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view the rest of the postsBuffett calculates the intrinsic value of a stock
the same way he calculates the intrinsic value of a
type of bond called a perpetuity. He believes there is
a select group of companies in the world (like Coke
and Gillette) whose cash flows are as reliable and
predictable as the coupons on a perpetuity bond. Thus,
Buffett uses the perpetuity formula to determine the
intrinsic value of such companies.
The formula for a
perpetuity is C / (r - g), where --
C is "owner
earnings (net income + depreciation + amortization -
capital expenditures),"
r is the discount rate
(historic 30-yr bond rate), and
g is the growth rate
of the owner earnings (if any).
(It's
important to note that the formula calculates the intrinsic
value one year PRIOR TO the beginning of the cash flow.
To compute the intrinsic value at the time of the
cash flow, multiply the IV by whatever g
is.)
Coke's year-end 1997 intrinsic value = [(net income +
depreciation + amortization - capital expenditures) /
(historic 30-yr bond yield - owner earnings' growth rate)]
* (1 + owner earnings' growth rate)
So
year-end 1997 IV = [($4,129 mil. + $384 mil. + $242 mil. -
$1,093 mil.) / (0.10 - 0.08)] * (1.08)
= $197,748
mil. (Coke's year-end 1997 INTRINSIC MARKET
CAP)
Divide $197,748 mil. by the number of Coke shares
outstanding as of 12/31/97, 2,470.718 million, to get a
per-share intrinsic value figure of $80 (I said $81 before
but I'm correcting myself).
Coke's actual
year-end 1997 market cap was $164,766 mil., which
represents a margin-of-safety of 17% vis-a-vis its intrinsic
market cap at the time of $197,748 mil. Coke was
undervalued by 17% at the end of 1997.
Now if you do
the above in Excel for each of the past 10 years, you
will see that Coke's intrinsic value, because its
business is growing, has actually led, rather than lagged,
Coke's market value. A lot of people wonder how Coke's
market price can go up every year as it has. The answer
is because Coke is a very strong company whose owner
earnings are growing every year and constantly raising
Coke's business value.
*********
Buffett
defined "owner earnings" in Berkshire's 1986 Annual
Report.
Buffett indicated 10% as the discount rate he uses in his
1991 Letter to Shareholders (see section labeled "Some
Valuation Math").
A growth rate of 8% is reasonable.
In his 1991 letter, Buffett identified the growth
rate to use for media franchises as 6%, and since Coke
is a better franchise in Buffett's view than the
Washington Post, it's only reasonable to assume Coke's
growth rate is higher. Incidentally, Buffett mentioned
in his 1991 Letter that all media companies' growth
rate would decrease dramatically in the future and,
consequently, so would their intrinsic values.
I've told you before that your formula for
valuing stocks is wrong. Let's see, you calculate a value
of $80 using a 10% discount rate and an 8% owner
earnings growth rate.
So what is the value if you
use a 15% owner earnings growth rate? Intrinsic value
should be higher if they grow faster, right?
Unfortunately, using that k - g formula (.10 - .15), you get a
negative value.
Why would you persist in using a
formula that clearly makes no sense for the application?
It is Saturday night and here you are on the KO board (me too.) What are we, old and married? Oh well, next week ought to be nothing less than interesting. Have a great weekend.
Kingfisher
Remember what a perpetuity is -- it's a bond
whose coupons are paid out FOREVER. No company can keep
its owner earnings (its "coupons") growing at 15%
forever. They can do it for a number of years, but
eventually it will fall below 10%. That is why you can use
the formula. If you found a company that indeed could
grow its owner earnings at 15% FOREVER, it would in
fact be worth infinite dollars.
You use a
two-stage dividend discount model for companies whose owner
earnings currently and temporarily exceed the risk-free
rate (10%). Then when the owner earnings fall to a
constant level below 10%, you apply the perpetuity
formula. Alternatively, you can make the conservative
assumption that owner earnings currently do not exceed 10%
at all but are presently growing at the rate at
which you expect them to grow forever (8% for Coke).
Then you don't have to use the two-stage dividend
discount model at all -- but you can immediately apply the
perpetuity formula.
