas may vary over time
2 The sample size may be inadequate
3 Betas are influenced by changing financial leverage and business risk
(see Rolling Beta for TGTxlsx)
13-17
Stability of Beta
bull Most analysts argue that betas are generally
stable for firms remaining in the same industry
bull That is not to say that a firmrsquos beta cannot
change
ndash Changes in product line
ndash Changes in technology
ndash Deregulation
ndash Changes in financial leverage
13-18
Determinants of Beta
bull Business Risk
ndash Cyclicality of Revenues
ndash Operating Leverage
bull Financial Risk
ndash Financial Leverage
bull Highly cyclical stocks have higher betas
ndash Retailers auto makers
bull Less cyclical
ndash Utilities
13-19
Example
bull Suppose the stock of Stansfield Enterprises a
publisher of PowerPoint presentations has a beta of
25 The firm is 100 equity financed
bull Assume a risk-free rate of 5 and a market risk
premium of 10
bull What is the appropriate discount rate for an expansion
of this firm
13-20
Example
Suppose Stansfield Enterprises is evaluating the
following independent projects Each costs $100 and
lasts one year
Project Project b Projectrsquos
Estimated Cash
Flows Next Year
IRR NPV at
30
A 25 $150 50 $1538
B 25 $130 30 $0
C 25 $110 10 -$1538
13-21
Using the SML
An all-equity firm should accept projects whose IRRs
exceed the cost of equity capital and reject projects whose
IRRs fall short of the cost of capital
Pro
ject
IRR
Firmrsquos risk (beta)
SML
5
Good
project
Bad project
30
25
A
B
C
13-22
What if project betas vary
bull If the firm has a single cost of capital but
considers projects of varying risk adjustments
should be made
ndash Different risk adjusted costs of capital should be used
for each project
bull Otherwise the firm will over invest in risky
projects
ndash Why - See the following example
13-23
Suppose the Conglomerate Company has a cost of capital
based on the CAPM of 17 The risk-free rate is 4 the
market risk premium is 10 and the firmrsquos beta is 13
17 = 4 + 13 times 10
This is a breakdown of the companyrsquos investment projects
13 Automotive Retailer b = 20
13 Computer Hard Drive Manufacturer b = 13
13 Electric Utility b = 06
average b of assets = 13
When evaluating a new electrical generation investment
which cost of capital should be used
Capital Budgeting amp Project Risk
13-24
Capital Budgeting amp Project RiskP
roje
ct I
RR
Projectrsquos risk (b)
17
13 2006
R = 4 + 06times(14 ndash 4 ) = 10
10 reflects the opportunity cost of capital on an investment in electrical generation given the unique risk of the project
10
24 Investments in hard
drives or auto
retailing should have
higher discount rates
SML
13-25
Capital Budgeting amp Project Risk
A firm that uses one discount rate for all projects may over
time increase the risk of the firm while decreasing its value
Pro
ject
IR
R
Firmrsquos risk (beta)
SML
rf
bFIRM
Incorrectly rejected
positive NPV projects
Incorrectly accepted
negative NPV projects
Hurdle
rate)( FMFIRMF RRβR
The SML can tell us why
13-26
The Weighted Average Cost of
Capital
bull The Weighted Average Cost of Capital is given
by
bull Because interest expense is tax-deductible we multiply the last term by (1 ndash TC)
RWACC = Equity + Debt
Equitytimes REquity +
Equity + Debt
Debttimes RDebt times(1 ndash TC)
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-27
Cost of Debt
bull Interest rate required on new debt issuance (ie yield to
maturity on outstanding debt)
bull Adjust for the tax deductibility of interest expense
bull In practice finding new debt issuances is tricky
bull For companies with publicly traded debt we can rely on
the yield to maturity of the debt
ndash Note that the coupon rate is NOT a measure of the cost of debt
today
bull httpfinanceyahoocombonds
13-28
Example Target Corp
bull First we estimate the cost of equity and the cost
of debt
ndash We estimate an equity beta to estimate the cost of
equity
ndash We can often estimate the cost of debt by observing
the YTM of the firmrsquos debt
bull Second we determine the WACC by weighting
these two costs appropriately
13-29
Example International Paper
bull The industry average beta is 082 the risk free rate is
3 and the market risk premium is 84
bull Thus the cost of equity capital is
RS = RF + bi times (RM ndash RF)
= 3 +82times84
= 989
13-30
Example International Paper
bull The yield on the companyrsquos debt is 8 and
the firm has a 37 marginal tax rate The
debt to value ratio is 32
834 is Internationalrsquos cost of capital
= 068 times 989 + 032 times 8 times (1 ndash 037)
= 834
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-31
Financial Leverage and Beta
bull Operating leverage refers to the sensitivity to the firmrsquos
fixed costs of production
bull Financial leverage is the sensitivity to a firmrsquos fixed
costs of financing
bull The relationship between the betas of the firmrsquos debt
equity and assets is given by
bull Financial leverage always increases the equity beta relative to the asset beta
bAsset = Debt + Equity
Debttimes bDebt +
Debt + Equity
Equitytimes bEquity
13-32
Example
Consider Grand Sport Inc which is currently all-equity
financed and has a beta of 090
The firm has decided to lever up to a capital structure of 1
part debt to 1 part equity
Since the firm will remain in the same industry its asset
beta should remain 090
However assuming a zero beta for its debt its equity beta
would become twice as large
bAsset = 090 = 1 + 1
1times bEquity bEquity = 2 times 090 = 180
13-14
Survey data on the risk premium
bull Most survey data is of academics and industry
professionals
ndash Average is about 55
ndash Has fallen in recent years from above 6
13-15
Estimation of Beta
Market Portfolio - Portfolio of all assets in the
economy In practice a broad stock market
index such as the SampP 500 is used to represent
the market
Beta - Sensitivity of a stockrsquos return to the return
on the market portfolio
13-16
Estimation of Beta
)(
)(
M
Mi
RVar
RRCovβ
bull Problems
1 Betas may vary over time
2 The sample size may be inadequate
3 Betas are influenced by changing financial leverage and business risk
(see Rolling Beta for TGTxlsx)
13-17
Stability of Beta
bull Most analysts argue that betas are generally
stable for firms remaining in the same industry
bull That is not to say that a firmrsquos beta cannot
change
ndash Changes in product line
ndash Changes in technology
ndash Deregulation
ndash Changes in financial leverage
13-18
Determinants of Beta
bull Business Risk
ndash Cyclicality of Revenues
ndash Operating Leverage
bull Financial Risk
ndash Financial Leverage
bull Highly cyclical stocks have higher betas
ndash Retailers auto makers
bull Less cyclical
ndash Utilities
13-19
Example
bull Suppose the stock of Stansfield Enterprises a
publisher of PowerPoint presentations has a beta of
25 The firm is 100 equity financed
bull Assume a risk-free rate of 5 and a market risk
premium of 10
bull What is the appropriate discount rate for an expansion
of this firm
13-20
Example
Suppose Stansfield Enterprises is evaluating the
following independent projects Each costs $100 and
lasts one year
Project Project b Projectrsquos
Estimated Cash
Flows Next Year
IRR NPV at
30
A 25 $150 50 $1538
B 25 $130 30 $0
C 25 $110 10 -$1538
13-21
Using the SML
An all-equity firm should accept projects whose IRRs
exceed the cost of equity capital and reject projects whose
IRRs fall short of the cost of capital
Pro
ject
IRR
Firmrsquos risk (beta)
SML
5
Good
project
Bad project
30
25
A
B
C
13-22
What if project betas vary
bull If the firm has a single cost of capital but
considers projects of varying risk adjustments
should be made
ndash Different risk adjusted costs of capital should be used
for each project
bull Otherwise the firm will over invest in risky
projects
ndash Why - See the following example
13-23
Suppose the Conglomerate Company has a cost of capital
based on the CAPM of 17 The risk-free rate is 4 the
market risk premium is 10 and the firmrsquos beta is 13
17 = 4 + 13 times 10
This is a breakdown of the companyrsquos investment projects
13 Automotive Retailer b = 20
13 Computer Hard Drive Manufacturer b = 13
13 Electric Utility b = 06
average b of assets = 13
When evaluating a new electrical generation investment
which cost of capital should be used
Capital Budgeting amp Project Risk
13-24
Capital Budgeting amp Project RiskP
roje
ct I
RR
Projectrsquos risk (b)
17
13 2006
R = 4 + 06times(14 ndash 4 ) = 10
10 reflects the opportunity cost of capital on an investment in electrical generation given the unique risk of the project
10
24 Investments in hard
drives or auto
retailing should have
higher discount rates
SML
13-25
Capital Budgeting amp Project Risk
A firm that uses one discount rate for all projects may over
time increase the risk of the firm while decreasing its value
