I would disagree with your point about stock issuance suggesting belief in the company. Issuing stock is usually a negative signal that not only is your company struggling with cash flow, but it can't issue debt at a reasonable cost. (Startups issue equity because it is difficult to borrow at such a risky stage of the company, but more established companies like Tesla issuing equity is usually a sign of difficulties with cash flow.) Read up on cost of equity vs cost of debt for more info.
But the buyback often increases the value of the shares because it allows investors to express their preferences better. If the company has a $1B business and $1B in cash, there is no option to invest in only the business, only the combined business+cash entity. If you think the business will give 9% returns and the cash 2% returns and you have an alternative investment that gives 6% returns, you won't invest in that company. But if they separate the cash from the business then you're willing to invest in the business, which makes the business worth more to investors and increases its share price.
Consider a company with value of $1000, with 100 shares outstanding. Each share is $10. Buying back 10 shares, the company spent $100, so the company is now worth $900 and has 90 shares outstanding. Each share is still $10.
This is the basic model that shows share price should be unaffected by buybacks, but there are other effects. The buyback could signal to investors that the company is unlikely to be inefficient with capital, so investors would value the company at $910 instead of $900.
Alternatively, in a demand/supply model of shares, the buybacks could have exhausted some of the supply of shares, so the valuation for the company settled on by the rest of the market is higher.
There's no clear answer here, but reality is probably somewhere between these models.
How would you buy 10% of the outstanding stock of a real company and pay exactly the market price for the entire block? On a public exchange, you'd need to bid higher than the market price for someone to sell you a block that big (otherwise it wouldn't be worth their while to sell).
If you're buying in the public market, other sellers will see that some party is willing to pay above the market price for this stock. They'll raise their own ask price as a result. In private, off-exchange sales, you'll be dealing with seasoned investors (family offices, hedge funds etc) where they're likely to know your situation, and you'll almost definitely pay a premium to acquire that stock.
The stock doesn't just vanish. It is held and owned by the company. So no, each share doesn't represent a larger percentage of the company. Unless the company retires the shares.
[1] https://en.m.wikipedia.org/wiki/Modigliani–Miller_theorem
I agree with the logic behind the arguments that a company buying its own stock should be a signal that the company believes in its business and valuation, but it also seems that many companies that also believe in their business and valuation also sell stock to raise money in order to expand, with the belief that the sale will result in individual stocks increasing in value even after the dilution. It seems hard for both cases to be true, but perhaps they are.
If this logic is sound, it seems that we should be at least somewhat concerned about this.
Also, I didn't understand how cheap credit is encouraging buybacks if companies aren't buying their own shares on credit. Would someone be able to explain this better than the article? (Thanks!)