Introduction
1. Corporate Finance – how decision
making affects “value”.
2. Corporate finance is not a number
“game”.
3. Focus: (a) practical issues that arise in
valuation, (b) taxes, (c) incentives of
different stakeholders.
1
Chapter 7
Risk, Return and the Cost of Capital
Final objective: Estimating the opportunity cost of
capital.
Explain and calculate
 Expected return
 Security risk
 Diversification
 Portfolio risk
 beta.
2
Capital Budgeting Example
• Capital Budgeting Decision
– Suppose you had the opportunity to buy a
tbill which would be worth $400,000 one
year from today.
• Interest rates on tbills are a risk free
7%.
– What would you be willing to pay for this
-$400,000
investment?
PV today:
0
1
2
$400,000 / (1.07) = $373,832
3
Cost of Capital
• Capital Budgeting Decision
– Suppose you are offered a construction
deal with similar cost and payoff.
– An important concept in finance is that a
risky dollar is worth less than a safe dollar.
– You are told that the risk is quantified by
the cost of capital, which is 12%.
NPV= -350,000+400,000/1.12 = $7,142
4
Calculating Returns
Suppose you bought 100 shares of BCE one
year ago today at $25. Over the last year, you
received $20 in dividends (= 20 cents per
share × 100 shares). At the end of the year, the
stock sells for $30. How did you do?
5
Holding Period Returns
The holding period return is the return that an
investor would get when holding an
investment over a period of n years, when the
return during year i is given as ri:
holding period return 
 (1  r1 )  (1  r2 )    (1  rn )  1
6
The Future Value of an Investment of $1 in
1957: Evidence from Canada
1000
$1 (1  r1957 )  (1  r1958)  (1  r2003)  $86.17
$42.91
$20.69
10
Common Stocks
Long Bonds
T-Bills
0.1
1957
1962
1967
1972
1977
1982
1987
1992
1997
2002
7
An Investment of $1 in 1900: US evidence
$100,000
$10,000
Common Stock
15,578
US Govt Bonds
$1,000
147
61
$100
$10
2004
$1
19
00
19
10
19
20
19
30
19
40
19
50
19
60
19
70
19
80
19
90
20
00
Dollars
T-Bills
Start of Year
8
An Investment of $1 in 1900: US evidence
Real Returns
$1,000
719
Equities
Bonds
Bills
Dollars
$100
$10
6.81
2.80
Start of Year
2004
19
00
19
10
19
20
19
30
19
40
19
50
19
60
19
70
19
80
19
90
20
00
$1
9
How does this relate to cost of capital?
• Suppose there is an investment project which
you know has the same risk as Standard and
Poor’s Composite Index.
• What rate should you use?
10
Rates of Return 1900-2003
Stock Market Index Returns
Percentage Return
80%
60%
40%
20%
0%
-20%
1900
1920
1940
1960
1980
2000
-40%
-60%
Year
Source: Ibbotson Associates
11
Measuring Risk
Histogram of Annual Stock Market Returns
# of Years
24
24
19
20
15
16
10
12
3
2
50 to 60
30 to 40
20 to 30
10 to 20
0 to 10
-10 to 0
-20 to -10
Return %
-30 to -20
1
-40 to -30
0
1
-50 to -40
4
4
40 to 50
8
13
12
12
Average Stock Returns and Risk-Free
Returns
• The Risk Premium is the additional return
(over and above the risk-free rate) resulting
from bearing risk.
• One of the most significant observations of
stock (and bond) market data is this longrun excess of security return over the riskfree return.
• The historical risk premium was 7.6% for the
US.
13
Average Market Risk Premia (by country)
10.7
Italy
UK
10
Japan
Germany
9.3
France
Ireland
Australia
Canada
8.6
South Africa
Spain
8.2
Sweden
Switzerland
Country
7.6
8.1
USA
5.9
6.6
Netherlands
5.9
6.4
Average
5.1
5.8
4.3
4.7
5.3
6.3
Belgium
11
10
9
8
7
6
5
4
3
2
1
0
Denmark
Risk premium, %
14
Measuring Risk
Variance - Average value of squared deviations
from mean. A measure of volatility.
Standard Deviation – Square root of variance.
