Hello Cynthia,
I am a REALTORĀ®, but I am not an attorney or a Residential Mortgage Loan Originator. You have a contract question, and you should certainly seek a qualified opinion.
If an appraisal was done, is it a function of Buyer's lender and financing? Please refer to your contract and any addendums. From my experience you can often negotiate a lower price with a "bargaining chip" at your disposal. If you are using a 3rd party financing addendum, there are paragraphs that reference Buyer credit approval and lender approval of the property. If your financing is dependent on a certain percentage down payment, the appraisal results determine the Loan to Value (LTV) ratio. in many cases, you can negotiate a new sales price based on the appraisal, or terminate because the Lender won't fund unless someone makes up the difference between the sale price and appraised price. If your contract has a special provision or a clause stating how you can terminate the contract, you can certainly negotiate a lower price, or terminate the contract.
Why did the appraisal came in lower than the contract purchase price? Without knowing how you determined the price of your offer, if you based your offer price on comps you or your buyer's agent pulled, compare the appraisal comps with your comps. Try to learn what the appraiser did and why the appraisal comps are better than yours.
If you are working with a Lender, and/or attorney, and/or a real estate license holder, be sure to ask them for guidance, as they will be knowledgeable of the terms of your contract.
Thanks,
Terry