Treasury said Tuesday in its two-year retrospective on the Troubled Asset Relief Program that the net cost of TARP’s AIG bailout at current market prices is $5.1 billion. The cost of the AIG bailout has been subject of considerable head scratching in recent days, with TARP winding down and the terms of federal assistance to AIG changing for the umpteenth time.

The New York-based insurance company and Treasury agreed last week to a swap in which the government will expand its AIG holdings in exchange for the liquidation of the Federal Reserve’s claims on AIG. Then the government, over time, will sell its AIG shares into the market in hopes of making taxpayers whole.

“The exit strategy announced today dramatically accelerates the timeline for AIG’s repayment and puts taxpayers in a considerably stronger position to recoup our investment in the company,” Treasury Secretary Tim Geithner said in a statement Sept. 30.

Treasury has said it believes the deal will allow the government to extract itself from the company over time, and that it sees a profit on the AIG bailout as possible assuming financial markets hold up and the economy doesn’t take another dive.

(Treasury says it is also making $22 billion on the conversion of some other AIG preferred shares to common — money it will use to bring the total cost of TARP to taxpayers down to $30 billion.)

Initially, last week’s restructuring will actually expand the company’s TARP borrowings to almost $70 billion from $48 billion previously. But because most of that sum is in preferred stock that will turn into AIG common stock, the net effect will be to raise Treasury’s ownership of the company to 92%.

Though the notion that the government could make money on bailouts of failing financial companies has been widely derided, Treasury shows in Tuesday’s report just how that math could work.

After the proposed restructuring of AIG, TARP will hold 1.09 billion shares of AIG common stock, plus preferred equity interests in SPVs of approximately $22.3 billion, against a cost basis of $69.8 billion. Valuing the common equity at the market close for October 1 of $38.86 per share implies a net cost of -$5.1 billion.

That’s not a bad outcome, considering that various arms of the government agreed to put up as much as $182.5 billion starting in 2008 to prop up AIG. And using Treasury’s math, AIG shares would have to climb only about 10% from current levels for taxpayers to break even – on paper, at least.