A measure of volatility.
15
Return Statistics
• The history of capital market returns can be
summarized by describing the
– average return
( R1    RT )
R
T
– the standard deviation of those returns
( R1  R) 2  ( R2  R) 2   ( RT  R) 2
SD  VAR 
T 1
16
Canada Returns, 1957-2003
Average
Investment
Canadian common stocks
Annual Return
10.64%
Standard
Deviation
Distribution
16.41%
Long Bonds
8.96
10.36
Treasury Bills
6.80
4.11
Inflation
4.29
3.63
– 60%
0%
17
+ 60%
Risk Statistics
There is no universally agreed-upon definition
of risk. A large enough sample drawn from a
normal distribution looks like a bell-shaped
curve.
18
Historically – Are Returns Normal?
S&P 500 Return Frequencies
16
16
Normal
approximation
Mean = 12.8%
Std. Dev. = 20.4%
12
12
12
11
10
9
8
6
5
Return frequency
14
4
2
1
1
2
2
1
0
0
0
-58% -48% -38% -28% -18%
-8%
2%
12%
Annual returns
22%
32%
42%
52%
62%
19
Expected Return, Variance, and covariance
Rate of Return
Scenario Probability Stock fund Bond fund
Recession
33.3%
-7%
17%
Normal
33.3%
12%
7%
Boom
33.3%
28%
-3%
Consider the following two risky asset worlds.
There is a 1/3 chance of each state of the
economy and the only assets are a stock fund
and a bond fund.
20
Expected Return, Variance, and Covariance
Scenario
Recession
Normal
Boom
Expected return
Variance
Standard Deviation
Stock fund
Rate of
Squared
Return Deviation
-7%
3.24%
12%
0.01%
28%
2.89%
11.00%
0.0205
14.3%
Bond Fund
Rate of
Squared
Return Deviation
17%
1.00%
7%
0.00%
-3%
1.00%
7.00%
0.0067
8.2%
21
The Return for Portfolios
Scenario
Recession
Normal
Boom
Expected return
Variance
Standard Deviation
Rate of Return
Stock fund Bond fund Portfolio
-7%
17%
5.0%
12%
7%
9.5%
28%
-3%
12.5%
11.00%
0.0205
14.31%
7.00%
0.0067
8.16%
squared deviation
0.160%
0.003%
0.123%
9.0%
0.0010
3.08%
The expected rate of return on the portfolio is
a weighted average of the expected returns
on the securities in the portfolio.
E (rP )  wB E (rB )  wS E (rS )
22
The Variance of a Portfolio
Scenario
Recession
Normal
Boom
Expected return
Variance
Standard Deviation
Rate of Return
Stock fund Bond fund Portfolio
-7%
17%
5.0%
12%
7%
9.5%
28%
-3%
12.5%
11.00%
0.0205
14.31%
7.00%
0.0067
8.16%
squared deviation
0.160%
0.003%
0.123%
9.0%
0.0010
3.08%
23
Portfolio Risk
1
2
3
STOCK
To calculate
portfolio
variance add
up the boxes
4
5
6
N
1
2
3
4
5
6
STOCK
N
24
Diversification
• The variance (risk) of the security’s return can
be broken down into:
– Systematic (Market) Risk
– Unsystematic (diversifiable) Risk
The Effect of Diversification:
– unsystematic risk will significantly diminish in
large portfolios
– systematic risk is not affected by
diversification since it affects all securities in
any large portfolio
25
Portfolio Risk as a Function of the Number
of Stocks in the Portfolio

In a large portfolio the variance terms are effectively
diversified away, but the covariance terms are not.
Diversifiable Risk;
Nonsystematic Risk;
Firm Specific Risk;
Unique Risk
Portfolio risk
Nondiversifiable risk;
Systematic Risk;
Market Risk
n
Thus diversification can eliminate some, but not all of the
risk of individual securities.
26
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%
Copyright 1996 by The McGraw-Hill
Companies, Ic
Expected
market
return
27
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.
Beta - Sensitivity of a stock’s return to the return
on the market portfolio.
28
Definition of Risk When Investors Hold
the Market Portfolio
• Researchers have shown that the best measure
of the risk of a security in a large portfolio is the
beta (b)of the security.
