dfilipek Posts: 1, Reputation: 1 New Member #1 Jul 4, 2009, 01:15 PM
How do I get the NPV of the following
I need to conduct a discounted cash flow calculation to determine the NPV of the following project, assuming a required rate of return of 0.2. The project will cost $75,000 but will result in cash inflows of$20,00, $25,000,$30,000,and \$50,000 in each of the next 4 years.

Please help and if you could show me how you did it that would be great so I know for the future.

Thanks,
Dan
 Stringer Posts: 3,733, Reputation: 770 Business Expert #2 Jul 4, 2009, 01:28 PM

Not sure if this is exactly what you are looking for, however this explains in detail how it is done:

Net present value - Wikipedia, the free encyclopedia
 ArcSine Posts: 969, Reputation: 106 Senior Member #3 Jul 5, 2009, 05:47 AM
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 outflows 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 $\frac{C_4}{(1.2)^4}$ or $C_4(1.2)^{\small-4}$, whichever you prefer ($C_4$ 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

$\displaystyle\sum_{i=0}^n \frac{C_i}{(1+r)^i}$

... where r is your discount rate (per period); $C_0$ is the initial cash flow; and after the initial cash flow there are n subsequent CFs.

Your particular case becomes

Project NPV = $-75,000 + 20K(1.2)^{\small-1} + 25K(1.2)^{\small-2} + 30K(1.2)^{\small-3} + 50K(1.2)^{\small-4}$

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,