It is not abnormal to see appraised values below purchase prices. We used to see a lot of those in recent years but is getting less and less lately. Lack of good comparables, unfamiliarity with the area, conservatism, recent 'bad sales' in the neighborhood etc. could be the reasons. The obvious choices for the buyer are: negotiate for the appraised value, come to a compromise on the agreed price or pay up the difference in cash at closing (if you really love the house). Sellers can always dispute the appraised value, get another appraisal done.