The Valuation and
Characteristics of Stock
Common Stock
Corporations are owned by common
stockholders
Stockholders choose directors
Most large companies are “widely held’
Ownership spread among many investors.
Investors don’t think of a role as owner
Interested mostly in future cash flows.
2
The Return on an
Investment in Common Stock
Income in a stock investment comes from:
dividends
gain or loss on the difference between the purchase and sale price
If you buy a stock for price P0, hold it for one year, receive a dividend
of D1, then sell it for price P1, you return, k, would be:
D 1 + P1 - P 0
k =
P0
or A capital gain (loss) occurs
k =
D1
+
P1 - P 0 if you sell the stock for a
P0 P0
price greater (lower) than
d iv id e n d y ie ld c a p ita l g a in s y ie ld
you paid for it.
3
The Return on an
Investment in Common Stock
Solve the previous equation for P0, the stock’s price
today:
k P 0 D 1 P1 P 0
P 0 k P 0 D 1 P1
1 k P0 D 1 P1
D 1 P1
P0
1 k
The return on a stock investment is the interest rate
that equates the present value of the investment’s
expected future cash flows to the amount invested
today, the price, P0
4
The Nature of Cash Flows
from Stock Ownership
Comparison of Cash Flows from Stocks and Bonds
For stockholders: For bondholders:
Expected dividends and future selling Interest payments are guaranteed,
price are not known with any precision constant
Similarity to bond cash flows is Maturity value is fixed
superficial – both involve a stream of At maturity, the investor receives face
small payments followed by a larger value from the issuing company.
payment
When selling, investor receives money
from another investor
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The Basis of Value
The basis for stock value is the present value of
expected cash inflows even though dividends
and stock prices are difficult to forecast
Make assumptions about future dividends and selling
price
Discount these assumptions at an appropriate interest
rate
0 2 D nk
F , V ,
P , D n
PP V
1
= V nkP
D 2k
V F F
PP
F n
1k ,
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The Basis of Value
Example 8.1
Q: Joe Simmons is interested in the stock of Teltex Corp. He feels it is
going to have two very good years because of a government contract,
but may not do well after that. Joe thinks the stock will pay a dividend
of $2 next year and $3.50 the year after. By then he believes it will be
selling for $75 a share, at which price he'll sell anything he buys now.
People who have invested in stocks like Teltex are currently earning
returns of 12%. What is the most Joe should be willing to pay for a
Example
share of Teltex?
7
The Intrinsic (Calculated) Value
and Market Price
A stock’s intrinsic value is based on
assumptions about future cash flows made
from fundamental analysis of the firm and
its industry
Different investors with different cash flow
estimates will have different intrinsic
values
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Growth Models of Common Stock
Valuation
Based on predicted growth rates since
forecasting exact future prices and
dividends is difficult
More likely to forecast a growth
rate of earnings rather than
cash flows
9
Developing Growth-Based Models
A stock’s value today is the sum of the present values of
the dividends received while the investor holds it and the
price for which it is eventually sold
D D D P
P= 1 22 nn nn
0
1 1
k k
1 1
k k
An Infinite Stream of Dividends
○ Many investors buy a stock, hold for awhile, then sell, as
represented in the above equation
• Not convenient for valuation purposes
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Developing Growth-Based Models
A person who buys stock at time n will hold it
until period m and then sell it
Their valuation will look like this:
D D P
= + … m- + m-
P n1+ +
n
+
1k +m +m
1k 1k
n
n
Repeating this process until infinity results in:
Di
P
1 + k
0 i
i=1
Conceptually it’s possible to replace the final
selling price with an infinite series of dividends
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The Constant Growth Model
If dividends are assumed to be growing at a constant rate forever and the last
dividend paid is, D0, then the model is:
D (1g i
)
P 0
(1k)i
0
i1
This represents a series of fractions as follows
1 g g
g 01 01
2 3
D D D
P=0
0
1
k
1
k
2
1
k
3
If k>g, the fractions get smaller (approach zero) as exponents get
larger
○ If k>g growth is normal
○ If k
• Can occur but lasts for limited time period
12
Working with Growth Rates
Example 8.2
Q. Apex Corp. paid a dividend of $3.50 this year. What are its
next three dividends if it is expected to grow at 7%?
