Corporate Finance

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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
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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
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