According to an article published in Fortune, billionaire investor Carl Icahn disposed of a full 13% of his position in Apple (NASDAQ:AAPL). This comes less than a year after he sent a letter to Apple CEO Tim Cook stating that he believed the stock was worth $240 per share, and urged the iDevice maker to be more aggressive about buying back stock when the shares traded for well north of $120 per-share.

Of course, even after unloading a bunch of Apple stock (and turning a handsome profit on the shares), the investor still owns more than 45 million shares after the sale. In light of this recent share sale, it's worth looking back at what Icahn had to say in his letter to Tim Cook, and why the investor may have unloaded those shares.

Icahn was expecting $12 per share in FY2016 -- probably not going to happen
In Icahn's letter, the investor justified his $240 price target as follows:

To arrive at the value of $240 per share, we forecast FY2016 EPS of $12.00 (excluding net interest income), apply a P/E multiple of 18x, and then add $24.44 of net cash per share.

Current analyst estimates call for Apple to deliver just $9.03 in earnings per share during fiscal year 2016, representing a slight contraction from the $9.22 that the company reported a year earlier. Even if we assume Icahn's earnings multiple of 18x is reasonable, this would still imply a price target of around $163 per share.

That would still represent substantial upside from current levels (the stock closed at $96.56 as of writing), but perhaps not the "no brainer" that Icahn had previously championed.

Is an 18x earnings multiple reasonable?
In addition to incorrectly predicting Apple's earnings per share in fiscal 2016, it would seem that the earnings multiple that Icahn believed that Apple stock should command turned out to be quite optimistic. 

Removing out the approximately $153 billion in net cash from Apple's market cap, the current implied enterprise value per share is approximately $69. The market currently values Apple at just 7.68 times projected earnings per share excluding cash, less than half of the multiple that Icahn believes that it deserves.

Although the case could be made for Apple commanding a richer multiple -- and if iPhone sales show signs of life in the coming cycle, it could very well get one -- it's important to understand that the iDevice maker is still fundamentally a hardware company operating in a very fierce competitive environment.

Against the backdrop of seemingly endless competition, the overall market for smartphones is also cooling off, which will make achieving future growth that much tougher.

Why Icahn's thesis didn't (and probably won't) work
Icahn's price target was based on unrealistic earnings-per-share growth coupled with a bet on significant earnings multiple expansion. As fiscal year 2016 plays out, it's quite obvious that neither of those things is really going to be "in play" this year.

Additionally, Icahn made reference to both an Apple-designed television set and an Apple-designed car both contributing to the company's revenue and earnings in the near term. It's doubtful that the TV will ever get made -- if it were ever actually a real project within Apple -- and the rumored car efforts seem to be years away -- if they ever actually make it to fruition.

As Icahn's thesis appears to be no longer intact, it's no surprise that the investor decided to take some profits. It'll be interesting to see if he takes additional profits in the quarters ahead.

Ashraf Eassa has no position in any stocks mentioned. The Motley Fool owns shares of and recommends Apple. Try any of our Foolish newsletter services free for 30 days. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.