15-1
Chapter 15
Required Returns
and the Cost of
Capital
15-2
Required Returns and
the Cost of Capital
? Creation of Value
? Overall Cost of Capital of the Firm
? Project-Specific Required Rates
? Group-Specific Required Rates
? Total Risk Evaluation
15-3
Key Sources of
Value Creation
Growth
phase of
product
cycle
Barriers to
competitive
entry
Other --
e.g,patents,
temporary
monopoly
power,
oligopoly
pricing
Cost
Marketing
and
price
Perceived
quality
Superior
organizational
capability
Industry Attractiveness
Competitive Advantage
15-4
Overall Cost of
Capital of the Firm
Cost of Capital is the required
rate of return on the various
types of financing,The overall
cost of capital is a weighted
average of the individual
required rates of return (costs).
15-5
Type of Financing Mkt Val Weight
Long-Term Debt $35M 35%
Preferred Stock $15M 15%
Common Stock Equity $50M 50%
$100M 100%
Market Value of
Long-Term
Financing
15-6
Cost of Debt is the required rate
of return on investment of the
lenders of a company.
ki = kd ( 1 - T )
Cost of Debt
P0 = Ij + Pj(1 + k
d)j
?
n
j =1
15-7
Assume that Basket Wonders (BW) has
$1,000 par value zero-coupon bonds
outstanding,BW bonds are currently
trading at $385.54 with 10 years to
maturity,BW tax bracket is 40%.
Determination of
the Cost of Debt
$385.54 = $0 + $1,000(1 + k
d)10
15-8
(1 + kd)10 = $1,000 / $385.54
= 2.5938
(1 + kd) = (2.5938) (1/10)
= 1.1
kd =,1 or 10%
ki = 10% ( 1 -,40 )
ki = 6%
Determination of
the Cost of Debt
15-9
Cost of Preferred Stock is the
required rate of return on
investment of the preferred
shareholders of the company.
kP = DP / P0
Cost of Preferred Stock
15-10
Assume that Basket Wonders (BW)
has preferred stock outstanding with
par value of $100,dividend per share
of $6.30,and a current market value of
$70 per share.
kP = $6.30 / $70
kP = 9%
Determination of the
Cost of Preferred
Stock
15-11
?Dividend Discount Model
?Capital-Asset Pricing
Model
?Before-Tax Cost of Debt
plus Risk Premium
Cost of Equity
Approaches
15-12
Dividend Discount Model
The cost of equity capital,ke,is
the discount rate that equates the
present value of all expected
future dividends with the current
market price of the stock.
D1 D2 D
(1+ke)1 (1+ke)2 (1+ke)+,,, ++P0 =
? ?
15-13
Constant Growth Model
The constant dividend growth
assumption reduces the model to:
ke = ( D1 / P0 ) + g
Assumes that dividends will grow
at the constant rate g forever.
15-14
Assume that Basket Wonders (BW) has
common stock outstanding with a current
market value of $64.80 per share,current
dividend of $3 per share,and a dividend
growth rate of 8% forever.
ke = ( D1 / P0 ) + g
ke = ($3(1.08) / $64.80) +,08
ke =,05 +,08 =,13 or 13%
Determination of the
Cost of Equity
Capital
15-15
Growth Phases Model
D0(1+g1)t Da(1+g2)t-a
(1+ke)t (1+ke)tP0 =
The growth phases assumption
leads to the following formula
(assume 3 growth phases):
? ????
t=1
a
t=a+1
b
t=b+1
? Db(1+g3)t-b
(1+ke)t
+
?
15-16
Capital Asset
Pricing Model
The cost of equity capital,ke,is
equated to the required rate of
return in market equilibrium,The
risk-return relationship is described
by the Security Market Line (SML).
ke = Rj = Rf + (Rm - Rf)?j
15-17
Assume that Basket Wonders (BW) has
a company beta of 1.25,Research by
Julie Miller suggests that the risk-free
rate is 4% and the expected return on
the market is 11.2%
ke = Rf + (Rm - Rf)?j
= 4% + (11.2% - 4%)1.25
ke = 4% + 9% = 13%
Determination of the
Cost of Equity
(CAPM)
15-18
Before-Tax Cost of Debt
Plus Risk Premium
The cost of equity capital,ke,is the
sum of the before-tax cost of debt
and a risk premium in expected
return for common stock over debt,
ke = kd + Risk Premium*
* Risk premium is not the same as CAPM risk
premium
15-19
Assume that Basket Wonders (BW)
typically adds a 3% premium to the
before-tax cost of debt,
ke = kd + Risk Premium
= 10% + 3%
ke = 13%
Determination of the
Cost of Equity (kd +
R.P.)
