By taking an ownership stake in the firms, the government can minimize the consequences of overpaying for the assets. It would own a piece of the very company that was benefited from the overpayment.There is, however, a significant problem with the warrant idea: It makes designing the auction to get the price right much harder.
Suppose that several banks own a particular type of mortgage-backed security. As I understand it, the Treasury would run a reverse auction to find which bank would sell the MBS at the lowest price. Competition among sellers should drive the price close to the actual value of the asset as judged by the banks.
But if each bank is required to sell the MBS together with a warrant on the bank's stock, then the items being sold are no longer comparable. A warrant on one bank does not have the same value as a warrant on another. How then can you run a competitive auction to find which bank is offering the best deal?
I suppose Treasury could hire option pricing experts to net out the value of the warrant from the price of the package to find the net price of the MBS. But doing so would certainly add noise to the process and make it harder for Treasury's auction experts to make sure the taxpayers is getting the best price for the securities it is buying.
Warren Buffett did not need to worry about this problem. He set the price for his position in Goldman based on his expert judgment, not an auction. But Treasury needs to find a more objective mechanism for setting prices of the things it buys. Auctions are precisely that mechanism, but they would do their job less well if an equity stake in each company is part of the deal.
Update: David's response.
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