SWAMPSCOTT – The school committee authorized a five-year agreement to continue educating Nahant middle and high school students at roughly $1.2 million a year, in a contract that uses a different formula to calculate per-pupil tuition costs but otherwise changes little from the current arrangement.”The only changes are the DESE (Department of Elementary and Secondary Education)said that this is the (per-pupil tuition) number they recommend, and the contract goes from seven years (previously) to five years,” said Swampscott District Budget Director Ed Cronin at the school committee’s Wednesday night meeting. “I believe it does represent the most fair number.”Nahant students attend Swampscott Public Schools for grades 7 through 12 because the town’s only school, The Johnson School, only offers grades Kindergarten through 6. The last agreement between Swampscott and Nahant was signed in 2003 and expired at the conclusion of this year. Cronin said that he and Nahant Superintendent Philip Devaux conducted negotiations and that the Nahant School Committee was scheduled to authorize the contract at its next meeting.Cronin told the school committee that rather than have Nahant pay 100 percent of a “target number” per pupil, the DESE recommended that the school base the per pupil expenditure on 100 percent of the “school choice” rate. This number – basically what Swampscott would be paid per pupil if it allowed “school choice,” or students from other districts to attend its schools – is part of a complex formula that incorporates numbers from the district’s annual financial reports.But some members of the Finance Committee expressed concern at their Nov. 9 meeting that Nahant did not pay some portion of the costs to construct the new high school, which opened in 2007.Cronin said after the meeting that the new formula – which he joked during the meeting would require three hours to explain and put everybody to sleep by minute 10″ – incorporated annual costs incurred for the high school such as the interest on the bond to pay for instruction. He acknowledged, however, that every meeting with the finance committee involves concerns about Nahant paying for some costs of school construction.”It is certainly something we can continue to look into if someone brings it up,” he said.But Superintendent Lynne Celli was more focused on the costs that Swampscott wouldn’t have to pay.”It’s important to note that special-ed(ucation) costs and home and hospital tutoring costs are incurred by Nahant,” Celli told the school committee. “These are numbers in a budget that in a day could throw a budget off with costs. It’s huge.”Cyrus Moulton can be reached at [email protected].