### No Slide Title

```Principles of Corporate Finance
Brealey and Myers

Sixth Edition
Introduction to Risk, Return, and the
Opportunity Cost of Capital
Slides by
Matthew Will
Irwin/McGraw Hill
Chapter 7
7- 2
Topics Covered
 72 Years of Capital Market History
 Measuring Risk
 Portfolio Risk
 Beta and Unique Risk
 Diversification
Irwin/McGraw Hill
7- 3
The Value of an Investment of \$1 in 1926
5520
Index
1000
S&P
Small Cap
Corp Bonds
Long Bond
T Bill
1828
55.38
39.07
14.25
10
1
0.1
1925
1933
1941
Source: Ibbotson Associates
Irwin/McGraw Hill
1949
1957
1965
1973
1981
1989
1997
Year End
7- 4
The Value of an Investment of \$1 in 1926
Index
1000
Real returns
S&P
Small Cap
Corp Bonds
Long Bond
T Bill
613
203
6.15
10
4.34
1
1.58
0.1
1925
1933
1941
Source: Ibbotson Associates
Irwin/McGraw Hill
1949
1957
1965
1973
1981
1989
1997
Year End
7- 5
Rates of Return 1926-1997
Percentage Return
60
40
20
0
-20
Common Stocks
Long T-Bonds
T-Bills
-40
-60 26
30
35
40
Source: Ibbotson Associates
Irwin/McGraw Hill
45
50
55
60
65
70
75
80
85
90
95
Year
7- 6
Measuring Risk
Variance - Average value of squared deviations from
mean. A measure of volatility.
Standard Deviation - Average value of squared
deviations from mean. A measure of volatility.
Irwin/McGraw Hill
7- 7
Measuring Risk
Coin Toss Game-calculating variance and standard deviation
(1)
(2)
(3)
Percent Rate of Return Deviation from Mean Squared Deviation
+ 40
+ 30
900
+ 10
0
0
+ 10
0
0
- 20
- 30
900
Variance = average of squared deviations = 1800 / 4 = 450
Standard deviation = square of root variance =
Irwin/McGraw Hill
450 = 21.2%
7- 8
Measuring Risk
Histogram of Annual Stock Market Returns
# of Years
Irwin/McGraw Hill
2
Return %
50 to 60
40 to 50
30 to 40
20 to 30
10 to 20
0 to 10
-30 to -20
3
-10 to 0
1
4
-20 to -10
1
2
-40 to -30
13
12 11 13
10
-50 to -40
13
12
11
10
9
8
7
6
5
4
3
2
1
0
7- 9
Measuring Risk
Diversification - Strategy designed to reduce risk by
spreading the portfolio across many investments.
Unique Risk - Risk factors affecting only that firm.
Also called “diversifiable risk.”
Market Risk - Economy-wide sources of risk that
affect the overall stock market. Also called
“systematic risk.”
Irwin/McGraw Hill
7- 10
Measuring Risk
(
(
)(
)(
Portfolio rate
fraction of portfolio
=
x
of return
in first asset
rate of return
on first asset
)
)
fraction of portfolio
rate of return
+
x
in second asset
on second asset
Irwin/McGraw Hill
7- 11
Portfolio standard deviation
Measuring Risk
0
5
10
15
Number of Securities
Irwin/McGraw Hill
7- 12
Portfolio standard deviation
Measuring Risk
Unique
risk
Market risk
0
5
10
15
Number of Securities
Irwin/McGraw Hill
7- 13
Portfolio Risk
The variance of a two stock portfolio is the sum of these
four boxes:
Stock1
Stock1
Stock 2
Irwin/McGraw Hill
x 12σ 12
x 1x 2σ 12 
x 1x 2ρ 12σ 1σ 2
Stock 2
x 1x 2σ 12 
x 1x 2ρ 12σ 1σ 2
x 22σ 22
7- 14
Portfolio Risk
Example
Suppose you invest \$55 in Bristol-Myers and \$45
in McDonald’s. The expected dollar return on
your BM is .10 x 55 = 5.50 and on McDonald’s it
is .20 x 45 = 9.90. The expected dollar return on
your portfolio is 5.50 + 9300 = 14.50. The
portfolio rate of return is 14.50/100 = .145 or
14.5%. Assume a correlation coefficient of 1.
