Have you ever lost something valuable that, given the chance and the means, you'd take back in a heartbeat? Well, payment processor Visa (NYSE:V) may have just such an opportunity: It's apparently making a push to acquire its onetime subsidiary, the similarly named Visa Europe.

According to a widely cited Bloomberg report, Visa and its counterpart across the Atlantic are in preliminary talks. The deal, if realized, could be worth up to $20 billion. And this blockbuster has been a long time coming.

Visa Stack Of Cards By Credit Karma

Image source: Credit Karma via Flickr.

What's in a name?
This rather odd situation came about because of Visa's rather odd history.

Despite its current size and power, Visa didn't start out as a stand-alone company. It started as the payment card operations of Bank of America (NYSE:BAC) -- hence the brand's original name, BankAmericard. What's now Visa was spun off into an entity owned and managed by a consortium of the card's issuers.

This eventually coalesced into the company we now know as Visa, initially a somewhat loose collection of regional operators. One of these was Visa Europe, which was spun out as a separate firm in advance of Visa's 2008 IPO.

Ever since then, Visa and Visa Europe have been solid business partners, albeit as individual entities. Like BankAmericard in the post-Bank of America era, Visa Europe is owned by a consortium of issuers (over 3,000, according to a recent count) and is not publicly traded. It operates under a permanent, irrevocable, exclusive license from its American counterpart.

That license doesn't come cheap: In Visa's Q2, Visa Europe paid $55 million for the privilege.

Put upon
The separation also granted the onetime subsidiary a potentially lucrative security. Since the split, Visa Europe has held a put option granted by Visa that, if exercised, would obligate the U.S. firm to buy it outright within roughly nine months.

The sale price is based on a complicated formula that takes into account a number of financial figures from both companies. According to the Bloomberg article, the two sides are discussing a price between $15 billion and $20 billion.

That's a lot of money, but the U.S. firm seems eager to spend it. The scuttlebutt is that Visa began the buyout negotiations. Of course, because it's not the holder of the put option, it can't pull the trigger on any buyout. Only a "yes" vote of at least 80% of Visa Europe's directors can do that.

Visa has the means to offer a sweet deal in order to sway them. The company has been a powerful, money-minting machine for some time; in Q2, for example, it posted a bottom line of nearly $1.6 billion on revenue of $3.4 billion for a net margin of almost 50%. The balance sheet is squeaky-clean, with zero debt.

In other words, Visa has a credit profile other companies dream of, at a time when interest rates are as low as they're going to get. Visa won't have much of a problem securing inexpensive financing to buy its European sibling.

Euro vision
Visa Europe would be a great addition to Visa's business. Visa Europe is a much smaller operation with a thinner profit margin, but it still does a thriving business. In fiscal 2014 it raked in $1.4 billion in revenue and just $242 million in bottom-line profit.

Better times should be ahead. Europe's economy has been weak in the years following last decade's financial crisis, but critical parts of the continent seem to be recovering steadily.

All in all, then, the potential fusing of Visa and Visa Europe seems like a well-timed move, although it has taken an awfully long time to get here -- particularly considering that they were once part of the same organization.

Eric Volkman has no position in any stocks mentioned. The Motley Fool both owns and recommends Bank of America and Visa. 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.