15-20
Constant Growth Model 13%
Capital Asset Pricing Model 13%
Cost of Debt + Risk Premium 13%
Generally,the three methods
will not agree,
Comparison of the
Cost of Equity
Methods
15-21
Cost of Capital = kx(Wx)
WACC =,35(6%) +,15(9%) +
.50(13%)
WACC =,021 +,0135 +,065
=,0995 or 9.95%
Weighted Average
Cost of Capital (WACC)
?
n
x =1
15-22
1,Weighting System
Marginal Capital Costs
Capital Raised in Different
Proportions than WACC
Limitations of the WACC
15-23
2,Flotation Costs are the costs
associated with issuing securities
such as underwriting,legal,listing,
and printing fees.
a,Adjustment to Initial Outlay
b,Adjustment to Discount Rate
Limitations of the WACC
15-24
Add Flotation Costs (FC) to the
Initial Cash Outlay (ICO).
Impact,Reduces the NPV
Adjustment to
Initial Outlay
(AIO)
NPV = ?
n
t=1
CFt
(1 + k)t- ( ICO + FC )
15-25
Subtract Flotation Costs from the
proceeds (price) of the security and
recalculate yield figures.
Impact,Increases the cost for any
capital component with flotation costs.
Result,Increases the WACC which
decreases the NPV.
Adjustment to
Discount Rate (ADR)
15-26
Use of CAPM in Project Selection:
? Initially assume all-equity financing.
? Determine project beta.
? Calculate the expected return.
? Adjust for capital structure of firm.
? Compare cost to IRR of project.
Determining Project-Specific
Required Rates of Return
15-27
Determining the SML:
? Locate a proxy for the project
(much easier if asset is traded).
? Plot the Characteristic Line relationship
between the market portfolio and the
proxy asset excess returns.
? Estimate beta and create the SML.
Difficulty in Determining
the Expected Return
15-28
Project Acceptance
and/or Rejection
SML
X
X
X
X
XX
X
O O
O
O
O
O
O
SYSTEMATIC RISK (Beta)
EX
PE
CT
ED
RA
TE
OF
R
ET
UR
N
Rf
Accept
Reject
15-29
1,Calculate the required return
for Project k (all-equity financed).
Rk = Rf + (Rm - Rf)?k
2,Adjust for capital structure of the
firm (financing weights).
Weighted Average Required Return =
[ki][% of Debt] + [Rk][% of Equity]
Determining Project-Specific
Required Rate of Return
15-30
Assume a computer networking project is
being considered with an IRR of 19%.
Examination of firms in the networking
industry allows us to estimate an all-equity
beta of 1.5,Our firm is financed with 70%
Equity and 30% Debt at ki=6%.
The expected return on the market is
11.2% and the risk-free rate is 4%.
Project-Specific Required
Rate of Return Example
15-31
ke = Rf + (Rm - Rf)?j
= 4% + (11.2% - 4%)1.5
ke = 4% + 10.8% = 14.8%
WACC =,30(6%) +,70(14.8%)
= 1.8% + 10.36% = 12.16%
IRR = 19% > WACC = 12.16%
Do You Accept the Project?
15-32
Use of CAPM in Project Selection:
? Initially assume all-equity financing.
? Determine group beta.
? Calculate the expected return.
? Adjust for capital structure of group.
? Compare cost to IRR of group project.
Determining Group-Specific
Required Rates of Return
15-33
Comparing Group-Specific
Required Rates of Return
Group-Specific
Required Returns
Company Cost
of Capital
Systematic Risk (Beta)
Ex
pe
ct
ed
R
at
e o
f R
et
ur
n
15-34
? Amount of non-equity financing
relative to the proxy firm,
Adjust project beta if necessary.
