Thanks Vladimir, good point indeed.

My expertise stops at the denominator of the CLV calculation I just wanted to explain it briefly since we need it to derive the CLV. Feel free to share here how that should be done but as far as I understand, you would/could indeed consider initial investment:

I would expect that any initial investment would be treated as a negative cash flow at time zero, since it is an upfront cost that has been incurred before revenue.

In my article, the NPV table we are using should then include a t=0 of (let's say 10000). Then in the calculation of NPV, I would expect to start with NPV = -10000 + M/(1+0.1) ...