NEW YORK (TheStreet) -- Billionaire and activist investor Carl Icahn believes Apple(AAPL) - Get Report shares are 50% undervalued. In an open letter to CEO Tim Cook he urged the acceleration of the iPhone maker's share repurchase activity through a tender offer. Icahn, who owns approximately 53 million shares of Apple, said he would volunteer to exclude his Apple shares from the proposed tender.

"[W]e ask you to present to the rest of the Board our request for the company to make a tender offer, which would meaningfully accelerate and increase the magnitude of share repurchases," Icahn said in the letter, posted on his Web site. He also thanked Cook for Apple's willingness to increase the company's share buyback activity in recent years, and noted the company has made opportunistic repurchases.

Watch the video below for Apple's response to Carl Icahn's open letter:

While Icahn's letter to Cook appeared to be intended to pressure Apple to increase repurchase activity, it also detailed the activist's analysis on Apple's valuation. Icahn believes Apple currently trades at only eight times its forecast 2015 earnings per share, significantly lower than the S&P 500 and the technology sector. He believes Apple should trade at a multiple of 19 times its forecast 2015 EPS, or roughly $203 a share.

"[W]e see Apple's P/E of just 8x our FY 2015 forecast as both irrational and transient in nature, especially since many actively managed mutual funds remain underweight Apple in their portfolios," Icahn said. 

He also included financial assumptions for Apple's newest products and some that continue to be the subject of speculation. Icahn forecast that Apple's recently announced Apple Watch will sell 20 million units in fiscal 2015, 45 million units in 2016 and 72.5 million units by 2017.

The activist investor also forecast that Apple Pay, the company's inclusion of near-field communication payments capabilities to its newest iPhone could generate $2.5 billion in revenue by 2017 if it reaches a 30% market share among debit and credit cards in the U.S.

Finally, Icahn also speculated on Apple's launch of a smart television by 2016.

"While Apple has not announced plans for a TV set and may never do so, we believe we have good enough reason to expect the introduction of an UltraHD TV set in FY 2016. We think television represents a large opportunity for Apple, one that reaches far beyond 'the hobby' that Apple TV currently represents," Icahn said.

-- Written by Antoine Gara in New York

Follow @AntoineGara