? Standard problems in the use of
CAPM,Potential insolvency is a
total-risk problem rather than
just systematic risk (CAPM).
Qualifications to Using
Group-Specific Rates
15-35
Risk-Adjusted Discount Rate
Approach (RADR)
The required return is increased
(decreased) relative to the firm’s
overall cost of capital for projects
or groups showing greater
(smaller) than average risk.
Project Evaluation
Based on Total
Risk
15-36
Probability Distribution
Approach
Acceptance of a single project
with a positive NPV depends on
the dispersion of NPVs and the
utility preferences of
management.
Project Evaluation
Based on Total
Risk
15-37
Firm Portfolio Approach
B
C
A
Indifference
Curves
STANDARD DEVIATION
EX
PE
CT
ED
VAL
UE
O
F N
PV
Curves show
HIGH
Risk Aversion
15-38
Firm Portfolio Approach
B
C
A
Indifference
Curves
STANDARD DEVIATION
EX
PE
CT
ED
VAL
UE
O
F N
PV
Curves show
MODERATE
Risk Aversion
15-39
Firm Portfolio Approach
B
C
A
Indifference
Curves
STANDARD DEVIATION
EX
PE
CT
ED
VAL
UE
O
F
NP
V
Curves show
LOW
Risk Aversion
15-40
?j = ?ju [ 1 + (B/S)(1-TC) ]
?j,Beta of a levered firm.
?ju,Beta of an unlevered firm
(an all-equity financed firm).
B/S,Debt-to-Equity ratio in
Market Value terms.
TC, The corporate tax rate.
Adjusting Beta for
Financial Leverage
15-41
Adjusted Present Value (APV) is the
sum of the discounted value of a
project’s operating cash flows plus the
value of any tax-shield benefits of
interest associated with the project’s
financing minus any flotation costs.
Adjusted Present Value
APV = UnleveredProject Value + Value ofProject Financing
15-42
Assume Basket Wonders is considering a
new $425,000 automated basket weaving
machine that will save $100,000 per year
for the next 6 years,The required rate on
unlevered equity is 11%,
BW can borrow $180,000 at 7% with
$10,000 after-tax flotation costs,Principal
is repaid at $30,000 per year (+ interest),
The firm is in the 40% tax bracket.
NPV and APV Example
15-43
What is the NPV to an all-equity-
financed firm?
NPV = $100,000[PVIFA11%,6] - $425,000
NPV = $423,054 - $425,000
NPV = -$1,946
Basket Wonders
NPV Solution
15-44
What is the APV?
First,determine the interest expense.
Int Yr 1 ($180,000)(7%) = $12,600
Int Yr 2 ( 150,000)(7%) = 10,500
Int Yr 3 ( 120,000)(7%) = 8,400
Int Yr 4 ( 90,000)(7%) = 6,300
Int Yr 5 ( 60,000)(7%) = 4,200
Int Yr 6 ( 30,000)(7%) = 2,100
Basket Wonders
APV Solution
15-45
Second,calculate the tax-shield benefits.
TSB Yr 1 ($12,600)(40%) = $5,040
TSB Yr 2 ( 10,500)(40%) =
4,200 TSB Yr 3 ( 8,400)(40%)
= 3,360 TSB Yr 4 ( 6,300)(40%)
= 2,520 TSB Yr 5 ( 4,200)(40%)
= 1,680 TSB Yr 6 ( 2,100)(40%)
= 840
Basket Wonders
APV Solution
15-46
Third,find the PV of the tax-shield benefits.
TSB Yr 1 ($5,040)(.901) = $4,541
TSB Yr 2 ( 4,200)(.812) =
3,410 TSB Yr 3 ( 3,360)(.731) =
2,456 TSB Yr 4 ( 2,520)(.659) =
1,661 TSB Yr 5 ( 1,680)(.593) =
996 TSB Yr 6 ( 840)(.535) =
449 PV =
$13,513
Basket Wonders
APV Solution
15-47
What is the APV?
