Chapter Seventeen
Cost of Capital
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PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan
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Chapter Organisation
17.1
The Cost of Capital: Some Preliminaries
17.2
The Cost of Equity
17.3
The Costs of Debt and Preference Shares
17.4
The Weighted Average Cost of Capital
17.5
Divisional and Project Costs of Capital
17.6
Flotation Costs and the Weighted Average Cost
of Capital
Summary and Conclusions
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PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan
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Chapter Objectives
• Apply the dividend growth model approach and the
SML approach to determine the cost of equity.
• Estimate values for the costs of debt and
preference shares.
• Calculate the WACC.
• Discuss alternative approaches to estimating a
discount rate.
• Understand the effects of flotation costs on WACC
and the NPV of a project.
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Cost of Capital: Preliminaries
• Vocabulary→ the following all mean the same
thing:
– required return
– appropriate discount rate
– cost of capital.
• The cost of capital depends primarily on the use of
funds, not the source.
• The assumption is made that a firm’s capital
structure is fixed—a firm’s cost of capital then
reflects both the cost of debt and the cost of equity.
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Cost of Equity
• The cost of equity, RE , is the return required by
equity investors given the risk of the cash
flows from the firm.
• There are two major methods for determining the
cost of equity:
– Dividend growth model
– SML or CAPM.
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The Dividend Growth Model
Approach
• According to the constant growth model:
D0 (1  g )
P0 
RE  g
Rearranging:
D1
RE 
g
P0
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Example—Cost of Equity:
Dividend Growth Model Approach
Jumbo Co. recently paid a dividend of 20 cents
per share. This dividend is expected to grow at a
rate of 5 per cent per year into perpetuity. The
current market price of Jumbo’s shares is $7.00
per share. Determine the cost of equity capital for
Jumbo Co.
$0.20 1.05
RE 
 0.05
$7.00
 0.08 or 8%
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PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan
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Estimating g
One method for estimating the growth rate is to use the historical
average.
Year Dividend Dollar Change % Change
2002 $4.00
2003 $4.40
$0.40
10.00%
2004 $4.75
$0.35
7.95%
2005 $5.25
$0.50
10.53%
2006 $5.65
$0.40
7.62%
Average growth rate  10.00  7.95  10.53  7.62/4
 9.025%
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The Dividend Growth Model
Approach—Evaluation
• Advantages
– Easy to use and understand.
• Disadvantages
–
–
–
–
Only applicable to companies paying dividends.
Assumes dividend growth is constant.
Cost of equity is very sensitive to growth estimate.
Ignores risk.
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The SML Approach
• Required return on a risky investment is dependent on three
factors:
– the risk-free rate, Rf
– the market risk premium, E(RM) – Rf
– the systematic risk of the asset relative to the average, .

RE  R f   E  RM  R f

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Example—Cost of Equity Capital:
SML Approach
• Obtain the risk-free rate (Rf) from financial press—
many use the 1-year Treasury note rate, say, 6 per
cent.
• Obtain estimates of market risk premium and security
beta:
– historical risk premium = 7.94 per cent (Officer, 1989)
– beta—historical
 investment information services
 estimate from historical data
• Assume the beta is 1.40.
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Example—Cost of Equity Capital:
SML Approach (continued)

RE  R f   E  RM  R f

 6%  1.40  7.94% 
 17.12%
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The SML Approach
• Advantages
– Adjusts for risk.
– Applicable in a wider range of circumstances (e.g. to
companies other than just those with constant dividend
growth).
• Disadvantages
– Requires two factors to be estimated: the market risk
premium and the beta co-efficient.
– Uses the past to predict the future, which may not be
appropriate.
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The Cost of Debt
• The cost of debt, RD, is the interest rate on new
borrowing.
• RD is observable:
– yields on currently outstanding debt
– yields on newly-issued similarly-rated bonds.
• The historic cost of debt is irrelevant—why?
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Example—Cost of Debt
Ishta Co. sold a 20-year, 12 per cent bond 10 years
ago at par ($100). The bond is currently priced at
$86. What is our cost of debt?
I  PV  NP/n
RD 
PV  NP/2
$12  $100  $86/10

