Why a dollar tomorrow is worth less than a dollar today
Money has a time value: a dollar received in five years is worth less than a dollar in hand now, because today’s dollar can be invested and grow. NPV makes that idea concrete by discounting each future cash flow — dividing it by (1 + r) raised to the number of periods away it sits — so distant cash is worth proportionally less than near-term cash. Add up all those present values and subtract what you have to pay upfront, and you are left with the net value the project adds in today’s money. Because the discount rate represents your required return, clearing zero means clearing your hurdle.
The net present value formula
NPV = Σ CFt / (1 + r)t
where CFt = the cash flow in period t(the initial outlay is CF₀, usually negative), r = the discount rate (your required return), and t = the period number, summed across every period of the project. A positive total means value created; a negative total means value destroyed.
What makes this calculator different
- Editable multi-year cash flows. Add, remove, and edit a cash flow for every period rather than being limited to a single fixed payment, so uneven and lumpy projects model correctly.
- It shows the per-period discounting. Each cash flow is listed with its discount factor and present value, so you can see exactly how distant dollars shrink — not just the final total.
- Profitability index, alongside. The PI (present value of inflows ÷ initial outlay) is reported so you can compare value per dollar invested, useful when capital is limited.
- The IRR, reported next to NPV. The internal rate of return is solved and shown beside the NPV, letting you read the break-even discount rate at a glance. For a deeper look, see theIRR calculator.
- A clear accept or reject. The verdict is stated plainly from the sign of the NPV, so the decision rule is never buried. To build the cash flows themselves from a full forecast, try the DCF calculator.
Frequently asked questions
What is net present value (NPV)?+
Net present value is the sum of every future cash flow an investment is expected to produce, each discounted back to today’s dollars, minus the upfront cost. The formula is NPV = Σ CF_t / (1 + r)^t, summed over each period t, where CF_t is the cash flow in that period and r is the discount rate. The initial outlay is simply CF₀, usually a negative number, so it enters the sum at t = 0 with a discount factor of one. The result is a single dollar figure: how much value, in today’s money, the project adds (or destroys) at your required rate of return.
How do you interpret an NPV result?+
The rule is simple. A positive NPV means the investment is expected to earn more than your required rate of return, so it creates value and should be accepted. A negative NPV means it earns less than that hurdle rate and would destroy value, so it should be rejected. An NPV of exactly zero means the project earns precisely your required return — break-even in present-value terms. When comparing mutually exclusive projects, the one with the higher NPV is generally preferred.
What discount rate should I use?+
The discount rate should reflect your required rate of return — the minimum return you need to justify tying up the capital, given its risk. For a company, this is typically the cost of capital, often the weighted average cost of capital (WACC) that blends the cost of debt and equity. For an individual, it might be the return you could earn on an alternative investment of similar risk (your opportunity cost). Riskier cash flows warrant a higher discount rate, which lowers their present value and makes the hurdle harder to clear.
What is the difference between NPV and IRR?+
NPV gives you a dollar amount of value created at a discount rate you choose, while the internal rate of return (IRR) gives you a single percentage — the discount rate at which NPV equals zero. They usually agree on whether to accept a standalone project: if IRR exceeds your required return, NPV is positive. They can disagree when ranking mutually exclusive projects of different scale or timing, and IRR can be ambiguous or undefined when cash flows change sign more than once. Most analysts treat NPV as the more reliable decision rule because it measures value directly and assumes reinvestment at the discount rate rather than at the IRR.
What is the profitability index?+
The profitability index (PI) is the present value of an investment’s future cash flows divided by the initial outlay. A PI above 1.0 corresponds to a positive NPV, and a PI below 1.0 corresponds to a negative NPV, so the accept/reject signal matches. Its advantage is that it expresses value per dollar invested, which helps rank projects when capital is rationed and you cannot fund everything with positive NPV. For example, a PI of 1.25 means the project returns $1.25 of present value for every $1.00 committed.
Disclaimer: This calculator is foreducation and illustration only. NPV depends entirely on the cash-flow estimates and discount rate you supply — small changes to either can flip the result — and it cannot capture every risk or real-world frictions. Its output is not a tradeable valuation. Nothing here is investment, tax, or trading advice.