APV = NPV + PV of TS - Flotation Cost
APV = -$1,946 + $13,513 - $10,000
APV = $1,567
Basket Wonders
NPV Solution
Chapter 15
Required Returns
and the Cost of
Capital
15-2
Required Returns and
the Cost of Capital
? Creation of Value
? Overall Cost of Capital of the Firm
? Project-Specific Required Rates
? Group-Specific Required Rates
? Total Risk Evaluation
15-3
Key Sources of
Value Creation
Growth
phase of
product
cycle
Barriers to
competitive
entry
Other --
e.g,patents,
temporary
monopoly
power,
oligopoly
pricing
Cost
Marketing
and
price
Perceived
quality
Superior
organizational
capability
Industry Attractiveness
Competitive Advantage
15-4
Overall Cost of
Capital of the Firm
Cost of Capital is the required
rate of return on the various
types of financing,The overall
cost of capital is a weighted
average of the individual
required rates of return (costs).
15-5
Type of Financing Mkt Val Weight
Long-Term Debt $35M 35%
Preferred Stock $15M 15%
Common Stock Equity $50M 50%
$100M 100%
Market Value of
Long-Term
Financing
15-6
Cost of Debt is the required rate
of return on investment of the
lenders of a company.
ki = kd ( 1 - T )
Cost of Debt
P0 = Ij + Pj(1 + k
d)j
?
n
j =1
15-7
Assume that Basket Wonders (BW) has
$1,000 par value zero-coupon bonds
outstanding,BW bonds are currently
trading at $385.54 with 10 years to
maturity,BW tax bracket is 40%.
Determination of
the Cost of Debt
$385.54 = $0 + $1,000(1 + k
d)10
15-8
(1 + kd)10 = $1,000 / $385.54
= 2.5938
(1 + kd) = (2.5938) (1/10)
= 1.1
kd =,1 or 10%
ki = 10% ( 1 -,40 )
ki = 6%
Determination of
the Cost of Debt
15-9
Cost of Preferred Stock is the
required rate of return on
investment of the preferred
shareholders of the company.
kP = DP / P0
Cost of Preferred Stock
15-10
Assume that Basket Wonders (BW)
has preferred stock outstanding with
par value of $100,dividend per share
of $6.30,and a current market value of
$70 per share.
kP = $6.30 / $70
kP = 9%
Determination of the
Cost of Preferred
Stock
15-11
?Dividend Discount Model
?Capital-Asset Pricing
Model
?Before-Tax Cost of Debt
plus Risk Premium
Cost of Equity
Approaches
15-12
Dividend Discount Model
The cost of equity capital,ke,is
the discount rate that equates the
present value of all expected
future dividends with the current
market price of the stock.
D1 D2 D
(1+ke)1 (1+ke)2 (1+ke)+,,, ++P0 =
? ?
15-13
Constant Growth Model
The constant dividend growth
assumption reduces the model to:
ke = ( D1 / P0 ) + g
Assumes that dividends will grow
at the constant rate g forever.
15-14
Assume that Basket Wonders (BW) has
common stock outstanding with a current
market value of $64.80 per share,current
dividend of $3 per share,and a dividend
growth rate of 8% forever.
ke = ( D1 / P0 ) + g
ke = ($3(1.08) / $64.80) +,08
ke =,05 +,08 =,13 or 13%
Determination of the
Cost of Equity
Capital
15-15
Growth Phases Model
D0(1+g1)t Da(1+g2)t-a
(1+ke)t (1+ke)tP0 =
The growth phases assumption
leads to the following formula
(assume 3 growth phases):
? ????
t=1
a
t=a+1
b
t=b+1
? Db(1+g3)t-b
(1+ke)t
+
?
15-16
Capital Asset
Pricing Model
The cost of equity capital,ke,is
equated to the required rate of
return in market equilibrium,The
risk-return relationship is described
by the Security Market Line (SML).
ke = Rj = Rf + (Rm - Rf)?j
15-17
Assume that Basket Wonders (BW) has
a company beta of 1.25,Research by
Julie Miller suggests that the risk-free
rate is 4% and the expected return on
the market is 11.2%
ke = Rf + (Rm - Rf)?j
= 4% + (11.2% - 4%)1.25
ke = 4% + 9% = 13%
Determination of the
Cost of Equity
(CAPM)
15-18
Before-Tax Cost of Debt
Plus Risk Premium
The cost of equity capital,ke,is the
sum of the before-tax cost of debt
and a risk premium in expected
return for common stock over debt,
ke = kd + Risk Premium*
* Risk premium is not the same as CAPM risk
premium
15-19
Assume that Basket Wonders (BW)
typically adds a 3% premium to the
before-tax cost of debt,
ke = kd + Risk Premium
= 10% + 3%
ke = 13%
Determination of the
Cost of Equity (kd +
R.P.)
