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Units, Constants and Useful Formulas
Dividend Discount Formula
-------------------------
The dividend model calculates the true value of a firm based on
the dividends the company pays its shareholders.
The market capitalization rate (expected return) can be obtained
from:
r_{E} = {D(1) + P(1) - P(0)}/P(0)
Therefore,
P(0) = {D(1) + P(1)}/(1 + r_{E}) and P(1) = {D(2) + P(2)}/(1 + r_{E})
Therefore, we can write:
P(0) = {D(1)/(1 + r_{E}) + {D(2) + P(2)}/(1 + r_{E})
This can be generalized to:
t = ∞
P(0) = Σ(D(t)/(1 + r_{E})^{t})
t = 1
Thus, P(0) is equal to the sum of discounted dividends from year
1 to the final period. For an infinite holding period the formula
reduces to:
P(0) = D(1)/r_{E}
Or, if the dividend is expected to grow:
P(0) = D(1)/(r_{E} - G)
where G is the dividend growth rate which can be obtained from:
G = ROE * Earnings Retention Ratio
ROE = EPS/Book value per share
Retention ratio = 1 - {D/EPS}
Example,
Price = $45
Dividend = 60c/share
EPS = $2.40
Book value = $15.00
Dividend yield = D(1)/P(0) = .60/45.00 = 1.3%
ROE = 2.40/15.00 = 16%
Retention ratio = 1 - 0.60/2.40 = 0.75
Therefore,
G = 0.16 * 0.75 = 12%
so
r_{E} = 0.60/45.00 + 0.12 = 13.3%
- r_{E} should not be based on one stock but on a large sample of
equivalent risk securities.
- May not apply to high growth rate companies since growth may
not be sustainable over the long haul.
The No Dividend Case
----------------------
What if the company doesn't pay a dividend or its dividend pattern
is irregular? Instead of looking at dividends, the DCF model uses
a company's discounted future cash flows to value the business. The
big advantage of this approach is that it can be used with a wide
variety of firms that don't pay dividends, and even for companies
that do pay dividends. The free cash flows are generally forecasted
for five to ten years, and then a terminal value is calculated to
account for all the cash flows beyond the forecast period. So, the
first requirement for using this model is for the company to have
predictable free cash flows, and for the free cash flows to be positive.
So, in order to use the DCF model most effectively, the target company
should generally have stable, positive and predictable free cash flows.