An asset is acquired by signing a note payable. The note does not indicate an interest rate, and the fair value of the asset cannot be reliably determined. At what amount should the asset be recorded?

Assets should be recorded at cost basis. To determine cost basis we should determine the price that the company paid for the asset. If the only record about the purchase transaction is the note payable, then we can assume that the amount specified in the note payable is the purchase cost of the asset. The cost basis doesn't include any type of interest, but since the note doesn't specify any interest, then we can assume that there is no interest charged.