Irwin/McGraw Hill
7- 15
Portfolio Risk
Example
Suppose you invest \$55 in Bristol-Myers and \$45 in McDonald’s. The
expected dollar return on your BM is .10 x 55 = 5.50 and on
McDonald’s it is .20 x 45 = 9.90. The expected dollar return on your
portfolio is 5.50 + 9300 = 14.50. The portfolio rate of return is
14.50/100 = .145 or 14.5%. Assume a correlation coefficient of 1.
Bristol- Myers
Bristol- Myers x 12σ 12  (.55) 2  (17.1) 2
McDonald's
Irwin/McGraw Hill
x 1x 2ρ 12σ 1σ 2  .55  .45
 1  17.1  20.8
McDonald's
x 1x 2ρ 12σ 1σ 2  .55  .45
 1  17.1  20.8
x 22σ 22  (.45) 2  ( 20.8) 2
7- 16
Portfolio Risk
Example
Suppose you invest \$55 in Bristol-Myers and \$45 in McDonald’s. The
expected dollar return on your BM is .10 x 55 = 5.50 and on
McDonald’s it is .20 x 45 = 9.90. The expected dollar return on your
portfolio is 5.50 + 9300 = 14.50. The portfolio rate of return is
14.50/100 = .145 or 14.5%. Assume a correlation coefficient of 1.
PortfolioValriance  [(.55)2 x(17.1)2 ]
 [(.45)2 x(20.8)2 ]
 2(.55x.45x
1x17.1x20.
8)  352.10
Standard Deviation 352.1  18.7%
Irwin/McGraw Hill
7- 17
Portfolio Risk
ExpectedPortfolioReturn (x1 r1 )  (x 2 r2 )
PortfolioVariance  x12σ 12  x 22σ 22  2(x1x 2ρ 12σ 1σ 2 )
Irwin/McGraw Hill
7- 18
Portfolio Risk
The shaded boxes contain variance terms; the remainder
contain covariance terms.
1
2
3
STOCK
To calculate
portfolio
up the boxes
4
5
6
N
1
2
3
4
5
6
N
STOCK
Irwin/McGraw Hill
7- 19
Beta and Unique Risk
1. Total risk =
diversifiable risk +
market risk
2. Market risk is
measured by beta,
the sensitivity to
market changes.
Expected
stock
return
beta
+10%
-10%
- 10%
+10%
-10%
Expected
market
return
Copyright 1996 by The McGraw-Hill Companies, Inc
Irwin/McGraw Hill
7- 20
Beta and Unique Risk
Market Portfolio - Portfolio of all assets in the
economy. In practice a broad stock market
index, such as the S&P Composite, is used
to represent the market.
return on the market portfolio.
Irwin/McGraw Hill
7- 21
Beta and Unique Risk
 im
Bi  2
m
Irwin/McGraw Hill
7- 22
Beta and Unique Risk
 im
Bi  2
m
Covariance with the
market
Variance of the market
Irwin/McGraw Hill
Principles of Corporate Finance
Brealey and Myers

Sixth Edition
Risk and Return
Slides by
Matthew Will
Irwin/McGraw Hill
Chapter 8
7- 24
Topics Covered
 Markowitz Portfolio Theory
 Risk and Return Relationship
 Testing the CAPM
 CAPM Alternatives
Irwin/McGraw Hill
7- 25
Markowitz Portfolio Theory
 Combining stocks into portfolios can reduce
standard deviation below the level obtained
from a simple weighted average calculation.
 Correlation coefficients make this possible.
 The various weighted combinations of stocks
that create this standard deviations constitute
the set of efficient portfolios.
Irwin/McGraw Hill
7- 26
Markowitz Portfolio Theory
Price changes vs. Normal distribution
Microsoft - Daily % change 1986-1997
600
# of Days
(frequency)
500
400
300
200
100
0
-10%
-8%
-6%
-4%
-2%
0%
2%
4%
6%
8%
10%
Daily % Change
Irwin/McGraw Hill
7- 27
Markowitz Portfolio Theory
Price changes vs. Normal distribution
Microsoft - Daily % change 1986-1997
600
# of Days
(frequency)
500
400
300
200
100
0
-10%
-8%
-6%
-4%
-2%
0%
2%
4%
6%
8%
10%
Daily % Change
Irwin/McGraw Hill
7- 28
Markowitz Portfolio Theory
Standard Deviation VS. Expected Return
Investment C
20
18
% probability
16
14
12
10
8
6
4
2
0
-50
0
50
% return
Irwin/McGraw Hill
7- 29
Markowitz Portfolio Theory
Standard Deviation VS. Expected Return
Investment D
20
18
% probability
16
14
12
10
8
6
4
2
0
-50
0
50
% return
Irwin/McGraw Hill
7- 30
Markowitz Portfolio Theory
 Expected Returns and Standard Deviations vary given
different weighted combinations of the stocks.
