You surely know the story: General Motors (NYSE: GM), after decades of mismanagement, was ushered into bankruptcy by the Obama administration at the height of the financial crisis and radically restructured -- with the help of some hefty loans from taxpayers.

Regardless of your feelings about the bailout (or the president, and it's worth noting that loans to GM were made under both Presidents Bush and Obama), here in 2012, it's clear that the restructuring was a big success from a business perspective.

GM is booking big profits and creating new jobs, and its latest models like the Chevy Cruze are extremely competitive with rival models from Toyota (NYSE: TM) and Honda (NYSE: HMC). The company is posting solid growth in overseas markets even as overall industry sales in places like China are slowing.

In many ways, General Motors has moved on -- successfully -- from the bailout and the dark days of early 2009. But in one big way, the bailout is still a big issue: Taxpayers haven't gotten their money back.

Technically, GM has already paid us back. But...
Under the terms of the loans made to GM under the Troubled Asset Relief Program during the financial crisis -- just under $50 billion worth in total -- GM was to pay part of the balance back in cash, and part with GM stock.

That has been done. GM had until 2015 to pay back the cash, but former CEO Ed Whitacre chose to do it early: The last payment, about $4.8 billion, was made two years ago. Meanwhile, the government was given a 60.8% equity stake in post-bailout GM. Officially speaking, that action settles the debt.

Here's the problem: The cash plus the stock hasn't (yet) added up to the $49.5 billion lent. So far, according to GM, about $23.1 billion has been "repaid or returned to the U.S. Treasury":

  • $6.7 billion in cash, the last of which was that payment made in April of 2010
  • $13 billion via GM's IPO, when the government sold about 45% of its stock holdings
  • $2.1 billion, when GM bought back some preferred stock from the Treasury in late 2010
  • About $800 million in interest and dividends on the loans and preferred stock.

That still leaves over $25 billion to be "repaid." But the government still holds 500 million shares of GM common stock, a 32% stake in the auto giant. At $25 a share, roughly where GM has been trading recently, that's $12.5 billion -- a bit less than half of what is needed to square accounts.

That's a problem.

What can GM do?
Simply put, not very much -- at least not right now.

As GM spokesman Selim Bingol wrote in a blog post on Wednesday, the timing of the government's sale of its remaining GM holdings is "anyone's guess (we have no say in the matter)." Unless GM stock soars, it's a safe bet that nothing will happen before the presidential election -- but after that, it's indeed anyone's guess.

What GM can do in the meantime is what CEO Dan Akerson and his team have already set out to do: Continue to fix and improve GM's global businesses and its balance sheet. More best-in-class vehicles, a global model-line consolidation patterned on Ford's (NYSE: F) successful approach, a fix to the money-burning European operation, and a resolution of GM's huge pension liability are all works that are very much in progress -- and all are likely to help improve GM's share price.

Boosting the share price will help reduce the gap between the stock's value and the amount owed, but it seems unlikely that GM stock will hit the price needed for the Feds to break even -- about $53 -- any time soon. More likely is that the government's eventual sale will still leave it several billion short.

What then? GM could offer to pay the difference in cash, and Akerson well might. A former Naval officer, Akerson is known to see his role at GM as something of a patriotic duty. GM won't be obligated to pay a cent, but paying back the government in full might well appeal to him – and the public.

GM has over $30 billion in cash now. Assuming that the company's pension situation can be resolved without a major payment that eats up a big part of that cash pile -- a big if -- GM's board might decide that using some of its hoard to pay the balance of its loan is in the company's best interest. We shall see.

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This article represents the opinion of the writer, who may disagree with the “official” recommendation position of a Motley Fool premium advisory service. We’re motley! Questioning an investing thesis -- even one of our own -- helps us all think critically about investing and make decisions that help us become smarter, happier, and richer.