

Financial
Management MGT201
VU
Lesson
17
COMMON
STOCK PRICING AND DIVIDEND
GROWTH MODELS
Learning
Objectives:
After
going through this lecture,
you would be able to have an
understanding of the following
topics
·
Common
Stock pricing
·
Dividend
Growth Models
In
this lecture, we continue
our discussion on the topic of stock
price valuation.
In
previous lecture, we have discussed
that there are two types of
Shares (or Stocks or
Equity
Securities)
1.
Preferred Stock:
These
stocks have regular Constant / Fixed
Future Dividends Certain for
the Preferred
Shareholders.
Use old Perpetuity Cash
Flow Pattern and formulas to
estimate theoretical
Fair
Stock Price.
2.
Common Stock:
Theses
stocks have variable future
dividends expected by the common shareholders.
Use Zero
&
Constant Growth Models to simplify
future Dividend forecasts in estimated
Theoretical Stock Price
(or
PV) equation. There dividend
depend upon the income earned by the
company and also upon
the
management
decision regarding the dividend
declaration.
Both
stocks represent ownership of Real
Assets in Company.
Dividends
are the Shareholder's portion of the
Distributed Net Income. The
value of direct
securities
(piece of paper) derived from the
cash flows generated from
the underlying real
assets.
There
are two types of Investment
Time Horizons
1.
Finite Investment:
In
this duration of our
investment is limited. Cash
inflow from Forecasted
Selling
Price
must be taken into account
in price estimate.
2.
Perpetual
Investment:
It
is very long term horizon
for long term investment. It is Perpetual
so Forecasted Selling Price
not
significant
and can be eliminated. If
you are planning to buy and
hold the share for 20 or 30
years then
you
can consider it as a long term assets.
Similarly, an investment in the share
for the period of one or
two
years
Value
of a Share (which is a Direct
Claim Security) can be estimated
based on the Cash Flows
that
is
generates. A Share generates
Cash Dividends just like a
Real Asset Project generates Cash
Income.
The
Formulas for the theoretical price
valuation vary depending
upon the time horizon. As
in
previous
lectures the formula for
preferred shares varies depending on
whether your time horizon
is
finite
or perpetual.
Let
us compare both common shares and
preferred shares with the
help of numerical
example.
Example:
Company
ABC has issued 2 Types of
Shares (both of Par Value =
Rs 10) and you
are
considering
Investing in both shares for
2 years because you think
the price will rise to Rs 13 by
then.
The
Market Risk Free Return
(Opportunity cost) is 10%
pa.
ABC
Preferred Shares:
Dividend
Fixed by the Company at Rs 2 per share
per year. Your required rate of
return for the
risky
preferred shares is 15%.
This is the rate of return that
you expect to get if you take
risk of
investing
the money in preferred shares. Preferred
shares are considered to be more risky
then the
deposit
in the bank. So, our
required rate of return in case of
preferred stock should be higher
then 10%.
ABC
Common Shares:
Dividend
varies. After analyzing the Company's
Annual Report, Balance Sheet,
Income & Cash
Flow
Statements, you forecast the
future Dividends to be Rs 2 in the first
year and Rs 4 in the second
year.
The required rate of return
does not have to be identical to the
required rate of return on
preferred
shares.
As, there is no guarantying you a
fixed rate of return on common shares.
Your required rate of
return
for the more risky common shares is
20% pa. Finally, based
upon the analysis of financial
statements
of the company you expect that the price
of share will rise to Rs. 13
after 2 years. You
planned
to look at different investment
cases you are interested in
estimating what the theoretical
market
price
of this share should be if
you invest perpetually and
you are also interested in the
price of the share
78
Financial
Management MGT201
VU
if
you invested for a short
period time. So, for the
case of preferred stock, we calculate the
expected
market
price for long term
investment would be.
Solution:
Preferred
Stock (Risky
Investment: rPE= 15%
> 10%=risk free)
Perpetual:
PV
= DIV1/ rPE
= 2 /
15% = 2/0.15
= Rs
13.33
Now
in case of finite
investment
2
Year (Finite): PV=2/1.15+ 2/
(1.15)2
+13/
(1.15)2
=Rs
13.08
Common
Stock Valuation (More
Risky Investment: rCE=
20%)
Perpetual
Investment: PV =? We don't have enough
Dividend forecast data in
order to calculate
the
value for 20 or 30 years
from now. We discuss the
solution of this problem
later in the lecture
.Here
1.2
= (1+20%). We use Rs 13 because we expect
to sell these shares for
Rs.13 after 2 Years.
2
Year (Finite): PV
=2/1.2
+ 4/
(1.2)2
+13/(1.2)2
= Rs
13.47
Interpretation:
In
our example, Common Stock
has higher Intrinsic Present
Value or Fair Value (or
Estimated
Market
Price) than Preferred Stock because
Common Stock offers higher expected
Dividends which
more
than compensates for the
higher risk of the common stock. We
discuss this in detail when
we
study
the topic of Risk and
Return.