Pro
ject
IR
R
Firmrsquos risk (beta)
SML
rf
bFIRM
Incorrectly rejected
positive NPV projects
Incorrectly accepted
negative NPV projects
Hurdle
rate)( FMFIRMF RRβR
The SML can tell us why
13-26
The Weighted Average Cost of
Capital
bull The Weighted Average Cost of Capital is given
by
bull Because interest expense is tax-deductible we multiply the last term by (1 ndash TC)
RWACC = Equity + Debt
Equitytimes REquity +
Equity + Debt
Debttimes RDebt times(1 ndash TC)
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-27
Cost of Debt
bull Interest rate required on new debt issuance (ie yield to
maturity on outstanding debt)
bull Adjust for the tax deductibility of interest expense
bull In practice finding new debt issuances is tricky
bull For companies with publicly traded debt we can rely on
the yield to maturity of the debt
ndash Note that the coupon rate is NOT a measure of the cost of debt
today
bull httpfinanceyahoocombonds
13-28
Example Target Corp
bull First we estimate the cost of equity and the cost
of debt
ndash We estimate an equity beta to estimate the cost of
equity
ndash We can often estimate the cost of debt by observing
the YTM of the firmrsquos debt
bull Second we determine the WACC by weighting
these two costs appropriately
13-29
Example International Paper
bull The industry average beta is 082 the risk free rate is
3 and the market risk premium is 84
bull Thus the cost of equity capital is
RS = RF + bi times (RM ndash RF)
= 3 +82times84
= 989
13-30
Example International Paper
bull The yield on the companyrsquos debt is 8 and
the firm has a 37 marginal tax rate The
debt to value ratio is 32
834 is Internationalrsquos cost of capital
= 068 times 989 + 032 times 8 times (1 ndash 037)
= 834
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-31
Financial Leverage and Beta
bull Operating leverage refers to the sensitivity to the firmrsquos
fixed costs of production
bull Financial leverage is the sensitivity to a firmrsquos fixed
costs of financing
bull The relationship between the betas of the firmrsquos debt
equity and assets is given by
bull Financial leverage always increases the equity beta relative to the asset beta
bAsset = Debt + Equity
Debttimes bDebt +
Debt + Equity
Equitytimes bEquity
13-32
Example
Consider Grand Sport Inc which is currently all-equity
financed and has a beta of 090
The firm has decided to lever up to a capital structure of 1
part debt to 1 part equity
Since the firm will remain in the same industry its asset
beta should remain 090
However assuming a zero beta for its debt its equity beta
would become twice as large
bAsset = 090 = 1 + 1
1times bEquity bEquity = 2 times 090 = 180
13-15
Estimation of Beta
Market Portfolio - Portfolio of all assets in the
economy In practice a broad stock market
index such as the SampP 500 is used to represent
the market
Beta - Sensitivity of a stockrsquos return to the return
on the market portfolio
13-16
Estimation of Beta
)(
)(
M
Mi
RVar
RRCovβ
bull Problems
1 Betas may vary over time
2 The sample size may be inadequate
3 Betas are influenced by changing financial leverage and business risk
(see Rolling Beta for TGTxlsx)
13-17
Stability of Beta
bull Most analysts argue that betas are generally
stable for firms remaining in the same industry
bull That is not to say that a firmrsquos beta cannot
change
ndash Changes in product line
ndash Changes in technology
ndash Deregulation
ndash Changes in financial leverage
13-18
Determinants of Beta
bull Business Risk
ndash Cyclicality of Revenues
ndash Operating Leverage
bull Financial Risk
ndash Financial Leverage
bull Highly cyclical stocks have higher betas
ndash Retailers auto makers
bull Less cyclical
ndash Utilities
13-19
Example
bull Suppose the stock of Stansfield Enterprises a
publisher of PowerPoint presentations has a beta of
25 The firm is 100 equity financed
bull Assume a risk-free rate of 5 and a market risk
premium of 10
bull What is the appropriate discount rate for an expansion
of this firm
13-20
Example
Suppose Stansfield Enterprises is evaluating the
following independent projects Each costs $100 and
lasts one year
Project Project b Projectrsquos
Estimated Cash
Flows Next Year
IRR NPV at
30
A 25 $150 50 $1538
B 25 $130 30 $0
C 25 $110 10 -$1538
13-21
Using the SML
An all-equity firm should accept projects whose IRRs
exceed the cost of equity capital and reject projects whose
IRRs fall short of the cost of capital
Pro
ject
IRR
Firmrsquos risk (beta)
SML
5
Good
project
Bad project
30
25
A
B
C
13-22
What if project betas vary
bull If the firm has a single cost of capital but
considers projects of varying risk adjustments
should be made
ndash Different risk adjusted costs of capital should be used
for each project
bull Otherwise the firm will over invest in risky
projects
ndash Why - See the following example
13-23
Suppose the Conglomerate Company has a cost of capital
based on the CAPM of 17 The risk-free rate is 4 the
market risk premium is 10 and the firmrsquos beta is 13
17 = 4 + 13 times 10
This is a breakdown of the companyrsquos investment projects
13 Automotive Retailer b = 20
13 Computer Hard Drive Manufacturer b = 13
13 Electric Utility b = 06
average b of assets = 13
When evaluating a new electrical generation investment
which cost of capital should be used
Capital Budgeting amp Project Risk
13-24
Capital Budgeting amp Project RiskP
roje
ct I
RR
Projectrsquos risk (b)
17
13 2006
R = 4 + 06times(14 ndash 4 ) = 10
10 reflects the opportunity cost of capital on an investment in electrical generation given the unique risk of the project
10
24 Investments in hard
drives or auto
retailing should have
higher discount rates
SML
13-25
Capital Budgeting amp Project Risk
A firm that uses one discount rate for all projects may over
time increase the risk of the firm while decreasing its value
Pro
ject
IR
R
Firmrsquos risk (beta)
SML
rf
bFIRM
Incorrectly rejected
positive NPV projects
Incorrectly accepted
negative NPV projects
Hurdle
rate)( FMFIRMF RRβR
The SML can tell us why
13-26
The Weighted Average Cost of
Capital
bull The Weighted Average Cost of Capital is given
by
bull Because interest expense is tax-deductible we multiply the last term by (1 ndash TC)
RWACC = Equity + Debt
Equitytimes REquity +
Equity + Debt
Debttimes RDebt times(1 ndash TC)
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-27
Cost of Debt
bull Interest rate required on new debt issuance (ie yield to
maturity on outstanding debt)
bull Adjust for the tax deductibility of interest expense
bull In practice finding new debt issuances is tricky
bull For companies with publicly traded debt we can rely on
the yield to maturity of the debt
ndash Note that the coupon rate is NOT a measure of the cost of debt
today
bull httpfinanceyahoocombonds
13-28
Example Target Corp
bull First we estimate the cost of equity and the cost
of debt
ndash We estimate an equity beta to estimate the cost of
equity
ndash We can often estimate the cost of debt by observing
the YTM of the firmrsquos debt
bull Second we determine the WACC by weighting
these two costs appropriately
13-29
Example International Paper
bull The industry average beta is 082 the risk free rate is
3 and the market risk premium is 84
bull Thus the cost of equity capital is
RS = RF + bi times (RM ndash RF)
= 3 +82times84
= 989
13-30
Example International Paper
bull The yield on the companyrsquos debt is 8 and
the firm has a 37 marginal tax rate The
debt to value ratio is 32
834 is Internationalrsquos cost of capital
= 068 times 989 + 032 times 8 times (1 ndash 037)
= 834
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-31
Financial Leverage and Beta
bull Operating leverage refers to the sensitivity to the firmrsquos
fixed costs of production
bull Financial leverage is the sensitivity to a firmrsquos fixed
costs of financing
bull The relationship between the betas of the firmrsquos debt
equity and assets is given by
bull Financial leverage always increases the equity beta relative to the asset beta
bAsset = Debt + Equity
Debttimes bDebt +
Debt + Equity
Equitytimes bEquity
13-32
Example
Consider Grand Sport Inc which is currently all-equity
financed and has a beta of 090
The firm has decided to lever up to a capital structure of 1
part debt to 1 part equity
Since the firm will remain in the same industry its asset
beta should remain 090
However assuming a zero beta for its debt its equity beta
would become twice as large
bAsset = 090 = 1 + 1
1times bEquity bEquity = 2 times 090 = 180
13-16
Estimation of Beta
)(
)(
M
Mi
RVar
RRCovβ
bull Problems
1 Betas may vary over time
2 The sample size may be inadequate
3 Betas are influenced by changing financial leverage and business risk
(see Rolling Beta for TGTxlsx)
13-17
Stability of Beta
bull Most analysts argue that betas are generally
stable for firms remaining in the same industry
