Converted detached garage to home office

I purchased my home in 2005 for $235,000 (current value is approx $250,000).  In June 2016, I converted a detached garage into a home office (new business use - I haven't claimed the home office expense in the past).  The cost of the conversion was $2,900.  The square footage of the house is about 3,000, the square footage of the detached garage is 300.

When I add the Home Office "Asset", I'm unclear what I should be entering for the "Cost".  Just the cost of the improvement?  Or the current market value of the house?  Also what should I be listing for the "Date purchased or acquired" (the date of the house purchase or the date of the improvement/conversion to the garage)?

It appears if I only deduct the cost of the improvement, then it's not depreciating a % of the value of the house.