In most cases, you cannot use one single home appraisal, however well-written and recent, at different banks. Historically, most banks are comfortable with a select few certified appraisers. Formerly, some banks occasionally accepted a recent well-documented appraisal by having one of their preferred appraisers "re-certify" the report, verifying the accuracy of the original appraisal and making any appropriate adjustments, up or down.
But, since new, stricter rules went into effect in 2010, banks often order appraisals from appraisal management firms, not specific appraisers. Even before these new rules, though, banks seldom accepted appraisals done specially for another bank.
TL;DR (Too Long; Didn't Read)
With few exceptions, you can't use the same appraisal at different banks because each lender uses its preferred appraiser or appraisal firm.
Homeowner- or Buyer-Ordered Appraisals
Banks will not accept an appraisal ordered by a homeowner or prospective buyer. This eliminates any possibility of buyer-appraiser collusion designed to arrive at a value helpful to the buyer. This rule has been followed for decades to help ensure a totally objective appraisal report and fair market value determination.
Since home appraisals are opinions of value based on recent sales data, the quality of the recent home sales used (called comparables) greatly influences the final opinion of value. Mortgage lenders need to trust the appraiser to arrive objectively at this opinion, without any buyer or homeowner influence.
Appraisal Management Companies
Appraisal management companies are firms that have relationships with fee-based certified appraisers. While they have existed for some years, since the 2010 rules that prohibited banks from hiring their own favorite appraisers, appraisal management companies have become more prominent. These firms solve the bank dilemma of getting an accurate appraisal without hiring their favorite appraisers.
By hiring an appraisal management company, lenders may receive a value report from any of the certified appraisers with relationships with the appraisal management firm. Unfortunately, unless your bank does business with the same appraisal management company, they will still not accept an appraisal ordered by another bank.
Real Estate Market Influences
The condition of the real estate market strongly influences the possibility that you could use an appraisal for different banks.
When the real estate market is "hot," with rapidly increasing home values, a well-documented appraisal completed within the past few months, may be accepted by another bank, since home values are increasing. The bank may believe the value on the original recent appraisal can only be higher, making the stated fair market value even more conservative.
A "cold" real estate market, with declining home values, typically renders an older appraisal almost useless in the bank's judgment, as the bank assumes that the property is over-valued.
Lender-Driven Appraisal Decisions
When you are buying or refinancing a home, your bank orders the appraisal, but you, the borrower, pay for it. Therefore, the bank does not increase their costs, but gets the appraisal they want. They want an original appraisal from an appraiser or appraisal management company they trust, not an appraisal used by another bank. Consequently, should you wish to apply for financing at more than one bank, be prepared to pay for as many appraisals as there are banks to which you apply.