future undiscount cash flow is remaining present value of the asset .

fair value is a rational and unbiased estimate of the potential market price of a good, service, or asset.Under US GAAP (FAS 157), fair value is the amount at which the asset could be bought or sold in a current transaction between willing parties, or transferred to an equivalent party, other than in a liquidation sale. This is used for assets whose carrying value is based on mark-to-market valuations; for assets carried at historical cost, the fair value of the asset is not used.

So fair value is more reliable than book value.