Floors all need replaced, as well as the kitchen and baths.other cosmetic repairs as well.

Went in and did repairs, but didn't pay the taxes for the next 3 years.Would the next investor have to pay for the repairs and back taxes the previous investor paid?

I used the lower end of prices as leasing price and after repair value based on the Zillow estimate.

It seems a little difficult at first when I have no idea how much to expect in repairs, vacancy rate, property management costs etc. 

You're going to need it to appraise for 20% (really should be higher) than what you have into it (purchase + repairs).

So I assumed the ARV would be $175,000Estimated Repair Cost: $2,500Downpayment: 10%Loan Interest Rate: 4.5%; pulled it out of the air.

You did not include insurance.  5% is too low for Vacancy, Repairs, and CapEx.  

When we do get it sold we would like to take back out the amount we bought it for and the money we put into it (we do not have a mortgage on it we bought it in cash and did all the repairs with cash).  

My question is if the purchase price is $50k and I need 100k for repairs is it 25% of just the puchase price or is it 25% of the purchase and rehab total?

Repairs/CapEx/Vacancy projections might be a little low.You should budget for property management, even if you're planning to self-manage.