There are several types and definitions of value sought by a ship/yacht appraisal. Some of the most common are:
Market value – The price at which an asset would trade in a competitive Walrasian auction setting. Market value is usually interchangeable with open market value or fair value. International Valuation Standards (IVS) define:
Market value – the estimated amount for which an asset or liability should exchange on the valuation date between a willing buyer and a willing seller in an arm's length transaction, after proper marketing and where the parties had each acted knowledgeably, prudently and without compulsion.
Value-in-use, or use value – The net present value (NPV) of a cash flow that an asset generates for a specific owner under a specific use. Value-in-use is the value to one particular user, and may be above or below the market value of a property. Investment value – is the value to one particular investor, and may or may not be higher than the market value of a property. Differences between the investment value of an asset and its market value provide the motivation for buyers or sellers to enter the marketplace. International Valuation Standards (IVS) define:
Investment value – the value of an asset to the owner or a prospective owner for individual investment or operational objectives. Insurable value – is the value of real property covered by an insurance policy. Generally, it does not include the site value. Liquidation value – may be analyzed as either a forced liquidation or an orderly liquidation and is a commonly sought standard of value in bankruptcy proceedings. It assumes a seller who is compelled to sell after an exposure period which is less than the market-normal time-frame.

PRICE VS VALUE

There can be differences between what the property is really worth (market value) and what it cost to buy it (price). A price paid might not represent that property's market value. Sometimes, special considerations may have been present, such as a special relationship between the buyer and the seller where one party had control or significant influence over the other party. In other cases, the transaction may have been just one of several properties sold or traded between two parties. In such cases, the price paid for any particular piece is not its market "value" (with the idea usually being, though, that all the pieces and prices add up to the market value of all the parts) but rather its market "price".