The asset acquisition value is affected by improve transactions on the first date of the asset acquisition, not on the date of the improvement transaction.  This is true for all reports EXCEPT those that contain a Calculate As Of filter.  Reports that include this filter are the Book Value report, the Asset Listing report and the Account Distribution report. 

For example:
Asset acquisition date: 01/01/2009
Acquisition value: $1000.00
Improvement transaction date: 06/15/2010
Improvement amount: $500.00

On the book value report, if you calculate as of a date prior to 06/15/2010, the acquisition value is $1000.00.  If you calculate as of 06/15/2010 or after, the acquisition value is $1500.00. 

If you run the Asset Transaction report, there is no calculate as of date.  Regardless of the date you run the report, the audition value of the asset is the full $1500.00.