Sell their position or push to sell the whole company?

That's the question private-equity firms are contemplating as they look to wrap up their experiment in bank investments that began at the height of the economic downturn. They got in low, but the recovery has taken longer than expected and regulation has been toughened. For some, now is the time to go.

Whether the firms float their stock or push for a sale of the entire company depends on several factors, including their sway over the board and market conditions. Rest assured, the astute investors are going to pick whatever results in the best payday.

"There are no general rules on how they exit and when they exit," says Thomas P. Vartanian, a partner at Dechert, speaking generally about private equity in banking. "It is a function of several things — the relationship with the entity, the short-term and long-term prospects and the condition of the market. In my experience, the big thing influencing exits and entrances has been the state of the market, and that is going to continue to be the case."

Add Sterling Financial (STSA) in Spokane to list the of private-equity-backed companies mulling its future. Last weekend Bloomberg News, citing two unnamed sources, reported the $9.9 billion-asset company is seeking takeover bids and has recently held talks with at least two potential bidders.

The news broke days after the third anniversary of Sterling's $730 million recapitalization, which included PE firms Warburg Pincus and Thomas H. Lee Partners. The firms invested a combined $342 million, giving each about a 23% stake in the company.

Sterling and Thomas H. Lee declined to comment, while Warburg Pincus did not return a call seeking comment.

Sterling's stock soared on the news, once the markets reopened after the Labor Day holiday. It has risen nearly 11 percent since Friday's close, finishing at $26.84 on Thursday.

Not surprising, say analysts. The market had built in a discount into the stock, expecting its private-equity holders to float their shares. That is what Warburg did with its stake in Webster Financial (WBS) starting late last year — culminating with a full exit in May.

Thomas H. Lee also said earlier this month it would reduce its stake First BanCorp (FBP) in San Juan, Puerto Rico. Essentially, the news of a potential sale was private equity going left when the market thought it would go right.

"Everyone really likes the Sterling story, but some investors are afraid to jump in because of this private-equity overhang," says Brett Rabatin, an analyst at Sterne Agee. "That issue was keeping the stock down — I'd say it was discounting the stock maybe two bucks."

Reiterating Vartanian's point, Rabatin says that investors shouldn't expect private-equity firms to stick to one path.

"Webster and Sterling are two different companies. You can't say, 'This is what they decided to do with this one, so that is the automatic template,'" Rabatin says.

At the time of the Webster exit, analysts said Warburg likely felt it had done all that it could do and that the returns in the next few years would likely be less attractive than they had been in the preceding few years.

However, Sterling is a growth story and has made a number of small acquisitions, including a pending one. Essentially, observers say, Warburg may have cashed out of Webster because it thought the stock price was about the best it could get, whereas the reported exploration of a Sterling sale suggests it thinks its holdings are undervalued.

The list of potential large suitors for Sterling includes Bank of the West, KeyCorp (KEY), New York Community Bank (NYCB), Rabobank, UnionBanCal and U.S. Bancorp (USB), analysts say. Jacquelynne Chimera, an analyst at Keefe, Bruyette & Woods, said in a research note that Umpqua Holdings (UMPQ) or Washington Federal (WAFD) could also be interested in some type of merger of equals. She suggested those banks would likely offer Sterling shareholders about 150% of its $18.49 tangible book value, or about $28 a share.

Rabatin says Sterling's board is probably looking for more than that — perhaps something closer to 170% of tangible book value.

Although private-equity players may go about their exits a few different ways, selling the company outright is their preference when they can do it, says Stephen Klein, a partner at Graham & Dunn in Seattle.

"I don't see how you're going to see the same premium selling your shares," Klein says. "If you can influence the sale of the company and you have a marketable commodity, you're far better off selling the whole company."