Yours is a multi stepped process. You have a long-term holding period.Beginning with the 2002 gift, your basis is usually the donor's basis for your fractional share. You will also need to know the Fair Market Value (FMV) of the land at the time of the gift (more on that later). Each example below builds on the previous one.
Ex: 2002 Land basis to your mother and husband before the gift: $100K Basis to all after the gift is $25k
In 2003 when your mother passes, the remaining 3 of you receive a stepped up basis in her share using the FMV at the date of death.
Ex: The FMV of her share is now worth $33K. Each of you will increase your basis by $11k for a total of $36k ($25k+ $11k) basis each.
In 2016 when her husband passes, your sister and you now receive another stepped up basis in his share using the FMV at the date of death.
Ex. The FMV of his share is now worth $60k. Each of you will increase your basis by $30k for a total of $66k ($36k + $30K) basis each.
In 2017 when you purchased your sister's share, you basis would then increase a final time by the cost of your purchase.
Ex. You purchased your sisters share for $80k. Your sole basis is now $66k + $80k = $146k basis.
Now in 2018 when you sell, the FMV at the time of the gift can come into play. This is because the IRS want's to make sure that donor losses are not shifted to the recipient. The rules can be challenging but I will attempt an explanation here:
If your sale resulted in a gain, then your basis used in the calculation is the same as the donor's basis - listed above in the examples and is generally the case for most taxpayers. However, if your sale resulted in a loss, then the FMV at the time of the gift is used. If this is your case, then comment back so I can explain further.
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