Yes. In most cases you will not have to pay for another appraisal if you change your mortgage company, and depending on the loan program typed, the first lender can transfer it to the new lender. Some appraisal firms may charge a small fee because additional clerical work is required to reflect the new mortgage company; this is called an "Appraisal Retype Fee". The original mortgage company has the right to refuse to transfer the appraisal to another lender. In this case, a new appraisal is needed.