bull That is not to say that a firmrsquos beta cannot
change
ndash Changes in product line
ndash Changes in technology
ndash Deregulation
ndash Changes in financial leverage
13-18
Determinants of Beta
bull Business Risk
ndash Cyclicality of Revenues
ndash Operating Leverage
bull Financial Risk
ndash Financial Leverage
bull Highly cyclical stocks have higher betas
ndash Retailers auto makers
bull Less cyclical
ndash Utilities
13-19
Example
bull Suppose the stock of Stansfield Enterprises a
publisher of PowerPoint presentations has a beta of
25 The firm is 100 equity financed
bull Assume a risk-free rate of 5 and a market risk
premium of 10
bull What is the appropriate discount rate for an expansion
of this firm
13-20
Example
Suppose Stansfield Enterprises is evaluating the
following independent projects Each costs $100 and
lasts one year
Project Project b Projectrsquos
Estimated Cash
Flows Next Year
IRR NPV at
30
A 25 $150 50 $1538
B 25 $130 30 $0
C 25 $110 10 -$1538
13-21
Using the SML
An all-equity firm should accept projects whose IRRs
exceed the cost of equity capital and reject projects whose
IRRs fall short of the cost of capital
Pro
ject
IRR
Firmrsquos risk (beta)
SML
5
Good
project
Bad project
30
25
A
B
C
13-22
What if project betas vary
bull If the firm has a single cost of capital but
considers projects of varying risk adjustments
should be made
ndash Different risk adjusted costs of capital should be used
for each project
bull Otherwise the firm will over invest in risky
projects
ndash Why - See the following example
13-23
Suppose the Conglomerate Company has a cost of capital
based on the CAPM of 17 The risk-free rate is 4 the
market risk premium is 10 and the firmrsquos beta is 13
17 = 4 + 13 times 10
This is a breakdown of the companyrsquos investment projects
13 Automotive Retailer b = 20
13 Computer Hard Drive Manufacturer b = 13
13 Electric Utility b = 06
average b of assets = 13
When evaluating a new electrical generation investment
which cost of capital should be used
Capital Budgeting amp Project Risk
13-24
Capital Budgeting amp Project RiskP
roje
ct I
RR
Projectrsquos risk (b)
17
13 2006
R = 4 + 06times(14 ndash 4 ) = 10
10 reflects the opportunity cost of capital on an investment in electrical generation given the unique risk of the project
10
24 Investments in hard
drives or auto
retailing should have
higher discount rates
SML
13-25
Capital Budgeting amp Project Risk
A firm that uses one discount rate for all projects may over
time increase the risk of the firm while decreasing its value
Pro
ject
IR
R
Firmrsquos risk (beta)
SML
rf
bFIRM
Incorrectly rejected
positive NPV projects
Incorrectly accepted
negative NPV projects
Hurdle
rate)( FMFIRMF RRβR
The SML can tell us why
13-26
The Weighted Average Cost of
Capital
bull The Weighted Average Cost of Capital is given
by
bull Because interest expense is tax-deductible we multiply the last term by (1 ndash TC)
RWACC = Equity + Debt
Equitytimes REquity +
Equity + Debt
Debttimes RDebt times(1 ndash TC)
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-27
Cost of Debt
bull Interest rate required on new debt issuance (ie yield to
maturity on outstanding debt)
bull Adjust for the tax deductibility of interest expense
bull In practice finding new debt issuances is tricky
bull For companies with publicly traded debt we can rely on
the yield to maturity of the debt
ndash Note that the coupon rate is NOT a measure of the cost of debt
today
bull httpfinanceyahoocombonds
13-28
Example Target Corp
bull First we estimate the cost of equity and the cost
of debt
ndash We estimate an equity beta to estimate the cost of
equity
ndash We can often estimate the cost of debt by observing
the YTM of the firmrsquos debt
bull Second we determine the WACC by weighting
these two costs appropriately
13-29
Example International Paper
bull The industry average beta is 082 the risk free rate is
3 and the market risk premium is 84
bull Thus the cost of equity capital is
RS = RF + bi times (RM ndash RF)
= 3 +82times84
= 989
13-30
Example International Paper
bull The yield on the companyrsquos debt is 8 and
the firm has a 37 marginal tax rate The
debt to value ratio is 32
834 is Internationalrsquos cost of capital
= 068 times 989 + 032 times 8 times (1 ndash 037)
= 834
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-31
Financial Leverage and Beta
bull Operating leverage refers to the sensitivity to the firmrsquos
fixed costs of production
bull Financial leverage is the sensitivity to a firmrsquos fixed
costs of financing
bull The relationship between the betas of the firmrsquos debt
equity and assets is given by
bull Financial leverage always increases the equity beta relative to the asset beta
bAsset = Debt + Equity
Debttimes bDebt +
Debt + Equity
Equitytimes bEquity
13-32
Example
Consider Grand Sport Inc which is currently all-equity
financed and has a beta of 090
The firm has decided to lever up to a capital structure of 1
part debt to 1 part equity
Since the firm will remain in the same industry its asset
beta should remain 090
However assuming a zero beta for its debt its equity beta
would become twice as large
bAsset = 090 = 1 + 1
1times bEquity bEquity = 2 times 090 = 180
13-17
Stability of Beta
bull Most analysts argue that betas are generally
stable for firms remaining in the same industry
bull That is not to say that a firmrsquos beta cannot
change
ndash Changes in product line
ndash Changes in technology
ndash Deregulation
ndash Changes in financial leverage
13-18
Determinants of Beta
bull Business Risk
ndash Cyclicality of Revenues
ndash Operating Leverage
bull Financial Risk
ndash Financial Leverage
bull Highly cyclical stocks have higher betas
ndash Retailers auto makers
bull Less cyclical
ndash Utilities
13-19
Example
bull Suppose the stock of Stansfield Enterprises a
publisher of PowerPoint presentations has a beta of
25 The firm is 100 equity financed
bull Assume a risk-free rate of 5 and a market risk
premium of 10
bull What is the appropriate discount rate for an expansion
of this firm
13-20
Example
Suppose Stansfield Enterprises is evaluating the
following independent projects Each costs $100 and
lasts one year
Project Project b Projectrsquos
Estimated Cash
Flows Next Year
IRR NPV at
30
A 25 $150 50 $1538
B 25 $130 30 $0
C 25 $110 10 -$1538
13-21
Using the SML
An all-equity firm should accept projects whose IRRs
exceed the cost of equity capital and reject projects whose
IRRs fall short of the cost of capital
Pro
ject
IRR
Firmrsquos risk (beta)
SML
5
Good
project
Bad project
30
25
A
B
C
13-22
What if project betas vary
bull If the firm has a single cost of capital but
considers projects of varying risk adjustments
should be made
ndash Different risk adjusted costs of capital should be used
for each project
bull Otherwise the firm will over invest in risky
projects
ndash Why - See the following example
13-23
Suppose the Conglomerate Company has a cost of capital
based on the CAPM of 17 The risk-free rate is 4 the
market risk premium is 10 and the firmrsquos beta is 13
17 = 4 + 13 times 10
This is a breakdown of the companyrsquos investment projects
13 Automotive Retailer b = 20
13 Computer Hard Drive Manufacturer b = 13
13 Electric Utility b = 06
average b of assets = 13
When evaluating a new electrical generation investment
which cost of capital should be used
Capital Budgeting amp Project Risk
13-24
Capital Budgeting amp Project RiskP
roje
ct I
RR
Projectrsquos risk (b)
17
13 2006
R = 4 + 06times(14 ndash 4 ) = 10
10 reflects the opportunity cost of capital on an investment in electrical generation given the unique risk of the project
10
24 Investments in hard
drives or auto
retailing should have
higher discount rates
SML
13-25
Capital Budgeting amp Project Risk
A firm that uses one discount rate for all projects may over
time increase the risk of the firm while decreasing its value
Pro
ject
IR
R
Firmrsquos risk (beta)
SML
rf
bFIRM
Incorrectly rejected
positive NPV projects
Incorrectly accepted
negative NPV projects
Hurdle
rate)( FMFIRMF RRβR
The SML can tell us why
13-26
The Weighted Average Cost of
Capital
bull The Weighted Average Cost of Capital is given
by
bull Because interest expense is tax-deductible we multiply the last term by (1 ndash TC)
RWACC = Equity + Debt
Equitytimes REquity +
Equity + Debt
Debttimes RDebt times(1 ndash TC)
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-27
Cost of Debt
bull Interest rate required on new debt issuance (ie yield to
maturity on outstanding debt)
bull Adjust for the tax deductibility of interest expense
bull In practice finding new debt issuances is tricky
bull For companies with publicly traded debt we can rely on
the yield to maturity of the debt
ndash Note that the coupon rate is NOT a measure of the cost of debt
today
bull httpfinanceyahoocombonds
