Net Present Value (NPV) Calculator

Understanding the net present value calculator — concept and principle

Net present value (NPV) answers a basic investment question: after allowing for the fact that money later is worth less than money now, does a project return more than it costs? Businesses use it to evaluate machinery, new products or property. Enter the initial investment, up to five yearly cash flows and a discount rate.

How it is calculated

NPV = −C₀ + CF₁ ÷ (1 + r)¹ + CF₂ ÷ (1 + r)² + … + CF₅ ÷ (1 + r)⁵

• C₀: initial investment, paid today (year 0).
• CFₜ: net cash flow at the end of year t.
• r: discount rate per year, as a decimal (8% = 0.08).

The calculator also shows PV of inflows = NPV + C₀, and the profitability index = PV of inflows ÷ C₀. The decision line says "accept" when NPV is above zero. Any currency works.

The principle

A dollar today can be invested to earn a return, so a dollar received in t years is worth only 1 ÷ (1 + r)ᵗ today. The discount rate represents the return you require: your cost of capital or the return of the best alternative with similar risk. Discounting every cash flow back to today puts them all on the same footing, so they can be added and compared with the investment. NPV is the value created, in today's money, beyond earning the required return.

Worked example

1. Investment $100,000; cash flows 30,000, 35,000, 40,000, 30,000, 20,000; r = 8%.
2. Year 1: 30,000 ÷ 1.08 = 27,777.78.
3. Year 2: 35,000 ÷ 1.08² = 30,006.86. Year 3: 40,000 ÷ 1.08³ = 31,753.29.
4. Year 4: 30,000 ÷ 1.08⁴ = 22,050.90. Year 5: 20,000 ÷ 1.08⁵ = 13,611.66.
5. PV of inflows = $125,200.49; NPV = 125,200.49 − 100,000 = $25,200.49.
6. Profitability index = 125,200.49 ÷ 100,000 = 1.25; NPV > 0, so the decision is accept (creates value).

How to read the result

Positive NPV: the project earns more than the required rate. Zero: it earns exactly that rate. Negative: it earns less. A profitability index of 1.25 means each dollar invested returns $1.25 in present value. Results are sensitive to the discount rate; in this example the NPV turns zero at roughly 17.6%, the project's internal rate of return. Try a higher rate to test how robust the decision is.

Common mistakes

• Using a discount rate that does not match the project's risk.
• Entering profits instead of cash flows (depreciation is not a cash outflow; capital spending is).
• Mixing nominal cash flows with a real (inflation-adjusted) rate, or vice versa.

Frequently asked questions

What discount rate should I use?

Usually your weighted average cost of capital or the return you could earn elsewhere at similar risk. Riskier projects warrant higher rates.

How is NPV different from IRR?

IRR is the rate that makes NPV zero. NPV gives value in money; IRR gives a percentage. When they disagree on ranking projects, finance textbooks generally favour NPV.

What if the project lasts more than five years?

This calculator handles five years. For longer projects, add later cash flows discounted the same way, or include a terminal value in year 5.

Sources: Brealey, Myers and Allen, Principles of Corporate Finance (McGraw-Hill)