Expected Return (%)
McDonald’s
45% McDonald’s
Bristol-Myers Squibb
Standard Deviation
Irwin/McGraw Hill
7- 31
Efficient Frontier
•Each half egg shell represents the possible weighted combinations for two
stocks.
•The composite of all stock sets constitutes the efficient frontier.
Expected Return (%)
Standard Deviation
Irwin/McGraw Hill
7- 32
Efficient Frontier
•Lending or Borrowing at the risk free rate (rf) allows us to exist outside the
efficient frontier.
Expected Return (%)
T
rf
S
Standard Deviation
Irwin/McGraw Hill
7- 33
Efficient Frontier
Example
Stocks
ABC Corp
Big Corp

28
42
Correlation Coefficient = .4
% of Portfolio
Avg Return
60%
15%
40%
21%
Standard Deviation = weighted avg = 33.6
Standard Deviation = Portfolio = 28.1
Return = weighted avg = Portfolio = 17.4%
Irwin/McGraw Hill
7- 34
Efficient Frontier
Example
Stocks
ABC Corp
Big Corp

28
42
Correlation Coefficient = .4
% of Portfolio
Avg Return
60%
15%
40%
21%
Standard Deviation = weighted avg = 33.6
Standard Deviation = Portfolio = 28.1
Return = weighted avg = Portfolio = 17.4%
Let’s Add stock New Corp to the portfolio
Irwin/McGraw Hill
7- 35
Efficient Frontier
Example
Stocks
Portfolio
New Corp

28.1
30
Correlation Coefficient = .3
% of Portfolio
Avg Return
50%
17.4%
50%
19%
NEW Standard Deviation = weighted avg = 31.80
NEW Standard Deviation = Portfolio = 23.43
NEW Return = weighted avg = Portfolio = 18.20%
Irwin/McGraw Hill
7- 36
Efficient Frontier
Example
Stocks
Portfolio
New Corp

28.1
30
Correlation Coefficient = .3
% of Portfolio
Avg Return
50%
17.4%
50%
19%
NEW Standard Deviation = weighted avg = 31.80
NEW Standard Deviation = Portfolio = 23.43
NEW Return = weighted avg = Portfolio = 18.20%
NOTE: Higher return & Lower risk
Irwin/McGraw Hill
7- 37
Efficient Frontier
Example
Stocks
Portfolio
New Corp

28.1
30
Correlation Coefficient = .3
% of Portfolio
Avg Return
50%
17.4%
50%
19%
NEW Standard Deviation = weighted avg = 31.80
NEW Standard Deviation = Portfolio = 23.43
NEW Return = weighted avg = Portfolio = 18.20%
NOTE: Higher return & Lower risk
How did we do that?
Irwin/McGraw Hill
7- 38
Efficient Frontier
Example
Stocks
Portfolio
New Corp

28.1
30
Correlation Coefficient = .3
% of Portfolio
Avg Return
50%
17.4%
50%
19%
NEW Standard Deviation = weighted avg = 31.80
NEW Standard Deviation = Portfolio = 23.43
NEW Return = weighted avg = Portfolio = 18.20%
NOTE: Higher return & Lower risk
How did we do that?
DIVERSIFICATION
Irwin/McGraw Hill
7- 39
Efficient Frontier
Return
B
A
Risk
(measured
as )
Irwin/McGraw Hill
7- 40
Efficient Frontier
Return
B
AB
A
Risk
Irwin/McGraw Hill
7- 41
Efficient Frontier
Return
B
AB
A
N
Risk
Irwin/McGraw Hill
7- 42
Efficient Frontier
Return
B
ABN AB
A
N
Risk
Irwin/McGraw Hill
7- 43
Efficient Frontier
Goal is to move
up and left.
