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The stock value multiplied by the number of shares outstanding _is_ the value of the company as set by the free market.
No, that is the potential value. My company was once trading at something like $20 a share. When it got bought out, it was at like $0.15 a share. According to your definition, both of those are the value of the company. Unless we're going to get into quantum finances, both of those can't be true.
No, that is absolutely true - the company is worth exactly what someone is prepared to pay for it at any time. (Just like anything else). Now a stock can't be worth $20 and $0.15 at exactly the same time, not in the same universe anyway. But a stock can change in value very quickly.
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At the same time, if you look at the stock market as betting on how much a company will eventually pay in dividends, other than semantic quibbling (which, don't get me wrong, I'm more than happy to do), this is the obvious explanation for how it all works.
The problem with that is that no one (here, at least) will commit to dividends being the ultimate reward.
Ok, I'll commit to that. Without the promise of dividends, the stock would have little value. The only value left would be to gain control of the company.
And this explains the $20 to $0.15 value changes. The moment a company looks as if it won't ever be able to make a profit and pay a dividend, all you are left with is the underlying value of tangible assets which generally isn't worth much when you divide it by millions of shares.
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