$100  $86/2
 14.4%
The yield to maturity is 14.4 per cent, so this is used
as the cost of debt, not 12 per cent.
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The Cost of Preference Shares
• Preference shares pay a constant dividend every
period.
• Preference shares are a perpetuity, so the cost is:
RP 
D
P0
• Notice that the cost is simply the dividend yield.
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Example—Cost of Preference
Shares
• A preference share issue paying an $8 dividend per
share was was sold 10 years ago for $60 per share.
It sells for $100 per share today.
• The dividend yield today is $8.00/$100 = 8 per cent,
so this is the cost of preference shares.
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The Weighted Average Cost of
Capital
Let:
E = the market value of equity = no.
of outstanding shares × share price
D = the market value of debt = no. of
outstanding bonds × price
V = the combined market value of debt
and equity
Then:
V=E+D
So:
E/V + D/V = 100%
That is:
The firm’s capital structure weights
are E/V and D/V.
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The Weighted Average Cost of
Capital
• Interest payments on debt are tax deductible, so
the after-tax cost of debt is:
After- tax cost of debt  RD  1  TC 
• Dividends on preference shares and ordinary
shares are not tax-deductible so tax does not
affect their costs.
• The weighted average cost of capital is therefore:
 V  R  DV  R
WACC  E
E
D
 1  TC 
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Example—Weighted Average Cost
of Capital
Gidget Ltd has 78.26 million ordinary shares on
issue with a book value of $22.40 per share and a
current market price of $58 per share. Gidget has
an estimated beta of 0.90. Treasury bills currently
yield 5 per cent and the market risk premium is
assumed to be 7.94 per cent. Company tax is 30
per cent.
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Example—Weighted Average Cost
of Capital (continued)
Gidget Ltd has four debt issues outstanding:
Bond
1
2
3
4
Coupon
6.375%
7.250%
7.635%
7.600%
Total
Book
Value
$499m
$495m
$200m
$296m
$1 490m
Market
Value
$501m
$463m
$221m
$289m
$1 474m
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Yield to
Maturity
6.32%
7.83%
6.76%
7.82%
17-21
Example—Cost of Equity
(SML Approach)