• Beta measures the responsiveness of a security
to movements in the market portfolio.
bi 
Cov( Ri , RM )
 ( RM )
2
29
Chapter 8
Risk and Return
• Markowitz Portfolio Theory
• Risk and Return Relationship
• Validity and the Role of the CAPM
30
Markowitz Portfolio Theory
• Given a certain level of risk, investors
prefer stocks with higher returns.
• Given a certain level of return, investors
prefer less risk.
• By combining stocks into a portfolio,
one can achieve different combinations
of return & standard deviation.
• Correlation coefficients are crucial for
ability to reduce risk in portfolio.
31
Markowitz Portfolio Theory
Expected Returns and Standard Deviations vary given
different weighted combinations of the stocks
Expected Return (%)
Coca Cola
40% in Coca Cola
Exxon Mobil
Standard Deviation
32
Efficient Frontier
Example
Stocks
ABC Corp
Big Corp

28
42
Correlation Coefficient = .4
% of Portfolio
Avg Return
60%
15%
40%
21%
33
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
34
Efficient Frontier
Example
Stocks
Return
ABC Corp
Big Corp
28
42
Portfolio
28.1

Correlation Coefficient = .4
% of Portfolio
Avg
60%
40%
15%
21%
17.4%
Let’s Add stock New Corp to the portfolio
35
Efficient Frontier
Example
Stocks
Portfolio
New Corp

28.1
30
New Portfolio 23.43
Correlation Coefficient = .3
% of Portfolio
Avg Return
50%
17.4%
50%
19%
18.20%
NOTE: Higher return & Lower risk
How did we do that?
DIVERSIFICATION
36
Efficient Frontier
Return
B
AB
A
Risk
37
Efficient Frontier
Return
B
AB
A
N
Risk
38
Efficient Frontier
Return
B
ABN AB
A
N
Risk
39
return
2-Security Portfolios - Various Correlations
100%
stocks
 = -1.0
 = 1.0
100%
bonds
 = 0.2

40
return
Efficient Frontier
minimum
variance
portfolio
Individual Assets
P
41
return
Riskless Borrowing and Lending
100%
stocks
Balanced
fund
rf
100%
bonds

Now investors can allocate their money
across the T-bills and a balanced mutual
42
fund
return
Market Equilibrium: CAPM
M
rf
P
43
return
Changes in Riskfree Rate
100%
stocks
1
f
0
f
r
r
First
Optimal
Risky
Portfolio
Second Optimal
Risky Portfolio
100%
bonds

44
Security Market Line
Return
Market Return = rm
.
Efficient Portfolio
Risk Free
Return
= rf
1.0
BETA
45
Security Market Line
Return
SML
rf
1.0
BETA
SML Equation = rf + B ( rm - rf )
46
Expected
return
Risk & Expected Return
13.5%
3%
βi  1.5
RF  3%
1.5
b
R M  10%
R i  3%  1.5  (10%  3%)  13.5%
47
Security Returns
Estimating b with regression
Slope = bi
Return on
market %
Ri = a i + biRm + ei
48
Estimates of Beta for Selected Stocks
Stock
Research in Motion
Nortel Networks
Bank of Nova Scotia
Bombardier
Investors Group.
Maple Leaf Foods
Roger
Communications
Canadian Utilities
TransCanada Power
Beta
3.04
3.61
0.28
1.48
0.36
0.25
1.17
0.08
0.08
49
CAPM versus Reality
1. Do investors care about mean and
variance?
2. Is there a security that is risk-free?
3. Short selling?
4. Transaction costs?
5. Most important: homogeneous
expectations?
50
Testing the CAPM
Beta vs. Average Risk Premium
Avg Risk Premium
1931-2002
30
20
SML
Investors
10
Market
Portfolio
0
1.0
Portfolio Beta
51
Testing the CAPM
Beta vs. Average Risk Premium
Avg Risk Premium
SML
1931-65
30
20
Investors
10
Market
Portfolio
0
1.0
Portfolio Beta
52
Testing the CAPM
Beta vs. Average Risk Premium
Avg Risk Premium
1966-2002
30
20
SML
Investors
10
Market
Portfolio
0
1.0
Portfolio Beta
53
Chapter 9 (part 1)
Capital Budgeting and Risk
Firm with
excess cash
Pay cash dividend
Shareholder
invests in
financial
asset
A firm with excess cash can either pay a
dividend or make a capital investment
Invest in project
Shareholder’s
Terminal
Value
Because stockholders can reinvest the dividend in risky financial assets,
the expected return on a capital-budgeting project should be at least as
great as the expected return on a financial asset of comparable risk.
