Popular (BPOP) could soon be $186 million closer to cashing out Uncle Sam.

Evertec (EVTC), a payments business Popular started 25 years ago, filed a secondary offering with the Securities and Exchange Commission on Monday to sell 20 million shares, including 9 million shares currently held by the $37 billion-asset Popular.

Based on Evertec's closing price before the offering's announcement, Popular could bring in $186 million after taxes, says Alexander Twerdahl, an analyst at Sandler O'Neill.

The move could help Popular exit the Treasury Department's Troubled Asset Relief Program, Twerdahl says. A recipient of $935 million in Tarp funds in 2008, Popular is the largest company still in the bailout program and it has been looking for a way to exit in the most shareholder-friendly way possible.

The proceeds would boost Popular's tangible common equity ratio to more than 10%, giving it ample room to repay Tarp and still have a 9.02% ratio, Twerdahl said in a research note. The company already has more than $400 million of cash and it could float a senior note to cover the rest of the repayment.

Popular has not made any announcements about what it plans to do with the expected proceeds.

Evertec has been a cash cow for Popular for several years now. Popular sold a 51% stake in the payments business to private-equity firm Apollo Management in 2010 to bring in some additional capital. Also, Popular earlier this year reduced its stake to 32% when Evertec went public.

Popular used the $171 million in gains from the initial public offering to offset a $135 million loss related to the writedown of nearly $600 million of nonperforming mortgages it planned to sell.

After the secondary offering, Popular would still own 21.3% of Evertec. That stake could be worth roughly $375 million based on Evertec's pre-announcement trading price, Twerdahl said.

Popular executives have an emotional attachment to Evertec, but if regulators wanted the company to have more capital before allowing it to cash out of Tarp, Popular would likely sell the remaining stake before doing a capital raise, Twerdahl says.