In the collections world, debt buying and liquidation involves several
aspects, but the application of NPV I would like discussion on and an
example of would be:  I have 'x' face value of debt (that I paid 'a'
for), should I sell it today if I can get 'y' or place it for
collection with an expected rate of future cashflows equal to 'z'
(cash flows will be discounted at a known rate since I have to pay a
collection agency a contingency fee for dollars collected).

There is some muddled thinking here.

|(cash flows will be discounted at a known rate since I have to pay a
collection agency a contingency fee for dollars collected).|

That does not make sense - those fees have nothing to do with the discount rate.

Realistically the 'discount rate' is pretty arbitrary, in essence one
is lending at a fixed rate, but changes in current rates make it a
moving target.

Let's get this really simple

Someone owes you money and they will pay it back over say 10 years
- to ensure the payment you have to use a collection agency that will
cost you per payment, but ensure income (by threatening remedial
dental bills)

Fine, you still have a flow of income, albeit reduced because of the thugs fee.

Now, the present value is the sum of money that you could go out and
borrow /today/ at fixed rates, with repayments that exactly match the
flow of nett income.

Maybe this is homework, but the first time I ran into DCF was in the
mid 1970's when working as an 'intern' for a large UK company.
- typically they confused 'one off' costs with the discount rate
- just as you are confusing your 'enforcers' fee with the rate of interest.

It is dead simple - match the 'problem' with a flow of expenditure