Quick answer
NPV = −initial investment + Σ cash flow ÷ (1 + r)ᵗ. Investing $1,000 for yearly cash flows of 300, 400, 500 and 600 at a 10% discount rate gives an NPV of $388.77, from total cash flows of $1,800.
Enter the discount rate, initial investment and yearly cash flows. The calculator returns the NPV and the sum of the cash flows. Use this net present value calculator to check your own figures.
Related tools: Present Value Calculator: Today's value of a future amount at a given discount rate. Present Value of Annuity Calculator: Present value of equal payments at the end of each period. Future Value of Annuity Calculator: Future value of equal payments at the end of each period.
How to use the Net Present Value Calculator
- Enter discount rate (%) (between -99 and 1000).
- Enter initial investment ($) (0 or more).
- Type cash flows (years 1, 2, 3 …), for example 300, 400, 500.
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Discount rate | A number, in % | ≥ -99, ≤ 1000 |
| Initial investment | A number, in $ | ≥ 0 |
| Cash flows (years 1, 2, 3 …) | Text, such as 300, 400, 500 | — |
Formula and method
Formula
NPV = −C₀ + Σ CFₜ ÷ (1 + r)ᵗ
IEEE-754 double precision; money shown to cents, rates to 4 decimals. Results are estimates, not financial advice.
Cash flows arrive at the end of years 1, 2, 3 and so on.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Discount rate = 10; Initial investment = 1000; Cash flows (years 1, 2, 3 …) = 300, 400, 500, 600.
| Result | Value |
|---|---|
| Net present value | $388.77 |
| Sum of cash flows | $1,800.00 |
Example 2
Inputs: Discount rate = 8; Initial investment = 5000; Cash flows (years 1, 2, 3 …) = 1000, 1000, 1000.
| Result | Value |
|---|---|
| Net present value | -$2,422.90 |
| Sum of cash flows | $3,000.00 |
Example 3
Inputs: Discount rate = 0; Initial investment = 100; Cash flows (years 1, 2, 3 …) = 50, 60.
| Result | Value |
|---|---|
| Net present value | $10.00 |
| Sum of cash flows | $110.00 |
The first line is the headline result (net present value). Below it the net Present Value Calculator lists sum of cash flows, which describe the same case from other angles. IEEE-754 double precision; money shown to cents, rates to 4 decimals. Results are estimates, not financial advice.
The decision rule
A positive NPV means the project earns more than the discount rate, so it adds value. Present values here are 272.73, 330.58, 375.66 and 409.81, totalling $1,388.77; subtracting the $1,000 outlay leaves $388.77.
Choosing the rate
The discount rate reflects the return you could earn elsewhere at similar risk. Higher rates lower NPV. Compare with the IRR calculator: here the IRR is 24.9%, well above 10%.
How the result changes with discount rate
Holding every other input at the first worked example, this table changes only discount rate. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Discount rate | Net present value | Sum of cash flows |
|---|---|---|
| 5 | $574.07 | $1,800.00 |
| 10 | $388.77 | $1,800.00 |
| 20 | $106.48 | $1,800.00 |
| 40 | -$243.23 | $1,800.00 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Cash flows (years 1, 2, 3 …): left empty shows "Enter cash flows (years 1, 2, 3 …)." beside that field and no result.
Choosing between the Net Present Value Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Present Value Calculator](/finance/present-value-calculator/) | future value, annual discount rate and years | Present value |
| [Present Value of Annuity Calculator](/finance/present-value-of-annuity/) | payment per period, rate per period and number of periods | Present value |
| [Future Value of Annuity Calculator](/finance/future-value-of-annuity/) | payment per period, rate per period and number of periods | Future value |
| [Investment Calculator](/finance/investment-calculator/) | initial amount, annual interest rate and years | Projected value |
| [Financial Calculator](/finance/financial-calculator/) | solve for, periods per year and payments | Future value (FV) |
Background: interest, saving and investing
A nominal rate (APR) does not include the effect of compounding; the annual percentage yield (APY) does: APY = (1 + r/n)^n − 1. A 5% nominal rate compounded annually is 5.000%, semi-annually about 5.063%, quarterly about 5.095% and monthly about 5.116%, so more frequent compounding helps, but with diminishing returns.
The rate you enter in a projection is an assumption, not a promise: real returns vary and can be negative. Fees and taxes are not modelled unless the page says so.
Assumptions and limitations
- Negative later cash flows are allowed
Results are estimates for planning, not financial advice. Lender terms, fees, taxes and rounding rules can change real figures, so confirm important numbers with your lender or a licensed adviser.
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for cash flows (years 1, 2, 3 …) to confirm this.
Frequently asked questions
What is the difference between NPV and PV?
NPV subtracts the initial cost.
Can cash flows be negative?
Yes, later negative flows are allowed.
What if NPV is zero?
The project earns exactly the discount rate.
What does the Net Present Value Calculator calculate?
NPV of an initial outlay and a series of yearly cash flows. It returns Net present value and Sum of cash flows.
What formula does the Net Present Value Calculator use?
NPV = −C₀ + Σ CFₜ ÷ (1 + r)ᵗ. Cash flows arrive at the end of years 1, 2, 3 and so on.
What do I need to enter in the net Present Value Calculator?
You enter Discount rate (%), Initial investment ($) and Cash flows (years 1, 2, 3 …).
How is the result rounded or limited?
IEEE-754 double precision; money shown to cents, rates to 4 decimals. Results are estimates, not financial advice. Negative later cash flows are allowed.
What is an example of a net Present Value result?
With discount rate 10, initial investment 1000 and cash flows (years 1, 2, 3 …) 300, 400, 500, 600, the net present value is $388.77.
Can I rely on this calculator for a decision?
Results are estimates for planning, not financial advice. Lender terms, fees, taxes and rounding rules can change real figures, so confirm important numbers with your lender or a licensed adviser. For this calculator in particular: Negative later cash flows are allowed.
Related calculators
- Present Value Calculator — Today's value of a future amount at a given discount rate.
- Present Value of Annuity Calculator — Present value of equal payments at the end of each period.
- Future Value of Annuity Calculator — Future value of equal payments at the end of each period.
- Investment Calculator — Project investment growth from a rate of return you choose.
- Financial Calculator — Time-value-of-money solver for N, rate, present value, payment or future value.
- IRR Calculator — Internal rate of return of an investment from its yearly cash flows.
Sources
- Standard time-value-of-money relations (e.g. Brealey, Myers & Allen, Principles of Corporate Finance)
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.