An increase in new student enrollment and projections that total enrollment will grow next year fueled a sharp rise Tuesday in the shares of online university Capella Education Co.

Shares rocketed up $5.36, or 18 percent, to close at $35.04 after the company reported first-quarter earnings that beat Wall Street expectations.

Analysts said the rally was driven by key trends pointing to rising profits at the online, for-profit university that has struggled with increased regulatory scrutiny and falling enrollment.

"Once total student volume growth becomes positive, the chances of earnings growth are a lot better," said Jerry Herman, an analyst at Stifel Nicolaus in Cleveland. Based on the first-quarter enrollment numbers, it appears that the new students needed for next year's total enrollment growth "are at least in the pipeline," Herman said.

First-quarter total enrollment dropped 3.1 percent to 36,405, the company said. While a financial recovery at Capella requires growing total enrollment, Capella's growing list of new students is likely to swell existing student ranks enough to achieve overall student growth by mid-2014, Herman said.

"We are pleased with our execution during the first quarter as we compete more effectively in a challenging market environment," Capella CEO Kevin Gilligan said in a statement. The company is increasingly confident its enrollment will grow again in the first half of next year, Gilligan said.

Capella, which does business under the name Capella University, earned $8.8 million, or 70 cents a share, in the first quarter, down 22.5 percent but good enough to beat analysts' expectations by 8 cents a share. Revenue was $105.2 million, down 3.8 percent.

Capella and its online competitors and traditional colleges have been struggling for several years with declining enrollments. Fall enrollment in all higher education institutions was down in 2011 and 2012, Herman said.

The recession and the financial crisis meant that some students couldn't afford college, and those who could were wary of going into debt, he said. At the same time job prospects were not great for college graduates. Consumers were calling into question the whole value proposition of higher education.

At the same time, Capella and the rest of the for-profit education industry have come under tighter regulatory scrutiny in recent years, which has crimped profit margins. In addition, private schools such as Capella face at least the possibility that online students could be drawn back to traditional colleges that have moved swiftly into online education in the last year and a half, Herman said.

"Capella has taken a more-sophisticated-than-average approach to driving the quality of their education product, their value proposition," Herman said. "They use key guiding factors, including affordability, increased speed to competency and greater alignment with employers. And there's been a lot of internal change at Capella that helped improve student retention.''