@Terron Winn there are a few items that I'd like to debunk based off the back-and-forth dialogue, and provide my input.
First of all, you can rent out a property with an FHA mortgage. When you apply for an FHA mortgage, it must be your primary; however, circumstances in life can change and you are able to rent the property without having to refinance. Typical FHA stipulations require you to live in the property for 12 months. The other thing you need to keep in mind is you can only have ONE FHA mortgage at any given time. This means, you couldn't apply for another FHA mortgage while you still had the existing mortgage on your first home.
Second, FHA loans in 2011 required MIP for 5 yrs (it's referred to as Mortgage Insurance Premium for FHA loans, and conventional loans use PMI, Private Mortgage Insurance). You cannot drop that insurance within that 5 yr period. FHA loans originated after June 3, 2013 had to pay MIP for the life of the loan if putting less than 10% down. If putting 10% or more down, MIP would be for 11 yrs.
Third, the consideration of rental income in your Debt-to-Income (DTI). This can be a little tricky if you don't have prior landlord experience. You definitely want to consider pro's and con's of each scenario before making any financial moves (ie. refinancing). It's a catch 22 because you want to pull cash out of your current equity; however, this can raise your DTI to the point where you couldn't qualify for the Investment loan or new home loan. This is where a detailed analysis of your financials is required to determine your options. Conventional loans only allow a max DTI of 45%. This means all your debts (housing, credit cards, car payments, student loans, child/spousal support, etc.) divided by your gross monthly pay (your wages/other income before taxes and deductions) cannot be greater than 45%. FHA allows up to 55%. Some HELOCs (home equity line of credit) allow up to 50%.
Fourth, Cash-out refi is limited to 80% Loan-to-Value (LTV) on primary homes and 75% on investment properties. Someone above mentioned only 75%, and that is typically the case with conventional/conforming loans for single family investment properties. If you refi while it's your primary then you can pull up to 80% LTV; however, most lenders have a document you sign stating you will live in the property for at least 12 months so you will run into issues if looking to purchase a new primary home after you recently refi'd your current home as a primary.
I have been in this situation many times, and have been able to successfully navigate all the guidelines and rules. Keep in mind, these rules change almost weekly. In this market, it's typically changing for the better (except FHA and primary conversion rule change in 2015).
Shoot me a message if you want to talk further and determine implications of one choice compared to the other. There is a lot more information needed to ensure you make the right decision.