13-28
Example Target Corp
bull First we estimate the cost of equity and the cost
of debt
ndash We estimate an equity beta to estimate the cost of
equity
ndash We can often estimate the cost of debt by observing
the YTM of the firmrsquos debt
bull Second we determine the WACC by weighting
these two costs appropriately
13-29
Example International Paper
bull The industry average beta is 082 the risk free rate is
3 and the market risk premium is 84
bull Thus the cost of equity capital is
RS = RF + bi times (RM ndash RF)
= 3 +82times84
= 989
13-30
Example International Paper
bull The yield on the companyrsquos debt is 8 and
the firm has a 37 marginal tax rate The
debt to value ratio is 32
834 is Internationalrsquos cost of capital
= 068 times 989 + 032 times 8 times (1 ndash 037)
= 834
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-31
Financial Leverage and Beta
bull Operating leverage refers to the sensitivity to the firmrsquos
fixed costs of production
bull Financial leverage is the sensitivity to a firmrsquos fixed
costs of financing
bull The relationship between the betas of the firmrsquos debt
equity and assets is given by
bull Financial leverage always increases the equity beta relative to the asset beta
bAsset = Debt + Equity
Debttimes bDebt +
Debt + Equity
Equitytimes bEquity
13-32
Example
Consider Grand Sport Inc which is currently all-equity
financed and has a beta of 090
The firm has decided to lever up to a capital structure of 1
part debt to 1 part equity
Since the firm will remain in the same industry its asset
beta should remain 090
However assuming a zero beta for its debt its equity beta
would become twice as large
bAsset = 090 = 1 + 1
1times bEquity bEquity = 2 times 090 = 180
13-18
Determinants of Beta
bull Business Risk
ndash Cyclicality of Revenues
ndash Operating Leverage
bull Financial Risk
ndash Financial Leverage
bull Highly cyclical stocks have higher betas
ndash Retailers auto makers
bull Less cyclical
ndash Utilities
13-19
Example
bull Suppose the stock of Stansfield Enterprises a
publisher of PowerPoint presentations has a beta of
25 The firm is 100 equity financed
bull Assume a risk-free rate of 5 and a market risk
premium of 10
bull What is the appropriate discount rate for an expansion
of this firm
13-20
Example
Suppose Stansfield Enterprises is evaluating the
following independent projects Each costs $100 and
lasts one year
Project Project b Projectrsquos
Estimated Cash
Flows Next Year
IRR NPV at
30
A 25 $150 50 $1538
B 25 $130 30 $0
C 25 $110 10 -$1538
13-21
Using the SML
An all-equity firm should accept projects whose IRRs
exceed the cost of equity capital and reject projects whose
IRRs fall short of the cost of capital
Pro
ject
IRR
Firmrsquos risk (beta)
SML
5
Good
project
Bad project
30
25
A
B
C
13-22
What if project betas vary
bull If the firm has a single cost of capital but
considers projects of varying risk adjustments
should be made
ndash Different risk adjusted costs of capital should be used
for each project
bull Otherwise the firm will over invest in risky
projects
ndash Why - See the following example
13-23
Suppose the Conglomerate Company has a cost of capital
based on the CAPM of 17 The risk-free rate is 4 the
market risk premium is 10 and the firmrsquos beta is 13
17 = 4 + 13 times 10
This is a breakdown of the companyrsquos investment projects
13 Automotive Retailer b = 20
13 Computer Hard Drive Manufacturer b = 13
13 Electric Utility b = 06
average b of assets = 13
When evaluating a new electrical generation investment
which cost of capital should be used
Capital Budgeting amp Project Risk
13-24
Capital Budgeting amp Project RiskP
roje
ct I
RR
Projectrsquos risk (b)
17
13 2006
R = 4 + 06times(14 ndash 4 ) = 10
10 reflects the opportunity cost of capital on an investment in electrical generation given the unique risk of the project
10
24 Investments in hard
drives or auto
retailing should have
higher discount rates
SML
13-25
Capital Budgeting amp Project Risk
A firm that uses one discount rate for all projects may over
time increase the risk of the firm while decreasing its value
Pro
ject
IR
R
Firmrsquos risk (beta)
SML
rf
bFIRM
Incorrectly rejected
positive NPV projects
Incorrectly accepted
negative NPV projects
Hurdle
rate)( FMFIRMF RRβR
The SML can tell us why
13-26
The Weighted Average Cost of
Capital
bull The Weighted Average Cost of Capital is given
by
bull Because interest expense is tax-deductible we multiply the last term by (1 ndash TC)
RWACC = Equity + Debt
Equitytimes REquity +
Equity + Debt
Debttimes RDebt times(1 ndash TC)
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-27
Cost of Debt
bull Interest rate required on new debt issuance (ie yield to
maturity on outstanding debt)
bull Adjust for the tax deductibility of interest expense
bull In practice finding new debt issuances is tricky
bull For companies with publicly traded debt we can rely on
the yield to maturity of the debt
ndash Note that the coupon rate is NOT a measure of the cost of debt
today
bull httpfinanceyahoocombonds
13-28
Example Target Corp
bull First we estimate the cost of equity and the cost
of debt
ndash We estimate an equity beta to estimate the cost of
equity
ndash We can often estimate the cost of debt by observing
the YTM of the firmrsquos debt
bull Second we determine the WACC by weighting
these two costs appropriately
13-29
Example International Paper
bull The industry average beta is 082 the risk free rate is
3 and the market risk premium is 84
bull Thus the cost of equity capital is
RS = RF + bi times (RM ndash RF)
= 3 +82times84
= 989
13-30
Example International Paper
bull The yield on the companyrsquos debt is 8 and
the firm has a 37 marginal tax rate The
debt to value ratio is 32
834 is Internationalrsquos cost of capital
= 068 times 989 + 032 times 8 times (1 ndash 037)
= 834
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-31
Financial Leverage and Beta
bull Operating leverage refers to the sensitivity to the firmrsquos
fixed costs of production
bull Financial leverage is the sensitivity to a firmrsquos fixed
costs of financing
bull The relationship between the betas of the firmrsquos debt
equity and assets is given by
bull Financial leverage always increases the equity beta relative to the asset beta
bAsset = Debt + Equity
Debttimes bDebt +
Debt + Equity
Equitytimes bEquity
13-32
Example
Consider Grand Sport Inc which is currently all-equity
financed and has a beta of 090
The firm has decided to lever up to a capital structure of 1
part debt to 1 part equity
Since the firm will remain in the same industry its asset
beta should remain 090
However assuming a zero beta for its debt its equity beta
would become twice as large
bAsset = 090 = 1 + 1
1times bEquity bEquity = 2 times 090 = 180
13-19
Example
bull Suppose the stock of Stansfield Enterprises a
publisher of PowerPoint presentations has a beta of
25 The firm is 100 equity financed
bull Assume a risk-free rate of 5 and a market risk
premium of 10
bull What is the appropriate discount rate for an expansion
of this firm
13-20
Example
Suppose Stansfield Enterprises is evaluating the
following independent projects Each costs $100 and
lasts one year
Project Project b Projectrsquos
Estimated Cash
Flows Next Year
IRR NPV at
30
A 25 $150 50 $1538
B 25 $130 30 $0
C 25 $110 10 -$1538
13-21
Using the SML
An all-equity firm should accept projects whose IRRs
exceed the cost of equity capital and reject projects whose
IRRs fall short of the cost of capital
Pro
ject
IRR
Firmrsquos risk (beta)
SML
5
Good
project
Bad project
30
25
A
B
C
13-22
What if project betas vary
bull If the firm has a single cost of capital but
considers projects of varying risk adjustments
should be made
ndash Different risk adjusted costs of capital should be used
for each project
bull Otherwise the firm will over invest in risky
projects
ndash Why - See the following example
13-23
Suppose the Conglomerate Company has a cost of capital
based on the CAPM of 17 The risk-free rate is 4 the
market risk premium is 10 and the firmrsquos beta is 13
17 = 4 + 13 times 10
This is a breakdown of the companyrsquos investment projects
13 Automotive Retailer b = 20
13 Computer Hard Drive Manufacturer b = 13
13 Electric Utility b = 06
average b of assets = 13
When evaluating a new electrical generation investment
which cost of capital should be used
Capital Budgeting amp Project Risk
13-24
Capital Budgeting amp Project RiskP
roje
ct I
RR
Projectrsquos risk (b)
17
13 2006
R = 4 + 06times(14 ndash 4 ) = 10
10 reflects the opportunity cost of capital on an investment in electrical generation given the unique risk of the project
10
24 Investments in hard
drives or auto
retailing should have
higher discount rates
SML
13-25
Capital Budgeting amp Project Risk
A firm that uses one discount rate for all projects may over
