The Valuation and
Characteristics of Stock
Chapter 7
© 2003 South-Western/Thomson Learning
Common Stock

Background

Stockholders own the corporation, but in many
instances the corporation is widely held
• Stock ownership is spread among a large number of people

Because of this, most stockholders are only
interested in how much money they will receive as a
stockholder
• Most equity investors aren’t interested in a role as owners
2
The Return on an Investment in
Common Stock

The future cash flows associated with stock ownership consists of



Dividends
The eventual selling price of the shares
If you buy a share of stock for price P0, hold it for one year during
which time you receive a dividend of D1, then sell it for a price P1,
you return, k, would be:
k=
D1+ P1 -P0 
P0
or
k=
D1
P0
dividend yield
+
P1-P0 
A capital gain (loss) occurs
if you sell the stock for a
price greater (lower) than
you paid for it.
P0
capital gains yield
3
The Return on an Investment in
Common Stock

We can solve the previous equation for P0, the stock’s
price today:
kP0  D1   P1  P0 
P0  kP0  D1  P1
1  k  P0  D1  P1
D1  P1
P0 
1  k 

The return on our 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

The expected receipt of dividends and the
future selling price of stock is similar to
what a bondholder expects in terms of
interest and principal repayment
• However, with bondholders:
•
•
•
•
A guarantee is associated with their interest payments
Interest payments are constant
The maturity value of a bond is fixed
When the bond matures, the investor receives contracted
par or face value from the issuing company
• When stock is sold, the investor receives money from another
investor
5
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

Must make assumptions about what the future
dividends and selling price will be
• Discount these assumptions at an appropriate interest rate
P0 = D1 PVFk,1   D2 PVFk,2  
 Dn PVFk,n   Pn PVFk,n 
6
The Intrinsic (Calculated) Value
and Market Price

A stock’s intrinsic value is based on
assumptions made by a potential investor

Must estimate future expected cash flows
• Need to perform a fundamental analysis of the
firm and the industry

Different investors with different cash flow
estimates will have different intrinsic
values
7
Growth Models of Common
Stock Valuation

Realistically most people tend to forecast
growth rates rather than cash flows

Because forecasting exact future prices and
dividends is very difficult
8
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
P0 =

D1
D2


2
1  k  1  k 

Dn
1  k 
n

Pn
1  k 
n
An Infinite Stream of Dividends

Many investors buy a stock, hold for awhile, then sell, as
represented in the above equation
• However, this is not convenient for valuation purposes
9
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:
Pn =

Repeating this process until infinity results in:

P0  
i=1

Dn + 1
Dm
Pm
+…+
+
m-n
m-n
1 + k 
1 + k 
1 + k 
Di
1 + k 
i
Conceptually it’s possible to replace the final
selling price with an infinite series of dividends
10
Working with Growth Rates

Growth rates work like interest rates

If growth is expected to be 6% next year
then $100 experiencing a 6% growth will
increase by $6, or $100 x 6%
• The ending value after 6% growth will be $106, or
$100 + $6, or $100 x (1.06)
11
The Constant Growth Model


If dividends are assumed to be growing at a constant rate forever
and we know the last dividend paid, D0, then the model simplifies
to:
1
 D 1 i
 
P0   0
i
i=1 1 + k 
Which represents a series of fractions as follows
P0 =

D0 1  g
1  k 

D0 1  g
1  k 
2
2
D0 1  g
3

1  k 
3


If k>g the fractions get smaller (approach zero) as the exponents
get larger


If k>g growth is normal
If k<g growth is supernormal
• Can occur but lasts for limited time period
12
Constant Normal Growth—The
Gordon Model

Constant growth model can be simplified
to
K must be
D1
P0 
k g

greater
than 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
13
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
14
The Expected Return

Can 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
15
Two Stage Growth

At times a firm’s future growth may not be
expected to be constant


For example, a new product may lead to temporary
high growth
The two-stage growth model allows us to value
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
16
Practical Limitations of Pricing
Models

Stock valuation models give approximate results
because the inputs are approximations of reality

Bond valuation is precise because inputs are exact
• With bonds future cash flows are contractually guaranteed in
amount and time

Actual growth rate can be VERY different from
predicted growth rates


Even if growth rates differ only slightly, it can make a big
difference in our decision
So, it’s best to allow a margin for error in your
estimations
17
Practical Limitations of Pricing
Models

Stocks That Don’t Pay Dividends


Some firms don’t pay dividends even if they are
profitable
Many companies claim they never intend to pay
dividends
• These firms can still have a substantial stock price

Firms of this type typically are growing and are using
their profits to finance their growth
• However rapid growth won’t last forever
• When growth slows, the firm will begin paying dividends
• It’s these distant dividends that impart value
18
Some Institutional Characteristics
of Common Stock

Corporate Organization and Control





Controlled by Board of Directors (elected by stockholders)
Board appoints top management who then appoint
middle/lower management
Board consists of: top management and outside members
(major stockholders, top executives at other firms, former
presidents, etc.)
In widely held corporations, top management is effectively in
control of the firm because no stockholder group has enough
power to remove them
Preemptive Rights


If firm issues new shares, existing shareholders have right to
purchase pro rata share of new issue
Common, but not required by law
19
Voting Rights and Issues

Each share of common stock has one
vote in the election of directors, which is
usually cast by proxy

A proxy fight occurs if parties with conflicting
interests solicit proxies at the same time
20
Majority and Cumulative Voting



Majority voting gives the larger group control of
the company
Cumulative voting gives minority interest a
chance at some representation on the board
Shares With Different Voting Rights

Different classes of stock can be issued with
different rights
• Some stock may be issued with limited or no voting rights
21
Stockholders’ Claim on Income
And Assets


Stockholders have claim on the firm’s net
income
What is not paid out as dividends is retained
(Retained Earnings) for investment in new
projects


Leads to future growth
Common stockholders are last in line to receive
income or assets, and bear more risk than
other investors

However, residual interest is large when firm does
well
22
Preferred Stock

Preferred stock is often referred to as a
hybrid between common stock and bonds
because:
No maturity date (like common stock)
 Fixed dividend payment (similar to bond
interest payment)

23
Valuation of Preferred Stock


There is no growth rate in preferred stock
dividends, so growth rate equals 0
The dividend at time 1 is the same as the
dividend at time 0, so there is usually no time
period associated with the numerator

Valuation is that of a perpetuity
P
p

D
p
k
24
Characteristics of
Preferred Stock

Cumulative Feature






Common dividends can’t be paid unless the dividends on cumulative
preferred are current
Preferred stock never returns principal (like a bond does upon
maturity)
Preferred stockholders cannot force a firm into bankruptcy (like
bondholders)
Preferred stockholders received preferential treatment over
common stockholders in the event of bankruptcy, but have a lower
priority than bondholders
Preferred stockholders do not have voting rights (like common
stockholders do)
Dividend payments to preferred stockholders are not tax
deductible to the firm
25
Securities Analysis




Securities analysis is the art and science of
selecting investments
Fundamental analysis looks at a company and
its business to forecast value
Technical analysis bases value on the pattern
of past prices and volumes
The Efficient Market Hypothesis says
information moves so rapidly in financial
markets that price changes occur immediately,
so it is impossible to consistently beat the
market to bargains
26