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By this point it should be clear that Icahn doesn't lack for confidence. But he is now embarking on what may be his biggest test yet. In squaring off against Apple, he is picking a fight--however gently and carefully--that is very different from the battles where he made his corporate-raider bones. Those typically pitted Icahn against companies with cancers lurking somewhere within, weakened in some way and vulnerable to--even in need of--an assertive investor. Apple, though, is an opponent practically unique in the annals of American capitalism. It is literally the world's most valuable company (even if a bad day in the stock market sometimes flips that honor temporarily back to the No. 2, ExxonMobil). More than that, though, Apple has a halo that few companies in history can match. Look around our smartphone-saturated, cloud-enabled and thoroughly digital world: Apple, many would argue, built the future.
How much chutzpah does it take to tell that company it's doing it wrong? Even Icahn may not have enough--which is why he appears to be approaching Project Apple with unusual (for him, at least) diplomacy. He chooses his words about Cook with care and takes pains to show respect for the company and its management. Icahn says his most recent conversation with Cook was a 20-minute phone call on Nov. 21--which Cook's assistant initially tried to schedule at 5 a.m. P.T. "That's usually when I go to bed," jokes Icahn, a notorious night owl. "This guy's tougher to get than the President!" he adds. "A lot of people say Steve Jobs probably wouldn't have talked to me, and maybe that's true. But I think he [Cook] found our conversation interesting. He said, 'Look, you've accomplished a lot, and we want to listen to you.'"
Icahn still has the option of withdrawing his proposal if he and Apple can come to terms. If they can't, though, the situation has the potential to turn into an old-fashioned proxy fight (the term refers to the ballots cast by shareholders unable to attend the annual meeting), even if it is not a particularly hostile or aggressive one. In that scenario, the two sides will vie to persuade stockholders to vote their way. If a significant number of shares are cast for Icahn's position, it would send a powerful signal to Cook and the Apple board. But even if some investors are antsy for Apple's next big hit product and want to get their hands on more of Apple's cash, it's far from clear that they'll be willing to second-guess such a world-class winner. Wall Street expects the company to earn $180 billion in revenue next year but would love to see another blockbuster on the order of the iPad.
Apple, for its part, is thinking hard about what to do with the cash hoard. In response to the Icahn precatory, Apple spokesman Steve Dowling told TIME, "Earlier this year we more than doubled our capital-return program to $100 billion, including the largest share-repurchase authorization in history. As part of our regular review process, we are once again actively seeking our shareholders' input on our program, and as we said in October, the management team and our board are engaged in an ongoing discussion about it, which is thoughtful and deliberate. We will announce any changes to our current program in the first part of calendar 2014."