Intermediate Corporate Finance
Spring 2007
Chapter 1-5 Review
Goal of the Manager of the Firm:
a)
b)
c)
d)
e)
f)
Maximize shareholder wealth
Minimize risk
Maximize profits (max dividends; max after-tax cash flows over time)
Maximize his or her salary
All of the above
All of the above, except d
Are these valid objectives?
Minimize Risk:
Maximize Profits:
What is S/H wealth and why does it weigh the risk/return trade-off?
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Stock Price = PV of future expected dividends. Why not include stock price
appreciation?
Summation formulas:
T
P0 = ∑[Dt/(1+rs)t] + PT/(1+rs)T
(1)
t=1
P0 = Div1 / (r –g)
(2)
r=
g=
–
–
Dividends reflect return (in dollar metric)
Discount rate of divs, r, reflects risk.
Another formula for Stock Price:
P0 = EPS1 / r + PVGO
(3)
EPS/r = capitalized value of earnings with no-growth policy
PVGO = NPV of growth opportunities (per share)
EXAMPLE:
Current stock price = $50
1 million shares outstanding
Managers accept a project with an NPV of $10 million.
What should the stock price be when S/H’s learn of the project?
When will the stock price react, assuming that the s/h’s correctly value the
project?
a) When rumors circulate about a positive NPV project available to the firm
b) When the S/H’s learn of mgmt’s decision to accept the project
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c) When the project is “officially” accepted (done deal: contracts signed, etc)
d) When the cash inflows from the project occur
Recall that P0 = EPS1 / r + PVGO. Can stock price ever be less than EPS1/r?
Such firms can become takeover targets. Why?
Moral to the Story:
What about the interests of other stakeholders of the firm (who has an interest in the
firm’s success other than the firm’s shareholders?) (pg 23-29)
•
What is the goal IF maximizing shareholder wealth conflicts other stakeholder
interests? (How could this happen?)
Percentage of firms in the given country that claim shareholder dividends come before
job security of employees: (figure 2.3)
•
•
•
•
•
Japan
France
Germany
UK
USA
•
•
•
•
•
3% dividends
40% dividends
41% dividends
89% dividends
89% dividends
Why is it important for US firms to understand corporate objectives for firms located
in other countries?
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Chapter 8: Risk, Return & the Opportunity Cost of Capital (OCC)
Chapter 8: Practice Questions: 11, 12, 22
(8th ed. Prin of Corp Fin text: Chapter 7: Practice question 2, 3 13)
Discount rates should reflect the project’s risk….but what kind of risk?
– Market risk?
– Business risk?
– Total risk?
How would you define the investor’s risk for a given investment?
____T-bills
____Government bonds (long-term)
____Common stocks
Which is riskier: Typical corporate bonds vs. long-term gov’t bonds?
Small firm stocks vs. avg firm stocks?
The Value of an Investment of $1 in 1900:
$1,000
719
Equities
Bonds
Bills
Dollars
$100
$10
6.81
2.80
2004
19
00
19
10
19
20
19
30
19
40
19
50
19
60
19
70
19
80
19
90
20
00
$1
Start of Year
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The Risk Premium (RP): Required rate in excess of the risk-free rate (to
compensate for added risk).
Add to RF rate to get a discount rate for projects, or use market risk premium and
project beta.
Historical average (1900-2000) for stocks:
Use arithmetic averages, not compound rates of return
Stock return = 11.7%; T-bill rate = 4.1%;
RISK PREMIUM for stocks = 11.7-4.1 = 7.6%
RP estimates differ; range: 5-8%
RP’s vary by country; from 4.3% in Denmark to 10.7% in Italy.
Do Risk Premiums vary over time?
•
Why would they?
– Reduced risk from availability of international investments
– Access to mutual funds (pension funds)
•
Why wouldn’t they?
– Investors do not diversify internationally as much as they should.
– No reason to expect stocks are getting riskier over time.
What effect does inflation have on returns?
On stock prices?
•
CAPM: E[Ri] = Rf + i [E(Rm) – Rf]
•
If risk premium is assumed constant, what effect will higher interest rates have on
the expected return of stock i?
•
What happens to stock prices, in general, when interest rates go up?
•
How can rates of return on stocks go up when prices go down?
Definitions:
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”,
“unsystematic risk” and “business risk”
Market Risk - Economy-wide sources of risk that affect the overall stock market.
Also called “systematic risk” and “undiversifiable risk”.
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Is there a limit to risk reduction through diversification? Or can we reduce all risk
(variability) by adding different investments into our portfolio?
Portfolio standard deviation
Note: Greater risk reduction going from 1 to 2 securities, than from 5 to 6 securities.
