Activist investor Carl Icahn, who owned 45 million shares of Apple (NASDAQ:AAPL) as of last August, claims that the stock could be worth over $203 per share. At $203, a 71% premium over its closing price on Feb. 2, Apple would have a whopping market cap of $1.12 trillion. While that would be wonderful news for Apple investors, we should check the math and logic behind Icahn's grand claim.

An Apple Store in Hong Kong. Source: Wikimedia Commons, WiNG.

The math doesn't add up
Apple currently trades at 16 times trailing earnings. Over the past two years, its P/E has fluctuated between 9 and 18.

Wall Street analysts, on average, expect Apple to respectively post earnings per share of $8.49 and $9.10 in fiscal 2015 and 2016. Assuming that Apple's P/E remains between 9 and 18, a "fair price" would fall between $76 and $153 for 2015, and between $82 and $164 for 2016. None of those prices come anywhere close to Icahn's $203 price target.

For Apple to hit $203 with a P/E of 18, Apple would need to post annual earnings of $11.28 per share. Apple is expected to post 32% year-over-year EPS growth in fiscal 2015, but just 7% in 2016, which means that earnings of $11.28 per share could be a tough target to hit.

Apple respectively posted gross and net margins of 40% and 24% last quarter. Last October, Argus Research analyst Jim Kelleher pointed out that if Apple maintains gross margins of 44%, net margins of 27%, and 12% annual earnings growth throughout fiscal 2016, that would still only generate earnings per share of $10.17.

Why Icahn believes that Apple could top $200
However, Icahn's model is likely based on Apple following his advice on boosting stock buybacks, which would inflate its earnings by reducing outstanding shares. Apple has already done so by funding buybacks with debt, since most of its cash remains overseas and would be heavily taxed if repatriated to the U.S.

Over the past 12 months, Apple has bought back over $44 billion in stock. As a result of funding buybacks and dividends with bond offerings, Apple's long-term debt has soared from nothing in 2012 to over $36 billion today. That's not much of a risk, since Apple still has $178 billion in cash and equivalents and trailing 12-month free cash flow of $60 billion. Apple clearly intends to stick with that plan -- it recently announced plans to sell $5 billion in additional debt to fund additional buybacks and dividends.

I'm not a big fan of buybacks, but they might help Apple shares hit $200 without causing its valuations to overheat.

Top line growth should remain a priority
Nonetheless, I would hate to see Apple completely propped up by buybacks. Some tech giants, like IBM (NYSE:IBM), get stuck in a cycle of spending cash better suited for revenue-boosting R&D and acquisitions on buybacks to appease shareholders. Therefore, Apple needs to keep launching new products, like Apple Watch, to diversify its top line away from the iPhone.

Icahn believes that Apple, like Samsung (NASDAQOTH: SSNLF), should launch 4K smart TVs. Last October, he claimed that Apple could sell 12 million 55-inch and 65-inch smart TVs in fiscal 2016, and 25 million in 2017 with an average selling price of $1,500. In a previous article, I highlighted the problems with that idea -- 4K TV prices are already plunging, margins are anemic, and it would be smarter for Apple to keep selling its lower cost Apple TV set-top boxes. 4K TVs might generate fresh revenue for Apple, but they would ruin its margins -- which would hurt earnings growth and the stock's chances of hitting $200.

Apple's set-top streaming box, Apple TV. Source: Apple.

The $200 question
I'm not saying that Apple stock will never be worth $200. However, the road to $200 will be a tough one which requires Apple's margins to keep expanding, top line growth to remain robust, and buybacks to continue.

Investors should focus on Apple's ability to grow revenue beyond the iPhone with new products like Apple Watch, and its ability to maintain its mix of high sales and high margins, instead of believing long-shot price targets from big investors who can move the market with open letters to companies and investors.

Editor's Note: A previous version of this article stated that Apple's cash and cash equivalents equates to $33 billion instead of the correct amount of $178 billion.