RE  R f   E  RM  R f

 5%  0.90  7.94% 
 12.15%
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Example—Cost of Debt
Bond
1
2
3
4
Market
Value
$501m
$463m
$221m
$289m
$1 474m
Weight
0.3399
0.3141
0.1499
0.1961
1.0000
Yield to
Maturity
6.32%
7.83%
6.76%
7.82%
Weighted
YTM
2.1482%
2.4594%
1.0133%
1.5335%
7.1544%
The weighted average cost of debt is 7.15 per cent.
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Example—Capital Structure
Weights and WACC
• Market value of equity = 78.26 million × $58 = $4.539
billion.
• Market value of debt = $1.474 billion.
V  $4.539 billion  $1.474 billion  $6.013 billion
D  $1.474b
 0.245 or 24.5%
V
$6.013b
E
V
 $4.539b
$6.013b
 0.755 or 75.5%
WACC  0.755 0.1215  0.245  0.0715 1  0.30
 0.104 or 10.4%
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WACC
• The WACC for a firm reflects the risk and the target
capital structure to finance the firm’s existing assets
as a whole.
• WACC is the return that the firm must earn on its
existing assets to maintain the value of its shares.
• WACC is the appropriate discount rate to use for
cash flows that are similar in risk to the firm.
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Divisional and Project Costs of
Capital
• When is the WACC the appropriate discount rate?
– When the project’s risk is about the same as the firm’s
risk.
• Other approaches to estimating a discount rate:
– divisional cost of capital—used if a company has more
than one division with different levels of risk
– pure play approach—a WACC that is unique to a
particular project is used
– subjective approach—projects are allocated to specific
risk classes which, in turn, have specified WACCs.
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The SML and the WACC
Expected
return (%)
SML
= 8%
16
15
14
B
Incorrect
acceptance
WACC = 15%
A
Incorrect
rejection
Rf =7
Beta
A = .60
firm = 1.0
B = 1.2
If a firm uses its WACC to make accept/reject decisions for all types of projects, it will have a
tendency towards incorrectly accepting risky projects and incorrectly rejecting less risky projects.
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Example—Using WACC for all
Projects
• What would happen if we use the WACC for all
projects regardless of risk?
• Assume the WACC = 15 per cent
Project
A
B
Required Return
15%
15%
IRR
14%
16%
Decision
Reject
Accept
• Project A should be accepted because its risk is
low (Beta = 0.60), whereas Project B should be
rejected because its risk is high (Beta = 1.2).
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The SML and the Subjective
Approach
Expected
return (%)
SML
= 8%
20
A
High risk
(+6%)
WACC = 14
10
Rf = 7
Low risk
(–4%)
Moderate risk
(+0%)
Beta
With the subjective approach, the firm places projects into one of several risk classes. The discount
rate used to value the project is then determined by adding (for high risk) or subtracting (for low risk)
an adjustment factor to or from the firm’s WACC.
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Flotation Costs
• The issue of debt or equity may incur flotation costs
such as underwriting fees, commissions, listing fees.
• Flotation costs are relevant cash flows and need to
be included in project analysis.
• To assist with this, a weighted average flotation cost
can be calculated:
f A  E  fE  D  fD
V
V
where f A  weighted averageflotationcost
f E  equity flotationcost
f D  debt flotationcost
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Example—Project Cost including
Flotation Costs
Saddle Co. Ltd has a target capital structure of 70 per
cent equity and 30 per cent debt. The flotation costs
for equity issues are 15 per cent of the amount raised
and the flotation costs for debt issues are 7 per cent.
If Saddle Co. Ltd needs $30 million for a new project,
what is the ‘true cost’ of this project?
f A  0.70  0.15  0.30  0.07
 12.6%
The weighted average flotation cost is 12.6 per cent.
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Example—Project Cost including
Flotation Costs (continued)
• Saddle Co. needs to raise $30 million for the project
after covering flotation costs.
Projectcost (ignoringflotationcosts)
T rue cost of project
1  f A 
$30m

1  0.126
 $34.32million
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Example—Flotation Costs & NPV
• Apollo Co. Ltd needs $1.5 million to finance a new
project expected to generate annual after-tax cash
flows of $195 800 forever. The company has a
target capital structure of 60 per cent equity and 40
per cent debt. The financing options available are:
– An issue of new ordinary shares. Flotation costs of equity
are 12 per cent of capital raised. The return on new
equity is 15 per cent.
– An issue of long-term debentures. Flotation costs of debt
are 5 per cent of the capital raised. The return on new
debt is 10 per cent.
• Assume a corporate tax rate of 30 per cent.
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Example—NPV (No Flotation Costs)
W ACC  0.6 15%  0.4  0.11  0.30
 0.118or 11.8%
$195800
NP V 
 $1500 000
0.118
 $159322
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Example—NPV (With Flotation
Costs)
f A  0.6  0.12  0.4  0.05
 0.092or 9.2%
$1500 000
T rue cost 
 $1 651982
1  0.092
NP V 
$195800
 $1 651982
0.118
 $7340
Flotation costs decrease a project’s NPV and
could alter an investment decision.
Note: If the flotation costs are tax-deductible, we can calculate an aftertax weighted average flotation cost, fAT = fA(1-TC)
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Summary and Conclusions
• The cost of equity is the return that equity investors
require on their investment in the firm.
• There are two approaches to determine the cost of
equity: the dividend growth model approach and the
SML approach.
• The cost of debt is the return that lenders require on
the firm’s debt.
• WACC is both the required rate of return and the
discount rate appropriate for cash flows that are
similar in risk to the overall firm.
• Flotation costs can affect a project’s NPV and alter
the investment decision.
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