Refinancing a paid off rental

[Lindsey Beeney]

I used a HELOC on my personal home to buy a duplex in cash. We're closing this week. Several improvements have already been done to the property and I'm almost positive an appraisal would come back higher than what I paid. My local bank lender tells me that even if it appraises for 50k over purchase price, they still have to refinance the lower value i.e. purchase price at 50k vs appraisal price at 100k. That doesn't seem correct. If it appraises for a higher amount, shouldn't I be able to refinance and cash out the 75% of the appraised value not 75% purchase price? I'm thinking I may need to shop around for another lender. Or is that how refinances are now if you do a quick turnaround? I was hoping to refinance in 45 days even after closing this week. Do I need to sit on it longer before I try to refinance?