What should I use as my cost basis? Inherited rental property...

[Ricky Stafford]

Parents built a house in the 80s and just built as they went - no record of what they paid. Parents deeded over property my sister and I in 2013. I renovated and started renting out 33% of the house in 2014. I have thus far not claimed any depreciation on this property but don't foresee ever selling it so that's not really an issue.

From what I've read, my cost basis is their cost basis which is the lesser of fair market value or cost + improvements. Since there's no way to know cost + improvements as they never kept a record, what do I do? I'm fine with with a super conservative estimate since something is obviously better than nothing, but don't even know where I should start?