Icahn buys $1bn more Apple shares lifting holding to $3.6bn Investor Carl Icahn Carl Icahn redoubled his challenge to Apple's board on Thursday, calling the iPhone maker "perhaps the most overcapitalised company in corporate history" in a 3,000-word letter arguing for a $50bn share buyback scheme. The veteran activist investor said in a Twitter posting that he had invested another $1bn into Apple in the last two weeks, taking his total holding to $3.6bn, or around 0.7 per cent of the company's $500bn market capitalisation. The stock, which had been trading lower until mid-afternoon on Thursday, closed 0.9 per cent higher at $556.18 after Mr Icahn's tweet. Mr Icahn, who on Wednesday revealed his push for Apple's Silicon Valley neighbour Ebay to spin off its PayPal unit, used the open letter to set out not only his financial arguments but his expectations of the company's opportunities in new product lines. Even if the story ended with Apple's existing product and software lines, we would still choose to make Apple our largest investment. But there is more to the story! Mr Icahn wrote. Despite his push for Ebay to divest PayPal, Mr Icahn said that a "revolutionary new payments solution is now a very real opportunity" for Apple to pursue. He suggested that a $1,600, ultra-high-definition Apple TV set could generate $40bn in annual revenues and $15bn in operating income. A smart watch could also be "compelling," he added, even as growth slows in the iPhone and iPad - the latest iterations of which he described as "evolutionary not revolutionary." Reports on Thursday created renewed speculation that Apple will launch new iPhones with larger screen sizes later this year as it competes with Samsung and other Asian rivals. Apple is due to report earnings next week. In language now familiar in boardrooms across America, Mr Icahn repeated his belief that investing in Apple is a "no brainer," comparing it to his team's successful bets on Netflix, the internet video service, Herbalife, the troubled nutrition company, and Chesapeake Energy. He wants Apple to borrow against its $130bn net cash hoard and $40bn in forecast annual earnings to pay out an additional $50bn to investors through share buybacks before the end of its fiscal year in September. Apple investors will be given the chance to vote on Mr Icahn's proposal at its annual meeting next month. Even after Mr Icahn scaled back his earlier demand for a $150bn share buyback, Apple's board has recommended shareholders vote against the proposal, saying it will revisit its $100bn capital return programme in the spring. In his first detailed response to Apple's December proxy statement, Mr Icahn said that he found its arguments that it needs to retain financial flexibility "overly conservative, almost to the point of being irrational." Opportunities for large acquisitions, which Mr Cook has previously said Apple has considered, are "difficult to identify," while suggesting that existing research and development investment could be funded from current earnings. Apple declined to comment beyond its earlier filings. Mr Icahn and Tim Cook, Apple's chief executive, have spoken on several occasions since the investor took a stake in the company in August last year. The corporate agitator praised Mr Cook and Sir Jonathan Ive, Apple's chief designer, but said its board was "doing a great disservice to its shareholders."