54
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)
55
Company Cost of Capital
Category
Speculativ e Ventures
Discount Rate
30%
New products
Expansion of existing business
20%
15% (Company COC)
Cost improvemen t, known tech nology
10%
56
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
57
Company Cost of Capital
If the firm is all equity financed, 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
Project Beta
58
Example
• Suppose the stock of Stansfield Enterprises,
a publisher of PowerPoint presentations,
has a beta of 2.5. The firm is 100-percent
equity financed.
• Assume a risk-free rate of 5-percent and a
market risk premium of 10-percent.
• What is the appropriate discount rate for an
expansion of this firm?
59
Example (continued)
Suppose Stansfield Enterprises is evaluating
the following non-mutually exclusive projects.
Each costs $100 and lasts one year.
Project
Project b
A
IRR
NPV at
30%
2.5
Project’s
Estimated Cash
Flows Next
Year
$150
50%
$15.38
B
2.5
$130
30%
$0
C
2.5
$110
10%
-$15.38
60
IRR
Project
Using the SML to Estimate the RiskAdjusted Discount Rate for Projects
Good
A
projects
30%
B
5%
C
SML
Bad projects
Firm’s risk (beta)
2.5
61
Capital Structure
Capital Structure - the mix of debt & equity
within a company
Expand CAPM to include CS (common shares)
R = r f + B ( rm - r f )
becomes
Requity = rf + B ( rm - rf )
62
Capital Structure & COC (company
cost of capital)
COC = rportfolio = rassets
rassets = rdebt (D) + requity (E)
(V)
(V)
Bassets = Bdebt (D) + Bequity (E)
(V)
(V)
IMPORTANT
requity = rf + Bequity ( rm - rf )
E, D, and V are
all market values
63
Capital Structure & COC
Expected Returns and Betas prior to refinancing
Expected
return (%)
20
Requity=15
Rassets=12.2
Rrdebt=8
0
0
0.2
0.8
Bdebt
Bassets
1.2
Bequity
64
The Firm versus the Project
Suppose the Conglomerate Company has a cost of capital,
based on the CAPM, of 17%. The risk-free rate is 4%, the
market risk premium is 10%, and the firm’s beta is 1.3.
17% = 4% + 1.3 × [14% – 4%]
This is a breakdown of the company’s investment projects:
1/3 Automotive retailer b = 2.0
1/3 Computer Hard Drive Mfr. b = 1.3
1/3 Electric Utility b = 0.6
average b of assets = 1.3
When evaluating a new electrical generation investment,
which cost of capital should be used?
65
SML
IRR
Project
Capital Budgeting & Project Risk
24%
Investments in hard
drives or auto retailing
should have higher
discount rates.
17%
10%
Firm’s risk (beta)
0.6
1.3
2.0
r = 4% + 0.6×(14% – 4% ) = 10%
10% reflects the opportunity cost of capital on an investment in
electrical generation, given the unique risk of the project.
66
Project
IRR
Capital Budgeting & Project Risk
The SML can tell us why:
SML
Incorrectly accepted
negative NPV projects
RF  βFIRM ( R M  RF )
Hurdle
rate
rf
bFIRM
Incorrectly rejected
positive NPV projects
Firm’s risk (beta)
67
Measuring Betas
Theoretically, the calculation of beta is
straightforward:
Cov( Ri , RM ) σ im
β
 2
Var ( RM )
σM
Problem 1: Betas may vary over time.
68
Measuring Betas
Dell Computer
Price data: May 91- Nov 97
R2 = .10
B = 1.87
Slope determined from plotting the
line of best fit.
69
Measuring Betas
Dell Computer
Price data: Dec 97 - Apr 04
R2 = .27
B = 1.61
Slope determined from plotting the
line of best fit.
