SARAJEVO, Sept 15 (Reuters) - British American Tobacco has bought a Bosnian regional government's 39.9 percent stake in tobacco factory Fabrika Duhana Sarajevo (FDS) for 42.7 million Bosnian marka ($24.4 million), BAT said on Thursday.

Bosnia's Bosniak-Croat Federation is attempting to privatise a number of state-owned enterprises to plug a hole in its budget.

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The world's second-biggest cigarette maker said in a statement it was willing to take over the remaining stake in the Bosnian company for 83.5 marka per share, the price per share it paid the regional government.

The remainder of FDS is owned by local subsidiaries of Austria's Raiffeisen Bank and Italy's UniCredit SpA , as well as investment funds and small shareholders.

BAT already owns plants in Serbia and Croatia.

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FDS' shares were trading at 65.98 marka on Thursday, up 3 percent on Wednesday's close. The company has a market capitalisation of 81.98 million marka.

($1=1.750 Bosnian marka) (Reporting by Maja Zuvela; editing by Susan Thomas)