How it works
NPV discounts each future cash flow back to today and subtracts the investment. In symbols, NPV = Σ CF_t / (1 + r)^t − I. CF_t is the net cash flow in year t, r is the discount rate per year, t runs from 1 to the project life N, and I is the investment at the start. Each cash flow is divided by (1 + r) once for every year it lies in the future. At 8%, a dollar received in ten years is worth 1 ÷ 1.08^10 = $0.46 today.
The discount rate carries most of the judgement. For project NPV it is usually the weighted average cost of capital, a blend of the after-tax cost of debt and the return equity requires. For equity NPV, the cash flows after debt service are discounted at the cost of equity. NPV is measured in money, so it shows how much value a project adds. IRR shows the rate at which it earns. The two can rank projects differently when they differ in size or life. In that case NPV gives the value created at the owner's cost of capital.
Why it matters
NPV tells an owner how much value a project adds after paying for its capital. A developer comparing two designs for the same site, such as more batteries or more solar, should choose the higher NPV even if its IRR is a little lower. A buyer can use it to compare a PPA with grid supply, treating the savings as the cash flow. Small changes in the discount rate move NPV a lot, so the rate should be agreed before results are compared.
A worked example
A plant costs $10 million and earns $1.2 million a year for 20 years. At 8%, the annuity factor is (1 − 1.08^−20) / 0.08 = 9.818. The cash flows are worth 1.2 × 9.818 = $11.78 million today. NPV = 11.78 − 10 = +$1.78 million. At 10%, the factor is 8.514, the cash flows are worth 1.2 × 8.514 = $10.22 million, and the NPV falls to +$0.22 million. The IRR is therefore a little above 10%.
Illustrative figures.