70
Measuring Betas
General Motors
Price data: May 91- Nov 97
R2 = .07
B = 0.72
Slope determined from plotting the
line of best fit.
71
Measuring Betas
General Motors
R2 = .29
GM return (%)
Price data: Dec 97 - Apr 04
B = 1.21
Slope determined from plotting the
line of best fit.
72
Estimated Betas
Beta
Burlington Northern &
Santa Fe
CSX Transportation
Norfolk Southern
Union Pacific Corp
Industry portfolio
equity
0.53
0.58
0.47
0.47
0.49
Standard
Error
0.2
0.23
0.28
0.19
0.18
73
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)
74
Using an Industry Beta
• It is frequently argued that one can better
estimate a firm’s beta by involving the whole
industry.
• If you believe that the operations of the firm
are similar to the operations of the rest of the
industry, you should use the industry beta.
• If you believe that the operations of the firm
are fundamentally different from the
operations of the rest of the industry, you
should use the firm’s beta.
75
Problems with Industry Beta
One must make sure that the firm is
comparable to other industry both in its
operation and its financing.
Question: Consider Grand Sport, Inc., which is currently allequity and has a beta of 0.90. The firm has decided to lever up
to a capital structure of 50% debt and 50% equity. Since the
firm will remain in the same industry, its asset beta should
remain 0.90.
Assuming a zero beta for its debt, what should the equity beta
be?
76
Beware of Fudge Factors
•
Common practice to make adjustments to
discount rate to offset worries.
Example:
1) A new drug won’t get FDA approval and won’t
be able to go on the market.
2) Unexpected weather condition would hurt the
crop.
77
Determinants of Beta
• Business Risk
– Cyclicality of Revenues
– Operating Leverage
• Financial Risk
– Financial Leverage
78
Cyclicality of Revenues
• Highly cyclical stocks have high betas.
– Empirical evidence suggests that retailers
and automotive firms fluctuate with the
business cycle.
– Transportation firms and utilities are less
dependent upon the business cycle.
79
Operating Leverage
• The degree of operating leverage measures
how sensitive a firm (or project) is to its fixed
costs.
• Operating leverage increases as fixed costs
rise and variable costs fall.
• Operating leverage magnifies the effect of
cyclicality on beta.
• The degree of operating leverage is given by:
Change in EBIT
Sales
DOL 

EBIT
Change in Sales
80
Operating Leverage
$
Total
costs
Fixed costs
 EBIT
 Volume
Fixed costs
Volume
Operating leverage increases as fixed costs rise
and variable costs fall.
81
Chapter 9: Q5
The following table shows estimates of the
risk of two well-known Canadian Stocks
STD
R^2
Beta
STD Beta
Alcan
24
0.15
0.69
0.21
Inco
29
0.22
1.04
0.26
a. What proportion was market risk, and what proportion unique risk?
b. What is the variance of market and unique variance of each stock?
c. What is the confidence level of the Inco’s beta?
d. What is expected return of Alcn if Rf=5% and market return=12%?
e. Suppose next year the market provides a zero return. What return to
you expect for each stock?
82
Chapter 9: Q9
You run a perpetual encabulator machine, which
generates revenues averaging $20 million per year.
Raw material costs are 50 percent of revenues.
These costs are variable – they are always
proportional to revenues. There are no other
operating costs. The cost of capital is 9 percent.
Your firm’s long-term borrowing rate is 6 percent.
Now you are approached by Studebaker Capital
Corp., which proposes a fixed-price contract to
supply raw materials at $10 million per year for 10
years.
a. What happens to the operating leverage and
business risk of the encabulator machine if you
agree to this fixed-price contact?
b. Calculate the present value of the encabulator
machine with and without the fixed-price contract?
83
Chapter 9 (part 2)
Capital Budgeting and Risk
Ct
CEQt
PV 

t
t
(1  r )
(1  rf )
84
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?
85
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%
Year
Cash Flow
PV @ 12%
1
100
89.3
2
100
79.7
3
100
71.2
Total PV
240.2
86
Risk,DCF and CEQ
Example
Project B cash flow is 94.6, 89.6, 84.8 in year 1-3 respectively.
