NEW YORK — Carl Icahn, the activist investor, has told Apple’s chief executive, Tim Cook, that the iPhone and iPad maker should launch a $150 billion stock buyback immediately and disclosed that he now owns 4.7 million shares in the company.
In a letter to Cook posted online Thursday, Icahn said that he has increased his stake in Apple by 22 percent, up from 3.9 million at the end of September. At Apple’s current stock price, that’s worth about $2.5 billion but amounts to less than a 1 percent stake in the company. He plans to increase his stake further.
Icahn wants Apple to launch the buyback at its current stock price, which closed at close to $525 on Wednesday when the letter was sent. He stressed that he does not plan to tender any of his shares in the buyback he is proposing.
‘‘There is nothing short term about my intentions here,’’ he wrote. Over the long term, Icahn said, he expects Apple’s stock price to increase to $1,250 if the company goes through with the buyback as proposed.
The highest value the stock has ever reached was $705.07.
Apple declined to comment.
Icahn said he wants to make it very clear that he supports Cook and Apple’s current management team, as well as the company’s culture and the innovative spirit it engenders.
But he believes that Apple’s current buyback plan — $60 billion over three years — is far too small.
Speaking of his proposal, Icahn wrote: ‘‘While this would certainly be unprecedented because of its size, it is actually appropriate and manageable relative to the size and financial strength of your company. Apple generates more than enough cash flow to service this amount of debt and has $147 billion of cash in the bank.’’
The billionaire investor posted the letter on a new website he launched Thursday, that is called Shareholders Square Table.