Using Land Equity for a C2P Loan

This C2P Loan process with land equity has been very confusing. Here is our scenario:

My wife and I have owned our lot for over a year. We paid approx 80k for it in early 2016. It doesn't have a current appraisal, but the value should have held. The initial quote that we received from our builder was approx $380k for a 2200 sqft home. This makes our total cost of construction $460k. Are we able to use the $80k in land equity as a down payment for our loan? We're worried about the final appraisal coming in low and we don't exactly know what would happen in this scenario. Would we have been better off keeping cash on hand instead of paying off our lot?

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