time increase the risk of the firm while decreasing its value
Pro
ject
IR
R
Firmrsquos risk (beta)
SML
rf
bFIRM
Incorrectly rejected
positive NPV projects
Incorrectly accepted
negative NPV projects
Hurdle
rate)( FMFIRMF RRβR
The SML can tell us why
13-26
The Weighted Average Cost of
Capital
bull The Weighted Average Cost of Capital is given
by
bull Because interest expense is tax-deductible we multiply the last term by (1 ndash TC)
RWACC = Equity + Debt
Equitytimes REquity +
Equity + Debt
Debttimes RDebt times(1 ndash TC)
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-27
Cost of Debt
bull Interest rate required on new debt issuance (ie yield to
maturity on outstanding debt)
bull Adjust for the tax deductibility of interest expense
bull In practice finding new debt issuances is tricky
bull For companies with publicly traded debt we can rely on
the yield to maturity of the debt
ndash Note that the coupon rate is NOT a measure of the cost of debt
today
bull httpfinanceyahoocombonds
13-28
Example Target Corp
bull First we estimate the cost of equity and the cost
of debt
ndash We estimate an equity beta to estimate the cost of
equity
ndash We can often estimate the cost of debt by observing
the YTM of the firmrsquos debt
bull Second we determine the WACC by weighting
these two costs appropriately
13-29
Example International Paper
bull The industry average beta is 082 the risk free rate is
3 and the market risk premium is 84
bull Thus the cost of equity capital is
RS = RF + bi times (RM ndash RF)
= 3 +82times84
= 989
13-30
Example International Paper
bull The yield on the companyrsquos debt is 8 and
the firm has a 37 marginal tax rate The
debt to value ratio is 32
834 is Internationalrsquos cost of capital
= 068 times 989 + 032 times 8 times (1 ndash 037)
= 834
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-31
Financial Leverage and Beta
bull Operating leverage refers to the sensitivity to the firmrsquos
fixed costs of production
bull Financial leverage is the sensitivity to a firmrsquos fixed
costs of financing
bull The relationship between the betas of the firmrsquos debt
equity and assets is given by
bull Financial leverage always increases the equity beta relative to the asset beta
bAsset = Debt + Equity
Debttimes bDebt +
Debt + Equity
Equitytimes bEquity
13-32
Example
Consider Grand Sport Inc which is currently all-equity
financed and has a beta of 090
The firm has decided to lever up to a capital structure of 1
part debt to 1 part equity
Since the firm will remain in the same industry its asset
beta should remain 090
However assuming a zero beta for its debt its equity beta
would become twice as large
bAsset = 090 = 1 + 1
1times bEquity bEquity = 2 times 090 = 180
13-20
Example
Suppose Stansfield Enterprises is evaluating the
following independent projects Each costs $100 and
lasts one year
Project Project b Projectrsquos
Estimated Cash
Flows Next Year
IRR NPV at
30
A 25 $150 50 $1538
B 25 $130 30 $0
C 25 $110 10 -$1538
13-21
Using the SML
An all-equity firm should accept projects whose IRRs
exceed the cost of equity capital and reject projects whose
IRRs fall short of the cost of capital
Pro
ject
IRR
Firmrsquos risk (beta)
SML
5
Good
project
Bad project
30
25
A
B
C
13-22
What if project betas vary
bull If the firm has a single cost of capital but
considers projects of varying risk adjustments
should be made
ndash Different risk adjusted costs of capital should be used
for each project
bull Otherwise the firm will over invest in risky
projects
ndash Why - See the following example
13-23
Suppose the Conglomerate Company has a cost of capital
based on the CAPM of 17 The risk-free rate is 4 the
market risk premium is 10 and the firmrsquos beta is 13
17 = 4 + 13 times 10
This is a breakdown of the companyrsquos investment projects
13 Automotive Retailer b = 20
13 Computer Hard Drive Manufacturer b = 13
13 Electric Utility b = 06
average b of assets = 13
When evaluating a new electrical generation investment
which cost of capital should be used
Capital Budgeting amp Project Risk
13-24
Capital Budgeting amp Project RiskP
roje
ct I
RR
Projectrsquos risk (b)
17
13 2006
R = 4 + 06times(14 ndash 4 ) = 10
10 reflects the opportunity cost of capital on an investment in electrical generation given the unique risk of the project
10
24 Investments in hard
drives or auto
retailing should have
higher discount rates
SML
13-25
Capital Budgeting amp Project Risk
A firm that uses one discount rate for all projects may over
time increase the risk of the firm while decreasing its value
Pro
ject
IR
R
Firmrsquos risk (beta)
SML
rf
bFIRM
Incorrectly rejected
positive NPV projects
Incorrectly accepted
negative NPV projects
Hurdle
rate)( FMFIRMF RRβR
The SML can tell us why
13-26
The Weighted Average Cost of
Capital
bull The Weighted Average Cost of Capital is given
by
bull Because interest expense is tax-deductible we multiply the last term by (1 ndash TC)
RWACC = Equity + Debt
Equitytimes REquity +
Equity + Debt
Debttimes RDebt times(1 ndash TC)
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-27
Cost of Debt
bull Interest rate required on new debt issuance (ie yield to
maturity on outstanding debt)
bull Adjust for the tax deductibility of interest expense
bull In practice finding new debt issuances is tricky
bull For companies with publicly traded debt we can rely on
the yield to maturity of the debt
ndash Note that the coupon rate is NOT a measure of the cost of debt
today
bull httpfinanceyahoocombonds
13-28
Example Target Corp
bull First we estimate the cost of equity and the cost
of debt
ndash We estimate an equity beta to estimate the cost of
equity
ndash We can often estimate the cost of debt by observing
the YTM of the firmrsquos debt
bull Second we determine the WACC by weighting
these two costs appropriately
13-29
Example International Paper
bull The industry average beta is 082 the risk free rate is
3 and the market risk premium is 84
bull Thus the cost of equity capital is
RS = RF + bi times (RM ndash RF)
= 3 +82times84
= 989
13-30
Example International Paper
bull The yield on the companyrsquos debt is 8 and
the firm has a 37 marginal tax rate The
debt to value ratio is 32
834 is Internationalrsquos cost of capital
= 068 times 989 + 032 times 8 times (1 ndash 037)
= 834
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-31
Financial Leverage and Beta
bull Operating leverage refers to the sensitivity to the firmrsquos
fixed costs of production
bull Financial leverage is the sensitivity to a firmrsquos fixed
costs of financing
bull The relationship between the betas of the firmrsquos debt
equity and assets is given by
bull Financial leverage always increases the equity beta relative to the asset beta
bAsset = Debt + Equity
Debttimes bDebt +
Debt + Equity
Equitytimes bEquity
13-32
Example
Consider Grand Sport Inc which is currently all-equity
financed and has a beta of 090
The firm has decided to lever up to a capital structure of 1
part debt to 1 part equity
Since the firm will remain in the same industry its asset
beta should remain 090
However assuming a zero beta for its debt its equity beta
would become twice as large
bAsset = 090 = 1 + 1
1times bEquity bEquity = 2 times 090 = 180
13-21
Using the SML
An all-equity firm should accept projects whose IRRs
exceed the cost of equity capital and reject projects whose
IRRs fall short of the cost of capital
Pro
ject
IRR
Firmrsquos risk (beta)
SML
5
Good
project
Bad project
30
25
A
B
C
13-22
What if project betas vary
bull If the firm has a single cost of capital but
considers projects of varying risk adjustments
should be made
ndash Different risk adjusted costs of capital should be used
for each project
bull Otherwise the firm will over invest in risky
projects
ndash Why - See the following example
13-23
Suppose the Conglomerate Company has a cost of capital
based on the CAPM of 17 The risk-free rate is 4 the
market risk premium is 10 and the firmrsquos beta is 13
17 = 4 + 13 times 10
This is a breakdown of the companyrsquos investment projects
13 Automotive Retailer b = 20
13 Computer Hard Drive Manufacturer b = 13
13 Electric Utility b = 06
average b of assets = 13
When evaluating a new electrical generation investment
which cost of capital should be used
Capital Budgeting amp Project Risk
13-24
Capital Budgeting amp Project RiskP
roje
ct I
RR
Projectrsquos risk (b)
17
13 2006
R = 4 + 06times(14 ndash 4 ) = 10
10 reflects the opportunity cost of capital on an investment in electrical generation given the unique risk of the project
10
24 Investments in hard
drives or auto
retailing should have
higher discount rates
SML
13-25
Capital Budgeting amp Project Risk
A firm that uses one discount rate for all projects may over
time increase the risk of the firm while decreasing its value
Pro
ject
IR
R
Firmrsquos risk (beta)
SML
rf