15-20
Constant Growth Model 13%
Capital Asset Pricing Model 13%
Cost of Debt + Risk Premium 13%
Generally,the three methods
will not agree,
Comparison of the
Cost of Equity
Methods
15-21
Cost of Capital = kx(Wx)
WACC =,35(6%) +,15(9%) +
.50(13%)
WACC =,021 +,0135 +,065
=,0995 or 9.95%
Weighted Average
Cost of Capital (WACC)
?
n
x =1
15-22
1,Weighting System
Marginal Capital Costs
Capital Raised in Different
Proportions than WACC
Limitations of the WACC
15-23
2,Flotation Costs are the costs
associated with issuing securities
such as underwriting,legal,listing,
and printing fees.
a,Adjustment to Initial Outlay
b,Adjustment to Discount Rate
Limitations of the WACC
15-24
Add Flotation Costs (FC) to the
Initial Cash Outlay (ICO).
Impact,Reduces the NPV
Adjustment to
Initial Outlay
(AIO)
NPV = ?
n
t=1
CFt
(1 + k)t- ( ICO + FC )
15-25
Subtract Flotation Costs from the
proceeds (price) of the security and
recalculate yield figures.
Impact,Increases the cost for any
capital component with flotation costs.
Result,Increases the WACC which
decreases the NPV.
Adjustment to
Discount Rate (ADR)
15-26
Use of CAPM in Project Selection:
? Initially assume all-equity financing.
? Determine project beta.
? Calculate the expected return.
? Adjust for capital structure of firm.
? Compare cost to IRR of project.
Determining Project-Specific
Required Rates of Return
15-27
Determining the SML:
? Locate a proxy for the project
(much easier if asset is traded).
? Plot the Characteristic Line relationship
between the market portfolio and the
proxy asset excess returns.
? Estimate beta and create the SML.
Difficulty in Determining
the Expected Return
15-28
Project Acceptance
and/or Rejection
SML
X
X
X
X
XX
X
O O
O
O
O
O
O
SYSTEMATIC RISK (Beta)
EX
PE
CT
ED
RA
TE
OF
R
ET
UR
N
Rf
Accept
Reject
15-29
1,Calculate the required return
for Project k (all-equity financed).
Rk = Rf + (Rm - Rf)?k
2,Adjust for capital structure of the
firm (financing weights).
Weighted Average Required Return =
[ki][% of Debt] + [Rk][% of Equity]
Determining Project-Specific
Required Rate of Return
15-30
Assume a computer networking project is
being considered with an IRR of 19%.
Examination of firms in the networking
industry allows us to estimate an all-equity
beta of 1.5,Our firm is financed with 70%
Equity and 30% Debt at ki=6%.
The expected return on the market is
11.2% and the risk-free rate is 4%.
Project-Specific Required
Rate of Return Example
15-31
ke = Rf + (Rm - Rf)?j
= 4% + (11.2% - 4%)1.5
ke = 4% + 10.8% = 14.8%
WACC =,30(6%) +,70(14.8%)
= 1.8% + 10.36% = 12.16%
IRR = 19% > WACC = 12.16%
Do You Accept the Project?
15-32
Use of CAPM in Project Selection:
? Initially assume all-equity financing.
? Determine group beta.
? Calculate the expected return.
? Adjust for capital structure of group.
? Compare cost to IRR of group project.
Determining Group-Specific
Required Rates of Return
15-33
Comparing Group-Specific
Required Rates of Return
Group-Specific
Required Returns
Company Cost
of Capital
Systematic Risk (Beta)
Ex
pe
ct
ed
R
at
e o
f R
et
ur
n
15-34
? Amount of non-equity financing
relative to the proxy firm,
Adjust project beta if necessary.
