The historical cost of an asset (which is what the owner originally paid for it) less its total depreciation (which is the portion of value removed each year for accounting purposes) up to that point. That is, the unamortized cost of an asset is the value of the asset that has not yet been subtracted for depreciation. This affects the owner's net asset value, but the unamortized cost often has only a rough relationship with the asset's actual fair market value.