Important to the buyer is your agent's comparative market analysis and when available, the fair market value established by a qualified appraiser. These values along with additional market information from your Agent will help you decide what your initial price offer will be, which may be at or below the appraised value. The final selling price can be any price agreed to by both you and the seller.
My advice is to contact a local realty firm and interview agents to represent you in the transaction and more fully explain the whole process before you proceed. You will also be happy to learn that as the buyer, your agent will be paid by the seller when the sale is closed.
Bill is correct.
Loans are based on the lessor of the purchase price or appraised value (unless you go with a private lender who can make up his/her own lending rules).
Every lender will require either a reduction in sales price to match the appraisal or the difference from you in cash.
It MIGHT be possible to talk the lender into ordering a new appraisal, hoping to obtain a higher value, but considering the current aversion to risk in the industry, it would be very unusual to persuade a lender to overlook the lower value in the first appraisal.
As Bill mentions, appraisals are reviewed by lenders for unusual risk (the most important being overvaluation) using software, a staff appraiser, or an outside party). Even if you are successful in obtainbing a higher value with a second appraisal... the higher value might be thrown out as too risky.
A bank, or financial institution, especially in this market, will probably lend only on the "appraised" value or will make the buyer (you) come up the difference in cash.
Of course you can always retain and pay for another appraisal on your own. But be sure that that appraiser is on the approved list of your bank or financial institution. Obtain the banks perfmission first as not to waste your money!
I was a former VA appraiser fo 20 years and generally each appraisal today goes through a "review process" befor it is issued. Hope this helps a bit