Fair value
Also called fair market value, FMV, mark, carrying value.
Fair value is the price that would be received to sell an investment in an orderly transaction between market participants at the measurement date. It is the standard under which a fund carries its portfolio, measured under ASC 820 for funds reporting under US GAAP, set by the general partner each quarter and reviewed by the auditor each year.
Example
A fund paid $3M for a 10% stake in a company two years ago. Last quarter the company raised a new round led by an outside investor at arm's length, and the price per share values the fund's stake at $7.5M. The fund marks the position to $7.5M and allocates a $4.5M unrealised gain across the partners' capital accounts. Had the round been an inside round at a flat price with no new investor, the price would be a weaker input, and the fund would calibrate it against comparable company multiples or a discounted cash flow before relying on it.
Confused with
Cost. Cost is what the fund paid. Fair value starts at cost and departs from it as evidence of value changes, in either direction.
Post-money valuation. The headline round valuation is a company-level number. The fair value of the fund's stake adjusts it for liquidation preferences, the rights attached to the class held and whether the round price is a reliable input at all.
In practice
ASC 820 ranks inputs by how observable they are, and almost every private fund position sits in the least observable tier, which is why the written valuation policy and its consistent application matter more than any single mark. Auditors test the inputs and the calibration. LPs look for marks that respond to bad news as quickly as to good, and for a policy that was not changed mid-fund without explanation.