A public "thought experiment" from Baird Equity Research analyst Colin Sebastian posits that eBay (EBAY 0.31%) might do better to combine with Google (GOOGL -1.97%) than to spin off PayPal, as activist investor Carl Icahn wants. Fool contributor Tim Beyers explains why he wouldn't support such a deal in the following video.

Sebastian didn't fervently advocate for a Google-eBay tie-up in his note. Rather, he raised the possibility of a combination because of how it might serve both companies. Google, in particular, could fill a sizable gap in its payments offering while adding a massive (and searchable!) index of products for sale.

That's important, Tim says, because Amazon.com (AMZN -1.65%) tends to be the go-to for product research conducted online. In fact, product revenue improved 22.9%, to $21.07 billion, in the fourth quarter. The site is the fifth most popular in the U.S. and 12th worldwide, according to Alexa. You can bet most of that is shopping traffic.

We can say the same for eBay.com, which ranks eighth and 26th, respectively, according to Alexa. The company also has more than 143 million active PayPal accounts, and processes some 9 million transactions daily. Imagine if Google had access to that volume. Not only would it improve search, but it would also give the company a new installed base for content and products sold via the Google Play store, Tim says.

So why not strike a deal? The price: eBay trades for near $69 billion in enterprise value. Paying a reasonable takeout premium would put Google's buy price at a minimum of $100 billion, Tim says. The search king only has half that in cash available as of this writing, meaning the remainder would have to be financed via stock, debt, or some combination thereof. Add it up, Tim says, and a Google-eBay merger looks ill-advised, especially with Square emerging as a fast-growing PayPal alternative that's likely to be had for far cheaper.

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