Return
WHY?
B
ABN AB
A
N
Risk
Irwin/McGraw Hill
7- 44
Efficient Frontier
Return
Low Risk
High Return
Risk
Irwin/McGraw Hill
7- 45
Efficient Frontier
Return
Low Risk
High Risk
High Return
High Return
Risk
Irwin/McGraw Hill
7- 46
Efficient Frontier
Return
Low Risk
High Risk
High Return
High Return
Low Risk
Low Return
Risk
Irwin/McGraw Hill
7- 47
Efficient Frontier
Return
Low Risk
High Risk
High Return
High Return
Low Risk
High Risk
Low Return
Low Return
Risk
Irwin/McGraw Hill
7- 48
Efficient Frontier
Return
Low Risk
High Risk
High Return
High Return
Low Risk
High Risk
Low Return
Low Return
Risk
Irwin/McGraw Hill
7- 49
Efficient Frontier
Return
B
ABN
AB
A
N
Risk
Irwin/McGraw Hill
7- 50
Security Market Line
Return
.
Efficient Portfolio
Risk Free
Return
= rf
Risk
Irwin/McGraw Hill
7- 51
Security Market Line
Return
Market Return = rm
Efficient Portfolio
Risk Free
Return
.
= rf
Risk
Irwin/McGraw Hill
7- 52
Security Market Line
Return
Market Return = rm
Efficient Portfolio
Risk Free
Return
.
= rf
Risk
Irwin/McGraw Hill
7- 53
Security Market Line
Return
Market Return = rm
.
Efficient Portfolio
Risk Free
Return
= rf
1.0
Irwin/McGraw Hill
BETA
7- 54
Security Market Line
Return
Market Return = rm
Security Market
Line (SML)
Risk Free
Return
= rf
1.0
Irwin/McGraw Hill
BETA
7- 55
Security Market Line
Return
SML
rf
1.0
BETA
SML Equation = rf + B ( rm - rf )
Irwin/McGraw Hill
7- 56
Capital Asset Pricing Model
R = r f + B ( r m - rf )
CAPM
Irwin/McGraw Hill
7- 57
Testing the CAPM
1931-65
SML
30
20
Investors
10
Market
Portfolio
0
1.0
Irwin/McGraw Hill
Portfolio Beta
7- 58
Testing the CAPM
1966-91
30
20
SML
Investors
10
Market
Portfolio
0
1.0
Irwin/McGraw Hill
Portfolio Beta
7- 59
Testing the CAPM
Company Size vs. Average Return
Average Return (%)
25
20
15
10
5
Company size
0
Smallest
Irwin/McGraw Hill
Largest
7- 60
Testing the CAPM
Book-Market vs. Average Return
Average Return (%)
25
20
15
10
5
Book-Market Ratio
0
Highest
Irwin/McGraw Hill
Lowest
7- 61
Consumption Betas vs Market Betas
Stocks
(and other risky assets)
Wealth = market
portfolio
Irwin/McGraw Hill
7- 62
Consumption Betas vs Market Betas
Stocks
(and other risky assets)
Market risk
makes wealth
uncertain.
Wealth = market
portfolio
Irwin/McGraw Hill
7- 63
Consumption Betas vs Market Betas
Stocks
(and other risky assets)
Market risk
makes wealth
uncertain.
Standard
CAPM
Wealth = market
portfolio
Irwin/McGraw Hill
7- 64
Consumption Betas vs Market Betas
Stocks
(and other risky assets)
Market risk
makes wealth
uncertain.
Wealth = market
portfolio
Irwin/McGraw Hill
Stocks
(and other risky assets)
Standard
CAPM
Consumption
7- 65
Consumption Betas vs Market Betas
Stocks
(and other risky assets)
Stocks
(and other risky assets)
Wealth is uncertain
Market risk
makes wealth
uncertain.
Standard
Wealth
CAPM
Consumption is uncertain
Wealth = market
portfolio
Irwin/McGraw Hill
Consumption
7- 66
Consumption Betas vs Market Betas
Stocks
(and other risky assets)
Stocks
(and other risky assets)
Wealth is uncertain
Market risk
makes wealth
uncertain.
