After months of hemming and hawing, it appears tech giant Apple (NASDAQ:AAPL) and its loudest (but by no means largest) shareholder, activist investor Carl Icahn, could be slowly nearing the endgame of their multimonth struggle.

Carl Icahn Twitter Pic

Source: Carl Icahn

How's that?

Recently, Apple filed its preliminary proxy statement with the SEC for its 2014 shareholders meeting. And as you can image, Icahn's shadow loomed large.

I think iCahn, I think iCahn
In the preliminary proxy statement, Apple detailed many of the items it plans to discuss and/or bring to a shareholder vote at its annual meeting next year. The document in its entirety isn't exactly a page-turner. But things do get slightly more interesting when you reach Shareholder Proposal No. 10 on page 62 (link here). Apple recounts the proposal as such:

RESOLVED, that the shareholders hereby approve, on an advisory basis, High River's proposal that Apple commit to completing not less than $50 billion of share repurchases during Apple's fiscal year ending September 27, 2014 (and increase the amount authorized for share repurchases under its Capital Return Program accordingly). 

As was expected, Icahn is making his presence felt. And as should also be expected at this point, Apple's management isn't having any of it. In the space below, Apple flatly recommends shareholders vote against Icahn's proposal for very familiar reasons.

It all comes down to overseas cash
Much of Apple's argument against Icahn's proposal comes across as the kind of typical boilerplate response for which Apple's PR and investor-relations teams have grown famous.

But after reading all of Apple's response, it appears their qualms with Icahn's proposal come down to its views on how to best manage its overseas cash. There's something to be said for that.

At the end of last quarter, Apple carried roughly $148 billion in cash and investments on its balance sheet. But only $35 billion of Apple's massive cash hoard was held domestically in the U.S. And that's the key sticking point.  

Apple notes that all dividends must be paid out of domestic cash, which could get dicey fast if it's suddenly required to have to fund a $50 billion buyback as well as fund its operations for the coming fiscal year. Of course, Icahn is acutely aware of this. If Icahn were to have his way, Apple would have to take on additional debt with which it could fund the buyback he's proposing by using its overseas cash as collateral.

He might be onto something here
Although they've surged in the second half of the year, Apple's shares are still dirt cheap, especially when compared to the rest of the market. Subtracting Apple's roughly $130 billion in net cash from its current market capitalization values the company's core operating business at $364 billion. Dividing by the $37 billion in profits Apple has booked over the last 12 months puts an overall valuation for Apple's actual business at just under 10x, versus 20x for the S&P 500 according to Robert Shiller.

We're talking rock-bottom valuation here, folks.

What's more, interest rates are still buoyed toward historic lows, although that will certainly change.

The point is that there is a very fair argument to be made that Apple could add value for its shareholders by leveraging its balance sheet a reasonable degree. At this point it's still hugely unclear whether Apple's shareholders will see the logic in the move.

Carl Icahn doesn't own nearly enough Apple stock to push this kind of initiative through on his own. This means investors and Apple observers will need to wait to see just how one of corporate America's most high-profile battles plays out.

Fool contributor Andrew Tonner owns shares of Apple. Follow Andrew and all his writing on Twitter at @AndrewTonnerThe Motley Fool recommends Apple. The Motley Fool owns shares of 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.