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Are you talking about qualifying for a loan to build a home, financing the construction along the way with draws, inspections, re-inspections, etc.? Or are you talking about buying a new home after it's been completed?
New construction financing is unique to the lender offering it, there is no standard guidelines that the entire industry plays by (unlike USDA, FHA, VA & conventional), if there was only 1 mortgage late, and it's over 12 months old by the time you apply though, then I'd say for a construction loan you should be OK, and if it was to buy a home at completion, you should also be OK for the permanent financing as well.