bFIRM
Incorrectly rejected
positive NPV projects
Incorrectly accepted
negative NPV projects
Hurdle
rate)( FMFIRMF RRβR
The SML can tell us why
13-26
The Weighted Average Cost of
Capital
bull The Weighted Average Cost of Capital is given
by
bull Because interest expense is tax-deductible we multiply the last term by (1 ndash TC)
RWACC = Equity + Debt
Equitytimes REquity +
Equity + Debt
Debttimes RDebt times(1 ndash TC)
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-27
Cost of Debt
bull Interest rate required on new debt issuance (ie yield to
maturity on outstanding debt)
bull Adjust for the tax deductibility of interest expense
bull In practice finding new debt issuances is tricky
bull For companies with publicly traded debt we can rely on
the yield to maturity of the debt
ndash Note that the coupon rate is NOT a measure of the cost of debt
today
bull httpfinanceyahoocombonds
13-28
Example Target Corp
bull First we estimate the cost of equity and the cost
of debt
ndash We estimate an equity beta to estimate the cost of
equity
ndash We can often estimate the cost of debt by observing
the YTM of the firmrsquos debt
bull Second we determine the WACC by weighting
these two costs appropriately
13-29
Example International Paper
bull The industry average beta is 082 the risk free rate is
3 and the market risk premium is 84
bull Thus the cost of equity capital is
RS = RF + bi times (RM ndash RF)
= 3 +82times84
= 989
13-30
Example International Paper
bull The yield on the companyrsquos debt is 8 and
the firm has a 37 marginal tax rate The
debt to value ratio is 32
834 is Internationalrsquos cost of capital
= 068 times 989 + 032 times 8 times (1 ndash 037)
= 834
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-31
Financial Leverage and Beta
bull Operating leverage refers to the sensitivity to the firmrsquos
fixed costs of production
bull Financial leverage is the sensitivity to a firmrsquos fixed
costs of financing
bull The relationship between the betas of the firmrsquos debt
equity and assets is given by
bull Financial leverage always increases the equity beta relative to the asset beta
bAsset = Debt + Equity
Debttimes bDebt +
Debt + Equity
Equitytimes bEquity
13-32
Example
Consider Grand Sport Inc which is currently all-equity
financed and has a beta of 090
The firm has decided to lever up to a capital structure of 1
part debt to 1 part equity
Since the firm will remain in the same industry its asset
beta should remain 090
However assuming a zero beta for its debt its equity beta
would become twice as large
bAsset = 090 = 1 + 1
1times bEquity bEquity = 2 times 090 = 180
13-22
What if project betas vary
bull If the firm has a single cost of capital but
considers projects of varying risk adjustments
should be made
ndash Different risk adjusted costs of capital should be used
for each project
bull Otherwise the firm will over invest in risky
projects
ndash Why - See the following example
13-23
Suppose the Conglomerate Company has a cost of capital
based on the CAPM of 17 The risk-free rate is 4 the
market risk premium is 10 and the firmrsquos beta is 13
17 = 4 + 13 times 10
This is a breakdown of the companyrsquos investment projects
13 Automotive Retailer b = 20
13 Computer Hard Drive Manufacturer b = 13
13 Electric Utility b = 06
average b of assets = 13
When evaluating a new electrical generation investment
which cost of capital should be used
Capital Budgeting amp Project Risk
13-24
Capital Budgeting amp Project RiskP
roje
ct I
RR
Projectrsquos risk (b)
17
13 2006
R = 4 + 06times(14 ndash 4 ) = 10
10 reflects the opportunity cost of capital on an investment in electrical generation given the unique risk of the project
10
24 Investments in hard
drives or auto
retailing should have
higher discount rates
SML
13-25
Capital Budgeting amp Project Risk
A firm that uses one discount rate for all projects may over
time increase the risk of the firm while decreasing its value
Pro
ject
IR
R
Firmrsquos risk (beta)
SML
rf
bFIRM
Incorrectly rejected
positive NPV projects
Incorrectly accepted
negative NPV projects
Hurdle
rate)( FMFIRMF RRβR
The SML can tell us why
13-26
The Weighted Average Cost of
Capital
bull The Weighted Average Cost of Capital is given
by
bull Because interest expense is tax-deductible we multiply the last term by (1 ndash TC)
RWACC = Equity + Debt
Equitytimes REquity +
Equity + Debt
Debttimes RDebt times(1 ndash TC)
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-27
Cost of Debt
bull Interest rate required on new debt issuance (ie yield to
maturity on outstanding debt)
bull Adjust for the tax deductibility of interest expense
bull In practice finding new debt issuances is tricky
bull For companies with publicly traded debt we can rely on
the yield to maturity of the debt
ndash Note that the coupon rate is NOT a measure of the cost of debt
today
bull httpfinanceyahoocombonds
13-28
Example Target Corp
bull First we estimate the cost of equity and the cost
of debt
ndash We estimate an equity beta to estimate the cost of
equity
ndash We can often estimate the cost of debt by observing
the YTM of the firmrsquos debt
bull Second we determine the WACC by weighting
these two costs appropriately
13-29
Example International Paper
bull The industry average beta is 082 the risk free rate is
3 and the market risk premium is 84
bull Thus the cost of equity capital is
RS = RF + bi times (RM ndash RF)
= 3 +82times84
= 989
13-30
Example International Paper
bull The yield on the companyrsquos debt is 8 and
the firm has a 37 marginal tax rate The
debt to value ratio is 32
834 is Internationalrsquos cost of capital
= 068 times 989 + 032 times 8 times (1 ndash 037)
= 834
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-31
Financial Leverage and Beta
bull Operating leverage refers to the sensitivity to the firmrsquos
fixed costs of production
bull Financial leverage is the sensitivity to a firmrsquos fixed
costs of financing
bull The relationship between the betas of the firmrsquos debt
equity and assets is given by
bull Financial leverage always increases the equity beta relative to the asset beta
bAsset = Debt + Equity
Debttimes bDebt +
Debt + Equity
Equitytimes bEquity
13-32
Example
Consider Grand Sport Inc which is currently all-equity
financed and has a beta of 090
The firm has decided to lever up to a capital structure of 1
part debt to 1 part equity
Since the firm will remain in the same industry its asset
beta should remain 090
However assuming a zero beta for its debt its equity beta
would become twice as large
bAsset = 090 = 1 + 1
1times bEquity bEquity = 2 times 090 = 180
13-23
Suppose the Conglomerate Company has a cost of capital
based on the CAPM of 17 The risk-free rate is 4 the
market risk premium is 10 and the firmrsquos beta is 13
17 = 4 + 13 times 10
This is a breakdown of the companyrsquos investment projects
13 Automotive Retailer b = 20
13 Computer Hard Drive Manufacturer b = 13
13 Electric Utility b = 06
average b of assets = 13
When evaluating a new electrical generation investment
which cost of capital should be used
Capital Budgeting amp Project Risk
13-24
Capital Budgeting amp Project RiskP
roje
ct I
RR
Projectrsquos risk (b)
17
13 2006
R = 4 + 06times(14 ndash 4 ) = 10
10 reflects the opportunity cost of capital on an investment in electrical generation given the unique risk of the project
10
24 Investments in hard
drives or auto
retailing should have
higher discount rates
SML
13-25
Capital Budgeting amp Project Risk
A firm that uses one discount rate for all projects may over
time increase the risk of the firm while decreasing its value
Pro
ject
IR
R
Firmrsquos risk (beta)
SML
rf
bFIRM
Incorrectly rejected
positive NPV projects
Incorrectly accepted
negative NPV projects
Hurdle
rate)( FMFIRMF RRβR
The SML can tell us why
13-26
The Weighted Average Cost of
Capital
bull The Weighted Average Cost of Capital is given
by
bull Because interest expense is tax-deductible we multiply the last term by (1 ndash TC)
RWACC = Equity + Debt
Equitytimes REquity +
Equity + Debt
Debttimes RDebt times(1 ndash TC)
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-27
Cost of Debt
bull Interest rate required on new debt issuance (ie yield to
maturity on outstanding debt)
bull Adjust for the tax deductibility of interest expense
bull In practice finding new debt issuances is tricky
bull For companies with publicly traded debt we can rely on
the yield to maturity of the debt
ndash Note that the coupon rate is NOT a measure of the cost of debt
today
bull httpfinanceyahoocombonds
13-28
Example Target Corp
bull First we estimate the cost of equity and the cost
of debt
ndash We estimate an equity beta to estimate the cost of
equity
ndash We can often estimate the cost of debt by observing
the YTM of the firmrsquos debt
bull Second we determine the WACC by weighting
