How could the price not go up? I understand buybacks as reverse dilution. Each share represents a larger percentage of the company, therefore it is more valuable and it's price should be higher. Is that wrong?

You're not accounting for the transfer of cash out of the company. If you have a company with a business worth a billion dollars and a billion dollars in cash, it should have a market cap of two billion dollars. If it uses half a billion dollars to buy back shares then it should have a market cap of $1.5B because it has $500M less cash. Then it also has 75% as many outstanding shares, so the value of each share is the same.

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.

The company becomes equally less valuable after a buyback.

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.

> Consider a company with value of $1000, with 100 shares outstanding. Each share is $10. Buying back 10 shares, the company spent $100

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.

I think you may be confusing market cap with share price. Market cap does not generally increase with buybacks, only share price does.

There are fewer shares, but the book value of the company goes down as well because it is spending cash to buy the shares. So it's not necessarily true that the price should go up.

Because the company cash to buy the stocks should decrease the amount of capital cash on hand by the same amount resulting in no change in the capitalized value of the 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.

A bigger percentage of a less valuable company, because buying the shares back costs money. Ignoring taxes and other “minor” details (like a discount applied go cash that could be “wasted”), if a company market cap is $10bn and it has $1bn in cash after a buyback investors in aggregate would still have $10bn after the cash is used to repurchase 10% of shares: $1bn in cash and $9bn in stock trading at the same price as before (there are 10% fewer shares, but the company is worth 10% less).

The simple version of the theory is that stock buybacks should be price neutral because shareholders effectively lose cash now (for the buyback) but get a higher proportion of future earnings for that cash. If the price of the stock is perfectly efficient, these values should be equal.

I recall learning this too. I never heard that prices shouldn't go up. Maybe the above person meant that the total valuation shouldn't go up? If so, that logic does check out.

I think we’re talking about Miller-Modigliani [1] which says that enterprise value should not change as capital structure changes. However it presumes many untrue aspects of the world in order to make this claim.

[1] https://en.m.wikipedia.org/wiki/Modigliani–Miller_theorem