A measure to allow student borrowers to refinance their college debt at current low interest rates would cost the federal government $51 billion over the next 10 years, the Congressional Budget Office reported Wednesday.

The bill, introduced by Sen. Elizabeth Warren, D-Mass., and other Senate Democrats, would let borrowers of federal and private student loans change the terms of the loans to those of new federal direct loans. For the 2014-2015, school year, the interest rate on new federal direct loans is 4.66 percent. That rate was determined by a student loan reform bill passed last summer that tied the rate on federal loans to the 10-year Treasury note.

Students who took out federal student loans in past years, in some cases, faced significantly higher rates, as did many borrowers of private student loans. The CBO, the nonpartisan budget scorekeeper for Congress, estimated that in the next few years $460 billion of federal student loans would be refinanced under the Warren measure — almost half of all outstanding federal student loans. Roughly half of private loans, or about $60 billion worth, also would be restructured if the program passed, according to the CBO.

Altogether, the CBO estimates, the program would cost $51 billion, including administrative costs. But the Warren measure, which is not expected to pass Congress, would include $72.5 billion in new taxes on Americans earning between $1 million and $2 million and would decrease the federal deficit.

But the underlying accounting is complicated. In the case of the $460 billion of federal student loans the CBO expects would be refinanced under the program, the federal government would lose out on $55.6 billion of interest income it otherwise would have earned.

For the $60 billion of private student loans, however, refinancing to federal loans would save the government $5 billion. That's because the private loans would be paid off and replaced with new federal student loans. Under government accounting, the interest the government would receive on those new loans would be greater than the cost of financing them.

The CBO is required by the Federal Credit Reform Act of 1990 to assess the cost of federal loan programs by discounting the cash flows expected from a given loan by interest rates on risk-free U.S. Treasuries. In an analysis using comparable market rates, however, the cost would appear to be significantly higher.

The CBO said last week that under such a fair-value method of accounting, the federal government's student loan programs would cost $88 billion over the next 10 years, even though they are supposed to save $135 billion under FCRA accounting.