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Deductions & credits
Add together the original purchase price + the cost of purchase + the cost of sale + any improvements = the cost basis which you split with the ex.
Then the sale should be reported on separate 1099-S forms so you each report 1/2 of the sale on your individual returns. Your 1/2 of the Sales price on the 1099 form - your half of the cost basis = profit/cap gains.
Then if you lived in the home for 2 of the last 5 years ending on the date of sale you each will be able to exclude up to $250K of profit.
Simple sample :
Purchase price $250K = $125 each
Sales price $1,050,000 = $525K each
525K - 125K = $400K
$400 - $250 exclusion(if eligible) = $150K profit x 20% tax = $30K tax on profit so this is the max amount of taxes on the return ... could be lower depending on the rest of your income.