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# The Coca-Cola Company Message Board

• Novalis_97 Novalis_97 Aug 20, 1998 3:40 AM Flag

## Beethoven_57: dividend discount model

Here is what I think you are looking for, an
explanation of why in the dividend discount model, g cannot
exceed r. The excerpt is from the finance textbook,
"Essentials of Investments," by Bodie, Kane, and Marcus;
McGraw-Hill; 1998; page 360:

"The constant growth DDM
(i.e., PV = C / (r - g)) is valid only when g is less
than r. If dividends were expected to grow forever at
a rate faster than r, the value of the stock would
be infinite. If an analyst derives an estimate of g
that is greater than r, that growth rate must be
unsustainable in the long run. The appropriate valuation model
to use in this case is a two-stage DDM."

So
you see, g may be greater than r in the short-run --
but not in the long run. As I mentionned before,
Buffett plugs in "owner earnings" instead of dividends as
"C" in PV = C / (r - g). Incidentally, you'll find a
similar paragraph like the above in every finance
textbook you open (look up "dividend discount model" in
the index).

being able to use the perpetuity formula when g is
greater than r is well-taken, however the case never
arises that a company's g will be greater than the
discount rate, r, in the long run. A company's g may be
greater than r temporarily but eventually it will fall
below r. The reason is because of a company's life
cycle, wherein a company will experience a growth or
"exponential" stage, followed by a slower "maturity" phase. For
such companies, a "two-stage" dividend discount model
is appropriate, the first stage corresponding to the
company's exponential phase, wherin g > r, and the
second stage corresponding to its maturity phase,
wherein g < r. Buffett himself often talks about
Berkshire not being able to grow at 24% forever. He cites
Carl Sagan's example of bacteria: though they could
double in mass every 20 minutes forever into the future,
they don't because the world (and bacterial substrate)
is finite. Likewise, any company's positive-NPV
projects are finite. Coke will reach its "maturity" phase
when every man, woman, and child on Earth drinks 10
Cokes a day (like I do).

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