Principles of
Corporate Finance
Chapter 9
Eighth Edition
Capital Budgeting
and Risk
Slides by
Matthew Will
McGraw-Hill/Irwin
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9- 2
Topics Covered
Company and Project Costs of Capital
Measuring the Cost of Equity
Setting Discount Rates w/o Beta
Certainty Equivalents
Discount Rates for International Projects
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Company Cost of Capital
A firm’s value can be stated as the sum of
the value of its various assets
Firm value  PV(AB)  PV(A)  PV(B)
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Company Cost of Capital
Category
Discount Rate
Speculativ e Ventures
30%
New products
20%
Expansion of existing business
15% (Company COC)
Cost improvemen t, known tech nology
10%
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Company Cost of Capital
A company’s cost of capital can be compared
to the CAPM required return
SML
Required
return
13
Company Cost
of Capital
5.5
0
1.26
McGraw-Hill/Irwin
Project Beta
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Measuring Betas
The SML shows the relationship between
return and risk
CAPM uses Beta as a proxy for risk
Other methods can be employed to
determine the slope of the SML and thus
Beta
Regression analysis can be used to find Beta
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Measuring Betas
Dell Computer
Dell return (%)
Price data: May 91- Nov 97
R2 = .10
B = 1.87
Slope determined from plotting the
line of best fit.
McGraw-Hill/Irwin
Market return (%)
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Measuring Betas
Dell Computer
Dell return (%)
Price data: Dec 97 - Apr 04
R2 = .27
B = 1.61
Slope determined from plotting the
line of best fit.
McGraw-Hill/Irwin
Market return (%)
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Measuring Betas
General Motors
GM return (%)
Price data: May 91- Nov 97
R2 = .07
B = 0.72
Slope determined from plotting the
line of best fit.
McGraw-Hill/Irwin
Market return (%)
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Measuring Betas
General Motors
GM return (%)
Price data: Dec 97 - Apr 04
R2 = .29
B = 1.21
Slope determined from plotting the
line of best fit.
McGraw-Hill/Irwin
Market return (%)
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Measuring Betas
Exxon Mobil
Exxon Mobil return (%)
Price data: May 91- Nov 97
R2 = .23
B = 0.57
Slope determined from plotting the
line of best fit.
McGraw-Hill/Irwin
Market return (%)
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Measuring Betas
Exxon Mobil
Exxon Mobil return (%)
Price data: Dec 97 - Apr 04
R2 = .18
B = 0.51
Slope determined from plotting the
line of best fit.
McGraw-Hill/Irwin
Market return (%)
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Estimated Betas
Burlington Northern &
Santa Fe
CSX Transportation
Norfolk Southern
Union Pacific Corp
Industry portfolio
McGraw-Hill/Irwin
Beta equity
Standard
Error
0.53
0.58
0.47
0.47
0.49
0.2
0.23
0.28
0.19
0.18
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Beta Stability
RISK
CLASS
% IN SAME
CLASS 5
YEARS LATER
% WITHIN ONE
CLASS 5
YEARS LATER
10 (High betas)
35
69
9
18
54
8
16
45
7
13
41
6
14
39
5
14
42
4
13
40
3
16
45
2
21
61
1 (Low betas)
40
62
Source: Sharpe and Cooper (1972)
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Company Cost of Capital
simple approach
Company Cost of Capital (COC) is based
on the average beta of the assets
The average Beta of the assets is based on
the % of funds in each asset
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Company Cost of Capital
simple approach
Company Cost of Capital (COC) is based on the average beta
of the assets
The average Beta of the assets is based on the % of funds in
each asset
Example
1/3 New Ventures B=2.0
1/3 Expand existing business B=1.3
1/3 Plant efficiency B=0.6
AVG B of assets = 1.3
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9- 17
Capital Structure
Capital Structure - the mix of debt & equity within a company
Expand CAPM to include CS
R = rf + B ( rm - rf )
becomes
Requity = rf + B ( rm - rf )
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Capital Structure & COC
COC = rportfolio = rassets
rassets = WACC = rdebt (D) + requity (E)
(V)
(V)
Bassets = Bdebt (D) + Bequity (E)
(V)
(V)
requity = rf + Bequity ( rm - rf )
McGraw-Hill/Irwin
IMPORTANT
E, D, and V are
all market values
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Capital Structure & COC
Expected Returns and Betas prior to refinancing
Expected
return (%)
20
Requity=15
Rassets=12.2
Rrdebt=8
0
0
McGraw-Hill/Irwin
0,2
0,8
Bdebt
Bassets
1,2
Bequity
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Asset Betas
B revenue
PV(fixed cost)
 Bfixed cost