Buffett calls Coke the greatest
company in the world. While its owner earnings are
currently growing about 20% a year, not even Buffett
assumes Coke will grow at this rate FOREVER. 8% is a
reasonable "forever" rate. Why? Because in Buffett's 1991
Shareholder Letter, he used 6% as the Washington Post's
"forever" growth rate, but Buffett considers Coke to be a
better franchise than the Washington Post so I assume 8%
is reasonable. By the way, Buffett also uses 10% as
his discount rate in this intrinsic value calculation
example, and I suggest you look at the 1991 Letter
(http://www.berkshirehathaway.com/letters/1991.html) to convince yourself that Buffett indeed uses the
perpetuity ("perpetual annuity") formula to compute
intrinsic value (look under the section entitled, "Some
Valuation Math"). To understand what Buffett's talking
about better, I'll do the math for you:
When
newspaper's growth rate = 6%:
PV = C / (r - g) = $1
mil. / (0.10 - 0.06) = $1 mil. / 0.04 = $1 mil. /
(1/25) = $1 mil. * 25 = $25 mil.
When newspaper's
growth rate has decreased to 6%:
PV = C / (r - g)
= $1 mil. / (0.10 - 0.00) = $1 mil. / 0.10 = $1
mil. / (1/10) = $1 mil. * 10 = $10 mil.
I here-by induct you into the society of ex farmer red necks of
Americia. The higest honor the Sgt at Arms can bestow.
notbuffett
Novalis did have an excellent post. Glad he will
join our redneckers society. How are you and your
stories? Hope I haven't missed any of them, especially the
tomato gravy one. I have had lots of homefolks at my
house for a couple of days and have been sorta lax
about reading the board, trying to cook for them and
all and sure did wish I could fix them some tomato
gravy but I didn't have the recipe. Please? Can't
believe 2HI admitted he didn't have an answer for
someone, maybe that Badger guy, I think. I usually skip
2hi's posts with all his 'supposin" and "what iffin"
but I did catch the one where he admitted to no
answer. While all the homefolks were here, I did have
plenty of coke to serve. We even had some chicken, too.
Where is John864 or 846? Do you know? Haven't seen him
for a couple of days. Do you think maybe that the
King in San Antonio would like to be a redneck, too?
He seems to be an OK kinda guy to me. How 'bout it
King? Best regards, Notbuffett to you and yours. Texie
But what you forgot to mention is that they have
defeated the business cycle. Unlike almost every other
major company in the entire world, they do quite well
in upturns and downturns of the economic cycle, and
this makes them quite unique among all
corporations.
Kingfisher
I wonder if Buffett is coming up with the same
answer as you are for the intrinsic value of Coke. In
his 1997 letter (1996 annual report) to shareholders,
when KO was quite a bit cheaper than it is now he said
the following:
"You can, of course, pay too
much for even the best of businesses. The overpayment
risk surfaces periodically and, in our opinion, may
now be quite high for the purchasers of virtually all
stocks, The Inevitables included (Coca Cola, Gillette,
etc.). Investors making purchases in an overheated
market need to recognize that it may often take an
extended period for the value of even an outstanding
company to catch up with the price they
paid."
This year Buffett is quietly reducing his allocation
to stocks. With this in mind, shouldn't we be doing
the same? By the way, your formula is great when you
want to hold KO for an infinite period, but what if
you want to get out sometime in the next five or ten
years rather than waiting for infinity.
Finally,
have you adjusted the net income for one time events
in 1997 like bottling transactions resulting in one
time capital gains and tax credits for option
exercises?
Also, does the fact that Buffett has not added to his
position in recent memory lead you to believe that Coke
might not be quite as good a buy relative to earnings
etc., as it was 10 years ago?
TOOHIGH2WIN
The relationship between intrinsic value and
market value is not static but changes over time. If you
plotted Coke's intrinsic value and market value on a
graph, you'd get two lines, both trending upwards over
time -- but sometimes intrinsic value is higher than
market value and other times (less frequently) market
value is higher than intrinsic value. Why does Coke's
intrinsic value increase in the first place (pulling Coke's
market value up roughly with it as it goes)? Because
Coke's owner earnings increase and, if C in PV = C / (r
- g) increases, then PV increases. While at
year-end 1996, Coke's intrinsic value was only slightly
above its market value, since then Coke's intrinsic
value is up about 65%, while Coke's market value is up
only 50%. Once again, Coke's intrinsic value is
outpacing its market value (what usually happens), creating
a potentially large margin-of-safety.
*****
Buffett is selling his Coke???
*****
It
doesn't matter how long you plan to own a stock -- the
stock costs the same to the investor who plans to keep
it just one day and to the investor who plans to
keep it forever.
*****
Buffett last
bought Coke in 1994.
*****
You have a
point about one-time gains. However, it is more than
offset by the fact that I used an intentionally low
owner earnings growth rate of 8%. In actuality, Coke's
owner earnings growth rate is closer to 20%, but
because I wanted to keep things simple and not use a
two-stage dividend discount model, I chose the very
conservative 8%.