0
5
10
15
Number of Securities
6
Portfolio standard deviation
Unique
risk
Market risk
0
5
10
15
Number of Securities
Chapter 9: Risk and Return, The CAPM, The SML, Other Models
Recommended problems Chapter 9: 6, 7, 8, 15 (not part a); challenge question 1
(8th ed. Prin of Corp Fin text: Chapter 8: Quiz 6 & ,7; Practice question 1 & 8 (not part a); Challenge
Question 1)
When and why is diversification desirable?
Individual perspective:
Corporate perspective:
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•
An investor fails to diversify her portfolio. She earns returns on this undiversified
investment based on:
a) Total Risk
b) Unique (business) risk only
c) Market risk only
What do YOU think?
An investor diversifies her portfolio nationally, but holds no foreign stocks. Her
expected portfolio returns are based upon:
A. The amount of risk in her portfolio assuming she had diversified to the
fullest extent, internationally
B. The amount of risk in her portfolio based on the amount of typical
international diversification for investors within her country
C. The amount of risk based on market risk within her country only
Firms in countries whose investors fail to diversify internationally have a higher cost
of capital (b/c their cost of equity is higher)
Note: this can make firms less competitive …higher WACC means more projects are
negative NPV.
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Stock Return Distributions
Standard Deviation VS. Expected Return
Investment A (top) and B (bottom)
20
18
16
14
12
10
8
6
4
2
0
-50
% return
0
50
20
18
16
14
12
10
8
6
4
2
0
-50
0
9
50
Investment C:
20
18
16
14
12
10
8
6
4
2
0
-50
0
50
Which is preferable, B or C?
Which has a greater variance, B or C?
Which has a higher beta, B or C?
Which offers the higher expected return, B or C?
Of A, B or C, which would be reasonable investments to recommend, assuming the
investor will not diversify further?
…what if you assume the investor is fully diversified?
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Return Distributions:




Stocks: symmetric, normal distributions
“flatness” of distribution indicates risk (std dev).
Mean return can be used to infer market risk (beta); (higher E[ret], higher beta.)
Non-symmetric distributions (skewed distributions):
Do Investors prefer (right / left) skewness?
What types of investments could have a skewed distribution?
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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
Project, firm or stock correlation:
•
a)
b)
c)
d)
You combine a low risk stock with a high risk stock* (50% invested in each) The
resulting risk of the portfolio will be__________
Between that of the high and low risk stocks
The average of that of the high and low risk stock
Less than that of the low risk stock
Potentially a, b or c
Implications for project risk:
Query: You are considering a project that is riskier than your firm’s average project (i.e.,
higher variance of after tax cash flows). Will the addition of the new project increase the
overall risk of your firm or decrease it? Is it possible to know with certainty from the
above information?
Now assume that the risky project is negatively correlated with the other lines of
business in our firm? Can we know whether the new project will increase or decrease the
overall risk of our firm?
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MUST the new project be negatively correlated to reduce the overall risk of our firm?
Will the addition of a new, higher-risk project increase our firm’s equity beta?
Portfolio return = weighted average return of all stocks in the portfolio =
x1 E[ret1] + x2 E[ret2]
Portfolio variance is the sum of the following boxes: (“x” is the % of the money
invested in stocks 1 and 2.)
Stock 1
Stock 1
Stock 2
x12 σ12
x1x 2 σ12 
x1x 2ρ12σ1σ 2
Stock 2
x1x 2 σ12 
x1x 2ρ12σ1σ 2
x 22 σ 22
Example
Suppose you invest 60% of your portfolio in Exxon Mobil and 40% in Coca Cola.
The expected dollar return on your Exxon Mobil stock is 10% and on Coca Cola is
15%. The expected return on your portfolio is:
Assume the same example above: The standard deviation of Exxon and Coca
Cola’s annualized daily returns are 18.2% and 27.3%, respectively. Assume a
correlation coefficient of 1.0 and calculate the portfolio variance.
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Efficient Frontier (a.k.a. mean variance efficient
frontier)
Expected Return (%)
T
Lending
Borrowing
M
MVP
rf
S
Standard Deviation
•Lending or Borrowing at the risk free rate (rf) allows us to exist outside the
efficient frontier.
Led to development of CAPM:
Best investment is some % in tangency portfolio (M), and rest in risk free asset or
engage in riskless borrowing
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.
What is done with the borrowed money (to obtain a point on the CML above M)?
Return exg:
RM = 20%; Rf = 5%,
$100 borrowed, $100 own
Ret = ($ ret on M – $ int) / own $
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SML: Plot of the CAPM:
Diagram:
Intercept:
Y-axis:
X-axis:
Slope:
.
Stocks (investments) that plot above the SML are:
a) overvalued
b) Undervalued
c) neither
What can we learn from the SML?
• Overvalued / Undervalued investments (Can use with project betas as well as
equity betas).
• Illustration of undiversifiable risk & beta
• Do returns plot, roughly around the actual SML? (If not, evidence against the
CAPM)
– Purists would say that you can’t test a model that measures expected
returns by plotting “actual returns.”
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