PV(revenue )
PV(variabl e cost)
PV(asset)
 B variable cost
 Basset
PV(revenue )
PV(revenue )
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Asset Betas
Basset  B revenue
PV(revenue ) - PV(variabl e cost)
PV(asset)
 PV(fixed cost) 
 B revenue 1 

PV(asset)


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Risk,DCF and CEQ
Ct
CEQt
PV 

t
t
(1  r )
(1  rf )
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Risk,DCF and CEQ
Example
Project A is expected to produce CF = $100 mil
for each of three years. Given a risk free rate of
6%, a market premium of 8%, and beta of .75,
what is the PV of the project?
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Risk,DCF and CEQ
Example
Project A is expected to produce CF = $100 mil for each of three years.
Given a risk free rate of 6%, a market premium of 8%, and beta of .75,
what is the PV of the project?
r  rf  B( rm  rf )
 6  .75(8)
 12%
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Risk,DCF and CEQ
Example
Project A is expected to produce CF = $100 mil for each of three years.
Given a risk free rate of 6%, a market premium of 8%, and beta of .75,
what is the PV of the project?
Project A
r  rf  B( rm  rf )
 6  .75(8)
 12%
McGraw-Hill/Irwin
Year
Cash Flow
PV @ 12%
1
100
89.3
2
100
79.7
3
100
71.2
Total PV
240.2
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Risk,DCF and CEQ
Example
Project A is expected to produce CF = $100 mil for each of three years.
Given a risk free rate of 6%, a market premium of 8%, and beta of .75,
what is the PV of the project?
Project A
Year
Cash Flow
PV @ 12%
1
100
89.3
2
100
79.7
3
100
71.2
Total PV
240.2
r  rf  B( rm  rf )
Now assume that the cash
flows change, but are
RISK FREE. What is the
new PV?
 6  .75(8)
 12%
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Risk,DCF and CEQ
Example
Project A is expected to produce CF = $100 mil for each of three years.
Given a risk free rate of 6%, a market premium of 8%, and beta of .75,
what is the PV of the project?.. Now assume that the cash flows
change, but are RISK FREE. What is the new PV?
Project B
Project A
Year
Cash Flow
PV @ 6%
1
94.6
89.3
Year
Cash Flow
PV @ 12%
1
100
89.3
2
100
79.7
2
89.6
79.7
3
100
71.2
3
84.8
71.2
Total PV
240.2
Total PV
240.2
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Risk,DCF and CEQ
Example
Project A is expected to produce CF = $100 mil for each of three years.
Given a risk free rate of 6%, a market premium of 8%, and beta of .75,
what is the PV of the project?.. Now assume that the cash flows
change, but are RISK FREE. What is the new PV?
Project B
Project A
Year
Cash Flow
PV @ 12%
Year
Cash Flow
PV @ 6%
1
100
89.3
1
94.6
89.3
2
100
79.7
2
89.6
79.7
3
100
71.2
3
84.8
71.2
Total PV
240.2
Total PV
240.2
Since the 94.6 is risk free, we call it a Certainty Equivalent
of the 100.
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Risk,DCF and CEQ
Example
Project A is expected to produce CF = $100 mil for each of three years.
Given a risk free rate of 6%, a market premium of 8%, and beta of .75,
what is the PV of the project? DEDUCTION FOR RISK
Year Cash Flow
McGraw-Hill/Irwin
CEQ
Deduction
1
100
94.6
for risk
5.4
2
100
89.6
10.4
3
100
84.8
15.2
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Risk,DCF and CEQ
Example
Project A is expected to produce CF = $100 mil for each of three years.
Given a risk free rate of 6%, a market premium of 8%, and beta of .75,
what is the PV of the project?.. Now assume that the cash flows
change, but are RISK FREE. What is the new PV?
The difference between the 100 and the certainty equivalent
(94.6) is 5.4%…this % can be considered the annual
premium on a risky cash flow
Risky cash flow
 certainty equivalent cash flow
1.054
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Risk,DCF and CEQ
Example
Project A is expected to produce CF = $100 mil for each of three years.
Given a risk free rate of 6%, a market premium of 8%, and beta of .75,
what is the PV of the project?.. Now assume that the cash flows
change, but are RISK FREE. What is the new PV?
100
Year 1 
 94.6
1.054
Year 2 
100
 89.6
2
1.054
100
Year 3 
 84.8
3
1.054
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International Risk
Brazil
Egypt
India
Indonesia
Mexioco
Poland
Thailand
South Africa
Ratio of Standard
Deviations
6.29
5.67
6.1
7.29
3.92
3.21
6.32
4.04
Correlation Coefficient
0.134
0.104
0.173
0.176
0.131
0.264
0.276
0.211
Beta
0.84
0.59
1.05
1.28
0.51
0.85
1.74
0.85
Source: The Brattle Group, Inc.
s Ratio - Ratio of standard deviations, country index vs. S&P composite
index
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