Trading equity in houses with original loans still owing?

How would one structure a pay off when we are selling our house to a friend at the same time purchasing a property from him. We are going to simply reduce our selling price by 50K and he’s going to do the same. We would both have to still pay off the existing loans though. In effect we’re both selling our properties 50k below the appraisal value. I know the loan to value would look good, but that leaves us with no cash downpayment for a mortgage to pay off. I’m just trying to wrap my head around this. Anybody have experience with this?
We would both have to obtain new mortgages to payoff our loans. But if we just switch equity, that leaves neither with cash for a down payment.

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