How would the new basis be determined?

I am determined to close on my first deal this year. 

Eligibility: The Housing Authority’s RoleThe Housing Authority's primary responsibility in the Section 8 program is to determine whether an applicant meets the eligibility requirements.

There is a tendency to focus on the rental price when that doesn't solely determine what ends up in your pocket!

Normally,  I determine the basis in the new property by subtracting the old mortgage from the new mortgage and then adding in certain costs such as Exchange fee that occurred outside the closing.  

By working with an expediter and an architect, they determined that resolving the open permits and lifting the Stop Work Order would take approximately four months.

The value of a note is determined by a lot of factors, so you'll want to partner with someone with expertise to set it to bring the most value.

Learn your market thoroughly and zoning, etc to be able to quickly determine ARVs and highest and best use. 

Given this, what’s the best way to determine competitive pricing?

It does not matter if the property is not livable, since the whole aim of the appraisal is to determine if your proposed renovations support the ARV.