Standard
Consumption
Wealth
CAPM
CAPM
Consumption is uncertain
Wealth = market
portfolio
Irwin/McGraw Hill
Consumption
7- 67
Arbitrage Pricing Theory
Alternative to CAPM
Expected Risk
- rf
= Bfactor1(rfactor1
Irwin/McGraw Hill
- rf) + Bf2(rf2 - rf) + …
7- 68
Arbitrage Pricing Theory
Alternative to CAPM
Expected Risk
- rf
= Bfactor1(rfactor1
Return
Irwin/McGraw Hill
- rf) + Bf2(rf2 - rf) + …
= a + bfactor1(rfactor1)
+ bf2(rf2) + …
7- 69
Arbitrage Pricing Theory
Estimated risk premiums for taking on risk factors
(1978-1990)
Factor
Interest rate
- .61
Exchange rate
- .59
Real GNP
.49
- .83
6.36
Inflation
Mrket
Irwin/McGraw Hill
Estimated Risk Prem ium
(rfactor  rf )
5.10%
Principles of Corporate Finance
Brealey and Myers

Sixth Edition
Capital Budgeting and Risk
Slides by
Matthew Will
Irwin/McGraw Hill
Chapter 9
7- 71
Topics Covered
 Measuring Betas
 Capital Structure and COC
 Discount Rates for Intl. Projects
 Estimating Discount Rates
 Risk and DCF
Irwin/McGraw Hill
7- 72
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)
Irwin/McGraw Hill
7- 73
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
Irwin/McGraw Hill
Project Beta
7- 74
Measuring Betas
 The SML shows the relationship between
return and risk.
 CAPM uses Beta as a proxy for risk.
 Beta is the slope of the SML, using CAPM
terminology.
 Other methods can be employed to determine
the slope of the SML and thus Beta.
 Regression analysis can be used to find Beta.
Irwin/McGraw Hill
7- 75
Measuring Betas
Hewlett Packard Beta
Hewlett-Packard return (%)
Price data - Jan 78 - Dec 82
R2 = .53
B = 1.35
Slope determined from 60 months of
prices and plotting the line of best
fit.
Irwin/McGraw Hill
Market return (%)
7- 76
Measuring Betas
Hewlett Packard Beta
Hewlett-Packard return (%)
Price data - Jan 83 - Dec 87
R2 = .49
B = 1.33
Slope determined from 60 months of
prices and plotting the line of best
fit.
Irwin/McGraw Hill
Market return (%)
7- 77
Measuring Betas
Hewlett Packard Beta
Hewlett-Packard return (%)
Price data - Jan 88 - Dec 92
R2 = .45
B = 1.70
Slope determined from 60 months of
prices and plotting the line of best
fit.
Irwin/McGraw Hill
Market return (%)
7- 78
Measuring Betas
Hewlett Packard Beta
Hewlett-Packard return (%)
Price data - Jan 93 - Dec 97
R2 = .35
B = 1.69
Slope determined from 60 months of
prices and plotting the line of best
fit.
Irwin/McGraw Hill
Market return (%)
7- 79
Measuring Betas
A T & T Beta
Price data - Jan 78 - Dec 82
A T & T (%)
R2 = .28
B = 0.21
Slope determined from 60 months of
prices and plotting the line of best
fit.
Irwin/McGraw Hill
Market return (%)
7- 80
Measuring Betas
A T & T Beta
Price data - Jan 83 - Dec 87
A T & T (%)
R2 = .23
B = 0.64
Slope determined from 60 months of
prices and plotting the line of best
fit.
Irwin/McGraw Hill
Market return (%)
7- 81
Measuring Betas
A T & T Beta
Price data - Jan 88 - Dec 92
A T & T (%)
R2 = .28
B = 0.90
Slope determined from 60 months of
prices and plotting the line of best
fit.
Irwin/McGraw Hill
Market return (%)
7- 82
Measuring Betas
A T & T Beta
Price data - Jan 93 - Dec 97
A T & T (%)
R2 = ..17
B = .90
Slope determined from 60 months of
prices and plotting the line of best
fit.
Irwin/McGraw Hill
Market return (%)
7- 83
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)
Irwin/McGraw Hill
7- 84
Capital Budgeting & Risk
Modify CAPM
(account for proper risk)
• Use COC unique to project,
rather than Company COC
• Take into account Capital Structure
Irwin/McGraw Hill
Company Cost of Capital
7- 85
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.