Example
A. SOLUTION: In this case D0 = $3.50 and g = .07, so
(1+g) = 1.07. Then
D1 = D0(1+g) = $3.50(1.07) = $3.75,
D2 = D1(1+g) = $3.75(1.07) = $4.01, and
D3 = D2(1+g) = $4.01(1.07) = $4.29.
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Constant Normal Growth —
The Gordon Model
Constant growth model can be simplified
to k must be
D1 greater
P0 than g.
k g
The Gordon Model is a simple expression
for forecasting the price of a stock that’s
expected to grow at a constant, normal
rate
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Constant Normal Growth—
The Gordon Model
Example 8.3
Q: Atlas Motors is expected to grow at a constant rate of 6% a year
into the indefinite future. It recently paid a dividends of $2.25 a
share. The rate of return on stocks similar to Atlas is about 11%.
What should a share of Atlas Motors sell for today?
D1
Example
A:
P0
k -g
$ 2 .2 5 ( 1 .0 6 )
.1 1 - .0 6
$ 4 7 .7 0
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The Zero Growth Rate Case —
A Constant Dividend
If a stock is expected to pay a constant,
non-growing dividend, each dollar
dividend is the same
Gordon model simplifies to:
D
P0
k
A zero growth stock is a perpetuity to the
investor
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The Expected Return
Recast Gordon model to focus on the return (k)
implied by the constant growth assumption
D1
k g
P0
The expected return reflects investors’
knowledge of a company
○If we know D0 (most recent dividend paid) and P0
(current actual stock price), investors’ expectations
are input via the growth rate assumption
17
Two Stage Growth
At times, a firm’s future growth may not be
expected to be constant
A new product may lead to temporary high growth
The two-stage growth model values a stock that is
expected to grow at an unusual rate for a limited
time
Use the Gordon model to value the constant portion
Find the present value of the non-constant growth
periods
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Two Stage Growth
Example 8.5
Q: Zylon Corporation’s stock is selling for $48 a share according to
The Wall Street Journal. We’ve heard a rumor that the firm will
make an exciting new product announcement next week. By
studying the industry, we’ve concluded that this new product will
support an overall company growth rate of 20% for about two
years. After that, we feel growth will slow rapidly and level off at
Example
about 6%. The firm currently pays an annual dividend of $2.00,
which can be expected to grow with the company. The rate of
return on stocks like Zylon is approximately 10%. Is Zylon a
good buy at $48?
A: We’ll estimate what we think Zylon should be worth given our
expectations about growth.
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Two Stage Growth
Example 8.5
We’ll develop a schedule of expected dividend payments:
Expected
Year Dividend Growth
1 $2.40 20%
Example
2 $2.88 20%
3 $3.05 6%
Next, we’ll use the Gordon model at the point in time where the
growth rate changes and constant growth begins. That’s year 2,
so:
D 35
.
$0
P
2 3
65
72
$.
-2 1-0
kg . 0. 6
20
Two Stage Growth
Example 8.5
Then we take the present value of D1, D2 and P2:
P 1 V ,1 + 2 V ,2 + 2 V ,2
k D PF PPF
0 DPF k k
$. 0PF,1 + 2 8PF,2 + 7. 5PF,2
2 V 0 $. V 0 $6 V 0
4 1 8 1 2 1
2 99 $. 86 $6 86
$. 0 . 01+ 2 8 . 24 + 7. 5 . 24
40 80 20
Example
$7 7
5
6.
Compare $67.57 to the listed price of $48.00.
If we are correct in our assumptions, Zylon
should be worth about $20 more than it is
selling for in the market, so we should buy
Zylon’s stock.
