If you knew what a house is valued at, how much higher than that would you offer??

Looking at a house. We know it's valued at 102,000. (this is alot for where we live). The owner started at 115,00 and has since dropped the price a few times to 107,000.

We're going to start offering at about 97,000. How much more than what a house is valued at would you be willing to spend?