The computation method that allows the most precise tracking of asset depreciation is Based on days per period. This method calculates depreciation based on the exact number of days the asset was in use during a specific period, resulting in a more accurate representation of the asset's value over time.

Here's a breakdown of the other methods:

• No Prorata: This method does not account for partial periods, meaning depreciation is calculated based on full periods, regardless of when the asset was acquired or disposed of during those periods. This can lead to inaccuracies, especially for assets acquired or disposed of mid-period.
• Constant Periods: This method assumes that all periods are of equal length, which may not be the case in reality. For example, some months have 30 days, while others have 31. This can also introduce inaccuracies in the depreciation calculation.  

Therefore, the Based on days per period method is generally considered the most precise for tracking asset depreciation.