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What: Shares of online and for-profit higher-education company Apollo Education Group Inc (NASDAQ:APOL) are up more than 16% on January 12 at 11:20 a.m. ET. This is one day after the company released less-than-stellar earnings for its first quarter, sending shares down about 5% on Monday.

So what: Today's rebound follows comments by management on yesterday's earnings call that they were exploring all their options, including merger and buyouts, for the company. And just that quickly, rumors surfaced that Apollo Global Management -- an unaffiliated private equity company -- is in talks to buy the beaten-down poster child of the for-profit education sector. 

Now what: If I were an Apollo Education shareholder, I would take this opportunity to cut my losses and move on. Yes, it's possible another buyer comes along and the price goes up, or that Apollo Global ends up paying more, but there's also a chance these rumors turn into nothing, or that the negotiations fall apart. If either of those happen, the stock will tank again, and probably even further than today's gain. That's just part of the reason I'd move on. 

The bigger issue? Fundamental concerns with Apollo Education's long-term potential, as it's not the only for-profit college educator in decline, with fellow big players DeVry Education Group Inc (NYSE:DV) and Strayer Education Inc (NASDAQ:STRA) all in a cyclical decline:

APOL Normalized Diluted EPS (TTM) Chart

APOL Normalized Diluted EPS (TTM) data by YCharts.

While challenges about the viability of their business models may be a bit overstated, there are certainly big challenges all three of these companies must face. The first is a generally strong and strengthening U.S. labor market. This is big, since it means fewer working adults will want to or need to increase their training or education. This has already started happening, and it's one factor behind the declining revenues Apollo Education, DeVry, and Strayer have all reported over the past five years. 

Moreover, a larger number of public colleges and universities are beginning to compete in the online education space that the for-profits have dominated for years. Not only are public institutions often lower-cost than for-profits, but they generally have better reputations and are often local to the students taking online courses. Add it all up, and the broad reach that has been a big competitive advantage for Apollo, DeVry, and Strayer for years is also weakening. 

Put it all together, and the future just doesn't look very bright for any of these companies in coming years. And that's why I'd be selling my shares of Apollo if I were a shareholder today. 

Jason Hall has no position in any stocks mentioned. The Motley Fool has no position in any of the stocks mentioned. 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.