This is called “adding freeboard.”. That’s especially prudent when building a new house. A new $250,000 house in a moderate or high risk flood zone, for instance, that has its lowest living floor four feet below base flood elevation, would have a $9,500 a year flood premium, FEMA notes.all notes the cost can run as much as $50,000 — at $30 to $35 a square foot for a concrete-block house — and as high as $200,000 or more for large houses. When Erika Brigham elevated her small 1925 cottage — a tiny creek runs behind it — on Ohio Place near downtown Sarasota, the cost was $17,000.