Beaten-down shares of Peloton Interactive (PTON -0.98%) caught a much-needed break this week, soaring on Monday following suggestions that it's a takeover target, then jumping again on Tuesday after the fitness equipment maker announced that a new CEO will lead a plan to cull $800 million in annual costs. After giving up 85% of its value in just a little over a year, as of Tuesday afternoon this stock is 53% higher than Friday's close.

Only time will tell how the cost-cutting program will fare with a new chief at the helm, and there's certainly no guarantee Peloton will actually be acquired -- that's only a vague rumor hinted at by The Wall Street Journal, citing "people familiar with the matter." But if three suggested buyers really are in fact mulling a buyout offer, I believe one of them would be a much better partner for Peloton than the other two.

These two team-ups are good, but not great

On the off chance you haven't heard, various news organizations have reported that Amazon (AMZN -2.56%), Apple (AAPL -1.22%) and Nike (NKE -1.26%) may all be interested in buying Peloton. Each of these prospective pairings make their own unique sense. Take Apple, for instance. The brand appeals to higher-end smartphone fans, and it's arguable that these bigger spenders are mostly the same crowd willing and able to spend more to own premium home-gym hardware.

Apple's iOS users certainly spend more on apps and digital subscriptions. Research outfit App Annie says iPhone (and iPad) users accounted for 65% of the global app market's revenue last year -- despite, according to data from GlobalStats, only owning about 30% of the world's actively used mobile devices.

Given that Peloton has evolved from being a fitness equipment maker that also sells trainer-led workout subscriptions to a subscription company that also sells fitness equipment, those are no meaningless statistics.

A man running on his Peloton treadmill.

Image source: Peloton Interactive.

Nike is another somewhat obvious candidate. It's the premier name in fitness apparel, and its customer base certainly seems like a crowd that would be interested in treadmills, exercise bikes, and rowing machines for their own homes. Nike's no stranger to digital ecosystems either.

Amazon stands to make the most of a merger

Of the three companies said to be kicking the tires, though, Amazon is the one that not only has the most to gain but also could do the most to leverage the Peloton brand name. Don't misread the message. Nike and Apple would be able to do something for Peloton it can't quite do for itself. However, Amazon is better-suited to such a deal for a couple of reasons.

Chief among these reasons? The king of e-commerce already has an enormous digital subscription customer base, including over 200 million Prime subscribers. And bear in mind that Prime isn't the only subscription-based product the company offers. Music and e-books are also stand-alone services offered by Amazon along with a few other subscription options. Adding a guided-workout subscription to the mix wouldn't be a big leap for the company.

Or better yet, Amazon could integrate Peloton's exercise video content into Prime's existing lineup, boosting subscriptions to Prime itself. This would matter for one big reason beyond workout-oriented revenue. Quartz estimates that Prime customers are spending two to three times more than non-Prime subscribers do at Amazon.com. Neither Apple nor Nike has such an easy cross-selling opportunity.

The other key reason Peloton would be in particularly good hands with Amazon is that Amazon isn't necessarily in a hurry to make a subsidiary profitable. It's typically more interested in leveraging a brand to establish dominance even if that means remaining in the red a little longer than most investors might like. It'll worry about profits after it expands a business's total footprint.

This is no small matter either, especially right now. While investors are celebrating Peloton's cost-cutting plans, it may ultimately undermine the fitness equipment brand at the worst possible time in its existence. Are the 2,800 positions to be culled actually more critical to the company's success than anyone fully understands? Is the planned $150 million reduction in capital spending going to limit much-needed production? Does the $800 million of savings include reductions in vital advertising spending?

We just don't know. What we do know is that Peloton may be foregoing a chance to deliver a knockout punch to budding competition. Under Amazon's leadership, the company may opt to play offense rather than defense.

Start thinking in these terms

These are all just possible outcomes of an Amazon/Peloton pairing, of course. Amazon might not buy the fitness equipment outfit. Indeed, it's entirely possible no suitor will end up popping the question. In the event of an acquisition, though, these ideas provide a potential lens through which investors might look at a deal.

Simply continuing to exist -- even at a smaller scale -- isn't really enough here. Peloton needs a partner to help it do what it can't do for itself on its own, but also needs a partnership that can do something clearly accretive for the buyer as well. It's arguable that Apple would seek to make Peloton more exclusive like it was in its early days, but also smaller in the process. Amazon, on the other hand, could seek to make the equipment more affordable to the masses. Meanwhile, Nike may be the world's leading fitness apparel brand, but home-gym hardware isn't exactly in its wheelhouse.

Amazon is not only the name with the most to gain from a deal, but also the only one of the three that's likely willing to use the sort of brute marketing force that the Peloton brand really needs at this point. Now, let's see if Amazon sees that too. In the meantime, remember that buying a stock just because it's deemed a possible buyout candidate is a lousy investment strategy.