However, these cash flows are RISK FREE. What is Project’s B
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
87
Risk,DCF and CEQ
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.
88
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 5.7%…this % can be considered the annual
premium on a risky cash flow
Risky cash flow
 certainty equivalent cash flow
1.057
89
Long lived assets and discount rates
Example (from text): The scientists at Vegetron have come up
with an electric mop and are ready to go ahead with pilot
production. The preliminary phase will take one year and
costs $125k. Management feels that there is only a 50%
chance that the pilot production will be successful. If the
project fails, the project will be dropped. If the project
succeeds Vegetron will build a $1million plant that would
generate an expected annual cash flow in perpetuity of
$250k.
Rf=7%, Risk Premium=9%. Regular projects of the firm have
a beta of 0.33, however due to the 50% probability of failure
management assumes a beta of 2 for the project.
1. What is NPV?
2. Is management correct about its approach for the NPV
calculation?
90
International Projects
• Investment projects abroad may be safer
than similar domestic investments.
• Remember: Beta measures risk relative to
investor’s portfolio (a good question would
be to ask who is the investor of the
company?)
• Not clear why home bias persists so
strongly (perhaps information, transaction
costs, etc.)
91
What is Liquidity?
• The idea that the expected return on a stock and
the firm’s cost of capital are positively related to
risk is fundamental.
• Recently a number of academics have argued
that the expected return on a stock and the
firm’s cost of capital are negatively related to the
liquidity of the firm’s shares as well.
• The trading costs of holding a firm’s shares
include brokerage fees, the bid-ask spread, and
market impact costs.
92
Liquidity, Expected Returns, and the Cost
of Capital
• The cost of trading an illiquid stock reduces the
total return that an investor receives.
• Investors thus will demand a high expected
return when investing in stocks with high trading
costs.
• This high expected return implies a high cost of
capital to the firm.
93
Liquidity and the Cost of Capital
Liquidity
An increase in liquidity, i.e., a reduction in trading costs,
lowers a firm’s cost of capital.
94
Liquidity and Adverse Selection
• There are a number of factors that determine the
liquidity of a stock.
• One of these factors is adverse selection.
• This refers to the notion that traders with better
information can take advantage of specialists
and other traders who have less information.
• The greater the heterogeneity of information, the
wider the bid-ask spreads, and the higher the
required return on equity.
95
What the Corporation Can Do
• The corporation has an incentive to lower
trading costs since this would result in a lower
cost of capital.
• A stock split would increase the liquidity of the
shares.
• A stock split would also reduce the adverse
selection costs thereby lowering bid-ask
spreads.
• This idea is a new one and empirical evidence is
not yet in.
96
What the Corporation Can Do
• Companies can also facilitate stock purchases
through the Internet.
• Direct stock purchase plans and dividend
reinvestment plans handled on-line allow small
investors the opportunity to buy securities
cheaply.
• The companies can also disclose more
information, especially to security analysts, to
narrow the gap between informed and
uninformed traders. This should reduce spreads.
97
Summary and Conclusions
• The expected return on any capital budgeting
project should be at least as great as the
expected return on a financial asset of
comparable risk. Otherwise the shareholders
would prefer the firm to pay a dividend.
• The expected return on any asset is
dependent upon b.
• A project’s required return depends on the
project’s b.
• A project’s b can be estimated by considering
comparable industries or the cyclicality of
project revenues and the project’s operating
and financial leverage.
98
Jones Family Mini-Case
Executive summary:
• The wildcat oil well is going to cost $5 million.
• The Jones geologists says there’s only 30% chance of a dry hole.
• If oil is found, the expectation is for 300 barrels of crude oil per day
(at a price of $25 per barrel)
• Sales will start next year.
• Production and shipping costs are $10 per barrel (Mr. Jones argues
that they are fixed).
• Production will start declining at 5% every year.
• Oil prices expected to grow at 2.5% per year, and pumping will
continue for 15 years.
• The interest rate is 6%, the beta is 0.8, and the risk premium is 7%.
99
Chapter 10: Decision Trees
• A fundamental problem in NPV analysis is
dealing with uncertain future outcomes.
• There is usually a sequence of decisions in
NPV project analysis.
• Decision trees are used to identify the
sequential decisions in NPV analysis.
