The federal and Ontario governments have got to hope that shares of General Motors multiply in value many times if Canadian taxpayers are to recoup their investment in the company.

The governments had invested more than $10 billion to keep GM afloat in the recession, hoping to get the money back by selling GM stock when the company recovered.

GM doesn't have any stock trading publicly yet, but that is expected to change later in November when the company completes an initial public offering.

U.S. media are reporting that the IPO will be priced at $26 US to $29 a share. At that price, "it looks to me like the [U.S.] government is going to lose at least $10 billion on this deal," said Megan McArdle, the business and economics editor for Atlantic magazine.

The shares owned by Ottawa and Ontario are worth between $1.5 billion and $1.7 billion, depending on the IPO value. The governments also hold preferred shares valued at about $400 million.

The governments will only be able to sell a fraction of their holdings in the IPO. The two governments have given GM about $9.3 billion (after the company repaid all its loans), so the gap between what they gave and what they'll get could be many billions.

The only way Canadians will get the rest of their $9.3-billion investment back is if the GM share price increases sharply.

To the rescue

The two governments and the U.S. government came to GM's rescue when it appeared the company was failing in 2008. In a complicated 2009 restructuring, GM was saved by massive infusions of government cash.

Most of the money came from the U.S. government, but Ontario said it invested $3.5 billion and combined with the federal government, Canada contributed a total of $10.8 billion.

Part of that was loans, but by April "General Motors completed the repayment of its entire $1.5-billion interim loan from Canada and Ontario ahead of schedule," the federal government said in September.

The governments said the bailout was necessary because the prospect GM failing would have cost 85,000 jobs in Ontario.

"Ontario is not a long-term investor but it will exit in a prudent manner and ensure optimal return for Ontario taxpayers," Scott Blodgett, a government spokesman said.

U.S. reports said the Treasury, which holds the U.S. government's GM stock, was going to book a loss on the share sale.