ForecastingStocks

Net present value — NPV, or VPL (valor presente liquido) in Portuguese — is the single most important decision tool in corporate finance. It tells you, in today's money, whether an investment creates or destroys value.

The formula

NPV is the sum of all cash flows, each discounted to today at the chosen rate i:

NPV = CF0 + CF1/(1+i)^1 + CF2/(1+i)^2 + ... + CFn/(1+i)^n

CF0 is usually negative (the upfront investment).

The decision rule

NPV greater than 0 — the project earns more than the discount rate. Accept it; it adds value.
NPV equal to 0 — it earns exactly the discount rate. Indifferent.
NPV less than 0 — it earns less than the discount rate. Reject it.

Worked example

The project from the cash flow lesson: invest 10,000 today, receive 4,000, 4,000, 5,000 over three years, discounted at 10%:

Year 0: -10,000
Year 1:  4,000 / 1.10      = 3,636.36
Year 2:  4,000 / 1.10^2    = 3,305.79
Year 3:  5,000 / 1.10^3    = 3,756.57

NPV = -10,000 + 3,636.36 + 3,305.79 + 3,756.57 = 698.72

The NPV is +698.72 units. At a 10% required return, the project is worth doing — it creates about 699 units of value today, even though the naive sum looked like +3,000.

The rate changes the verdict

Recompute at 15%:

NPV = -10,000 + 4000/1.15 + 4000/1.15^2 + 5000/1.15^3
NPV = -10,000 + 3,478.26 + 3,024.57 + 3,287.58 = -209.59

Now NPV is negative — at a 15% hurdle, reject it. The exact rate at which NPV crosses zero has a name: the internal rate of return, our next lesson.