SAN FRANCISCO ( TheStreet) -- The Treasury Department will auction its last remnant of ownership in Wells Fargo ( WFC) this week, by selling warrants to purchase 110.3 million shares of common stock.

The warrants are related to the government's initial $25 billion TARP investment in Wells Fargo in October 2008. With a minimum bid price of $6.50, the offering will reel in at least $716.7 million in proceeds for taxpayers.

The bidding will take place on Thursday, May 20, beginning at 8 a.m., Eastern time in a modified Dutch auction overseen by book-running manager Deutsche Bank ( DB).

Wells Fargo is one of the last of the U.S. banking titans to rid itself entirely of TARP. Goldman Sachs ( GS) and Morgan Stanley ( MS) repurchased their warrants last summer when repaying the TARP investment. JPMorgan Chase ( JPM) was the first bank to hold an auction later in 2009, while Bank of America ( BAC) sold its warrants in a public auction in March. The government doesn't have warrants in Citigroup ( C) any longer, because its preferred stock investment was transferred into a large block of common shares, which the Treasury Department has been selling off periodically.

As previously reported by TheStreet, the process was delayed for Wells because of scheduling issues, and because the bank had initially tried to repurchase the warrants on its own to avoid diluting shareholders further. Ultimately, the two sides couldn't come to terms on price, and Wells management decided to auction the securities instead.

Given recent pricing, and the returns from other auctions, it's likely that taxpayers will receive a premium over the $6.50 minimum bid. For instance, the Treasury auctioned 2.53 million warrants for the small regional bank Valley National ( VLY) on Tuesday, with a minimum bid price of $1.70 apiece. The warrants garnered nearly 30% more value, selling for $2.20 apiece, and yielding net proceeds of $5.42 million.

Linus Wilson, a finance professor at the University of Louisiana at Lafayette, believes taxpayers will net at least $702 million in proceeds, and at most $1.76 billion in proceeds, from the transaction. His median estimate is $1 billion. Wilson has become something of a default expert on TARP warrant valuations, and pinpointed the Valley warrants at $2.20 apiece before the deal.

A Wells Fargo spokeswoman said the firm didn't have any comment on its warrant auction. In morning trading, shares of the San Francisco-based bank were down 2.8% at $29.74.

-- Written by Lauren Tara LaCapra in New York.
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