My mother died in 1980 without a will. The house was split 4 ways and my father was one of the 4. in 1990, he signed his share over to the three kids and has lived there rent free
For the past 17 years. Now he is moving and we need to sell the house. He showed me
An appraisal done at my mothers death at $5000. With all the improvements he has made the appraisal now is $55,000. I believe that the appraisal in 1980 was erroneous.
My question is how much tax would we have to pay on the sale of the house split three ways and what would we use as the basis?

The basis is the value of the house at the time of your mother's death plus the cost of improvements made over the past 27 years. You didn't say how much this was - hopefully your father kept some records. Since there are 3 owners, none of whom used the house as a primary residence, I believe you will have to split any appreciation (minus selling costs) 3 ways and each pay capital gains tax on your portion of the increase in value. This assumes the three kids will split the proceeds evenly.

If you think the appraisal done back in 1980 is erroneous, not sure how you would come up with an alternate appraisal so many years later - perhaps tax assessment records?

Getting a proper FMV evaluation seventeen years late will be most difficult. However, if your estimate is close to comparative values for similar houses, you should little problem with the IRS.

It could take some work, but if the neighborhood is stable, you can look through the county records to see what similar houses actually sold for in 1980. In my county, I can do that on-line.

Agree with Pacific NW.