I bought my house from my father-in-law for $20,000 last year. Why is it appraised for $80,000?

The appraised value of your property for ad valorem tax purposes is based upon current market value. Market value is the most probable price that a property would bring if exposed to the open market for a reasonable period of time. It is the price that a willing buyer and a willing seller would agree upon under usual and ordinary circumstances in the open market.