Yes, it matters!
The cost of your home is being requested in order to set up the home as a depreciable asset, so that the home office percentage of depreciation can be included in your expenses each year.
Refinancing is not part of this calculation. The value of an asset for depreciation is not based on appraisals, but arms-length transactions that established value. The cost of your home is what you paid for it, plus any adjustments to basis since your original purchase date, such as a new roof, upgraded HVAC system, etc.
