The NPV formula
Net present value answers a deceptively simple question: is this project worth more than it costs, once you account for the fact that a dollar tomorrow is worth less than a dollar today? It discounts every future cash flow back to the present and subtracts what you paid up front:
Where C₀ is the initial investment (a year-0 outflow), CFt is the cash flow received in year t, and r is the discount rate. Dividing by (1 + r) raised to the year shrinks distant cash flows more than near ones — that's the time value of money at work.
- NPV > 0 — the project earns more than your required return; it creates value.
- NPV = 0 — it exactly meets your required return.
- NPV < 0 — it earns less than the discount rate; it destroys value.
Worked example
Invest $10,000 today, expect $4,000 a year for 3 years, with a 10% discount rate:
NPV vs IRR
NPV's close cousin is the internal rate of return (IRR) — the discount rate at which NPV equals zero. In the example above the IRR is just under 10%, which is exactly why NPV came out slightly negative at a 10% rate. NPV tells you the dollar value created; IRR tells you the break-even rate. For deciding between mutually exclusive projects, NPV is generally the more reliable guide.