General Motors Co.’s initial public offering showed that while U.S. President Barack Obama’s administration may lose billions on the auto-industry bailout, the national budget and economy might be better off for it.

The U.S. sold almost half of its stake in the nation’s largest automaker for $33 a share - about $10 less than it needs to break even. The remaining shares will need to sell for about $20 higher to make up the difference. GM opened at $35 and stayed within $1.11 of that price all day. Selling the remaining shares at that price would produce a loss of about $9 billion.

That may go down as a bargain. The U.S. would have lost $28.6 billion in spending on social services and missing tax revenue if not for the bailout of GM, its former lending arm and Chrysler Group LLC, according to a study released Nov. 17 by the Center for Automotive Research in Ann Arbor, Michigan.

“GM ends up an economic contributor to the U.S. economy,” said Barry Ritholtz, author of “Bailout Nation” and chief executive officer of New York investment research firm FusionIQ. “It’s manufacturing products, it’s creating jobs, it’s buying wholesale parts, it’s doing what an industrial company is supposed to do.”

Since the Treasury sold almost half of its stake at $33 a share, the government needs future offerings to sell for an average of $53.07 a share to break even, according to data compiled by Bloomberg.

GM rose $1.19, or 3.6 percent, to $34.19 yesterday in New York Stock Exchange composite trading.

Recouping Investment

The aid to GM and Chrysler was politically unpopular. In an Oct. 7-10 Bloomberg National Poll, 41 percent of adults said they believed the automaker bailout would weaken the economy, while 34 percent said it would strengthen the economy. About 45 percent of likely voters said they were less likely to support a congressional candidate who voted in favor of the aid.

“The American taxpayer should never be compelled to finance a corporate bailout, even if it may produce short-term benefits,” Senator Richard Shelby, an Alabama Republican, said in an e-mail.

GM wants to get rid of the government as a shareholder as well. Chairman Ed Whitacre said in August that he was eager for the U.S. to sell its shares because it would boost employee morale and help Detroit-based GM sell more vehicles.

“We don’t like this label of Government Motors,” said Whitacre, 69.

‘Obama Number’

The Treasury needs to sell GM’s stock for an average of $43.67 a share to recoup the $49.5 billion investment, including the $13.4 billion that the Bush administration put into GM. While planning the IPO, the Obama administration calculated that GM stock would need to sell for $29.15 a share, referred to as “the Obama number,” to recover just what it invested in GM, said two people familiar with the matter.

The government may lose $5 billion to $7 billion on its rescue of the auto industry, Steven Rattner, the former head of the U.S. Automotive Task Force, said in a Nov. 17 interview on Bloomberg Radio.

The government has said it will collect $9.5 billion in loan payments, interest and preferred stock dividends from GM. The Treasury has agreed with GM’s underwriters not to sell more shares for six months.

GM will have a harder time winning high prices when the Treasury goes back to the market to sell more stock, said Maryann Keller, who runs a self-named consulting firm in Stamford, Connecticut. There will be less hype and investors will have more information to use when making investment decisions, she said.

‘Next Time Around’

“You will probably need continuous improvement in the stock market,” Keller said. “Everything will have to be firing on all cylinders the next time around.”

Obama and his advisers figured the government may lose as much as half of its investment as they evaluated options for the automaker in early 2009, two people familiar with the deliberations said yesterday. They decided to save the carmakers because the cost of losing so much of the auto industry was too grave, the people said.

There was a lot of concern that job losses would continue, costing the nation, said the people, who asked not to be named because the discussions were private. The administration thought that Michigan’s unemployment fund could go broke and require the federal government to pick up the bill, one of the people said.

At the time, Evercore Partners, a New York financial advisory firm that counseled GM on the IPO, gave a fairness opinion that said the U.S. and Canadian governments would be putting up a combined $59 billion for a company worth $38 billion, said a person familiar with the study.

Breakeven Scenario

Now that GM is profitable and paying off debt, the automaker and its bankers can see a scenario when the stock gets above $50 a share and allows the government to break even, said one of the people familiar with the situation.

Obama said yesterday at the White House that taxpayers are in a position to recoup more than his administration put into GM. Letting the U.S. auto industry fail was an unacceptable option that would have resulted in “economic chaos” and devastated communities across the country, he said.

“We are finally beginning to see some of these tough decisions that we made in the midst of crisis pay off,” Obama said. “And I am absolutely confident that we’re going to keep on making progress.”