Legislation introduced in the Senate Thursday would wind down Fannie Mae and Freddie Mac within 10 years and turn over the remnants to the private sector.

The Mortgage Finance Act of 2011, sponsored by Sen. Johnny Isakson (R-Ga.), would also pay back taxpayers the funds used to place the two entities into conservatorship.

Isakson, himself a former real estate broker, said the bill would change the current course of taxpayers "bailing out the mortgage industry to the tune of hundreds of billions of dollars."

"My bill would shut down Fannie Mae and Freddie Mac through an orderly transition, and it will repay the taxpayers," Isakson said in a release. "I invite my colleagues in Congress, both Democrat and Republican, to move this bill forward to strengthen our nation's housing finance system and our nation's economy."

If the bill becomes law, the two government-sponsored entities would be placed in receivership within 18 months and rebranded the Mortgage Finance Agency.

The agency would charge "guarantee fees" on issuers of qualified mortgage-backed securities. Those fees would be used to fund the agency and a catastrophic fund to cover any losses.

The board of the new agency would draw up a plan within three years on how to go private. The plan would take effect within five years and privatization within 10 years, and sale proceeds would go to the general fund of the Treasury Department.

The bill also includes a provision to lower the required down payment to 5% on a qualified single-family residential mortgage. A proposal issued in March would require at least 20% down from the borrower on such mortgages.

Isakson, along with Sen. Kay Hagan (D-N.C.) and Sen. Mary Landrieu (D-La.), wrote a letter in June asking regulators to scale back the rule. The three drafted the section of the Dodd-Frank Act that requires a risk-retention rule.

Regulators continue their work on the rule. Online lending exchange LendingTree reported Thursday that no state averages at least 20% down on mortgages.