Corporate
Finance FIN 622

**VU**

**Lesson
07**

**COMMON
STOCK VALUATION (Dividend
Models)**

A
company can raise capital
from variety of sources. We already
covered the loans as a potential
source of

capital
enhancement. Bonds are a
kind of loan that is different
form a bank loan.

In this
segment, we know that a
company may sell its
shares to general public (primary
market) to gather

funds
needed for investment purposes.
These shares are significantly
different from the Bonds in
many

aspects.
For example, the salient
features of a stock or share
are as under:

No
promised cash flow for
dividend

No
date of maturity Investment
for ever

Problems
in observing rate of return

Common
stock, also referred to as common shares,
is as the name implies the most
usual and commonly

held
form of stock in a corporation.
The other type of shares
that the public can hold in
a corporation is

known
as preferred stock. Common stock that
has been re-purchased by the
corporation is known as

treasury
stock and is available for a
variety of corporate uses.

Common
stock typically has voting
rights in corporate decision matters,
though perhaps different
rights

from
preferred stock. In order of priority in
a liquidation of a corporation, the
owners of common stock
are

near
the last. Dividends paid to the
stockholders must be paid to preferred
shares before being paid to

common
stock shareholders.

**COMMON
STOCK VALUATION:**

The
following models are commonly
used to valuate the common
stock:

**DIVIDEND
DISCOUNT MODEL:**

It is
not an easy job to predict or
forecast future stock
price.

Dividend
discount model states that today's
price is equal to the present
value of all future
dividends.

After
One year

P0 = Div + P1 / (1 +
r)

After
2 years the value of stock
is:

=div1/ (1+r) + div2+P2/ (1+r) 2

After
3 years the value of stock
is:

=div1/(1+r) + div2/(1+r)2
+ div3+P3/(1+r)3

When
the time horizon is infinitely far,
then we do not consider the
final price as it has no
present value

today.
This mean the PV of stock
depends only on future
dividends.

**DIVIDEND
GROWTH MODELS:**

Assumed
NO GROWTH by the company

Company
pays out all as dividend
what it earns every
year.

It
means that NOTHING is reinvested in
business.

It
means that investors may
forecast that future dividends
will not increase. Dividends
over the

years
are at the same level
perpetuity.

If the
value of stock is the PV of all
future dividend then

PV = DIV /
r

When
company pay out everything as
dividend then earnings and
dividend will be equal and
PV can be

calculated
as:

PV =
EPS / r

**CONSTANT
GROWHT MODEL:**

Assume
that dividends will grow at a constant
growth rate. For example 5%
per year.

It
means that Dividend of Rs. 2
per share at 5% constant
growth rate is

Div1 = 2

22

Corporate
Finance FIN 622

**VU**

Div2 = 2 x 1.05 = 2.10

2

Div3 = 2 x (1.05) = 2.205

Fitting
these into formula:

= D1/1+r + D1(1+g)/(1+r) + D1(1+g) /(1+r) ....

2

2

3

2

3

=
2/1.12 + 2.10/ (1.12) +
2.205/ (1.12) = 1.79 + 1.67
+ 1.57 + ....

Although
the number of terms is infinite, the PV of
dividend is proportionately smaller
than the preceding

term
and this will continue as
long as growth rate is less
than the discount rate.

Because
the far distant dividends will be close
to zero, the sum of all of
these terms is finite
despite the fact

that
an infinite number of dividends will be
paid.

So we
can write equation
as:

P0 = D1 x (1+g) / (r
g)

This
is known as Constant-growth Dividend
Discount Model or Gordon
Growth Model.

For
example:

2 x
1.05 / .12 - .05 =
30.00

Gordon
model is valid as long as g < r

**Example:**

Dividend
paid = Rs. 2.30

Growth
rate = 5%

Required
return = 13%

What
will be the value of stock after
five years?

5

D5 = 2.30 X (1.05) =
2.935

P5 = 2.935 x 1.05 / (.13
-.05) = 38.53

**Example:**

The
next dividend of a company
will be Rs 4 per share. Investors
demand 16 percent return on
share

having
same risk level as of this company. The
dividend growth is 6% per
year. Calculate the value of
this

company's
stock today and in four
years using dividend growth
model.

**Solution:**

Next
dividend has already been
given:

Po = D1 / (r
g)

Po = 4 / (.16 -.06)

Po = 40

Price
in 4 years:

D4 = 4 x (1.06) = 4.764

3

P4 = 4.764 x 1.06 / (0.16
-0.06) = 50.50

23