• Decision trees allow us to graphically represent
the alternatives available to us in each period
and the likely consequences of our actions.
• This graphical representation helps to identify
the best course of action.
100
Example of Decision Tree
Open circles represent decisions to be made.
“A”
Pay
wizard
$1000?
Study
finance
“B”
Filled circles represent
receipt of information
e.g., a test score in this
class.
“C”
Do not
study
The lines leading away
“D” from the circles represent
the alternatives.
“F”
101
Stewart Pharmaceuticals
• The Stewart Pharmaceuticals Corporation is considering
investing in developing a drug that cures the common
cold.
• A corporate planning group, including representatives
from production, marketing, and engineering, has
recommended that the firm go ahead with the test and
development phase.
• This preliminary phase will last one year and cost $1
billion. Furthermore, the group believes that there is a
60% chance that tests will prove successful.
• If the initial tests are successful, Stewart
Pharmaceuticals can go ahead with full-scale production.
This investment phase will cost $1,600 million.
102
Production will occur over the next four years.
Stewart Pharmaceuticals NPV of Full-Scale Production following
Successful Test
Investment
Year 1
Years 2-5
Revenues
$7,000
Variable Costs
(3,000)
Fixed Costs
(1,800)
Depreciation
(400)
Pretax profit
$1,800
Tax (34%)
(612)
Net Profit
Cash Flow
$1,188
-$1,600
4
NPV  $1,600  
t 1
$1,588
$1,588
 $3,433.75
t
(1.10)
Note that the NPV is calculated as of date 1, the date at which the
investment of $1,600 million is made. Later we bring this number
back to date 0.
103
Stewart Pharmaceuticals NPV of Full-Scale Production following
Unsuccessful Test
Investment
Year 1
Years 2-5
Revenues
$4,050
Variable Costs
(1,735)
Fixed Costs
(1,800)
Depreciation
(400)
Pretax profit
$115
Tax (34%)
(39.10)
Net Profit
$75.90
Cash Flow
-$1,600
$475
4
$475.90
 $91.461
t
t 1 (1.10)
NPV  $1,600  
Note that the NPV is calculated as of date 1, the date at which the
investment of $1,600 million is made. Later we bring this number104
back to date 0.
Decision Tree for Stewart Pharmaceutical
The firm has two decisions to make:
To test or not to test.
To invest or not to invest.
Success
Test
Invest
NPV  $3,433.75m
Do not
invest
NPV = $0
Failure
Do not
test
NPV  $91.461m
NPV  $0
Invest
105
Stewart Pharmaceutical: Decision to Test
• Let’s move back to the first stage, where the decision
boils down to the simple question: should we invest?
• The expected payoff evaluated at date 1 is:
Expected  Prob.
Payoff
Payoff
  Prob.
  
 


payoff
 sucess given success   failure given failure
Expected
payoff



 .60  $3,433.75  .40  $0  $2,060.25
• The NPV evaluated at date 0 is:
NPV  $1,000 
$2,060.25
 $872.95
1.10
So we should test.
106
Real Options
• One of the fundamental insights of modern finance
theory is that options have value.
• The phrase “We are out of options” is surely a sign of
trouble.
• Because corporations make decisions in a dynamic
environment, they have options that should be
considered in project valuation.
107
Options
The Option to Expand
• Static analysis implicitly assumes that the scale of the
project is fixed.
• If we find a positive NPV project, we should consider the
possibility of expanding the project to get a larger NPV.
• For example,the option to expand has value if demand
turns out to be higher than expected.
• All other things being equal, we underestimate NPV if we
ignore the option to expand.
The Option to Delay
• Has value if the underlying variables are changing with a
favourable trend.
108
The Option to Expand: Example
• Imagine a start-up firm, Campusteria, Inc. which plans
to open private (for-profit) dining clubs on university
campuses.
• The test market will be your campus, and if the concept
proves successful, expansion will follow nationwide.
• Nationwide expansion, if it occurs, will occur in year
four.
• The start-up cost of the test dining club is only $30,000
(this covers leaseholder improvements and other
expenses for a vacant restaurant near campus).
