After banks make an offer, Treasury will decide whether to make a counteroffer, subject to a private appraisal if the two sides cannot agree on a fair price.
The administration has established the process for determining the price for millions of stock warrants the government holds that represent the final ties many large banks have to the $700 billion bailout program.
The Treasury Department said Friday the banks will make an offer for the warrants, and Treasury then decides whether to make a counteroffer.
If the government and a bank cannot agree on a fair price for the warrants, the two sides will have the right to use private appraisers.
Some of the nation's largest banks, including JPMorgan Chase & Co. and Morgan Stanley, have been eagerly awaiting Treasury's decision. They were among a group of 10 banks that repaid a total of $68 billion in bailout funds last week.
Taxpayers are expected to receive billions of dollars in exchange for the warrants, but negotiations on how to value them have taken longer than expected.
That's partly because the value of the underlying bank stock has fluctuated during the financial crisis. Treasury has wanted more money for the warrants it holds than the banks have been willing to pay.
Under the Treasury guidelines, the banks will have 15 days from when they repaid their bailout funds to submit an offer for what they would be willing to pay to buy back the stock warrants.
Treasury will then have 10 days to respond. If Treasury objects to the bank's offer, it can make a counteroffer, using a range of pricing methods.
If the two sides cannot agree on a price, appraisers for each side will be appointed. If those appraisers remain apart, then a third appraiser will be brought in, according to Treasury's guidelines.
Treasury's guidelines also leave as an option that if the two sides remain apart on a price, the government has the right to put the warrants up for sale in an auction process in which third parties would be invited to bid.
The department received $68 billion in repayments of bailout funds on June 17. The largest amounts were $25 billion from JPMorgan Chase & Co., and $10 billion each from Goldman Sachs Group Inc. and Morgan Stanley. They now have until the end of June to make an offer for the warrants.
The stock warrants allow Treasury to buy the banks' stock at a fixed price at some future date. The Government Accountability Office released a report last week calling for more transparency regarding the warrants and the repayment process.
Until the banks buy back the stock warrants that Treasury holds, they remain entangled in a program that has subjected them to limits on executive pay and other restrictions. The banks have complained that the government-imposed rules could hurt their profits and prevent them from hiring or keeping top talent.
Besides JPMorgan, Goldman and Morgan Stanley, the other seven big institutions repaying funds last week were: U.S. Bancorp, Capital One Financial Corp., American Express Co., BB&T Corp., Bank of New York Mellon Corp., Northern Trust Corp. and State Street Corp.
In addition to the $68 billion in bailout funds repaid by the 10 large institutions, another $2 billion has been repaid by smaller banks.
In addition to the money they are returning, the banks have paid Treasury more than $2 billion in dividends mandated under the bailout program passed by Congress last October at the height of the financial crisis.