Shares of Peloton (PTON 4.89%) finally had a good week this week as reports swirled the company could be a private equity takeover target. According to data provided by S&P Global Market Intelligence, shares jumped as much as 31.5% this week and are up 23% for the week as of 2:30 p.m. ET on Friday afternoon.

Buyers circle Peloton?

Last week, Peloton reported what can only be called a disappointing earnings report. The core-equipment and premium-subscription segment is doing well, but the app that was supposed to allow Peloton to scale is struggling with high churn and low sign-ups.

But that was forgotten this week when reports emerged that the company has gotten interest from private equity firms. This may make sense given the extremely low churn rate of about 1% for the core-content subscription, but management has been pouring money into expanding the app, and that's why the company hasn't yet been profitable.

A private equity firm would be more likely to cut costs further and narrow the focus to what's working at Peloton, which is why a deal may make some sense for everyone.

A deal may not materialize

As much as the market got excited about a potential buyout early in the week, shares faded as the week wore on and no offers emerged. It's possible there is no buyout offer or management is unwilling to entertain a buyout given what they see in the business. So, this pop could fade.

The good news for investors is Peloton is finally free-cash-flow positive and has a core that's working as hoped. More cost cuts are on the way, and if the company stays focused, this could be a solid company long term even if it's not the growth stock investors hoped it would be.