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# Berkshire Hathaway Inc. Message Board

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• Novalis_97 Novalis_97 Aug 16, 1998 6:17 PM Flag

## The intrinsic value of Pepsi

The purpose of the newspaper example was to show
how an estimate for intrinsic value can dramatically
change if the assumption for earnings growth rate
changes. He's saying that if the newspaper's earnings
growth rate changes from 6% to 0%, the intrinsic value
estimate changes dramatically from \$25 mil. to only \$10
mil. He's definitely using the "perpetual annuity (aka
perpetuity)" formula. He says, "(in the past) ownership of a
media property could be construed as akin to owning a
perpetual annuity set to grow at 6% a year." Look at the
math and you'll see that he really is using the
perpetuity formula.

In the first case, when g =
6%:

PV = C / (r - g) = \$1 mil. / (0.10 - 0.06) = \$1 mil.
/ 0.04 = \$1 mil. / (1/25) = \$1 mil. * 25 = \$25
mil.

In the second case, when g has been reduced to
0%:

PV = C / (r - g) = \$1 mil. / (0.10 - 0.00) = \$1 mil.
/ 0.10 = \$1 mil. / (1/10) = \$1 mil. * 10 = \$10
mil.

There's no debate that Buffett uses the perpetual annuity
formula to calculate intrinsic value. In the 1992
Shareholder Letter, Buffett states that in his book, "The
Theory of Investment Value," John Burr Williams set
forth the "equation for value." And what is this
equation? It's the equation for a perpetuity! Go look it up
yourself! Except that Williams uses dividends as C, while
Buffett in his 1986 Annual Report stated he uses "owner
earnings."

In the newspaper example, Buffett doesn't give a
reason for why he uses 10%. He just uses it. He says,
"Say that a discount rate of 10% was used to determine
the present value of that earnings stream." I've
already pointed out that this is higher than the 7.7%
long-bond yield at the time. If Buffett uses it, it's good
enough for me!

If you recognize what a perpetuity
is, that its coupons are paid out FOREVER, you'd want
to make sure your discount rate, r, reflects what
the interest rate is not just now (or in the past
several years) but out until Judgment Day. If you're
using 7% as your discount rate, you're saying that, on
average, the discount rate from now until Judgment Day
will stay at 7%. But you don't know this and,
furthermore, it's not likely to stay at 7% in the future.
Essentially, you're making a prediction about future interest
rates but, as you said yourself, no one knows what
future interest rates will be. Just because interest
rates have been low in recent years doesn't mean they
will continue to be low in the future.

To be
on the safe side -- not because I or Buffett can
predict future interest rates -- you want to use a
conservative (i.e., higher) discount rate. If Buffett uses 10%
-- which is the historical average -- then people
who want to calculate intrinsic value like he does
should use it, too. By using 10%, you aren't using an
unrealistically conservative discount rate, either. You're just
using a rate that, over time, will likely better
reflect future rates than 7%, based on history. As a
result, your IV calculation based on 10% is likely to be
accurate rather than an underestimate. On the other hand,
the danger of using 7% is that your IV estimate is
likely to be an overestimate and, even if you cut that
IV by 50%, you're not going to end up truly buying a
company for 50% of its true IV.

Here's what
Buffett said not too long ago at the Univ. of
Washington:

�There�s no magic to evaluating any financial
instrument...If every financial asset were valued properly, they
would all sell at a price that reflected all of the
cash that would be received from them forever until
Judgment Day, discounted back to the present at the same
interest rate. There wouldn�t be a risk premium, because
you�d know what coupons were printed on this �bond�
between now and eternity. That method of valuation is
exactly what should be used whether you�re in 1974 or
you�re in 1998.�

We want to use a discount rate
that reflects not just recent years but will reflect
what the likely rate will be from now until Judgment
Day.

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