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Practical Limitations of
Pricing Models
Stock valuation models give estimated
results since the inputs are approximations
of reality
Actual growth rate can be VERY different
from predicted growth rates
Even if growth rates differ slightly, it can be a
big difference in the decision
Allow for a margin for error in estimations
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Practical Limitations of Pricing
Models
Comparison to Bond Stocks That Don’t Pay Dividends
Valuation Have value because of expectation
Bond valuation is precise that they will someday pay them.
because the inputs are Some firms don’t pay dividends
precise. even if they are profitable
Future cash flows are Firms are growing and using profits to
guaranteed in amount and finance the growth
time, unless firm
defaults.
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Some Institutional Characteristics of
Common Stock
Corporate Organization and Control
Controlled by Board of Directors
elected by stockholders
Board appoints top management who
appoint middle/lower management
Board consists of top managers and outside
directors (may include major stockholders)
In widely held corporations, top management in
“control”
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Stockholders’ Claim on
Income And Assets
Stockholders have a residual claim on income
and assets
What is not paid out as dividends is retained for
reinvestment in the business (retained earnings)
Common stockholders are last in line, they bear
more risk than other investors
25
Preferred Stock
A hybrid security with characteristics of
common stock and bonds
Pays a constant dividend forever
Specifies the initial selling price and the
dividend
No provision for the return of capital to the
investor
26
Valuation of Preferred Stock
Since securities are worth the present value of
their future cash flows, preferred stock is worth
the present value of the indefinite stream of
dividends.
D p
P p
k
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Preferred Stock
Example 8.6
Q: Roman Industries’ $6 preferred originally sold for $50. Interest
rates on similar issues are now 9%. What should Roman’s
preferred sell for today?
Example
A: Just substitute the new market interest rate into the preferred
stock valuation model to determine today’s price:
$6
P
0 $6 7
6
6.
0
.9
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Characteristics of
Preferred Stock
Cumulative Feature - can’t pay common dividends
unless cumulative preferred dividends are current
Never returns principal
Stockholders cannot force bankruptcy
Receives preferential treatment over common
stock in bankruptcy
Lower priority than bondholders
No voting rights
Dividend payments not tax deductible to the firm
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Securities Analysis
The art and science of selecting investments
Fundamental analysis looks at a
company’s business to forecast value
Technical analysis bases value on
the pattern of past prices and
volume
The Efficient Market Hypothesis (EMH) -
financial markets are efficient since new
information is instantly disseminated
Impossible to consistently beat the market
30
Options and Warrants
Options and warrants make it possible to
invest in stocks without holding shares
Options Warrants
Gives the holder the Similar but less common
temporary right to buy
or sell an asset at a
fixed price
Speculate on price
changes without holding
the asset
31
Stock Options
Stock options speculate on stock price
movements
Trade in financial markets
Call option — option to buy
Put option — option to sell
Options are Derivative Securities
Derive value from prices of underlying securities
Provide leverage – amplifying returns
32
Writing Options
People write options for the premium income, hoping
that the option will never be exercised
Option writers give up what option buyers make
Covered option — writer owns underlying stock
Naked option — writer does not own the underlying
stock
Purchase it at the current price if exercised
33
Warrants
Options Warrants
Trade between investors, Issued by underlying company
not between the When exercised – new stock is
companies that issue the issued and company receives the
underlying stocks exercise price
Secondary market Primary market instruments while
instruments options are secondary market
instruments
34
Warrants
Similar to calls with a longer expiration
period (several years vs. months)
Issued as a “sweetener” (especially for
risky bonds)
Can generally be detached from another
issue and sold separately
35
Employee Stock Options
More like warrants than traded options
Expire after several years
Strike price set far out of the money
May receive options in lieu of salary increases
Wanted if future expectations are good
Companies offering options may pay lower
salaries
Attract employees not otherwise affordable
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Employee Stock Options
Executive Stock Option Problem
Senior executives may receive most of the
stock options
Provide an incentive for executives to
misstate financial statements and inflate
stock prices
Negatively impacts a firm’s pension plan if heavily
invested in its own stock
As a result of overhauling financial reporting,
companies must recognize employee stock options as
expenses when they are issued
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