109
Campusteria pro forma Income Statement
Investment
Year 0
Revenues
Years 1-4
$60,000
Variable Costs
($42,000)
Fixed Costs
($18,000)
Depreciation
($7,500)
Pretax profit
($7,500)
Tax shield 34%
$2,550
–$4,950
Net Profit
Cash Flow
–$30,000
4
$2,550
$2,550
NPV  $30,000  
 $21,916.84
t
t 1 (1.10)
We plan to sell 25 meal
plans at $200 per
month with a 12-month
contract.
Variable costs are
projected to be
$3,500 per month.
Fixed costs (the lease
payment) are
projected to be
$1,500 per month.
We can depreciate
(straight line) our
capitalized leaseholder
improvements. 110
The Option to Expand: Valuing a Start-Up
• Note that while the Campusteria test site has a
negative NPV, its negativity is relatively small.
• If we expand, we project opening 20 Campusterias in
year four and the size of the project may grow 20 folds.
• The value of the project is in the option to expand.
• If we hit it big, we will be in a position to score large.
• We won’t know if this has value if we do not try. Thus, it
seems that we may want to take on this test project
and see what it delivers.
111
Discounted Cash Flows and Options
• We can calculate the market value of a project as the
sum of the NPV of the project without options and the
value of the managerial options implicit in the project.
M = NPV + Opt
 A good example would be comparing the
desirability of a specialized machine versus a more
versatile machine. If they both cost about the same
and last the same amount of time the more
versatile machine is more valuable because it
comes with options.
112
The Option to Abandon: Example
• The option to abandon a project has value if demand
turns out to be lower than expected.
• Suppose that we are drilling an oil well. The drilling rig
costs $300 today and in one year the well is either a
success or a failure.
• The outcomes are equally likely. The discount rate is
10%.
• The PV of the successful payoff at time one is $575.
• The PV of the unsuccessful payoff at time one is $0.
113
The Option to Abandon: Example
(continued)
Traditional NPV analysis would indicate rejection of the project.
Expected = Prob. × Successful + Prob. × Failure
Payoff
Success Payoff
Failure Payoff
Expected
= (0.50×$575) + (0.50×$0) = $287.50
Payoff
NPV = –$300 +
$287.50
1.10
= –$38.64
114
The Option to Abandon: Example
Traditional NPV analysis overlooks the option to abandon.
Success: PV = $575
Sit on rig; stare
at empty hole:
PV = $0.
Drill
 $300
Failure
Do not
drill
NPV  $0
Sell the rig;
salvage value
= $250
The firm has two decisions to make: drill or not, abandon or115
stay.
The Option to Abandon: Example
(continued)
• When we include the value of the option to abandon, the
drilling project should proceed:
Expected = Prob. × Successful + Prob. × Failure
Payoff
Success Payoff
Failure Payoff
Expected
= (0.50×$575) + (0.50×$250) = $412.50
Payoff
NPV = –$300 +
$412.50
1.10
= $75.00
116
Valuation of the Option to Abandon
• Recall that we can calculate the market value of a
project as the sum of the NPV of the project without
options and the value of the managerial options implicit
in the project.
M  NPV  Opt
$75.00  38.64  Opt
$75.00  38.64  Opt
Opt  $113.64
117
The Option to Delay: Example
Year
0
1
2
3
44
Cost
$ 20,000
$ 18,000
$ 17,100
$ 16,929
16,760
$$ 16,760
PV
$ 25,000
$ 25,000
$ 25,000
$ 25,000
25,000
$$ 25,000
NPV tt
$ 5,000
$ 7,000
$ 7,900
$ 8,071
8,240
$$8,240
NPV 0
$ 5,000
$ 6,364
$7,900
$ 6,529 $6,529 
(1.10) 2
$ 6,064
$ 5,628
• Consider the above project, which can be undertaken
in any of the next 4 years. The discount rate is 10
percent. The present value of the benefits at the time
the project is launched remain constant at $25,000, but
since costs are declining the NPV at the time of launch
steadily rises.
• The best time to launch the project is in year 2—this
schedule yields the highest NPV when judged today.118
Option issues to consider
Things to remember in these types of analysis:
• Cost of the testing
• Expected future cash flows given the outcome
of the test
• Probability of success of the testing
• Discount rate
119