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The Wonders and Horrors of Compounding

Google Price Target: $16,578.90 Some of you will immediately recognize this headline is a joke. For the rest of you, I was kind of hoping the ninety cents part would give it away. If you're reading this because you're interested in what I have to say about Google (GOOG), you can stop now.

I'm not going to say anything interesting about Google. Rather, I'm going to say something (that I hope is) very interesting about the wonders of compounding. Warren Buffett's annual letter to shareholders was released on Saturday. For now, I'm just going to pull out one little nugget: "Between December 31, 1899 and December 31, 1999, to give a really long-term example, the Dow rose from 66 to 11,497 (Guess what annual growth rate is required to produce this result; the surprising answer is at the end of this section.)" I knew what Warren was up to, and had some idea of the historical growth rate for the Dow, so I guessed 6%.

"Here's the answer to the question posted at the beginning of this section: To get very specific the Dow increased from 65.73 to 11,497.12 in the 20th century, and that amounts to a gain of 5.3% compounded annually. (Investors would also have received dividends, of course).

To achieve an equal rate of gain in the 21st century, the Dow will have to rise by December 31, 2099 to - brace yourself - precisely 2,011,011.23. But I'm willing to settle for 2,000,000; six years into this century, the Dow has gained not at all." I wish I could tell you that my guess was close.

But, it wasn't even in the right ballpark. The difference between a 5.3% annual gain and a 6% annual gain may look relatively small.

In fact, the difference is not small. If, during the 20th century, the Dow had achieved a gain of 6% compounded annually rather than a gain of 5.3% compounded annually, on the eve of Y2K, the index would have been sitting at 22,302.

33. The rallying cry of the bubble years would have been Dow 20,000. And what of Dow 10,000? The index would have added its fifth figure in 1987.

That's right, if the Dow had achieved a gain of 6% compounded annually during the 20th century, the index would have broken the 10,000 mark while the Berlin Wall was still standing. Over a century, that extra 0.7% really adds up. I recently wrote an email to a member of my family who had just had her first child. You would think that blathering on as I do here each day, I would have a sea of investing advice to offer.

In fact, I provided only a single drop: Time trumps money. If you want to have more money than you will ever need, your best bet is to find a few places where you can deploy large sums of money that will earn good returns for a great many years, and will not require you to share any of the spoils with Uncle Sam until you are done accumulating said spoils. To do this, you will have to own a business either in part or in whole. I'm an investor, not an entrepreneur; so, let's stick to the economics of becoming part owner of a business. It's time to discuss Google.

I have a price target of $16,578.90 on Google. Does that sound reasonable? No. Well, I may have forgotten to mention this is a 50-year price target? So, does it sound reasonable now? Don't answer. First, we need to see what it would take for Google's share price to reach $16,578.90.

Last I checked, each share of Google had a book value of $31.87. Everyone says Google's a great business.

They may be right. But, I like all my surprises to be of the pleasant variety. So, I'm going to start by chucking the idea of Google being an extraordinary business. For now, let's just call it average.

Who would want stock options in an average business? Let's pretend no one would. Since there's no downside, I think everyone would; but, let's just ignore that inconvenient fact. We're going to pretend Google won't be diluting its shares at all. For the next fifty years, there will be no new shares and no stock splits. As a public company, Google has earned an above average return on equity.

It hasn't been an earth shattering return on equity (it's no Timberland), but it's been better than most. Of course, with Google, you're not paying up for the current return on equity - you're paying up for all the ridiculously profitable growth to come. I'm willing to meet the Google bulls halfway on this one.

I'll give you growth, but no unusual profitability. You're going to get a 12% return on equity, but there will be no limit to your growth. In my model, Google can literally conquer the world. With something like $9 billion in equity to start with, a 12% return on equity, and the reinvestment of all earnings in the business, Google would get awfully big. Don't believe me? I know a 12% return on equity looks ridiculously low, but watch what happens. In 2056, Google will be a $312 billion company.