these two costs appropriately
13-29
Example International Paper
bull The industry average beta is 082 the risk free rate is
3 and the market risk premium is 84
bull Thus the cost of equity capital is
RS = RF + bi times (RM ndash RF)
= 3 +82times84
= 989
13-30
Example International Paper
bull The yield on the companyrsquos debt is 8 and
the firm has a 37 marginal tax rate The
debt to value ratio is 32
834 is Internationalrsquos cost of capital
= 068 times 989 + 032 times 8 times (1 ndash 037)
= 834
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-31
Financial Leverage and Beta
bull Operating leverage refers to the sensitivity to the firmrsquos
fixed costs of production
bull Financial leverage is the sensitivity to a firmrsquos fixed
costs of financing
bull The relationship between the betas of the firmrsquos debt
equity and assets is given by
bull Financial leverage always increases the equity beta relative to the asset beta
bAsset = Debt + Equity
Debttimes bDebt +
Debt + Equity
Equitytimes bEquity
13-32
Example
Consider Grand Sport Inc which is currently all-equity
financed and has a beta of 090
The firm has decided to lever up to a capital structure of 1
part debt to 1 part equity
Since the firm will remain in the same industry its asset
beta should remain 090
However assuming a zero beta for its debt its equity beta
would become twice as large
bAsset = 090 = 1 + 1
1times bEquity bEquity = 2 times 090 = 180
13-24
Capital Budgeting amp Project RiskP
roje
ct I
RR
Projectrsquos risk (b)
17
13 2006
R = 4 + 06times(14 ndash 4 ) = 10
10 reflects the opportunity cost of capital on an investment in electrical generation given the unique risk of the project
10
24 Investments in hard
drives or auto
retailing should have
higher discount rates
SML
13-25
Capital Budgeting amp Project Risk
A firm that uses one discount rate for all projects may over
time increase the risk of the firm while decreasing its value
Pro
ject
IR
R
Firmrsquos risk (beta)
SML
rf
bFIRM
Incorrectly rejected
positive NPV projects
Incorrectly accepted
negative NPV projects
Hurdle
rate)( FMFIRMF RRβR
The SML can tell us why
13-26
The Weighted Average Cost of
Capital
bull The Weighted Average Cost of Capital is given
by
bull Because interest expense is tax-deductible we multiply the last term by (1 ndash TC)
RWACC = Equity + Debt
Equitytimes REquity +
Equity + Debt
Debttimes RDebt times(1 ndash TC)
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-27
Cost of Debt
bull Interest rate required on new debt issuance (ie yield to
maturity on outstanding debt)
bull Adjust for the tax deductibility of interest expense
bull In practice finding new debt issuances is tricky
bull For companies with publicly traded debt we can rely on
the yield to maturity of the debt
ndash Note that the coupon rate is NOT a measure of the cost of debt
today
bull httpfinanceyahoocombonds
13-28
Example Target Corp
bull First we estimate the cost of equity and the cost
of debt
ndash We estimate an equity beta to estimate the cost of
equity
ndash We can often estimate the cost of debt by observing
the YTM of the firmrsquos debt
bull Second we determine the WACC by weighting
these two costs appropriately
13-29
Example International Paper
bull The industry average beta is 082 the risk free rate is
3 and the market risk premium is 84
bull Thus the cost of equity capital is
RS = RF + bi times (RM ndash RF)
= 3 +82times84
= 989
13-30
Example International Paper
bull The yield on the companyrsquos debt is 8 and
the firm has a 37 marginal tax rate The
debt to value ratio is 32
834 is Internationalrsquos cost of capital
= 068 times 989 + 032 times 8 times (1 ndash 037)
= 834
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-31
Financial Leverage and Beta
bull Operating leverage refers to the sensitivity to the firmrsquos
fixed costs of production
bull Financial leverage is the sensitivity to a firmrsquos fixed
costs of financing
bull The relationship between the betas of the firmrsquos debt
equity and assets is given by
bull Financial leverage always increases the equity beta relative to the asset beta
bAsset = Debt + Equity
Debttimes bDebt +
Debt + Equity
Equitytimes bEquity
13-32
Example
Consider Grand Sport Inc which is currently all-equity
financed and has a beta of 090
The firm has decided to lever up to a capital structure of 1
part debt to 1 part equity
Since the firm will remain in the same industry its asset
beta should remain 090
However assuming a zero beta for its debt its equity beta
would become twice as large
bAsset = 090 = 1 + 1
1times bEquity bEquity = 2 times 090 = 180
13-25
Capital Budgeting amp Project Risk
A firm that uses one discount rate for all projects may over
time increase the risk of the firm while decreasing its value
Pro
ject
IR
R
Firmrsquos risk (beta)
SML
rf
bFIRM
Incorrectly rejected
positive NPV projects
Incorrectly accepted
negative NPV projects
Hurdle
rate)( FMFIRMF RRβR
The SML can tell us why
13-26
The Weighted Average Cost of
Capital
bull The Weighted Average Cost of Capital is given
by
bull Because interest expense is tax-deductible we multiply the last term by (1 ndash TC)
RWACC = Equity + Debt
Equitytimes REquity +
Equity + Debt
Debttimes RDebt times(1 ndash TC)
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-27
Cost of Debt
bull Interest rate required on new debt issuance (ie yield to
maturity on outstanding debt)
bull Adjust for the tax deductibility of interest expense
bull In practice finding new debt issuances is tricky
bull For companies with publicly traded debt we can rely on
the yield to maturity of the debt
ndash Note that the coupon rate is NOT a measure of the cost of debt
today
bull httpfinanceyahoocombonds
13-28
Example Target Corp
bull First we estimate the cost of equity and the cost
of debt
ndash We estimate an equity beta to estimate the cost of
equity
ndash We can often estimate the cost of debt by observing
the YTM of the firmrsquos debt
bull Second we determine the WACC by weighting
these two costs appropriately
13-29
Example International Paper
bull The industry average beta is 082 the risk free rate is
3 and the market risk premium is 84
bull Thus the cost of equity capital is
RS = RF + bi times (RM ndash RF)
= 3 +82times84
= 989
13-30
Example International Paper
bull The yield on the companyrsquos debt is 8 and
the firm has a 37 marginal tax rate The
debt to value ratio is 32
834 is Internationalrsquos cost of capital
= 068 times 989 + 032 times 8 times (1 ndash 037)
= 834
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-31
Financial Leverage and Beta
bull Operating leverage refers to the sensitivity to the firmrsquos
fixed costs of production
bull Financial leverage is the sensitivity to a firmrsquos fixed
costs of financing
bull The relationship between the betas of the firmrsquos debt
equity and assets is given by
bull Financial leverage always increases the equity beta relative to the asset beta
bAsset = Debt + Equity
Debttimes bDebt +
Debt + Equity
Equitytimes bEquity
13-32
Example
Consider Grand Sport Inc which is currently all-equity
financed and has a beta of 090
The firm has decided to lever up to a capital structure of 1
part debt to 1 part equity
Since the firm will remain in the same industry its asset
beta should remain 090
However assuming a zero beta for its debt its equity beta
would become twice as large
bAsset = 090 = 1 + 1
1times bEquity bEquity = 2 times 090 = 180
13-26
The Weighted Average Cost of
Capital
bull The Weighted Average Cost of Capital is given
by
bull Because interest expense is tax-deductible we multiply the last term by (1 ndash TC)
RWACC = Equity + Debt
Equitytimes REquity +
Equity + Debt
Debttimes RDebt times(1 ndash TC)
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-27
Cost of Debt
bull Interest rate required on new debt issuance (ie yield to
maturity on outstanding debt)
bull Adjust for the tax deductibility of interest expense
bull In practice finding new debt issuances is tricky
bull For companies with publicly traded debt we can rely on
the yield to maturity of the debt
ndash Note that the coupon rate is NOT a measure of the cost of debt
today
bull httpfinanceyahoocombonds
13-28
Example Target Corp
bull First we estimate the cost of equity and the cost
of debt
ndash We estimate an equity beta to estimate the cost of
equity
ndash We can often estimate the cost of debt by observing
the YTM of the firmrsquos debt
bull Second we determine the WACC by weighting
these two costs appropriately
13-29
Example International Paper
bull The industry average beta is 082 the risk free rate is
3 and the market risk premium is 84
bull Thus the cost of equity capital is
RS = RF + bi times (RM ndash RF)
= 3 +82times84
= 989
13-30
Example International Paper
bull The yield on the companyrsquos debt is 8 and
the firm has a 37 marginal tax rate The
