Thinking this through.
What happens to the value of shares of public stock if the company buys some of the stock back in the marketplace?
Think of it first as a simple accounting matter, and let's assume for simplicity's sake that the actual or potential buyers of the stock in the marketplace (who constitute the market demand) know and care about the book value on the balance sheet: that is, the equity as defined by the formula Assets - Liabilities = Equity.
Suppose the company has 1,000 shares of stock outstanding, each selling for $50. Its market capitalization, then, is $50,000.
Now, it uses some of its own cash (an asset) to buy back some of the shares of stock. This decreases the amount of stock still available to a would-be buyer. So if 100 shares are retired and 900 are left, as a first approximation -- assuming demand for the stock stays the same, we might well expect the value of those to increase to $55.55 per.
BUT something else has taken place, too. The company has depleted itself of cash. If it offered no premium on the market value of those shares, it bought 100 shares at $50 each, depleting itself of $5,000 worth of cash.
Since A - L = E, we would of course expect this hit to the asset side of the balance sheet to show up as a reduction in equity too. We've assumed the buyers care about such things. Why would the market not notice this and adjust for it?
Since the equity (book value) is reduced by the amount that the cash is reduced than the company is no longer worth $50,000: it is worth $45,000.
There are now 900 shares outstanding of stock in a company with a book value of $45,000. If that is reflected in the market value, then the market value will end up at: $50. Which is where we started.
Second approximation, then, the buyback should have no consequence at all for stock price, because the two effects one would immediately presume it will have (lessening the supply of the stock in circulation and lessening the book value of the company, thus the market demand for the stock) would exactly offset one another.
As a third approximation, there is this: Palak Raval.