Ahh, I think I got it now. In my calculations, I was assuming you pay off the refinance for the previous house but you leave each house with the refinance. I've put together a breakdown of a cash and mortgage example running through the 3rd house.
Adding it here if it's helpful for anyone else to get a sense for what the picture looks like on the 2nd, 3rd house, etc.
Thanks Matt and Whitney for your help!
BRRR Cash Example
Home 1
Home: $55k cash
Rehab: $15k
ARV: $100k
Refinance 1 @ 75%: $75k
Home 2
Home: $55k using Refinance 1
Rehab: $15k using Refinance 1
ARV: $100k
Refinance 2 @75%, $75k
Status: 2 homes ARV of $200k, Refinance 1 & 2 outstanding for $150k
Home 3
Home: $55k using $ from Refinance 2
Rehab: $15k using $ from Refinance 2
ARV: $100k
Refinance 3 @ 75%: $75k
Status: $70k of your cash initially in, 3 homes ARV of $300k, Refinance 1, 2, & 3 outstanding for $225k
BRRRR Mortgage Example
Home 1
Home: $55k
Deposit: $11k
Mortgage 1: $44k
Rehab: $18k
ARV: $100k
Refinance 1 @ 75%: $75k
Home 2
Home: $55k
Deposit: $11k using Refinance 1
Mortgage 2: $44k
Rehab: $18k using Refinance 1
Leftover $ from Refinance 1 = $46k, payoff Mortgage 1
ARV: $100k
Refinance 2 @75%, $75k
Status: 2 homes ARV of $200k, Refinance 1 & 2 outstanding for $150k
Home 3
Home: $55k
Deposit: $11k using Refinance 2
Mortgage 3: $44k
Rehab: $18k using Refinance 2
Leftover $ from Refinance 2 = $46k, payoff Mortgage 2
ARV: $100k
Refinance 3 @ 75%: $75k
Status: $29k of your cash initially in, 3 homes with an ARV of $300k, debt from Refinance 1, 2, & 3 and mortgage 3 totaling $269k