Merrill Lynch & Co told the Government in 2008 that it would cost €16.4 billion at most to rescue the Irish banks, a quarter of the eventual bill for bailing out the country's financial system.
A report on the Bloomberg financial news service said that Merrill produced the estimate in a 45-page presentation to the Department of Finance on November 18, 2008.
This is according to documents released by the Government after a Freedom of Information request by Sinn Féin's Pearse Doherty.
The Government had paid the firm €7.3m for banking advice in 2008 and 2009.
Taxpayers were forced to pledge about €64 billion to rescue the country's banks after the worst property crash in Western Europe.
In November 2010, the country sought an international bailout as it struggled with the mounting cost of propping up the banks.
The Government is preparing to hold an inquiry into the banking crisis.
Ireland's then government hired Merrill Lynch to advise on options for its struggling lenders in September 2008 before introducing a guarantee of most of its banks' liabilities, totalling about €440 billion.
A spokeswoman for Bank of America Corp declined to comment on the report. The North Carolina-based bank agreed to buy Merrill in September 2008, two months before its advice to the government.
The State's contract with Merrill ended in June 2009, according to the Bloomberg report.
In the November 2008 presentation, Merrill estimated the recapitalisation costs at between €6.5 billion and €16.4 billion.
The firm weighed a series of merger options between Irish lenders as well as the creation of a nationalised bank to wind down toxic commercial property loans.
The government, led by then Taoiseach Brian Cowen, decided to set up a bad bank, known as the National Asset
Management Agency, in April 2009.
Banks lost about €40 billion transferring risky loans to NAMA. Further bad loan losses were uncovered during two Central Bank stress tests in 2010 and 2011.
Merrill estimated that the now-defunct Anglo Irish Bank would cost €5.63 billion to rescue, a fifth of its final cost.
It assumed AIB, the country's second largest lender, would need €5.62 billion. Within three years, the State had injected almost €21 billion into the bank, in which it now has a 99.8% stake.
The investment bank's €4 billion Bank of Ireland projection was near to its €4.8 billion taxpayer rescue, which has since been recouped by the Government.
Merrill's advice was based on increasing banks' core Tier 1 capital ratio, a measure of financial strength, to 8.5%.
The Troika had demanded in 2010 that enough capital be injected into the lenders to ensure the measure remained above 10.5%.
AIB's ratio stood at 15% at the end of 2013, while Bank of Ireland had a ratio of 12.2%.