A decision by Popular (BPOP) in San Juan, Puerto Rico, to reduce its stake in a former technology subsidiary could help it exit the Troubled Asset Relief Program.

Evertec (EVTC), a payments company Popular founded 25 years ago, filed a secondary offering with the Security and Exchange Commission to sell roughly 15.3 million shares, or more than $322 million of stock, at $21.09 a share.

Popular plans to sell about 5.8 million shares, or $122 million of stock. Brian Klock, an analyst at Keefe, Bruyette & Woods, wrote in a note to clients Thursday that the sale would reduce Popular's stake in Evertec to 14.8% from 21.3%. The sale could allow Popular to exit Tarp without having to sell its own common stock, Klock added.

Popular has $935 million of outstanding Tarp, representing the largest stake of any company remaining in the program.

Popular has already raised a portion of the money it would need to exit Tarp by whittling down its Evertec stake. It sold a 51% stake in the company to Apollo Management in 2010, and it gained about $171 million in Evertec's April initial public offering. The $34.5 billion-asset Popular used those proceeds to cover a $135 million loss on the writedown of nearly $600 million of bad loans.

In September, Popular sold another block of Evertec stock worth about $186 million.

Popular has not stated what it plans to do with proceeds from the upcoming offering, though Klock wrote in his note that the sale "gives us additional conviction in our belief that exiting Tarp will likely be a near-term event."

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