Icahn said in a tweet Tuesday that he had pushed Apple CEO Tim Cook on Monday evening for a $150 billion share buyback, adding that the two would continue the discussion at another time.
"Had a cordial dinner with Tim last night. We pushed hard for a 150 billion buyback. We decided to continue dialogue in about three weeks," Icahn's tweet said.
In a CNBC interview, however, Icahn emphasized how strongly he feels about an increased buyback.
"It's a no-brainer and it makes no sense for this company with their multiple being so low not to do a major major buyback. And there's another reason that I mention, that I think might go forgotten, the fact that you can borrow money so cheaply today. I don't think we are going to see this again," Icahn said on CNBC's "Halftime Report."
"They have a golden opportunity to go borrow money."
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With Apple trading at about $482 per share, a repurchase of this kind would mean buying more than 300 million shares. Apple currently only has about 900 million shares outstanding, so a buyback of this size would be a reduction of more than than one-third.
In April, Apple announced that it would return as much as $100 billion to shareholders by the end of 2015, $60 billion of which would be through a share buyback program. It also raised its dividend 15 percent. By June, Apple had already purchased about $16 billion worth of its own stock.
While a $150 billion buyback program is well above the current buyback, Apple likely wouldn't have trouble funding an increased buyback.