I'm having trouble understanding your lack of understanding when so many examples of value have been given!

Owning part of a company has intrinsic value. You own part of its infrastructure and assets, its patents and copyrights, its trademarks and brands. All of those have some value. You also own part of its future profits and losses.

The expectation is that the company will be profitable. When that happens it will pay out dividends. Except, sometimes it is better for a company to invest in itself instead. This is frequently the case with emerging business sectors where companies compete to garner market-share - the expectation is that the larger the market share that a company has, the more product it can sell, and since it aims to make profit from each unit of product, the more profits it will generate. If they can gain a large enough market share they may be able to gain an effective monopoly, allowing them to dictate prices and profit margins (eg Microsoft) So the company grows, increasing its intrinsic value, making your share of the company worth more and more. Stable business sectors usually contain companies that pay dividends.

You can _always_ sell your share back to the company for its intrinsic value.

Yes, I did just write that.

Note that I didn't say that you could go and knock on the CEO's door and ask to 'redeem' it. But if you were, he would almost certainly buy it from you. He'd have to be drinking Kool-Aid to not do so.

Why?

Because the intrinsic value of a share is nearly always significantly less than the market value. The company could buy that share from you and resell it for an easy profit. But why would you sell it to back to the company when you could get a better price on the open market yourself? (Unless _you_ were drinking the Kool-Aid)

The intrinsic value of a share is based on the tangible assets of a company. The moment that the market price drops below the intrinsic value, the company is going to buy back shares. The major stockholders are going to demand it - each share removed from the market increases their percentage of control and profit. Eventually, if the market price stayed forever below the intrinsic value (which raises for each share removed from the market), you'd end up with a handful of stockholders holding all the remaining stock, at which point they'd probably liquidate the company to extract its intrinsic value straight into their bank accounts.

But of course - how could this happen? It obviously cannot. Stockholders get smart and realise that they could be amongst those getting the big payouts, and refuse to sell for that price. Other non-owners realise that they could buy stock and be amongst them too. Supply, demand. The market price quickly rises to an equilibrium.

The market price is based upon the intrinsic value and other intangible factors, such as expected profits, market share, market outlook, etc. As such, the market price defines the perceived value of the company, which fluctuates as perceptions shift. Obviously, the company itself can affect these perceptions. That is why the SEC exists, to bring regulate how a company must report its accounts and financial outlook, and also prevent employees with privleged information from profiting on the stock market due to that knowledge.

Stock Exhanges are a convenience. Since the company does not participate in most transactions, forcing buyers and sellers to move their transactions through the company would be inconvenient. You'd need to contact each company that you'd want to trade in. Originally this was the case. It soon became apparent that there was money to be made in being a broker or dealer of several stocks, and soon after that groups of brokers and dealers collected together to form clubs dedicated to extracting money from brokering and dealing in stocks. Thus begun the stock exchanges that became a far more efficient vehicle for buying and selling stocks than dealing with the company directly. This is the reason that you don't redeem stocks to the company. It's too inefficient. Companies basically outsource this process to the stock exchanges and participate to buy and sell stock in the open market when appropriate (eg IPOs and buy-backs)