The city’s four new public upper schools are on target to open Sept. 4 for the first day of school, district administrators say, but reconstruction at three of them faces delays and a leap in the first estimated price.

The King School at 100 Putnam Ave.; King Open at 850 Cambridge St.; and Tobin School  at 197 Vassal Lane; have long been targeted for reconstruction — the fourth school at 70 Rindge Ave. is not included in long-term renovation plans — that would result in years of student relocations, with the Longfellow school that closed in 2003 as “swing” space for whatever campus population is uprooted at the time.

The timeline for construction always stretched years into the future, but now the start of the processes are delayed, according to a memo from City Manager Robert W. Healy issued at a May 16 budget hearing with the City Council and School Committee.

The city intended to put $33 million for design and construction into the Putnam Avenue school, but “now that the designer selection process has been completed and a feasibility study under way, these numbers have been revised substantially upward to a possible $76 million,” Healy wrote.

Given the cost of recent city renovations — $26 million for the War Memorial Recreation Center, but $90 million for the Cambridge Main Library and $112 million for the high school — the early estimate for the first upper school was taken by most to be exactly that: an early estimate. “I don’t think anybody really though the $30 million was going to be an accurate figure,” member Marc McGovern said. “I think everybody kind of thought it’d be more.”

But even the current Putnam Avenue estimate has been given mid-study.

What looked to be the fall hiring of an architect to look at the Cambridge Street building now seems to be moved to fall of 2014, and what looked like design work to be begun at Vassal Lane that year now looks to be pushed to 2015. Healy’s memo suggested that while “no city in the commonwealth has invested as much local dollars in school-building programs than Cambridge,” not knowing how much state money would be available for the projects is having an effect on the construction schedule.

“I have made the statement that ‘It is likely that the financing viability of future school construction projects would necessitate some SBA participation.’ Whether that is a possibility is not known at this time. It is hopeful that some positive indications might be forthcoming, and we will be able to continue the program, albeit, perhaps, on a less aggressive timeline,” Healy said.

“This is not a retraction of a commitment to the elementary school building program. I have consistently stated that the schools would need state assistance,” Healy said. But “projecting fiscal capacity and state participation that far into the future is not possible at this time.”

Superintendent Jeffrey Young got city official’s okay in December to file a “statement of interest” in funding with the Massachusetts School Building Authority.

The council asked Healy for a long-term plan for the elementary schools more than two years ago. Four schools have been rebuilt in the past two decades, but that leaves seven basically untouched since construction — although the older ones, up to six decades old, are doing better than those built in the 1970s. “The King and the Tobin are in tough shape,” then Mayor David Maher said in October 2010. “Not the oldest, but the one that has probably gone the longest without renovations, is the Graham & Parks School, which is just a good building that is suffering from age.”

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