CHICAGO — The Chicago Public Schools on Monday proposed a $6.4 billion budget for the next year that includes $600 million of bonds and would drain the district’s $190 million fund balance to help erase $370 million of red ink.

The release of the proposed budget will be the subject of hearings before the Chicago Board of Education votes on it later this month. Its marks the culmination of a months-long process that began with the district’s dire warning of a looming $1 billion shortfall.

About $400 million was trimmed off that figure by state pension reform legislation that reduced the size of district pension payments over the next three years.

Then CPS was spared $230 million in budget cuts from Illinois. That left the hole at $370 million. The district is seeking teacher concessions on contractual 4% pay increases, but so far those talks have failed.

Further adding to the fiscal strains, the state is $236 million behind in grant payments, as it faces its own liquidity crisis. Illinois closed out fiscal 2010 in June with $6 billion of bills that don’t have to be paid until the end of the year.

To achieve a balanced budget, CPS will cut more than 1,000 administrative positions, require non-union employees to take 15 unpaid furlough days, reduce some school programs, and eliminate 800 teacher positions.

Administrative cuts will save $266 million and school-based cuts $104 million. The reductions will boost high school class sizes, while elementary sizes will remain the same.

“These reductions are unsustainable, and our situation will be further exacerbated if the state does not make good on its past and future commitments to the district,” CPS chief executive officer Ron Huberman said in budget documents.

“While we do not want to revisit the decisions we have made to preserve class size and programs, the state’s failure to fulfill its obligations will force our hand,” he added.

Because the state is behind, Huberman wants to draw down the district’s fiscal 2010 ending balance of $190 million to balance the budget.

The fund balance serves as an informal reserve and eases cash-flow ­management.

Even as CPS has struggled annually with deficits, its fund balance has met an internal policy of 5% to 10% of its operating and debt-service budget. The balance is cited by rating agencies as a key credit strength.

Budget documents note that if Illinois caught up, the fund balance would top $426 million, representing 7.5% of appropriations.

The district is seeking board approval to take two years to restore the balance to at least 5% since the status of state payments is dependent on legislative action.

The district could move to restore the balance sooner if lawmakers approve an income tax increase for education sought by Gov. Pat Quinn. No action is expected before the November ­election.

At the city level, Mayor Richard Daley is considering a move to free up $700 million of surplus tax-increment financing revenues for use by various taxing bodies. CPS would receive about half the funds.

To keep a long-term $5 billion capital program on track, the budget includes plans to borrow $600 million to support an $807 million fiscal 2011 capital budget for new school construction, ongoing facility maintenance, and other upgrades.

CPS has an allocation under the federal stimulus to sell $257 million of qualified school construction bonds in 2011. It issued $254 million in fiscal 2010.

The district has $4.6 billion of outstanding debt and $477 million in the fiscal 2011 budget will go to cover debt service.

The Board of Education’s debt is rated AA-minus by Fitch Ratings and Standard & Poor’s and Aa2 by Moody’s Investors Service. All assign stable outlooks.

The board in June voted during an emergency meeting to authorize the establishment of an $800 million line of credit to boost its liquidity.

It also approved other measures ­giving Huberman extraordinary powers to manage through the district’s budget crisis.

CPS operates more than 670 schools that serve 409,000 students.

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