Irwin/McGraw Hill
Company Cost of Capital
7- 86
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 Plant efficiency B=0.6
AVG B of assets = 1.3
Irwin/McGraw Hill
7- 87
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 )
Irwin/McGraw Hill
7- 88
Capital Structure & COC
COC = rportfolio = rassets
Irwin/McGraw Hill
7- 89
Capital Structure & COC
COC = rportfolio = rassets
rassets = WACC = rdebt (D) + requity (E)
(V)
(V)
Irwin/McGraw Hill
7- 90
Capital Structure & COC
COC = rportfolio = rassets
rassets = WACC = rdebt (D) + requity (E)
(V)
(V)
Bassets = Bdebt (D) + Bequity (E)
(V)
(V)
Irwin/McGraw Hill
7- 91
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 )
Irwin/McGraw Hill
7- 92
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 )
Irwin/McGraw Hill
IMPORTANT
E, D, and V are
all market values
7- 93
Capital Structure & COC
Expected Returns and Betas prior to refinancing
20
Expected
return (%)
Requity=15
Rassets=12.2
Rrdebt=8
0
0
Irwin/McGraw Hill
0.2
0.8
Bdebt
Bassets
1.2
Bequity
7- 94
Pinnacle West Corp.
Requity = rf + B ( rm - rf )
= .045 + .51(.08) = .0858 or 8.6%
Rdebt = YTM on bonds
= 6.9 %
Irwin/McGraw Hill
7- 95
Pinnacle West Corp.
Irwin/McGraw Hill
BostonElectric
Beta Standard. Error
.60
.19
CentralHUdson
Consolidated Edison
.30
.65
.18
.20
DT E Energy
.56
.17
Eastern UtilitiesAssoc .66
GPU Inc
.65
.19
.18
NE ElectricSystem
.35
.19
OGE Energy
P ECO Energy
.39
.70
.15
.23
P innacleWest Corp
.43
.21
P P & LResources
P ortfolioAverage
.37
.51
.21
.15
7- 96
Pinnacle West Corp.
COC  rassets
D
E
 rdebt  requity
V
V
 .35(.08)  .65(.10)
 .093or 9.3%
Irwin/McGraw Hill
7- 97
International Risk
Correlation
 Ratio
Beta
coefficient
Argentina
3.52
.416
1.46
Brazil
3.80
.160
.62
Kazakhstan 2.36
.147
.35
T aiwan
3.80
.120
.47
Source: The Brattle Group, Inc.
 Ratio - Ratio of standard deviations, country index vs. S&P composite index
Irwin/McGraw Hill
7- 98
Unbiased Forecast
 Given three outcomes and their related
probabilities and cash flows we can determine
an unbiased forecast of cash flows.
Possible
cash flow
1.2
1.0
0.8
Irwin/McGraw Hill
Probabilit y
.25
.50
.25
Prob weighted
cash flow
.3
.5
.2
Unbiased
forecast
\$1.0 million
7- 99
Asset Betas
Cash flow = revenue - fixed cost - variable cost
PV(asset) = PV(revenue) - PV(fixed cost) - PV(variable cost)
or
PV(revenue) = PV(fixed cost) + PV(variable cost) + PV(asset)
Irwin/McGraw Hill
7- 100
Asset Betas
Brevenue
PV(fixedcost)
 Bfixed cost

PV(revenue)
PV(variable cost)
PV(asset)
 Bvariablecost
 Basset
PV(revenue)
PV(revenue)
Irwin/McGraw Hill
7- 101
Asset Betas
Basset  B revenue
P V(revenue) - P V(variable cost )
P V(asset )
 P V(fixedcost )
 B revenue 1 

P
V(asset
)


Irwin/McGraw Hill
7- 102
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?
Irwin/McGraw Hill
7- 103
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%
Irwin/McGraw Hill
7- 104
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?
P rojectA
Year Cash Flow P V @ 12%
r  rf  B( rm  rf )
 6  .75(8)
 12%
Irwin/McGraw Hill
1
100
89.3
2
3
100
100
79.7
71.2
T otalP V
240.2
7- 105
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?
