Capital Gains and Losses
Capital Gains Tax Questions? Ask a Tax Advisor for Answers ASAP
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Assuming you, your mother-in-law, and the property are in Canada. her estate pays capital gain taxes on the deemed sale of the 1/3 of the cottage she owned at death. In your hands, the basis is 1/3 of the value at death + 2/3 of (the cost at acquisition + improvements before her death) + improvements after her death.
If you need more clarification, don't hesitate to ask.
Technically, that's not a "Capital Gains" question, and it's not formally in my field of expertise, but it isn't in the probate estate.
If the probate estate (or the estate managed by the executor, which might be slightly larger) is inadequate to pay the capital gains taxes, the CRA (or whatever it's called now) can go after the beneficiaries.
My apologies, but it's time for me to go to bed. I'll have an opportunity to answer any followup questions in about 6 hours, but my access will be intermittent after that point.