Billionaire investor Carl Icahn has penned a letter to Apple CEO Tim Cook that urges Cook to buy back more shares of Apple.

While Icahn is certainly not happy with Apple's stock price, the letter more resembles a letter of support than a letter of disapproval.

"As a large Apple shareholder with approximately 53 million shares, we applaud you and the rest of management, especially in light of recent launches and announcements which further validate our view that you are the ideal CEO for Apple," said Icahn in the open letter. "It is truly a watershed moment, with Apple poised to take market share from Google (Android) in the premium device market as iPhone 6 becomes Apple's flagship device among a growing collection of products and services that work together to form an increasingly dominant mobile ecosystem."

Despite the appreciation, Icahn went on to talk about Apple's shares and what he feels like they should be trading at.

"Our valuation tells us that Apple should trade at $203 per share today," continued Icahn. Apple's shares currently trade at around $101.

The billionaire investor says that he expects Apple's revenue to show growth of 25 percent in fiscal 2015 and that earnings per share should grow 44 percent. With the success of the iPhone 6, Apple is, according to Icahn, set to show earnings growth of 30 percent in both fiscal year 2016 and 2017.

To help fuel this growth there will be a number of other successful Apple products, including the Apple Watch and eventually an iOS Ultra HD TV.

Despite Icahn's valuations, some analysts are suggesting that they may not come true because of the nature of the technology industry.

"In the tech landscape, trends can shift relatively quickly," said Colin Gillis, an analyst at BGC Partners.

For example, Icahn says that Apple could sell 72.5 million smart watches in fiscal year 2017, but that may end up being completely unrealistic.

"Apple remains primarily the iPhone company and they are bucking the trend by raising prices as the average sale price drops," continued Gillis.

The call from Icahn is just the latest of his suggestions in the tech industry. Icahn suggested that eBay spin off PayPal as a separate company months before it actually happened. Last year he went on the offensive against Dell founder Michael Dell, saying that the company should be made private. He then dropped those claims, but still said that Dell was undervalued. 

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