President Obama inspects a Chevrelot Silverado during a visit to the DC Auto Show, Jan. 31, 2012 in Washington, D.C. Obama touted his bailout of General Motors and Chrysler three years ago.

When the Treasury Department sold its last remaining shares in insurance giant AIG recently, it announced that it had earned a profit on the controversial bailout that began in 2008. That will not be the case for General Motors.

Treasury has finalized a plan to sell its remaining stake in the nation's biggest automaker over the next 15 months, beginning with GM buying back 200 million shares from the Treasury by the end of this year. That will leave the government holding about 19 percent of GM's shares, which it plans to sell throughout 2013 and perhaps into 2014.

The government's final exit from GM will mark the start of a new era for the carmaker, which has struggled to overcome its "Government Motors" image and chafed under rules that limit executive pay and perks. During this year's presidential campaign, Republican candidate Mitt Romney said he'd sell all the government's shares in GM as quickly as possible — even at a steep loss — to get the feds out of the private sector.

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President Barack Obama was more circumspect, though he now seems to be following Romney's advice. CEO Dan Akerson, meanwhile, has complained that GM's status as a "political punching bag" hurts sales.

But once the government sells its shares, GM will still be tainted by the fact that it failed to pay back all the taxpayer money used to save it back in 2009. GM initially got $49.5 billion from the U.S. government, and it paid back $23.1 billion of that after its stock went public in 2010. That left $26.4 billion GM still owed the government.

GM's shares have been trading around $25. The buyback will occur at a share price of $27.50, or a total of $5.5 billion for 200 million shares. But for taxpayers to get their money back, the government would have to sell at an average price of about $52. So by simple math, the total break-even price for those first 200 million shares would be about $10.4 billion. The $5.5 billion sale price amounts to roughly a $5 billion loss for taxpayers.

The exit itself could help boost GM's stock price, since some investors have been reluctant to buy shares in a company that's potentially subject to political manipulation. Treasury's move "provides a significant amount of clarity on one of the major overhangs on the share price," says Credit Suisse analyst Chris Ceraso, "particularly with the government articulating that it intends to fully exit over the next 12 to 15 months." And sure enough, GM shares rose on the news from Treasury.

GM has a few things going for it. Since the 2009 bailout and subsequent bankruptcy proceeding, GM has become a profitable, healthy company with about $38 billion in cash on hand. A new deal with the United Auto Workers allows GM to hire new workers at considerably lower wages than older ones earn, which ought to reduce labor costs over time. GM's product lineup is vastly improved and a new batch of pickups and SUVs — its biggest moneymakers — comes out in 2013. Plus, GM's operation in China is a roaring success.

But GM still has some deep problems, too, and it's hard to see its stock price getting close to the $52 breakeven price any time soon. GM's biggest albatross is its money-losing European operation, which is plagued with high costs, inflexible labor unions, and a recessionary European economy. GM says it plans to stop the losses there within three or four years, but it has whiffed on such promises before. GM is also behind Ford in terms of streamlining its global supply chain. And competition remains brutal in GM's home market, thanks to ever-rising quality and upstarts such as Hyundai and Kia.

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GM's stock price is likely to drift upward in 2013, with analysts forecasting a share price of $33 on average within 12 months, according to S&P Capital IQ. If the Treasury were able to sell its remaining shares at that price, it would represent another $6 billion or so loss for taxpayers. So unless there's an unexpected surge in GM stock, the net cost of the GM bailout to taxpayers will be around $10 billion to $12 billion.

Supporters of the company point out that the GM bailout saved much more than one automaker. Because GM is so large, keeping it alive also kept hundreds of suppliers in business. The Center for Automotive Research in Ann Arbor, Mich., says the auto bailouts (which also included lifelines for Chrysler and others) saved 1.4 million jobs, which is more than 15 times the number of Americans who work for GM.

Still, GM will go down as one of the costliest bailouts in U.S. history. Most of the banks that got bailout money following the 2008 financial crisis have paid it back, and of those that haven't, none required the amount of money GM got. The only companies who owe taxpayers more at this point are the wrecked housing agencies Fannie Mae and Freddie Mac. GM can only hope taxpayers don't remember that.

Rick Newman is the author of Rebounders: How Winners Pivot From Setback To Success. Follow him on Twitter: @rickjnewman.