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view the rest of the postsI don't think Hagstrom is far off the mark. In
the 1991 Letter to Shareholders, Buffett used 10% as
his discount rate in an example to find the intrinsic
value of a newspaper, but at year-end 1991, the 30-yr
bond rate was 7.7%. So Buffett was additing 2.3% to
the discount rate at the time to do the discounting.
Remember what the discount rate is used for: it's used as
the discount rate in the perpetual annuity formula,
PV = C / (r - g). A perpetuity's coupons are paid
yearly FOREVER, so you want to make sure the discount
rate, r, accurately reflects what the discount rate
will be not just now but from now until
eternity.
Buffett made comments a few months ago saying that if
both interest rates stayed low and ROE's stayed high,
current high stock prices could be justified. But he said
it's not likely that either of these conditions will
continue to be true in the future, so to be on the safe
side, you should jack up the discount rate. 10% is good
(and even higher than Hagstrom's) because Buffett
himself used it in his 1991 Shareholder letter example
(see the section entitled, "Some Valuation Math.")
I understand your logic and I appreciate your
reply to my message. However, you are off the mark a
little.
First, the Buffett example about the
newspaper valuation was not supposed to be an exact example
of how he does it. He was using that as an example
of how the market values stocks generally.
I've
read that section about 50 times and nowhere does he
specifically come out and say that's how he does it or how he
figures out the discount rate. I have read quotes by him,
however, in which he says you should not use any risk
premium, but use a margin of safety when estimating future
growth in earnings. Come to think of it, even the
Hagstrom book quotes Buffett as saying that. The reason
Hagstrom's valuations all came out so low (i.e. for Disney,
Coke, ABC, etc.) is because Hagstrom didn't cut 50% off
the intrinsic value as an acceptable buy price. He
just took the full I.V. using the 9% rate as the buy
price, which of course was higher than the current
market price of those stocks. Almost ANY stock has an
I.V. higher than the market price if you do it this
way. Go ahead and discount Coke's earnings out right
now using a 12% growth rate for 10 years and 5% after
that, and a 9% discount rate. You'll see what I mean.
It gives an I.V. higher than today's market price.
Would you then conclude that Coke is undervalued at 51
times earnings?
Of course not. You have to discount
Coke's earnings out at about 7%, and then take 50% of
the I.V. as an acceptable buy price. Even then, it's
overvalued.
If you try to predict earnings AND future interest
rates, you're trying to do the inhuman. No one can
predict future interest rates more than a few months out.
In 1991, if rates were 7.7% when Buffett wrote his
piece and he used a 10% discount rate, that would be a
30% premium over the then current long bond rate.
Today's long bond rate is 5.6%, and 30% above that is
about 7.25%. You have to use the percentage premium he
used, not the absolute number. Otherwise, the logic is
flawed. So I guess maybe I should be using 7.25% instead
of 7%, but again the Buffett example was not meant
to be that specific.
I still say you can't
predict something like interest rates, whether they'll go
up or down, and so the only thing you can do is use
the current rate and go off that. It's hard enough to
predict future earnings. Use a margin of safety for that.
If interest rates go down from here (they just
might), you may be using a margin of safety on your
discount rate that prevents you from buying some great
stocks at bargain prices.
Forgot to include it in the title again.
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.
One of the problems with using the perpetuity
formula for anything during times of very low interest
rates, (such as now, as the long bond is at the lowest
rates since being issued in the 70's), is that prices
can quickly approach infinity. This is due to the
convex nature of a bond's yield. I am sure most of you
are familiar with basic bond math, so suffice it to
say that it takes a correspondingly greater increase
in the price of a bond to go from 6% to 5% than from
10% to 9%.
Let's say that we are now in a
period where interest rates will remain permanently low,
due to, say, massive global oversupply, Asia's
recession, whatever. Now, if you were to use the long bond's
yield of 5.537% to discount your growth rate of 5%, the
prices approach absurd levels. At these rates, every
dollar of earnings would be valued at over 186 dollars!
The same dollar using a discount of 7% would be worth
50 dollars, still not cheap. And as rates go lower,
the problem becomes worse, especially when you
consider what happens if (when) rates start to rise again.
These astronomically high valuations quickly plummet to
earth, causing massive asset devaluations.
So,
if you have a company expected to grow at 5%
forever, and rates continue to go lower, how do you use
this equation effectively??? Even if you use the 50%
of intrinsic value method, you still are paying high
prices for stocks.
And, my record speaks for itself.
The answer is you use 10% like Buffett, not 5.5%. You use the historical average.