In addition to the reputation of the artist, appraisers review the physical characteristics of an artwork such as its condition, subject matter, size, materials, and quality. Facts such the year the work was produced, the history of ownership, and exhibitions, are also taken into consideration.
Appraised value is based on the recent market for similar works and how much buyers have been willing to spend on them. The price-point of an artwork can be a reflection of desirability & exclusivity, current politics and economics, nostalgia, and changes in taste.
One artwork may have multiple values, depending on the purpose of the appraisal. An estimated replacement cost for insurance is usually not the price the work would sell for.
Learn more about the different types of appraisals here.