P rojectA
Year Cash Flow P V @ 12%
1
100
89.3
2
3
100
100
79.7
71.2
T otalP V
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%
Irwin/McGraw Hill
7- 106
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?
P rojectA
Year Cash Flow P V @ 12%
1
100
89.3
2
3
100
100
79.7
71.2
T otalP V
240.2
Irwin/McGraw Hill
P roject B
Year Cash Flow P V @ 6%
1
94.6
89.3
2
3
89.6
84.8
79.7
71.2
T otalP V
240.2
7- 107
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?
P rojectA
Year Cash Flow P V @ 12%
P roject B
Year Cash Flow P V @ 6%
1
100
89.3
1
94.6
89.3
2
3
100
100
79.7
71.2
2
3
89.6
84.8
79.7
71.2
T otalP V
240.2
T otalP V
240.2
Since the 94.6 is risk free, we call it a Certainty Equivalent
of the 100.
Irwin/McGraw Hill
7- 108
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
Irwin/McGraw Hill
7- 109
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
100
Year 2 
 89.6
2
1.054
Year 3 
Irwin/McGraw Hill
100
 84.8
3
1.054
7- 110
Risk,DCF and CEQ
 The prior example leads to a generic certainty
equivalent formula.
Ct
CEQt
PV 

t
t
(1  r )
(1  rf )
Irwin/McGraw Hill
Principles of Corporate Finance
Brealey and Myers

Sixth Edition
A Project Is Not a Black Box
Slides by
Matthew Will
Irwin/McGraw Hill
Chapter 10
7- 112
Topics Covered
 Sensitivity Analysis
 Break Even Analysis
 Monte Carlo Simulation
 Decision Trees
Irwin/McGraw Hill
7- 113
How To Handle Uncertainty
Sensitivity Analysis - Analysis of the effects of
changes in sales, costs, etc. on a project.
Scenario Analysis - Project analysis given a
particular combination of assumptions.
Simulation Analysis - Estimation of the
probabilities of different possible outcomes.
Break Even Analysis - Analysis of the level of
sales (or other variable) at which the company
breaks even.
Irwin/McGraw Hill
7- 114
Sensitivity Analysis
Example
Given the expected cash flow
forecasts for Otoban Company’s
Motor Scooter project, listed on
the next slide, determine the
NPV of the project given
changes in the cash flow
components using a 10% cost of
capital. Assume that all
variables remain constant, except
the one you are changing.
Irwin/McGraw Hill
7- 115
Sensitivity Analysis
Example - continued
Investment
Sales
Variable Costs
Fixed Costs
Depreciation
P retaxprofit
.T [email protected] 50%
P rofitafter tax
Operatingcash flow
Net Cash Flow
Year 0
- 15
Years1 - 10
37.5
30
3
1.5
3
1.5
1.5
- 15
3.0
3
NPV= 3.43 billion Yen
Irwin/McGraw Hill
7- 116
Sensitivity Analysis
Example - continued
Possible Outcomes
Range
Variable Pessim istic Expected Optim istic
MarketSize
.9 mil
51 mil
1.1mil
MarketShare
.04
.1
.16
Unit price
350,000 375,000 380,000
Unit Var Cost
360,000 300,000 275,000
Fixed Cost
4 bil
3 bil
2 bil
Irwin/McGraw Hill
7- 117
Sensitivity Analysis
Example - continued
NPV Calculations for Pessimistic Market Size Scenario
Investment
Sales
Variable Costs
Fixed Costs
Depreciation
P retaxprofit
.T [email protected] 50%
P rofitafter tax
Operatingcash flow
Net Cash Flow
Irwin/McGraw Hill
Year 0
- 15
Years1 - 10
41.25
33
3
1.5
3.75
1.88
1.88
- 15
3.38
 3.38
NPV= +5.7 bil yen
7- 118
Sensitivity Analysis
Example - continued
NPV Possibilities (Billions Yen)
Range
Variable Pessim istic Expected Optim istic
MarketSize
1.1
3.4
5.7
MarketShare
- 10.4
3.4
17.3
Unit price
- 4.2
3.4
5.0
Unit Var Cost
- 15.0
3.4
11.1
Fixed Cost
0.4
3.4
6.5
Irwin/McGraw Hill
7- 119
Break Even Analysis
 Point at which the NPV=0 is the break even point.
