I would think that you would treat it like this. The permanent loan, when there is a 2x close construction/permanent loan, is still a purchase loan or reporting, even if the permanent loan is technically refinancing the construction loan.
3. Construction and permanent financing. A home purchase loan includes both a combined construction/permanent loan or line of credit, and the separate permanent financing that replaces a construction-only loan or line of credit for the same borrower at a later time.
It would be a cash out refinance in the secondary market, as the original loan funds were not used to purchase the property, but that is only if you price or underwriting your Limited Cash Out and Cash-Out Refinances differently. Since this is a home improvement loan, neither would apply.
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