AIB's market value rose 5.7 per cent to €12.9 billion on its first day back on the main Irish and London stock markets after 7½ years under nearly complete State ownership.
The successful re-privatisation of AIB, which had been bailed out by the Irish government during the financial crisis, was priced at €4.40 a share on Thursday.
It starts the repayment process of the near €21bn the State invested in propping up a stricken AIB almost seven years ago - although the Government views €6.6bn having already been repaid through dividend and government guarantee payments, the redemption of preference shares, and bank levy payments.
"A successful transaction would represent an important milestone in our journey to dispose of our banking investments and ultimately recover all the money the Irish state has invested in AIB", Noonan said.
THE DEPARTMENT OF Finance has announced that 25% of AIB shares have €4.40 each, raising €3 billion for the state. That would imply a market capitalization of 13.3 billion euros at the upper end of the range.
AIB will be listed on the Dublin and London stock exchanges.
Irish taxpayers came within touching distance of breaking even on their €20.8 billion (£18.3 billion) bailout of big four lender Allied Irish Banks today after it returned to the stock market.
"This is a landmark day for the bank", AIB chief executive Bernard Byrne said in a statement.
The lender also reported an annual pre-tax profit of 1.7 billion euro earlier this year, and delivered a dividend for the first time in nine years. "The level of investor interest and support is a great vote of confidence in the strength of the turnaround in the bank and the wider economy". Noonan said last month it would probably take eight to 10 years to return AIB fully to private ownership.
The government has meanwhile stated its intention to use the proceeds of the sale to pay down a small portion of its €200-billion national debt, which ranks among the highest in the eurozone.
The state now has an option to sell a further 3% stake in the coming weeks, which would raise a further €400 million.