What if we expect that future returns
will grow, with inflation and as an investment
progresses? If returns grow at a constant rate
(g), the DCF formula produces one of the most
often-used formulas in stock valuation -- known
as the "Gordon-Shapiro dividend discount
model" or the "Gordon model."
P0 =D0×(1+g)1
/ (1+i)1 +D0×(1+g)2
/ (1+i)2 + ... + D0×(1+g)inf
/ (1+i)inf
P0 = D1
/ (i - g)
or
P0 = D0
(1 +g) / (i - g)
|
P0 |
present value of common stock
(with constant growth returns) |
D0 |
most recent per-share dividend |
D1 |
per-share dividend after one period of growth
[D1 = D0 (1 + g)] |
i |
required return (discount rate) for each
year t |
g |
rate of growth |
inf |
infinite time period |
Notice that this model makes heroic (assuredly
wrong) assumptions about the flat continuity of
growth and that extrapolation from past earnings
reflects likely future earnings. But at least
it's a start. |
Example
Company is growing. It pays most of its
earnings as dividends, but retains some
earnings for future growth. The practice
has worked well, as its history of growth
suggests.
What is the value of Company stock, based
on dividend returns? (More>>) |
Year |
Dividend/Share |
1 |
1.00 |
2 |
1.06 |
3 |
1.15 |
4 |
1.25 |
5 |
1.36 |
6 |
1.44 |
7 |
1.59 |
|
|
1.3.5 Present Value of a Perpetuity