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* Price range set at 0.30 to 0.33 euros a share
* Fairfax-led group has committed to buying 47 pct of issue
* Bookbuilding to run April 25-29
* Peer National Bank sells five-year bond at 4.5 pct (Adds details, background, NBG bond issue)
By George Georgiopoulos
ATHENS, April 24 (Reuters) - Greece's third-largest lender Eurobank has set a tight price range for its 2.86 billion euro ($3.96 billion) share offering, aiming to fill the order book quickly as it seeks the funds to plug a capital shortfall.
Eurobank, which is 95 percent-owned by Greece's bank bailout fund HFSF and has a current market value of 2.29 billion euros, set the range at 0.30 to 0.33 euros per share - a discount of 15 percent to 23 percent on Thursday's closing price on the Athens Stock Exchange.
Reflecting growing confidence that bailed-out Greece has turned the corner, Eurobank is the third of its lenders to tap international markets after peers Alpha Bank and Piraeus raised 2.95 billion euros between them.
The country's biggest lender National Bank of Greece (NBG), which also plans to tap markets with a 2.5 billion euro share issue next month, on Thursday sold 750 million euros of senior bonds, borrowing funds at a lower cost than the government earlier in the month.
NBG's five-year bond with a 4.375 percent coupon was priced to yield 4.50 percent, 45 basis points below the yield on Greece's 3-year bond issued earlier in the month.
Eurobank's capital shortfall was revealed in a health check last month by the Greek central bank to see whether last year's recapitalisation of the top four banks had left them with enough cash to withstand rising loan losses. It showed that Eurobank needed an extra 2.95 billion euros.
Bookbuilding for Eurobank's cash call will run from April 25 to 29, with 10 percent offered to local investors.
An investment group led by Canada's Fairfax already agreed earlier this month to be anchor investors in the share sale, committing to take up 47 percent of the issue at 0.30 euros a share.
If Eurobank raises the full 2.86 billion euros from markets, it would ease Greece's debt burden because the HFSF would not have to dip into its remaining 11 billion euro capital buffer to support the lender. The HFSF has been endowed with 50 billion euros under Greece's international bailout.
If the final price after the bookbuilding process equals that offered by the anchor investors, each is guaranteed to be allocated shares for the amount committed. If the price proves to be higher, the anchor investors can either match it or pull out and receive a fee of 1.5 percent on their commitment amount.
Current shareholders, including the HFSF, will waive rights to the share issue, which will dilute the rescue fund's stake to 34.7 percent if the shares are placed at 0.30 euros.
Barclays, Deutsche Bank and JP Morgan will lead the bookbuilding aimed at international investors. ($1 = 0.7231 Euros) (Editing by Harry Papachristou and David Goodman)