It is tough to say whether U.S. taxpayers will ever get back the $50 billion the government has committed to General Motors. The plan for doing so is to let GM rise from the ashes, watch the stock soar, and then sell the government’s 60 percent share when the market fully embraces GM’s new value. Is there any chance of this happening?

A thorough analysis would assess prospects for global auto demand, predict the quality of GM’s new management, and figure out the odds that GM can catch up with its competitors at home and abroad. It is not hard to see why some analysts take a shortcut instead: figure out whether a new high market value seems reasonable by comparing it to GM’s past experience. Peter Cohan crunches the numbers and notes that at GM’s peak market value, in 2000, the company was worth roughly $57 billion.

As it turns out, since $8.8 billion of the [government’s] $50 billion will remain in the form of loans, the U.S. will convert $41.2 billion worth into its 60 percent equity stake. This means that in order to break even on that $41.2 billion equity portion of our investment—this does not even take into account getting a profit for taxpayers after taking on the risk—the new GM would need to have a market capitalization of $68.7 billion—20 percent higher than the old GM was at its peak.

While Cohan decides it is very unlikely taxpayers will see their money again, it turns out that even then he is excessively optimistic. Before making that case, though, there is one count on which he undersells GM’s prospects. A peak value of $57 billion, in 2000 dollars, is roughly equal to $71 billion in current dollars. That would suggest that the necessary value of $68.7 billion falls just within the realm of past experience.

GM’s peak value turns out to have been 12 percent reality and 88 percent empty optimism.

And now the problems begin. GM was never worth $71 billion, whether we adjust for inflation or not. Yes, there was a moment when investors were willing to pay that much, but they were deluded. Now that GM has entered bankruptcy, we can calculate with some finality what GM was worth at any given point.

It can sometimes seem as if the value of a stock or a company depends entirely on the whims of market gamblers. In fact, though, stocks have intrinsic value. Owning stock gives you the right to a share of the company’s profits. Someone who bought GM’s stock at its April 2000 peak of roughly $93 per share received GM profits through the company’s dividend payments. GM paid out 50 cents per share every quarter until February 2006, when it cut its dividend in half. Dividends stopped after the payment of May 2008.

Usually, for going concerns, there is a fair amount of uncertainty about what will happen with future profits and dividends. For GM, however, that has now all been laid to rest. The buy-and-hold investor who climbed on board in April 2000 will receive nothing more after bankruptcy. For them, the books are closed.

The government has just pumped into GM more than five times what the company was worth to its owners over the last decade.

That means we can calculate how much GM was really worth back then. To take the present value of those payments, we need an interest rate. We can use the yield on ten-year Treasury bonds at the time (an alternative investment that our stockholder might have made). That was 6.23 percent. After a few spreadsheet calculations and conversion into current dollars, voilà: GM’s value was really just over $8.5 billion.

This, of course, relies on 20/20 hindsight. The investors who pegged GM’s value at $71 billion at the time were infused with hope for a much brighter future. But, like so many other bubble victims, they were dramatically wrong. GM’s peak value turns out to have been 12 percent reality and 88 percent empty optimism.

This means, incidentally, that the government has just pumped into GM more than five times what the company was worth to its owners over the last decade.

For GM to earn back the government’s investment, it must not only return to past profitability, it must fill investors with unfounded optimism, of the sort they felt back in 2000. Once investors again feel that giddy sense of limitless possibility, the government will have a company to sell them.

Philip I. Levy is a resident scholar at the American Enterprise Institute.

FURTHER READING: Levy wrote “How to Help Detroit” in December about why declaring bankruptcy was the least bad option for the Big Three automakers, and “Public Outrage as a Systemic Risk” on how without bankruptcy, it is hard to avoid rewarding failure.

Image by Darren Wamboldt/Bergman Group.