No typo. A year ago they had authorized $140 billion, and had already repurchased more than $80 billion.

https://www.apple.com/pr/library/2015/04/27Apple-Expands-Cap...

($175 million would be less than three hundredths of one percent of Apple's market cap.)

Ah, thanks. Kind of a hard to parse sentence; I read it as buying back $175bn this quarter. Which would be 30% of their market cap and represent all their cash on hand.

They do not have that much cash on hand. Apple already has over $100B in common and exotic debt that has been used to pay for both dividends and this buy back program. So that pile of cash sitting overseas? On its way to being mostly spent. And if the Congress critters start pressing companies to repatriate, a big tax bill looms too.