It seems to me that the property should be assessed more or less as it was when the property changed hands. $80k in improvements shouldn’t be a part of the original assessment.
Unless the $80k in improvements were new construction (or of an extent that would trigger reassessment). If you added to the house, then yes the addition should be assessed at fair market value. $80k in construction could easily raise the fair market value more than $80k. Although it still seems unlikely that $80k in construction would add $350k in value.
Keep in mind that I know next to nothing about appraisals or tax law. Just enough to get myself into trouble.
