Fair value is measured at an exit price, so the entity's intention to hold an asset or to settle a liability is not relevant to the measurement. The definition is the same in IFRS 13 and ASC 820. The title of IFRS 13 is "Fair Value Measurement," and the United States also calls it fair value.
Consider a hypothetical example of a bond with an acquisition price of 100. If it can be sold for 92 in an active market at the measurement date, its fair value is 92, which is 8 lower than the acquisition price. If it can be sold for 108 in the market, its fair value is 108, which is 8 higher than the acquisition price. The acquisition price is an entry price and is not the basis for determining fair value.
In valuation articles, the value calculated for a position as the result of a valuation is not the same thing as accounting fair value. The two differ in definition.