? Standard problems in the use of
CAPM,Potential insolvency is a
total-risk problem rather than
just systematic risk (CAPM).
Qualifications to Using
Group-Specific Rates
15-35
Risk-Adjusted Discount Rate
Approach (RADR)
The required return is increased
(decreased) relative to the firm’s
overall cost of capital for projects
or groups showing greater
(smaller) than average risk.
Project Evaluation
Based on Total
Risk
15-36
Probability Distribution
Approach
Acceptance of a single project
with a positive NPV depends on
the dispersion of NPVs and the
utility preferences of
management.
Project Evaluation
Based on Total
Risk
15-37
Firm Portfolio Approach
B
C
A
Indifference
Curves
STANDARD DEVIATION
EX
PE
CT
ED
VAL
UE
O
F N
PV
Curves show
HIGH
Risk Aversion
15-38
Firm Portfolio Approach
B
C
A
Indifference
Curves
STANDARD DEVIATION
EX
PE
CT
ED
VAL
UE
O
F N
PV
Curves show
MODERATE
Risk Aversion
15-39
Firm Portfolio Approach
B
C
A
Indifference
Curves
STANDARD DEVIATION
EX
PE
CT
ED
VAL
UE
O
F
NP
V
Curves show
LOW
Risk Aversion
15-40
?j = ?ju [ 1 + (B/S)(1-TC) ]
?j,Beta of a levered firm.
?ju,Beta of an unlevered firm
(an all-equity financed firm).
B/S,Debt-to-Equity ratio in
Market Value terms.
TC, The corporate tax rate.
Adjusting Beta for
Financial Leverage
15-41
Adjusted Present Value (APV) is the
sum of the discounted value of a
project’s operating cash flows plus the
value of any tax-shield benefits of
interest associated with the project’s
financing minus any flotation costs.
Adjusted Present Value
APV = UnleveredProject Value + Value ofProject Financing
15-42
Assume Basket Wonders is considering a
new $425,000 automated basket weaving
machine that will save $100,000 per year
for the next 6 years,The required rate on
unlevered equity is 11%,
BW can borrow $180,000 at 7% with
$10,000 after-tax flotation costs,Principal
is repaid at $30,000 per year (+ interest),
The firm is in the 40% tax bracket.
NPV and APV Example
15-43
What is the NPV to an all-equity-
financed firm?
NPV = $100,000[PVIFA11%,6] - $425,000
NPV = $423,054 - $425,000
NPV = -$1,946
Basket Wonders
NPV Solution
15-44
What is the APV?
First,determine the interest expense.
Int Yr 1 ($180,000)(7%) = $12,600
Int Yr 2 ( 150,000)(7%) = 10,500
Int Yr 3 ( 120,000)(7%) = 8,400
Int Yr 4 ( 90,000)(7%) = 6,300
Int Yr 5 ( 60,000)(7%) = 4,200
Int Yr 6 ( 30,000)(7%) = 2,100
Basket Wonders
APV Solution
15-45
Second,calculate the tax-shield benefits.
TSB Yr 1 ($12,600)(40%) = $5,040
TSB Yr 2 ( 10,500)(40%) =
4,200 TSB Yr 3 ( 8,400)(40%)
= 3,360 TSB Yr 4 ( 6,300)(40%)
= 2,520 TSB Yr 5 ( 4,200)(40%)
= 1,680 TSB Yr 6 ( 2,100)(40%)
= 840
Basket Wonders
APV Solution
15-46
Third,find the PV of the tax-shield benefits.
TSB Yr 1 ($5,040)(.901) = $4,541
TSB Yr 2 ( 4,200)(.812) =
3,410 TSB Yr 3 ( 3,360)(.731) =
2,456 TSB Yr 4 ( 2,520)(.659) =
1,661 TSB Yr 5 ( 1,680)(.593) =
996 TSB Yr 6 ( 840)(.535) =
449 PV =
$13,513
Basket Wonders
APV Solution
15-47
What is the APV?
APV = NPV + PV of TS - Flotation Cost
APV = -$1,946 + $13,513 - $10,000
APV = $1,567
Basket Wonders
NPV Solution
