As the federal government gets ready to sell the last of its shares in General Motors Co., a research institute has calculated the final bill on the auto industry bailout and says that taxpayers were net winners.

The Center for Automotive Research, a Michigan nonprofit organization that analyzes auto industry issues, said Monday that the U.S. government will lose about $13.7 billion on its bailout of GM and Chrysler Group.

But the think tank said those funds “saved or avoided the loss of $105.3 billion in transfer payments and the loss of personal and social insurance tax collections — or 768 percent of the net investment.”

Additionally, the center said the bailouts saved about 2.6 million jobs in the U.S. economy in 2009 and $284.4 billion in personal income over 2009 and 2010.

In the report, “The Effect on the U.S. Economy of the Successful Restructuring of General Motors,” researchers Sean McAlinden and Debra Maranger Menk wrote that the value of the bailouts can’t be considered just by what the taxpayers will lose in the sale of GM’s stock.

“Any complete cost-benefit assessment of the federal assistance to GM in its restructuring must consider the total net returns to the public investment in GM in the U.S. economy,” they said. “In other words, the U.S. government is not a simple investor in companies but an active participant, when needed, in the overall U.S. economy on the behalf of all of the U.S. citizenry.”

As the auto industry went into crisis in 2008, the federal government stepped in, lending billions of dollars to GM and Chrysler. The federal help allowed both companies to restructure their businesses through bankruptcies. Today, both companies are profitable.

A shutdown of the two automakers would have spilled into the rest of the auto industry and caused catastrophic economic damage, the report said.

Other analysts said it was hard to judge the net effect of the bailouts.

“If you only count the things that make you look good and don’t count the things that make you look bad, any investment will look good and any investment will be profitable,” said Dan Mitchell, senior fellow at the Cato Institute.