Investors & landlords

How would things differ if the house were sold six months after its inheritance to allow time for several home improvements (i.e. upgraded kitchen and bathrooms)?    I assume I'd need to identify the "stepped up" cost basis at the time the life tenant dies, and then at the time of the sale determine a "current" cost basis (stepped up basis plus cost of permanent improvements) ?   Would capital gains then be the sale price-"current" cost basis, less any closing costs?