 Otoban Motors has a breakeven point of 8,000 units
sold.
PV Inflows
Break even
400
NPV=9
PV (Yen)
Billions
PV Outflows
200
19.6
Sales, 000’s
85
Irwin/McGraw Hill
200
7- 120
Monte Carlo Simulation
Modeling Process
 Step 1: Modeling the Project
 Step 2: Specifying Probabilities
 Step 3: Simulate the Cash Flows
Irwin/McGraw Hill
7- 121
Decision Trees
960 (.8)
Turboprop
-550
+150(.6)
NPV=
+30(.4)
?
220(.2)
930(.4)
140(.6)
800(.8)
-150
+100(.6) or
410(.8)
0
Piston
-250
NPV=
Irwin/McGraw Hill
?
100(.2)
180(.2)
220(.4)
+50(.4)
100(.6)
7- 122
Decision Trees
960 (.8)
Turboprop
-550
+150(.6)
NPV=
+30(.4)
?
220(.2)
930(.4)
-150
+100(.6) or
NPV=
Irwin/McGraw Hill
?
100(.2)
410(.8)
0
-250
456
140(.6)
800(.8)
Piston
812
180(.2)
660
364
220(.4)
+50(.4)
100(.6)
148
7- 123
Decision Trees
960 (.8)
Turboprop
-550
+150(.6)
NPV=
+30(.4)
?
220(.2)
930(.4)
-150
+100(.6) or
NPV=
Irwin/McGraw Hill
?
100(.2)
410(.8)
0
-250
456
140(.6)
800(.8)
Piston
812
180(.2)
660
364
220(.4)
960 .80+50(.4)
 220 .20  812
100(.6)
148
7- 124
Decision Trees
Turboprop
-550
NPV=
?
960 (.8)
660 +150(.6)
 150  450
1.10
220(.2)
930(.4)
+30(.4)
800(.8)
-150
+100(.6) or
331
Irwin/McGraw Hill
?
100(.2)
410(.8)
0
Piston
NPV=
456
140(.6)
*450
-250
812
180(.2)
660
364
220(.4)
+50(.4)
100(.6)
148
7- 125
Decision Trees
960 (.8)
NPV=888.18
Turboprop
-550
+150(.6)
NPV=
+30(.4)
?
220(.2)
930(.4)
*450
NPV=
Irwin/McGraw Hill
?
800(.8)
-150
or
331
100(.2)
410(.8)
0
Piston
-250
456
140(.6)
NPV=444.55
812
NPV=550.00
 150
 888+100(.6)
.18
1.10
812
180(.2)
660
364
220(.4)
+50(.4)
NPV=184.55
100(.6)
148
7- 126
Decision Trees
960 (.8)
NPV=888.18
Turboprop
-550
+150(.6)
NPV=
+30(.4)
?
220(.2)
710.73
930(.4)
NPV=550.00
800(.8)
-150
+100(.6) or
100(.2)
410(.8)
NPV=
Irwin/McGraw Hill
?
660
180(.2)
 888403.82
.18  .60
331  444.55  .40
0
-250
456
140(.6)
NPV=444.55
*450
Piston
812
364
220(.4)
+50(.4)
NPV=184.55
100(.6)
148
7- 127
Decision Trees
960 (.8)
NPV=888.18
+150(.6)
Turboprop
-550
NPV=96.12
220(.2)
710.73
930(.4)
+30(.4)
NPV=550.00
+100(.6) or
-250
NPV=117.00
Irwin/McGraw Hill
800(.8)
-150
100(.2)
410(.8)
0
710 .73
180(.2)
331
 550  96.12
403.82
220(.4)
1.10
+50(.4)
NPV=184.55
456
140(.6)
NPV=444.55
*450
Piston
812
100(.6)
660
364
148
7- 128
Decision Trees
960 (.8)
NPV=888.18
+150(.6)
Turboprop
-550
NPV=96.12
220(.2)
710.73
930(.4)
+30(.4)
*450
NPV=550.00
800(.8)
-150
+100(.6) or
NPV=117.00
+50(.4)
Irwin/McGraw Hill
NPV=184.55
331
100(.2)
410(.8)
0
Piston
403.82
456
140(.6)
NPV=444.55
-250
812
180(.2)
660
364
220(.4)
100(.6)
148