An automobile was purchased for total price of $10k. The down payement of $1k was deferred. What would the asset value be for depreciation.

Cost concept. Assets are recorded at the cost at which they are purchased. Payment has nothing to do with it.

Unless you're somewhere besides the U.S. where the rules are different. I don't know what you even mean by deferring the down payment. If it's deferred, how can it be a down payment? So that makes me a little suspicious about where you're located.