Look at a whole bunch of my past posts, I've gone into this in a fair bit of detail before... mostly on CLH mind but some on PNC.
The fair value initially will be the price paid for the parcel of debt. After that a DCF is used by PNC as there is no readily observable market price. That DCF will estimate the future cash flows based on the underlying characteristics of the portfolio etc. How much will we collect and when and then discount.
Note that the costs of collection aren't included in the valuation of a financial asset (i.e. your points in 6 aren't appropriate).
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