debt to value ratio is 32
834 is Internationalrsquos cost of capital
= 068 times 989 + 032 times 8 times (1 ndash 037)
= 834
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-31
Financial Leverage and Beta
bull Operating leverage refers to the sensitivity to the firmrsquos
fixed costs of production
bull Financial leverage is the sensitivity to a firmrsquos fixed
costs of financing
bull The relationship between the betas of the firmrsquos debt
equity and assets is given by
bull Financial leverage always increases the equity beta relative to the asset beta
bAsset = Debt + Equity
Debttimes bDebt +
Debt + Equity
Equitytimes bEquity
13-32
Example
Consider Grand Sport Inc which is currently all-equity
financed and has a beta of 090
The firm has decided to lever up to a capital structure of 1
part debt to 1 part equity
Since the firm will remain in the same industry its asset
beta should remain 090
However assuming a zero beta for its debt its equity beta
would become twice as large
bAsset = 090 = 1 + 1
1times bEquity bEquity = 2 times 090 = 180
13-27
Cost of Debt
bull Interest rate required on new debt issuance (ie yield to
maturity on outstanding debt)
bull Adjust for the tax deductibility of interest expense
bull In practice finding new debt issuances is tricky
bull For companies with publicly traded debt we can rely on
the yield to maturity of the debt
ndash Note that the coupon rate is NOT a measure of the cost of debt
today
bull httpfinanceyahoocombonds
13-28
Example Target Corp
bull First we estimate the cost of equity and the cost
of debt
ndash We estimate an equity beta to estimate the cost of
equity
ndash We can often estimate the cost of debt by observing
the YTM of the firmrsquos debt
bull Second we determine the WACC by weighting
these two costs appropriately
13-29
Example International Paper
bull The industry average beta is 082 the risk free rate is
3 and the market risk premium is 84
bull Thus the cost of equity capital is
RS = RF + bi times (RM ndash RF)
= 3 +82times84
= 989
13-30
Example International Paper
bull The yield on the companyrsquos debt is 8 and
the firm has a 37 marginal tax rate The
debt to value ratio is 32
834 is Internationalrsquos cost of capital
= 068 times 989 + 032 times 8 times (1 ndash 037)
= 834
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-31
Financial Leverage and Beta
bull Operating leverage refers to the sensitivity to the firmrsquos
fixed costs of production
bull Financial leverage is the sensitivity to a firmrsquos fixed
costs of financing
bull The relationship between the betas of the firmrsquos debt
equity and assets is given by
bull Financial leverage always increases the equity beta relative to the asset beta
bAsset = Debt + Equity
Debttimes bDebt +
Debt + Equity
Equitytimes bEquity
13-32
Example
Consider Grand Sport Inc which is currently all-equity
financed and has a beta of 090
The firm has decided to lever up to a capital structure of 1
part debt to 1 part equity
Since the firm will remain in the same industry its asset
beta should remain 090
However assuming a zero beta for its debt its equity beta
would become twice as large
bAsset = 090 = 1 + 1
1times bEquity bEquity = 2 times 090 = 180
13-28
Example Target Corp
bull First we estimate the cost of equity and the cost
of debt
ndash We estimate an equity beta to estimate the cost of
equity
ndash We can often estimate the cost of debt by observing
the YTM of the firmrsquos debt
bull Second we determine the WACC by weighting
these two costs appropriately
13-29
Example International Paper
bull The industry average beta is 082 the risk free rate is
3 and the market risk premium is 84
bull Thus the cost of equity capital is
RS = RF + bi times (RM ndash RF)
= 3 +82times84
= 989
13-30
Example International Paper
bull The yield on the companyrsquos debt is 8 and
the firm has a 37 marginal tax rate The
debt to value ratio is 32
834 is Internationalrsquos cost of capital
= 068 times 989 + 032 times 8 times (1 ndash 037)
= 834
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-31
Financial Leverage and Beta
bull Operating leverage refers to the sensitivity to the firmrsquos
fixed costs of production
bull Financial leverage is the sensitivity to a firmrsquos fixed
costs of financing
bull The relationship between the betas of the firmrsquos debt
equity and assets is given by
bull Financial leverage always increases the equity beta relative to the asset beta
bAsset = Debt + Equity
Debttimes bDebt +
Debt + Equity
Equitytimes bEquity
13-32
Example
Consider Grand Sport Inc which is currently all-equity
financed and has a beta of 090
The firm has decided to lever up to a capital structure of 1
part debt to 1 part equity
Since the firm will remain in the same industry its asset
beta should remain 090
However assuming a zero beta for its debt its equity beta
would become twice as large
bAsset = 090 = 1 + 1
1times bEquity bEquity = 2 times 090 = 180
13-29
Example International Paper
bull The industry average beta is 082 the risk free rate is
3 and the market risk premium is 84
bull Thus the cost of equity capital is
RS = RF + bi times (RM ndash RF)
= 3 +82times84
= 989
13-30
Example International Paper
bull The yield on the companyrsquos debt is 8 and
the firm has a 37 marginal tax rate The
debt to value ratio is 32
834 is Internationalrsquos cost of capital
= 068 times 989 + 032 times 8 times (1 ndash 037)
= 834
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-31
Financial Leverage and Beta
bull Operating leverage refers to the sensitivity to the firmrsquos
fixed costs of production
bull Financial leverage is the sensitivity to a firmrsquos fixed
costs of financing
bull The relationship between the betas of the firmrsquos debt
equity and assets is given by
bull Financial leverage always increases the equity beta relative to the asset beta
bAsset = Debt + Equity
Debttimes bDebt +
Debt + Equity
Equitytimes bEquity
13-32
Example
Consider Grand Sport Inc which is currently all-equity
financed and has a beta of 090
The firm has decided to lever up to a capital structure of 1
part debt to 1 part equity
Since the firm will remain in the same industry its asset
beta should remain 090
However assuming a zero beta for its debt its equity beta
would become twice as large
bAsset = 090 = 1 + 1
1times bEquity bEquity = 2 times 090 = 180
13-30
Example International Paper
bull The yield on the companyrsquos debt is 8 and
the firm has a 37 marginal tax rate The
debt to value ratio is 32
834 is Internationalrsquos cost of capital
= 068 times 989 + 032 times 8 times (1 ndash 037)
= 834
RWACC = S + B
Stimes RS +
S + B
Btimes RB times(1 ndash TC)
13-31
Financial Leverage and Beta
bull Operating leverage refers to the sensitivity to the firmrsquos
fixed costs of production
bull Financial leverage is the sensitivity to a firmrsquos fixed
costs of financing
bull The relationship between the betas of the firmrsquos debt
equity and assets is given by
bull Financial leverage always increases the equity beta relative to the asset beta
bAsset = Debt + Equity
Debttimes bDebt +
Debt + Equity
Equitytimes bEquity
13-32
Example
Consider Grand Sport Inc which is currently all-equity
financed and has a beta of 090
The firm has decided to lever up to a capital structure of 1
part debt to 1 part equity
Since the firm will remain in the same industry its asset
beta should remain 090
However assuming a zero beta for its debt its equity beta
would become twice as large
bAsset = 090 = 1 + 1
1times bEquity bEquity = 2 times 090 = 180
13-31
Financial Leverage and Beta
bull Operating leverage refers to the sensitivity to the firmrsquos
fixed costs of production
bull Financial leverage is the sensitivity to a firmrsquos fixed
costs of financing
bull The relationship between the betas of the firmrsquos debt
equity and assets is given by
bull Financial leverage always increases the equity beta relative to the asset beta
bAsset = Debt + Equity
Debttimes bDebt +
Debt + Equity
Equitytimes bEquity
13-32
Example
Consider Grand Sport Inc which is currently all-equity
financed and has a beta of 090
The firm has decided to lever up to a capital structure of 1
part debt to 1 part equity
Since the firm will remain in the same industry its asset
beta should remain 090
However assuming a zero beta for its debt its equity beta
would become twice as large
bAsset = 090 = 1 + 1
1times bEquity bEquity = 2 times 090 = 180
13-32
Example
Consider Grand Sport Inc which is currently all-equity
financed and has a beta of 090
The firm has decided to lever up to a capital structure of 1
part debt to 1 part equity
Since the firm will remain in the same industry its asset
beta should remain 090
However assuming a zero beta for its debt its equity beta
would become twice as large
bAsset = 090 = 1 + 1
1times bEquity bEquity = 2 times 090 = 180
