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Detroit Public Schools expects to be millions of dollars short on payrolls through most of the remaining school year, documents obtained by the Free Press show.

he district’s shortfall is projected at $21.6 million on the March 17 pay date, $16.1 million on April 14, $17.4 million on May 12 and $21.3 million on June 9, according to reports the district files with the state under a consent agreement.

In addition, the district has at least $42 million in overdue bills as of Jan. 29 — double the arrears reported in November. The shortage includes $9.2 million in retirement payments to the Michigan Public School Employees Retirement System.DPS has options to cover payroll for its 13,633 employees. Among them: borrow from a bank against future state aid payments, arrange to participate in a state borrowing pool, ask the state for an advance on state aid or work out a new payment schedule with unions. But such measures would likely worsen the district’s financial picture in the long run.

“Most districts that are going to have a cash-flow problem…. borrow to make payroll,” said David Martell, executive director of Michigan School Business Officials. “Who would want to loan them the money? That might be an issue.”

It’s one of the first challenges to await Robert C. Bobb, a former city manager and school board president in Washington expected to take control of the DPS budget on March 2.

Mattie Majors, spokeswoman for the district, said officials are not sure how the problem will be resolved.

DPS has lost 45% of its enrollment in the past 10 years, contributing to a $139-million deficit for 2008 and a $3.7-million deficit for 2007, according to the 2008 comprehensive annual financial report. The district expects to lose more students and funding next year.

The state has already extended DPS two advances this fiscal year, according to the Michigan Department of Education.

In August, unions in the district agreed to be paid one day later than scheduled to allow DPS to avoid taking out a loan to cover payroll. That reportedly saved DPS $1 million.

For employees, there are few funding problems as jarring as this one.

“People are not going to work for free,” said Keith Johnson, president of the Detroit Federation of Teachers.