When the cash flows are uneven, as in your case (i.e. they don't form an 'annuity'), the general idea is that you discount each individual cash flow, and add up the results. Be sure to treat cash

**out**flows as negative values (these are commonly the "cost" of the project, occurring immediately).

Each cash flow is discounted by (

*1 + required discount rate*), after first compounding this amount by the number of periods into the future the cash flow occurs.

For example, the PV of a cash flow occurring 4 years away from "today" (and assuming that you're working with 'years' as your 'periods'), with a required discount rate of 20% per year, would be

or

, whichever you prefer (

simply denotes the cash flow occurring at the time-point four years away).

In the conventional 'shorthand' notation, the whole thing in general form is

... where

*r *is your discount rate (per period);

is the initial cash flow; and after the initial cash flow there are

*n *subsequent CFs.

Your particular case becomes

**Project NPV** =

Knock that one out on Excel or your favorite pocket calculator, and you're good to go. Hope that helped a bit, Dan. Best of luck with it,