The formula
NPV = Σ flow ÷ (1 + r)^period
Where it comes from
Net present value discounts every future cash flow back to today and adds them up, investment included. A positive NPV means the project beats the return you demanded; a negative one means you would do better elsewhere, even if the raw total looks like a profit.
How to work it out by hand
- Write the flows in order, with the investment first and negative
- Divide each flow by (1 + discount rate) raised to its period
- Add all the discounted values together
- Positive means it creates value at that rate; negative means it does not
What is worth knowing
The example is worth staring at: 1,000 in, 1,200 out, and the answer is still no. The raw profit is 200, but the money is tied up for three years and you demanded 10% a year for that. Discounted, the 1,200 is worth 994.74 today. This is exactly why undiscounted return figures mislead, and why the discount rate is the assumption to argue about. Drop it to 9% and the same project turns positive. NPV also assumes intermediate cash flows can be reinvested at the discount rate, which is a real limitation when comparing projects of very different lengths.