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:

๏ฟฝThere๏ฟฝs 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๏ฟฝt be a risk premium, because

you๏ฟฝd know what coupons were printed on this ๏ฟฝbond๏ฟฝ

between now and eternity. That method of valuation is

exactly what should be used whether you๏ฟฝre in 1974 or

you๏ฟฝre in 1998.๏ฟฝ

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.