The FHA 203k to the rescue again.
That is correct, and if you purchased a 1-4 unit property that you are living in or want to live in, within the last six months and can close the new loan prior to that six month anniversary you get to include the money you already put down as though you had just put it down now. If it was after that anniversary and you put 20% or more down you may still be able to get your construction money with no more money out of your pocket. This is a wonderful refinance and renovation program.
Remember that refinances can only go up to 100% of the appraised value and not the 110% like purchases can. If you need a refinance and renovation loan we can recommend Danny Fitzpatrick of Wells Fargo
This loan program is also an excellent way of financing construction when contractors need to assist the borrower in finding the money to pay them. There are also programs for investors (not FHA 203k)