Cash out refi or HELOC for new property down payment

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So My wife any I have quite a bit of equity in our house.(primary residence)  We want to pull the trigger on buying our first rental property but I need to decide on a course of action for the down payment.  Initially my wife was pushing for the heloc as the method to get our down payment money but I insisted on as closely as possible comparing the numbers to the cash out refi.  I gathered the numbers from the banks on both and she inputted everything into her excel sheet.  

current house value $620k

remainng balance $194k

credit over 800

looking at pulling $150000 or $200000 out for investing

When comparing the same increased monthly payment on both options over 30 years  we ending up seeing quite a difference.   

With the $150k heloc vs cash out refi, the heloc would save you quite bit of money over the life of the term and increase our monthly payments around $600

If we go for the $200k option,  the cashout refi saves quite a bit over the life of the term and increases our monthly payments by around $900

Does this make sense to others who have looked into the numbers?

The other consideration is order of operations.  Is it preferable to refi the house and then later get a heloc for more investing?  Or can we get a heloc now and have it not effect refi ing the house later for more inversting?

Any questions or advise always welcome 

I just took out a HELOC on my primary residence and used that for a down payment on a duplex. The only reason I did a HELOC, is because I plan to Refinance the duplex in 6 months (sooner if possible) and pay off the HELOC balance. Then I will be able to utilize that money again for another property.

also, I know it can be very difficult to get a HELOC out of an investment property.

Ya that makes sense. I didn't take that into account when I was figuring things. I suppose that would be the smartest way to do it to keep our primary residence payment the same and at a lower interest rate than current rates. Not having done a BRRRR deal yet, how long do you have to wait to refinance the rental. You said six months. Is that just how long you think it will take to rehab it. And how much can you pull out during the refi?