Share
Values:
Fair
Value VS Market
Price
Fair
Value:
It
is estimated from PV Equation. We calculate
this from NPV equation
based on a required rate
of
return as the discount rate or r in the
equation. This is very
important to understand because the
ROR
is
our personal ROR and its value varies
depending on the investor who is
doing the calculation.
Every
person
has a different Risk
Profile. Therefore, Fair
Value varies depending on the investor
who is doing
the
calculation and his/her Personal
Required Return.
Market
Price:
It
is actual price at which it is bought or
sold. It is determined by Share's
Demand/Supply &
Investor
Perceptions & Psychology about the
company behind the share. Market Price is
almost
identical
for everyone.
In
Efficient
Markets where investors
have almost equal information, Fair
Value will basically
match
Market Price. But, temporarily
they can differ. Then
what happens? Usually, you
think that
whether
the price of the thing purchased by
you have that much price or
not. Similar question will
be
asked
in share trading
If
Market
Price < Fair Value: then
Stock is under valued by the
Market. It is a bargain and
investors
will rush to buy it.
Therefore, Share's Demand will rise and
Market Price will rise to match
the
Fair
Value. Dynamic
Equilibrium.
If
Market
Price > Fair Value then
Stock is Over Valued
Share
Price Valuation Perpetual Investment in Common
Stock:
Perpetual
Investment in Common Stock
The
PV Formula would require us to make
Dividends Forecast for every
year in future. Which
is
not feasible for us?
Therefore, we can not use
the old version of PV formula. We
use 2 approaches to
solve
this problem.
Zero
Growth Dividends
Model:
In
this we assume Perpetual Dividends at
Zero Growth i.e. Constant Perpetual
Dividends.
Similar
to Preferred Stock Valuation Formula
i.e. DIV1 = DIV 2 = DIV3 In this method
the
simplification
we made is this
In
this there is a Fixed Regular
Dividends Cash Flow Stream
for every year in
future.
This
is very simple method as the dividend
for first year and the last
year remains identical. It is
a
simple
perpetuity model. Therefore we
use Perpetuity
Formula.
Which is Similar to Preferred
Stocks
(Perpetual
Investment) except Preferred Dividends
(which are declared by the Company)
not same as
Common
Stock Dividends (which are
estimated).
The
Formula for common stock
PV
= Po*= DIV1 /
(1+ rCE) + DIV1 /
(1+ rCE) 2 + DIV1 /
(1+ rCE) 3 +
... +...
79
Financial
Management MGT201
VU
=
DIV
1 / rCE.
Po*
is the Expected (Theoretical) Present Price.
The Price depends on DIV1 which is
the
Expected
Future Dividend for Year 1
(and all other years in
future).There is difference in case
of
common
stock & preferred stock. In common stock we assume
the constant growth but in
preferred
stock
the company has assured the preferred
stockholder that he will get
fixed rate of dividend.
Constant
Growth Dividends
Model:
In
this, we need only to
forecast the next year
dividend and assume constant
dividends Growth
at
Inflationary Growth Rate "g"
which equals 5  10% pa
(depending on country).
DIVt+1
=
DIVt
x (1 + g)
t.
t =
time in years i.e. If g =
10%
Dividends
Cash Flow Stream grows
according to the Discrete Compound Growth
Formula
DIVt+1
= DIVt x (1 + g) t.
t
= time in years.
So
if you have estimated the present
Dividend (DIVo) or the next
year's Dividend (DIV1)
then
you
can estimate all future
dividends using this
formula. In this, the trick is
how to pick the right
growth
rate.
Generally, we pick the rate of growth of
inflation. As common stock holders we assume
that the
dividends
are continue to grow at
constant rate which is equal to rate of
growth of inflation. If
inflation
rate
is 10% then the dividend
will grow at 10%.you have
dividend of Rs 10 in first year then
you will
have
dividend of Rs 10 plus 10% of Rs 10
which is equal to Rs.11.
Estimate
Growth Rate = "g" using:
1.
Financial Statements (calculate
Dividends' growth rate)
2.
Inflationary Growth Rate of
Economy (say 5  10%
pa)
Formula:
PV
= Po* =DIV1 (1+g) /(1+
rCE ) +DIV1
(1+g)2 / (1+ rCE )2 +
DIV
1 (1+g)3 / (1+ rCE )3 +
...
=
DIV
1 / (rCE  g)
DIVI=
dividend for first
year
In
this we can derive the
answer as sum of geometric
series. Growing Perpetuity
formula.
Example:
You
are considering making a
very long term investment in the common
stock of Company ABC.
Your
Required Return on the investment
(based on risk) is 20%
(rCE). The present
Dividend
offered
by Company ABC is Rs 4. Par
Value is Rs 10.
Dividend
Yield Pricing for Common
Stock under Perpetual
Investment
Zero
Growth Model
Pricing
PV
= Po* = DIV1 / rCE
= 4 /
0.20 = Rs 20
Constant
Growth Model Pricing (assume
g=10%)
PV
= Po* = DIV1 / (rCE
g) =
4 / (0.20.1) = Rs 40
Interpretation
of Result:
Constant
Growth Pricing gives a
higher Estimate of Present Price because
it assumes perpetual
10%
compounded growth in dividends
forever
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