Purchasing with a solid HML will limit your initial cash outlay, and your refinancing bank will count your new built in equity as your down payment.

I have about $20k in equity in the house now.

@AJ Harris you may have $30k in equity but you likely will only be able to get refinance at 75% LTV which would be about $86K, so you would only be left with $6K after paying the original mortgage off. 

That is the annual increase in equity metric compared YOY as if you were going to sell minus sales cost and taxes.

He still has a $50k "equity" - was the work he invested worth $50k in equity?

Here' how I would do it with $100K using a BRRRR Strategybuy a 4 Plex for we will say 250K / 20% down = $50K DPPut $20K into renovations, it helps if you can do some or most of the work yourself (Sweat Equity) Rent out three of the units and house hack by staying in the 4th unit so essentially you would have $0 living expenses if done properly.Get the property appraised after making the renos, we will say it gets reappraised at 325K.Refinance for 75% of the new appraised value (325K*0.75)= $243,750KPay back the original mortgage of $200K You end up spending $50K DP + $20K Renos = $70k to get the property and you'd get back $243,750K - $200K (original mortgage) tax free back plus $81,250 in equity in the home that is tax free as well since you'd be getting refinanced at 75% of the total mortgage you'd receive the remaining 25% equity in the newly appraised value of the home ($325K *0.25) = $81,250 in Equity plus $43,750 in cash. 

I have 70g in equity and the home I want to purchase is only 15g. 

We have roughly $2 Million in equity today and generate enough cash flow each year to support our chosen lifestyle (which is admittedly pretty low key). 

Go find a private lender that has no interest in equity participation, Philip!

Currently I have a duplex with $45,000 in equity.