Billionaire "activist investor" Carl Icahn has revealed his latest attempt to convince Apple's board to move aggressively on a stock buyback. Today Icahn published a letter he sent to Tim Cook reaffirming his insistence to have the company immediately offer a $150 billion buyback. He says in the letter that "we find it difficult to imagine why the board would not move more aggressively to buy back stock by immediately announcing a $150 Billion tender offer," adding "It is our belief that a company’s board has a responsibility to recognize opportunities to increase shareholder value, which includes allocating capital to execute large and well-timed buybacks."

Icahn also reveals that his firm now owns 4,730,739 Apple shares, worth $2.5 billion, which he says is "reflecting our belief the market continues to dramatically undervalue the company." Apple has already announced a $60 billion buyback program over the next three years, but Icahn wants the company to move immediately on a buyback more than twice as large, saying "The timing for a larger buyback is still ripe, but the opportunity will not last forever." Apple has $147 billion of cash on hand, and Icahn calls for the company to use some of it — or a massive loan — to purchase $150 billion worth of shares at an offer price of $525 per share (a price near where it trades today). He adds that his firm expects Apple's share price to reach $1,250 over the next three years.

It's clear that Icahn's proposal is in his best interests — he hopes for Apple to boost the share price after he's acquired a large position. He says in the letter that "commencing this buyback immediately would ultimately result in further stock appreciation of 140 percent for the shareholders who choose not to sell into the proposed tender offer," adding "to invalidate any possible criticism that I would not stand by this thesis in terms of its long term benefit to shareholders, I hereby agree to withhold my shares from the proposed $150 Billion tender offer. There is nothing short term about my intentions here." Whether Apple agrees with Icahn remains to be seen.