DETROIT  A government report released Monday concludes that taxpayers will probably never recoup all  or even close to all  of the $67 billion that the Treasury Department lent to General Motors and Chrysler in the last year to prevent their collapse.

The report, by the Government Accountability Office, estimates that G.M. and Chrysler would need to be worth a combined $121.7 billion, or roughly 30 percent more than their values about a decade ago, for the Treasury to break even on its investments. The report said it already was assuming that $6.4 billion of the money lent to the carmakers before their bankruptcies would not be repaid.

“Treasury is unlikely to recover the entirety of its investment in Chrysler or G.M., given that the companies’ values would have to grow substantially above what they have been in the past,” the report said.

The companies’ current value and recent financial performance are unknown because neither one is publicly traded. The report said that G.M. had agreed to file a third-quarter and 2009 full-year earnings report by March 31, 2010, but that there was no such agreement with Chrysler. Both companies must file frequent financial summaries with the Treasury as long as their loans are outstanding, however.