* Posts 2013 net profit of 2.92 bln eur on goodwill write-back
* Excluding write-back, posts 304 mln eur 2013 loss
* Non-performing loans ease to 32.7 pct of book from 32.9 pct in Q3 (Adds CEO comment, details)
By George Georgiopoulos
ATHENS, March 10 (Reuters) - Greece's fourth-largest lender Alpha Bank reported a profit in 2013, thanks to an accounting gain on its acquisition of Emporiki Bank, but without the one-off it was loss-making as provisions for bad debt weighed.
Greek banks struggled with bad loans because of a deep recession last year. Record unemployment of nearly 28 percent has made it hard for borrowers to service their loans, forcing lenders to provision for bad debt, although the pace of rise is slowing.
Non-performing loans (NPLs) were the focus of a health check the country's central bank ran to assess whether Greece's top banks are adequately capitalised to absorb further credit deterioration.
Alpha, 81.7 percent owned by Greece's HFSF bank rescue fund, said that including an upwardly revised 3.3 billion euro goodwill write-back on Emporiki booked in the first quarter, it posted a net profit of 2.92 billion euros ($4.05 billion) last year.
Excluding the write-back, Alpha narrowed its loss to 304 million euros last year from a loss of 1.08 billion in 2012.
Provisions for non-performing loans - credit in arrears for more than 90 days - rose 15.4 percent to 1.92 billion euros, with NPLs decreasing to 32.7 percent of its book from 32.9 percent in the end of the third quarter.
Based on central bank data, non-performing loans held by Greek banks rose to 31.2 percent of their total loan book at the end of the third quarter last year from 29.3 percent at the end of the first half.
"In 2014 we expect further improvement to our core revenues from decreased funding costs," Alpha's Chief Executive Dimitris Mantzounis said in a statement.
Net interest income rose 19.8 percent last year compared to 2102, helped by lower wholesale funding costs and a drop in deposit rates, with Alpha saying it expected the trend to continue in the next quarters.
Alpha, with a current market value of 7.6 billion euros, had the lowest capital shortfall - 262 million euros - among the country's top four banks, a stress test by the central bank showed last week.
The bank plans a share offering of up to 1.2 billion euros to boost its capital and pay back 940 million euros of preferred shares owned by the state.
The equity offering, without pre-emption rights for its existing shareholders and underwritten by Citigroup and J.P. Morgan, will increase its free-float and the liquidity of its stock. ($1 = 0.7214 euros)