Inherited property has stepped-up basis - that is a fair market value of the property at the time the decedent died - so if the fair market value is $200,000 - that would be the basis.
Assuming - you will spend $10,000 for renovations - that will bring the basis to $210,000
If you sell the property - let's say for $225,000 - the capital gain will be calculated as $225,000 - $210,000 = $15,000 - and it will be taxable as long term capital gain - at reduced rate - not more than 15%
Additional NJ income taxes will be due on that amount.
Please be aware that all numbers above are very raw estimations and are for illustrations only.
Let me know if you need any clarifications.
Yes - any gain is calculated as a difference between the sale price and the basis.
If you do not do any improvements - and sell shortly after the decedent died - the selling price will be considered as a fair market value and as the basis of the property -so there will not be any capital gain.
If you do improvements - the fair market value will likely increase, but the basis will be a fair market value at the time of death (not selling price) plus improvement expenses.