President Barack Obama is considering the sale of all or part of the Tennessee Valley Authority, the largest publicly owned U.S. power company, in a deal that may raise as much as $35 billion as the administration seeks to reduce the national debt.

A potential sale is part of a “strategic review” of the Knoxville, Tenn.-based nonprofit, which faces increasing capital costs, according to the administration’s fiscal 2014 budget proposal released Wednesday. A sale may yield $30 billion to $35 billion in cash and reduced government debt obligations, said Travis Miller, a Chicago-based analyst for Morningstar.

The 80-year-old authority, created during the Great Depression to bring electricity to rural communities, will probably exceed its $30 billion debt cap to pay for needed infrastructure improvements and meet new environmental rules, according to the budget proposal. U.S. utilities face rising costs to replace aging power lines and generators and install pollution controls to meet stringent air-quality standards.

“We expect potential buyers will have big concerns about the huge pension and asset retirement liabilities that TVA faces,” Miller said in an e-mail Thursday. “That future uncertainty could depress the prices buyers are willing to pay.”

The power authority’s bonds fell on news of a potential sale, which was criticized as “one more bad idea in a budget full of bad ideas,” by Sen. Lamar Alexander, R-Tenn.

TVA’s $1 billion of 3.5 percent bonds due December 2042 declined to 95.7 cents on the dollar from 98.6 cents Wednesday to yield 3.74 percent, or 74.3 basis points more than similar- maturity Treasuries on Thursday afternoon, according to Trace, the bond-price reporting system of the Financial Industry Regulatory Authority. The spread widened from 57.5 basis points Wednesday.

Standard & Poor’s said it would review its AA+ rating on the debt if there was a “change in TVA’s role or link to the federal government.” S&P said its rating is based on the “very high likelihood” the U.S. government would support TVA if it got into financial distress.

The announcement was a surprise to the authority, which is self-financing. CEO Bill Johnson said TVA would work with the administration to provide requested information during the strategic review.

“Reducing or eliminating the federal government’s role in programs such as TVA, which have achieved their original objectives and no longer require federal participation, can help put the nation on a sustainable fiscal path,” according to the budget proposal.

TVA was created in 1933 as part of President Franklin Roosevelt’s New Deal to lift the nation out of an economic depression. The agency now provides power to 9 million people in parts of seven southeastern states including most of Tennessee, according to its website. TVA owns 29 hydropower plants, 11 coal plants and three nuclear plants.

By capacity, its 38,040 megawatts make TVA the third-largest U.S. power producer, according to a Bloomberg calculation. Duke Energy, the largest, has a market value of $51.6 billion. Southern, the second-biggest, is valued $41.4 billion.

“Depending on the price, I would expect a considerable amount of interest,” Paul Patterson, a New York-based utility analyst at Glenrock Associates, said in a phone interview Wednesday. “A possible sale sounds like an interesting idea, but as usual the devil will be in the details.”

The authority funds its operations through power sales and bond financing. TVA recorded $11.2 billion in sales last year and had $25.5 billion in total debt as of Dec. 31, according to regulatory filings.

“It is unclear that the sale of TVA’s assets would bring significant additional revenues to the federal coffers once its debt and ‘debt-like obligations’ are repaid,” Stephen Smith, executive director of the Southern Alliance for Clean Energy, said in an e-mailed statement Thursday. “It is extremely unlikely that this proposed strategic review will lead to any real desire by the Obama administration to pursue selling TVA.”

The authority paid the Treasury Department $27 million last year as part of annual payments it has made since 1961 to repay the federal government for $1 billion in power generation, according to a Securities and Exchange Commission filing.

The Treasury Department also provided TVA with a $250 million line of credit, which it hasn’t yet tapped, according to the filing.

A sale of TVA would cost taxpayers money and may boost electricity rates, Alexander said in an e-mailed statement Wednesday. Both of Tennessee’s Republican senators oppose a sale.

“There is by law no federal taxpayer liability for TVA debt,” the senator said. “And after deducting its debt, selling TVA would probably cost taxpayers money.”

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With assistance from Charles Mead, Jim Polson and Jody Shenn in New York.