Of course, the big question is: do I mean market cap or revenue? I mean profits! At a P/E of 15, Google would have a market cap of $4.68 trillion. Yes, with a "t". That same Google share that was quoted on Friday at $378.18 would be worth $16,578.90.

Google's EPS would be $1,105.26. You read that last part right. Each Google share would be earning three times its current (lofty) price. So, what's the catch? There are two problems with this scenario. One, in 2056, it's more likely Britney Spears and Kevin Federline will be celebrating 50+ years of marital bliss together than it is that Larry Page and Sergey Brin will be celebrating 50+ years of 100% retained earnings at Google.

For that matter, I'd say it's more likely Larry Page and Sergey Brin will be celebrating 50 years of marital bliss together in 2056 - which is to say it isn't very likely Google will be able to retain all of its earnings for the next half century (unless you know something about Larry and Sergey that I don't). The second problem is much less amusing. You see, if on Monday, you were to shell out the $378.18 for a share of Google, when the stock reached $16,578.90 in 2056, you'd be able to brag to Britney and K-Fed about your annual compound gain of.drum roll please.

7.85%. And that's before taxes and inflation. Google would have a $4.68 trillion empire, and you'd have an annual return of 7.85% - how can that be? Time turns molehills into mountains and mountains into molehills.

In the very long-term, growth that only earns ordinary profits leads to stocks that only yield ordinary gains. But, isn't Google's (lofty) price the problem? It's part of the problem. However, it's probably a smaller part than you think.

Right now, Google is trading at about twelve times book. What would your return be if you bought Google at book value? 13.32%. That's a good return (fifty years from now, it'll probably be considered a great return).

Still, it's somewhat unsatisfying. I mean, if you had the prescience to buy a $4.68 trillion behemoth when it was just a $10 billion company (remember, you're paying book this time) all you'd get for your trouble is 13.32%. Think of it this way.

At $31.87 a share, 85% of your purchase price would be backed by cold, hard cash and you'd be buying a stock with a P/E of 6.3. A P/E of 6.3 is insanely cheap. So, why would buying a stock trading at a P/E of 6.

3 and growing earnings per share at 11.4% a year for fifty years only yield a 13.32% return? Where are the insane gains? Return on equity is the puppet master here.

Take another look at the numbers. They're doing something strange; they're converging. Everything is getting closer and closer to 12%. Why? Because that's your destiny. If you buy a business that earns 12% a year and you hold it long enough, guess where your returns are headed? Here's one last excerpt from Buffett's letter.

He's writing about all businesses, but a long-term holding in a single business works in much the same way: "True, by buying and selling that is clever or lucky, investor A may take more than his share of the pie at the expense of investor B. And, yes, all investors feel richer when stocks soar. But an owner can exit only by having someone take his place.

If one investor sells high, another must buy high. For owners as a whole, there is simply no magic - no shower of money from outer space - that will enable them to extract wealth from their companies beyond that created by the companies themselves." It is now obvious I picked Google just to get your attention.

Google may very well earn a return on equity much greater than 12% for the next fifty years. It has already earned "extraordinary profits". Even if it does grow at a phenomenal rate, it will, during the next half century, likely shed excess equity by paying dividends, buying back stock, or transforming itself into a holding company. I don't see a way the company could possibly put more than $2.

5 trillion in equity to good use in search and related businesses. In nominal terms, that's well more than California's GSP (Gross State Product). In 2006 dollars, it would still be something like $600 billion.

Armies have been raised for less. So, if Google really does want to conquer the world, it could just try doing it the old fashioned way. I will attempt to provide some semblance of sobriety by letting Ovid express in three words what has taken me more than sixteen hundred. TEMPUS EDAX RERUM.

Geoff Gannon writes a daily value investing blog and produces a twice weekly (half hour) value investing podcast at Gannon on Investing.

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