After you purchase a home lenders usually want you to own the home for a certain amount of time, called "seasoning", before they will use an appraised value that was higher than your purchase price. Typically that seasoning period is 12 months. However keep in mind that Fannie Mae & Freddie Mac, who back the conforming loan programs that lenders make, do not have any seasoning requirements, so the time you must own your home will be solely determined by the mortgage lender you are applying with ("overlay" guidelines they are called).
However taking cash out of your home's equity is usually capped at 80-85% of your home's appraised value, not to 100% of your home's appraised value, so even when the new value can be used it may not be able to get you the cash out you are thinking.
However if you are looking to get funds to renovate a home you should look into purchase the home with an FHA 203(k) rehab loan or Fannie Mae HomeStyle renovation loan program. Both will finance the cost of improvements into your loan, assuming the "as completed" appraised value supports the funds you need to purchase + renovations.
Extensive info on FHA's 203(k) rehab loan: http://www.hud.gov/offices/hsg/sfh/203k/203kabou.cfm