Refinancing a rental property

[Anthony Finger]

Hello BP community! This is my first post as I am a newbie to the real estate game. I have been bitten by the rental property bug and have challenged myself with buying my first property in the San Antonio area by the end of 2018.

I am struggling with the refinancing portion of the BRRRR strategy. Can someone please help me out with this word problem?

I buy a $100,000 house with a 20% down conventional loan and put 10,000 dollars of rehab into it. After 12 to 18 months when I am able to refinance the property it appraises at $120,000. In order to get rental income above the mortgage price I am learning that 20% down is generally the way to go; which means I have to put $24,000 down on the refi. That means I am keeping $16,000 (20K down plus 20K in appreciation minus 24K down leaves me with 16K) and not getting all of my money back out of the deal.

Is my math wrong or am I looking at this scenario incorrectly? Any and all help will be greatly appreciated! I look forward to networking with the San Antonio and BiggerPockets community.