CEO Bob Benmosche says U.S. taxpayers will earn up to $10 billion on the $182 billion rescue of American International Group , the insurance company he runs. Of course, that depends on how one defines profit.

How much AIG actually borrowed after it was saved from bankruptcy in late 2008, how much it still owes and questions about the point at which the U.S. Treasury breaks even on its shares all complicate any calculation about how much the government will make on the insurer's bailout.

It even is possible, under some (disputed) scenarios, that all of the profits go to the Federal Reserve and the losses go to the U.S. Treasury, netting a gain for the government as a whole.

Either way, though, even critics of the way the bailout has been handled concede something is better than nothing.

Now is that a great return relative to other investments in the stock market? Not really, said Linus Wilson, an assistant professor of finance at the University of Louisiana-Lafayette, who has calculated the returns from the bailout. We'll take breaking even after a huge holding period, rather than a huge loss.

Benmosche, in an interview with CNBC's Jim Cramer Monday night, was adamant AIG would repay its bailout in full and that between all the branches of government that participated, a profit of $5 billion to $10 billion would result.

That is a far cry from two years ago, when the Congressional Budget Office estimated the government would lose $36 billion on the rescue.

But where the government's cost ends and the taxpayers' profit begins is sort of an open question.

A chart on AIG's website walks through the bailout step by step - $182.3 billion in total funds authorized, to be exact, less $20.9 billion that was never used or expired before it could be used. In other words, an actual draw of $161.4 billion.

Various sums have been repaid since in a variety of ways, mostly through asset sales. AIG says all of those repayments were on their own profitable, after factoring in interest and the dividends that were paid on the various credit facilities and preferred shares.

With those repayments done, some $44.7 billion is left to be recovered, according to AIG -- $35.7 billion worth of common stock and about $9 billion in a Federal Reserve vehicle known as Maiden Lane III.

MAIDEN LANE MATH

This, however, is where it gets even more complicated than usual. The Fed created the legal entity called Maiden Lane III and lent it money, which the entity then used to buy collateralized debt obligations from AIG's counterparties. That relief let AIG terminate insurance contracts against the CDOs, easing its liquidity burdens.

Maiden Lane III is non-recourse to AIG, though; AIG is not obliged to make the Fed whole on its loans under any circumstance. As it stands, that is not an issue, as the portfolio's holdings are worth nearly twice the loan balance.

In addition to Maiden Lane III, there was also Maiden Lane II, a Fed vehicle to relieve AIG of $20.5 billion in mortgage-backed securities. The last of its holdings were sold off recently, for a net gain to the New York Fed of $2.85 billion.

Combine that with the paper profit the Fed is looking at on Maiden Lane III as of today and you get a return of $11.3 billion -- a tidy sum, particularly since the early 2011 deal to recapitalize AIG was intended, in part, to buy out the central bank's portion of the rescue.

AND THEN THE SHARES

But leaving aside the Maiden Lane entities, there is still a fierce debate about the common stock. The U.S. Treasury still holds a 70 percent stake in AIG, or 1,248,141,410 shares. As of Monday's close that was worth $36.27 billion, for a profit to the Treasury of $570 million, give or take.

That assumes, though, that the Treasury's break-even point on the stock is $28.73 per share. That is what the Treasury says on its website, factoring in all the money that was disbursed in exchange for shares and the total number of shares the Treasury ended up holding. However, the former inspector general of the Troubled Asset Relief Program disagrees, forcefully.

In Neil Barofsky's view, there are two sets of shares: those the Treasury got in exchange for its TARP bailout funds, and those new shares the Treasury got in early 2011 when AIG was recapitalized.

The government says the TARP cost basis was $43.53, and to Barofsky, that means the TARP program is losing money when the Treasury sells AIG stock at $29, as it has done twice in the last 10 months. (Were the Treasury to sell all 1.1 billion of the original TARP shares for $29, it would in theory lose about $16 billion on that investment.)

My complaint with Treasury is when they put out their break-even number for the sale of common shares, instead of using 1.1 billion as the denominator they used 1.6 billion and described that as the Treasury investment, Barofsky said in an interview.

I'm not critical of the notion that the taxpayer may break even on the AIG bailout, my problem is the transparency issue, he said, adding: I hope Benmosche is 100 percent right.

The Treasury, to put it mildly, disagrees with Barofsky's assessment of the math. To the government, the TARP math is irrelevant, since the new shares from the recapitalization had zero cost, and therefore lowered the Treasury's cost basis in the stock dramatically to the $28.73 figure.

In the dark days of the financial crisis, when commitments to AIG totaled $182 billion, few would have believed that we'd already be able to reduce that amount by more than 75 percent, or that we may be able to recover every single dollar invested in the company, Assistant Secretary for Financial Stability Tim Massad said in a statement last week.

The ultimate answer, though, may come from the investment banker who led much of AIG's rescue -- Jim Millstein, the former chief restructuring officer of the U.S. Treasury and now chairman of his own firm, Millstein & Co.

He's just nitpicking and he's missing the bigger point, Millstein said of Barofsky. The bigger point is that the federal government actually did something important and effective and it was controversial and people have a lot of ambivalence about it, but had the government not done it - over two administrations - effectively we'd be in a much worse position than we are today.

(Reporting By Ben Berkowitz; Editing by Dan Grebler)

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