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If the property does not appraise than the price can be re-negotiated or the contract cancelled by the buyer. In the financing section of most P&S contracts it is subject to the buyer obtaining financing for $X and if it doesn't appriase that is when it can be negotiated. In most builder contracts there is no such provision.
However, if you have a strong sellers market then the seller may, or may not, renegotiate the purchase price to meet the appraised value.
@TnTNYC wrote:ezdriver, wouldn't OP have the opportunity to return to the seller with the appraisal and renegotiate the sale price to fall in line with that? We are in the process of buying our first home and our agent advised the contract should be contingent upon the home appraising at or above our purchase price, otherwise we need to go back to the table. That is, rather than have to come up with an additional $3K, which amounts to a penalty for buying a home not worth the price paid.
Once the appraisal falls short of the purchase price, there are several options that are available to the buyer [eg: cancel contract, renegotiate contract, accept and pay the difference, etc]. I responded only to the specific questions asked by the OP.
Thanks for the responses everyone! I really, really appreciate it!