The Treasury Department said Wednesday that it will sell its remaining stake in General Motors by early 2014, writing the final chapter of a $50 billion bailout that saved the auto giant but stoked a heated national debate about the government’s role in private industry.

Taxpayers are sure to lose billions of dollars in the deal, even though GM has bounced back from the darkest days of 2008, when it almost ran out of cash.

The company has racked up $16 billion in profits during the past three years and added more than 2,000 American workers. Now GM is looking forward to the day when it can shed the stigma of government ownership and bury the derisive moniker of “Government Motors,” which it says kept customers away from dealerships.

“This is very attractive to the company and to our shareholders,” GM Chief Financial Officer Dan Ammann said. The deal is “obviously good for the business in terms of continuing to remove the perception of government involvement in the company, which is going to be good for sales.”

When the government sells its last GM shares, the Treasury Department projects that autos will be the biggest money-loser of all the corporate bailouts connected to the Great Recession. The government already lost more than $1 billion on the bailout of Chrysler, which has repaid all its loans.

“There should be no expectation about getting back the taxpayers’ money,” said Phillip Swagel, professor of public policy at the University of Maryland and a former assistant treasury secretary under President George W. Bush who authorized the first installment of GM’s bailout.

Under the deal, GM will spend $5.5 billion to buy back 200 million shares from the Treasury, with the sale closing before year’s end. That will leave the government with 300 million shares, or a 19 percent stake, which it plans to sell during the next 12 to 15 months.

The Treasury Department has held the stock for more than two years while awaiting a better price. In a statement issued Wednesday, it said the bailout protected the business at a critical time.

“The auto industry rescue helped save more than a million jobs during a severe economic crisis,” said Timothy Massad, Treasury’s assistant secretary for financial stability. “The government should not be in the business of owning stakes in private companies for an indefinite period of time.”

Treasury officials declined to answer questions from The Associated Press about why the government is selling now.

The government clearly waited until after the presidential election to unload the stake and close the bailout, which was a contested issue in the campaign between President Barack Obama and Republican challenger Mitt Romney. Yet the sale comes as U.S. auto sales are rising, and many analysts predict a higher GM stock price in the coming years.

GM shares sold for $33 each when the company returned to the public markets two years ago. Analysts expected further growth, and the shares rose shortly after the sale. But they fell dramatically early this year as the U.S. economy slowed and Europe headed toward recession.

Citi analyst Itay Michaeli said the government ownership has held down the stock price because investors feared the Treasury would flood the market with big blocks of shares. The government, he said, is probably expecting a big price bump because of the GM buyback.

“The thinking is perhaps you sell some of it now, that starts to lift the overhang and that potentially allows a better exit (price) for the remaining shares,” he said.

GM will buy the 200 million shares at $27.50 each, about an 8 percent premium over Tuesday’s closing price of $25.49. The shares shot up more than 9 percent Wednesday to $27.91, the highest price of the year, before falling back somewhat.

Breaking even would require selling the remaining 300 million shares for an average of about $70 each — more than double the current trading price.

The government bailed out GM during the financial crisis in 2008 and 2009, when the economy teetered on the brink of a depression. Without government help, the wheezing automaker would likely have been auctioned off in pieces. At the time, GM was a sick company, racking up more than $86 billion in losses since 2005. It had $53 billion in debt, burdensome labor contracts and a weak lineup of cars at a time when global markets were shifting to smaller vehicles.

Even during GM’s 2009 bankruptcy, government officials said they never expected to get all the bailout money back. Former auto czar Steve Rattner conceded in 2009 that the government would lose billions bailing out Chrysler and GM. But he said saving thousands of jobs and keeping the industrial Midwest alive was worth the money.

The government sold 412 million shares in the 2010 initial public offering. The shares rose shortly after the IPO, but then slid as the U.S. economic recovery faltered and Europe’s economy took a turn for the worse. As the shares fell, the government balked at further sales.

Even with the government ownership, GM has made money for 11 straight quarters. But there are signs of trouble. It has lost money in Europe for a dozen years, and its U.S. sales aren’t growing as fast as competitors or the overall market.

The company has never been prohibited from paying a dividend to shareholders, but so far has decided against it.

Government-ordered pay restrictions will remain in effect until the Treasury completes the sale of its remaining 19 percent stake. CEO Dan Akerson has complained the pay limits have hurt the company in its efforts to recruit top talent.

Although GM is paying a premium for the government shares, GM’s other shareholders could benefit because the number of shares on the market will be reduced about 11 percent. That should increase the value of the remaining shares.

The bailouts of GM and rival Chrysler were part of the Troubled Asset Relief Program created by Congress to save banks during the 2008 financial crisis. So far, the government has recovered 92 percent of the $418 billion in funds disbursed through the TARP.

Last week, Treasury sold its final shares of insurance giant American International Group, which had received the largest amount of government support. The government actually made money on its bailout of big banks, and it expects to recoup all but $1.8 billion of the $14.6 billion supplied to smaller banks.

But in the end, TARP programs are expected to lose $42.1 billion, including a $45.6 billion loss on programs supporting homeowners who are battling foreclosure.

Mark Zandi, chief economist at Moody’s Analytics, said Treasury’s estimate of final losses from TARP is overstated because much of the money for homeowners will never be used.

Private economists rated the TARP effort as an unqualified success in stabilizing the banking system during the crisis.

“It was a slam-dunk success,” Zandi said. “It was vitally necessary and proved to be a key to ending the financial panic and jump-starting an economic recovery.” He expects the final government loss on TARP to be $24 billion.

“No one liked bailing out the banks,” Zandi added. “But without a banking system on solid ground, the economy would have never found its footing.”