The private company that runs Chicago’s parking meters could be in for another windfall under a deal proposed by Chicago Mayor Rahm Emanuel, according to an analysis by one Chicago alderman.

A day before the first City Council hearing on the proposal, Alderman Scott Waguespack (32nd), a frequent Emanuel critic, also suggested the administration lowballed by millions of dollars the amount of money Chicago Parking Meters LLC would make off of drivers who would have to feed the meters longer under the mayor’s plan.

“It’s purely a political move by the mayor to make sure that this free Sunday thing gains traction, but (it’s wrong) calling it a wash or saying the city’s not losing any money here,” Waguespack said, referring to Emanuel’s plan to allow free Sunday parking in most neighborhoods.

Emanuel’s office did not comment on the alderman’s analysis.

The mayor has repeatedly said he’s hoping to “make a little lemonade out of a big lemon” by negotiating free Sunday parking in neighborhoods, and dramatically reducing the amount of reimbursement money the paid to the private company each year for meters the city takes out of service.

But in exchange, Emanuel is asking drivers to feed meters for three extra hours, until midnight, near downtown, and for one more hour in most Chicago neighborhoods.

The City Council Finance Committee on Friday is set to begin the first of two days of hearings on Emanuel’s proposed revisions to the much-hated $1.15 billion, 75-year lease of the city’s parking meters. The privatization has since become politically toxic, and aldermen are wary of any deal that could mean more money for CPM.

But Waguespack said the proposed amendment could be worse than the initial 2008 deal, which former Mayor Daley crammed through the City Council just days after it was introduced.

The alderman predicts an extension of parking meter hours - from 9 p.m. to midnight near downtown, and until 10 p.m. in most neighborhoods - could reap between $11 million and $12.9 million a year for CPM, according to a draft of the analysis obtained by WBEZ.

The Emanuel administration had predicted CPM would make only $7.4 million off of the extra meter hours, but Waguespack said City Hall used three low-traffic months in making its projections.

When the longer meter hours, new pay-by-cellphone fees and the give-back of parking spots to CPM are taken into account, Waguespack says the city would be losing out on nearly $1.9 million a year under Emanuel’s plan. That assumes CPM will take $2 million on the pay-by-cell fees, though neither the city nor the company have provided an estimate.

His more aggressive projection, which assumes a lot more revenue from the extended parking meter hours, has CPM coming out more than $9.5 million ahead of the city.

Waguespack is challenging the Emanuel administration claim that the city is getting the better end of the deal: free Sunday parking will cost CPM $8.4 million in lost revenue, it says, while it will make only the $7.4 million off the extra hours. That doesn’t factor in the roughly $20 million a year City Hall says it won’t have to pay in reimbursement costs.

Waguespack did praise Emanuel’s administration for trying to bring down the reimbursement costs, though he questions the claim that it will save the city $1 billion over the life of the contract.

Aldermen will hold a second hearing on Emanuel’s proposal on Tuesday, with a vote by the full City Council expected in mid-June.

Alex Keefe covers politics for WBEZ. Follow his @akeefe