Cost of Capital
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PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan
17-1

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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PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan
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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 , R
E
, 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:
P
0

D
0
(1
 g
R
E
 g
)
Rearranging:
R
E

D
1
P
0
 g
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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.
R
E

$0.20

1.05


0.05
$7.00

0.08
or 8%
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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
2004 $4.75
2005 $5.25
2006 $5.65
-
$0.40
$0.35
$0.50
$0.40
-
10.00%
7.95%
10.53%
7.62%
Average growth rate


10.00

7.95

10.53

7.62

/4

9.025%
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PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan
17-8

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, R f
– the market risk premium, E ( R
M
) – R f
– the systematic risk of the asset relative to the average, 
.
R
E

R f
 
E


R
M

R f

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Example —Cost of Equity Capital:
SML Approach
• Obtain the risk-free rate ( R f
) 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)
R
E

R f


6 %


E


R
M

1 .
40

7

R
.
94 % f



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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17-13

The Cost of Debt
• The cost of debt , R
D
, is the interest rate on new borrowing.
• R
D 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?
R
D


I


PV



PV

$12


NP
NP

/2

/ n
$100

$86
$100

$86

/2

/10

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:
R
P

D
P
0
• 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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17-17

The Weighted Average Cost of
Capital
Let:
Then:
So:
That is:
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
V = E + D
E / V + D / V = 100%
The firm’s capital structure weights are E / V and D / V .
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2007 McGraw-Hill Australia Pty Ltd
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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

R
D


1

T
C

• 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:
WACC

 
V

R
E

 
V

R
D


1

T
C

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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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17-20

Example —Weighted Average Cost of Capital (continued)
Gidget Ltd has four debt issues outstanding:
Bond
1
2
3
4
Coupon Book
Value
Market
Value
6.375%
7.250%
7.635%
$499m
$495m
$200m
$501m
$463m
$221m
7.600% $296m $289m
Total $1 490m $1 474m
Yield to
Maturity
6.32%
7.83%
6.76%
7.82%
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Example —Cost of Equity
(SML Approach)
R
E

R f
 
E


R
M

R f


5 %


0 .
90

7 .
94 %


12 .
15 %
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Example —Cost of Debt
Bond Weight
4
1
2
3
Market
Value
$501m
$463m
$221m
$289m
$1 474m
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
V
 $1.474b
$6.013b

0.245
or 24.5%
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 (%)
16
15
14 A
B
SML
= 8%
Incorrect acceptance
WACC = 15%
Incorrect rejection
R f
=7
B
= 1.2
Beta
A
= .60
firm
= 1.0
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 Decision
14% Reject
16% 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 (%)
= 8%
SML
20
A
High risk
(+6%)
WACC = 14
10
R f
= 7
Moderate risk
(+0%)
Low risk
(
–4%)
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
V
 f
E
 D
V
 f
D where f
A f
E
 weighted average flotation
 equity flotation f
D
 debt flotation
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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

12.6%
0.30

0.07

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.
T rue cost of project

P roject cost (ignoring flot at ion

1
 f
A


$30m

1

0 .126


$34.32
million
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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


0.118
or 11.8%
NP V

$195 800
0.118

$1 500 000

$159 322
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Example —NPV (With Flotation
Costs) f
A


0.6

0.12
0.4

0.05


0.092
or 9.2%
T rue cost

$1

1
500

000
0.092


$1 651 982
NP V

$195 800
0.118

$1 651 982

$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, f
AT
= f
A
(1T
C
)
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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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