Republic Airways (NASDAQOTH:RJETQ) is in the midst of a significant business transition, as the company recently agreed to sell its Frontier Airlines subsidiary to private equity firm Indigo Partners. This will allow Republic to concentrate on its core business of flying regional jets and turboprops for legacy carriers.

The Frontier sale process has added a significant amount of complexity to interpreting Republic's financial results. However, beneath all this "noise", Republic is generating strong earnings per share growth that is likely to continue for the next several years. Today, investors can buy into that growth at a great price that's less than 10 times earnings.

Digging into earnings
Republic recently reported adjusted earnings per share of $0.34 for Q3. At first glance, that appears to fall well short of the average analyst estimate for earnings per share of $0.70. However, Republic classified all earnings from the Frontier subsidiary as income from discontinued operations beginning with Q3. It was therefore excluded from adjusted earnings per share. Without this accounting change, Republic's earnings per share would have reached approximately $0.90, well ahead of analyst estimates and the company's original guidance.

Looking just at continuing operations (i.e. excluding Frontier), Repubic's adjusted earnings per share more than doubled year over year in Q3 from $0.13 to $0.34. Earnings are up on a year-to-date basis as well. Republic posted $0.46 earnings per share from continuing operations in the first three quarters of 2012, compared to $0.84 year to date.

The American growth opportunity
The biggest growth driver for Republic right now is the expansion of large regional jet flying at AMR's (NASDAQOTH:AAMRQ) American Airlines. Prior to AMR's bankruptcy filing, its pilot contract severely restricted the company's use of large regional jets. However, the AMR pilot contract has since been modified, which could potentially allow AMR to add hundreds of large regional jets to its fleet over the next several years.

Republic won the first contract for AMR's expanded regional jet operations, and began operating flights under the American Eagle brand in August, flying four Embraer E-175 jets for AMR at the end of Q3. This figure will grow to 16 by the end of the year, and top out at 47 by mid-2015.

Flying these large regional aircraft is the largest and most profitable part of Republic's business. At the end of Q3, Republic's subsidiaries operated 167 aircraft with between 69 and 99 seats. Republic's new flying for AMR will grow this total by around 25% in less than two years. Furthermore, AMR can potentially add another 200-plus large regional jets to its fleet in the future, and Republic has a good chance to win some of this business.

Risk factors
Republic is on a growth path right now, but the airline business is still quite risky. The biggest risk Republic faces is that it could be forced to idle some of its aircraft next year. The company has 41 small regional jets on short-term capacity purchase agreements that end in 2014, and there is no guarantee that these agreements can be renewed. Furthermore, Republic has five 99-seat E-190 aircraft that have been flying for Frontier, a service that is already winding down.

Neither of these risks is unmanageable. CEO Bryan Bedford stated on Republic's earnings call that he believes (based on conversations with the company's partners) that it will be possible to renew all of the small regional jet contracts for another year. However, Republic may decide to reduce the number of small regional jets it operates next year in order to free up pilots for the growing American Airlines E-175 business.

As for Republic's E-190s, the company may be able to sell or sublease them to another airline. If that is not possible, Republic may be able to use them for charter service. For example, last year, Republic won a three-year contract to provide charter service for Caesars Entertainment with five E-190s that had also formerly been operated for Frontier.

The other big risk factor for Republic shareholders is that the company has heavy near-term capital commitments, relative to its size. Republic has ordered 40 Bombardier CSeries jets that will start arriving in 2015, but this plane does not fit into the company's current business model. So far, Republic has not provided much detail on its plans for these new jets, but it may operate them under its own brand in a low-cost-carrier format.

Good upside for the risk
While Republic Airways stock comes with a good helping of risk, it currently trades for just eight times forward earnings. (Its closest peer, SkyWest trades for 11 times forward earnings, and probably faces even more business risks.)

A single-digit-earnings multiple is rare for a company with as much growth potential as Republic has. With the Frontier sale nearly complete, Republic's management team can devote its full attention to pursuing growth opportunities and mitigating the major risks Republic faces. These efforts are likely to pay off very nicely for shareholders.

Fool contributor Adam Levine-Weinberg has no position in any stocks mentioned. The Motley Fool recommends Embraer-Empresa Brasileira. 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.