It took eight months, but activist investor Carl Icahn has finally won his battle with eBay (NASDAQ:EBAY): Late last month, the company announced that it would spin its PayPal division off entirely, creating a second, publicly traded entity in the process.

But Icahn isn't finished. Shortly after eBay made the announcement, he went further, calling for PayPal to lead a wave of consolidation in the payment space -- either by acquiring another firm, or merging with another company.

But Peter Thiel disagrees. As a successful venture capitalist, and the founder of PayPal, Thiel's words carry some weight. In fact, much of his new book, Zero to One, is drawn from the lessons he learned while running PayPal in its early days. In a recent telephone interview, Thiel told me that, although he agrees with eBay's decision to spin the company off, he thinks PayPal would be better served remaining an independent firm.

The only two situations where mergers make sense
Thiel isn't completely opposed to tech mergers, but he is skeptical. In fact, according to Thiel, there are only two situations where mergers make sense -- and PayPal doesn't fit the bill for either.

"Acquisitions only make sense for two main reasons. [The first is] deep synergies ... the other is cost-cutting ... If you sort of think of PayPal and the rest of the tech world, I can't think of any reason you'd really get [either] of those two. eBay has the most synergies, it's just less [than it was in the past]. I think the synergies with anyone else would be much less than they are with eBay. Cost-cutting would [make sense] if you had a company like PayPal that was just as big, and you sort of combine them, make them more efficient ... but I don't think [such a company] exists."

Still, a PayPal merger is not far-fetched. Analyst Colin Sebastian argued earlier this year that Google would benefit from buying PayPal, as the search giant's attempts at cracking mobile and digital payments have largely floundered. At the same time, Apple's (NASDAQ:AAPL) new Apple Wallet initiative has shaken up the space and, after making a deal with PayPal earlier this year, rival Samsung could emerge as a potential suitor. Yet Thiel disagrees.

"It's certainly not what I'd do if I was running those two companies. It's so far from their core business. Competing in something you're not that strong in doesn't seem to make sense. It's certainly the way these things get pitched by investment bankers that want to do deals, but it doesn't make sense for anyone other than the bankers that get fees on these things."

A buyer for PayPal?
But just because Thiel believes it's misguided, doesn't mean it won't happen -- especially with Icahn agitating for it. In addition to Google and Samsung, many other major tech firms have been seen as potential buyers, including Amazon and Facebook.

In his note, Icahn specifically suggested eBay consider a reverse Morris Trust structure -- a somewhat rare, tax-advantageous move that involves eBay selling PayPal to another firm in an all-stock deal, then issuing shares of the combined company to eBay shareholders.

Doing such a deal would require eBay finding a buyer that was somewhat smaller than PayPal, but not so small as to make the deal untenable. As an independent company, PayPal would likely trade with a market cap around $35 billion. There aren't many payment companies of the appropriate size, but a few do exist, notably Discover Financial Services ($29 billion). China's Alipay might also make sense, though it's valuation is difficult to discern.

PayPal could be about to shine
Unfortunately for eBay shareholders, the stock has fallen somewhat significantly since the announcement -- eBay shares are down more than 6.50% since it said it would spin-off PayPal, worse than the Nasdaq composite.

That fall was exacerbated by an earnings release that fell short of expectations -- eBay's revenue last quarter came in weaker than analysts had anticipated, and its forward guidance was light. But its PayPal unit remains strong -- sales rose 20%. And though new competitors have emerged, PayPal remains the dominant form of online payments, accounting for roughly one out of every six dollars spent online.

Investors could use the dip to accumulate eBay shares, knowing that they'll eventually receive stock in a dynamic payments company (PayPal as an independent entity, or PayPal combined with a smaller firm). Or they could wait for PayPal to begin trading (if they wish to avoid owning a piece of a somewhat stagnant online marketplace). But regardless of what happens to PayPal, it's certainly one of the most interesting assets in an industry that appears to be undergoing significant upheaval.

Sam Mattera has no position in any stocks mentioned. The Motley Fool recommends, Apple, eBay, Google (A shares), and Google (C shares). The Motley Fool owns shares of, Apple, Discover Financial Services, eBay, Google (A shares), and Google (C shares). 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.