Actually, when buying back stock you're essentially reducing the number of shares outstanding, which, all else equal, would translate into a higher stock price.
That confuses me. When the company buys back shares they don't just disappear, do they? With 1 million outstanding shares owning 50% of a company and the company buys back 500k, then there are 500k shares owning 25%. Why would those shares' value increase?
Yes, the shares disappear. A company cannot own itself, at least not directly. If a company had 3 million shares outstanding, then buys back 1 million shares, there would then be 2 million shares.
Yes. When a company buys back shares, those who do not sell end up owning a larger percentage. It would be the same if you were paid a dividend and then used that dividend payment to buy additional shares of stock.