Cobb County commissioners took a small step toward financing the new Atlanta Braves stadium on Tuesday, approving a move to refinance bonds issued years ago to pay for the Cobb Energy Center.

The Cobb-Marietta Coliseum Authority issued $57 million in bonds to build that facility in 2004. Refinancing the remaining $41 million in debt at a lower interest rate will net about a $400,000 annual savings to the county.

That money will be applied to the $19.7 million annual debt service payments the county will make as part of its contribution to the Braves stadium.

The Braves announced last month they will move to a new stadium in Cobb County, near I-75 and I-285, for the 2017 season. The county will carry just under half of the debt for the $672 million stadium, along with about $1.2 million a year in maintenance costs.

Jim Pehrson, finance director for the county, said the $400,000 annual savings from refinancing of the Cobb Energy Center bonds was planned all along to be a part of the county’s share.

Other public funds to be used include $8.67 million in redirected property taxes; $5.15 million from a new tax on businesses and apartments in the Cumberland Community Improvement District; $2.74 million from a new nightly hotel room fee in the district; $400,000 from a new rental car tax in unincorporated portions of the county; and $940,000 from existing hotel-motel taxes.

The $400,000 savings is part of that hotel-motel tax figure.

“We have a three-percent requirement savings criteria that we look at to see if” bonds should be refinanced, Pehrson said. “These do that, and we’ll keep the same expiration date, so we’re just going to refinance for whatever period is left.”

The Cobb Energy Center bonds will be paid off in 2029. The annual payment will be reduced to $3.3 million, from the current $3.7 million. Those amounts fluctuate over time, but the average annual savings remains $400,000.

The commission’s vote to refinance the bonds was not controversial. It was placed on the county’s consent agenda, meaning it was voted on at the same time with multiple other agenda items and without discussion.

Pehrson said the county should be ready to sell bonds for the Braves stadium in the Spring.