Equity Valuation Formulas
1
Consider a company that pays expected dividends
D
1
,
D
2
,
D
3
going out forever. The
price of this company would then be:
P
0
=
D
1
1 +
r
+
D
2
(1 +
r
)
2
+
D
3
(1 +
r
)
3
+
· · ·
.
where
r
is the discount rate for investments of similar risk. Its hard to forecast dividends
for every period going forward. So we begin with some simplifying assumptions.
Constant Dividends
Suppose that the stock pays the same
dividend every year forever:
P
0
=
D
1 +
r
+
D
(1 +
r
)
2
+
· · ·
What would the price be in this case?
P
0
=
D
r
This formula can be related to the priceearnings ratio. To do this, say that the relation
ship between earnings and dividends is approximated by
D
= (1

b
)
E
where
b
denote the
plowback ratio
– the portion of earnings that is kept in the firm. 1

b
is paid out as dividends. Substituting in
P
0
=
(1

b
)
E
r
Then, the priceearnings ratio equals:
P
0
E
=
1

b
r
1
Notes for Finance 100 (sections 301 and 302) prepared by Jessica A. Wachter.
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Constant Dividend Growth
In reality, some companies grow faster than others. A model of firm value based on
level dividends alone will fail to take this into account. Suppose
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 Fall '09
 Finance, Valuation, Dividend, Financial Ratio, Dividend yield, P/E ratio, Equals sign

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