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Deductions & credits
RE: #6 - Can you clarify? If the $26,500 were treated as a FMV, if I add the $31,000 (which was legitimately all improvements according to IRS guidelines), wouldn't the basis be $57,500? Not sure how the $8,833, $3,000, or $5,833 for each sibling factor into the basis - but good to know for the gift aspect of the situation. (Sorry if I am overlooking something obvious.)
Because you did not inherit the entire house (because the will was unsigned). Each sibling inherited 1/3 of the house, so each sibling gets 1/3 of the basis. If the FMV (the stepped up basis) was $26,500, then your starting basis for your 1/3 ownership was $8,833. (If I buy a bunch of 3 bananas at the grocery store for $1 and give you and your siblings each 1 banana, the bananas are worth 33 cents each.)
The question then becomes, how much additional basis did you acquire when you acquired the other 2/3 ownership. At a minimum, you obtained $3000 additional basis from each sibling for their share (what you actually paid). You might have acquired the full $8,333 of your sibling's bases, if we take into account both the payment and the gift basis.
So your basis before improvements was at the lowest $14,833 and at the highest, $26,500 (assuming $26,500 is the true FMV.)