NPV calculator
Discount a stream of cash flows to today.
- Formula and assumptions shown
- Table and CSV export
- Runs in your browser
How it works
NPV discounts each future cash flow, including any negative later amounts, back to the starting period and subtracts the initial outlay. A positive result means the entered net future cash flows exceed the initial outlay at the chosen discount rate.
NPV = − initial outlay + Σ(annual cash flow at year t ÷ (1 + annual discount rate)^t), with later cash flows at each year end.
The calculation assumes equally spaced periods. Use a consistent period rate and remember that NPV is only as useful as the cash-flow and discount-rate assumptions.
Assumptions
- Cash flows occur at regular periods.
- The discount rate matches the cash-flow period.
- The initial outlay occurs at time zero.
- The model excludes taxes, terminal-value judgments, probabilities, and irregular dates.
Worked example
$1,000 now for $1,100 next year
At a 5% discount rate, NPV is −$1,000 + $1,100 ÷ 1.05 = about $47.62.
Step by step
- Find the discount factor. At 5%, a dollar received one year from now is worth 1 ÷ 1.05 = 0.952381 of a dollar today.
- Discount the cash flow. $1,100 × 0.952381 = $1,047.62, shown as Present value of future cash flows and in the year 1 row of the table.
- Subtract the initial outlay. $1,047.62 − $1,000 = $47.62, the headline net present value.
- Read the positive result. $1,000 earning 5% would grow to $1,050 in a year. The project pays $1,100, which is $50 more, and $50 received in a year is worth $50 ÷ 1.05 = $47.62 today.
How to read your result
The headline is net present value. The secondary results show the initial outlay, the present value of all later cash flows, and the discount rate used. The table lists each year’s cash flow and its present value, and the chart plots those present values by year, which shows how discounting shrinks amounts that arrive later.
A positive NPV means the cash flows return more than the discount rate after repaying the outlay; zero means they return exactly that rate, which is the IRR; negative means less. The dollar figure is value today above the outlay, not total profit. In the default inputs, $10,000 now followed by $3,000, $3,500, $4,000, and $4,500 has $15,000 of undiscounted inflows but a present value of $12,261.43 at 8%, for an NPV of $2,261.43.
Every later cash flow is treated as arriving at the end of its year, and the outlay at time zero. This differs from Excel’s NPV function, which discounts its first value by one period, so spreadsheet users usually add the time-zero outlay separately. Taxes, inflation, risk adjustments, and a terminal value are included only if they are built into the cash flows or the rate entered.
What changes the result most
- Discount rate
- The same $1,100 is worth less at higher rates. NPV is $47.62 at 5%, $18.52 at 8%, $0 at 10%, and −$17.86 at 12%.
- Timing
- Receiving the $1,100 in year 2 instead of year 1 (cash flows "0, 1100") lowers its present value at 5% to $997.73, and NPV turns negative at −$2.27.
- Size and distance of later amounts
- In the default series at 8%, the year 4 inflow of $4,500 has a present value of $3,307.63, about 73.5% of its face value, while the year 1 inflow of $3,000 keeps $2,777.78 (92.6%).
Questions
What does a positive NPV mean?
Under the entered assumptions, discounted net future cash flows exceed the initial outlay. It does not guarantee a profitable or suitable investment.
Can I enter monthly cash flows?
This form labels later values as annual cash flows. A monthly schedule would need matching monthly timing and a matching period rate, which this form does not provide.
Does NPV include IRR?
No. NPV tests one discount rate. IRR solves for the rate that makes NPV zero.
What is the NPV formula?
NPV = −initial outlay + CF1 ÷ (1 + r) + CF2 ÷ (1 + r)² + … + CFn ÷ (1 + r)ⁿ, where r is the discount rate per period and CFt is the net cash flow at the end of period t. With one $1,100 cash flow at 5%, NPV = −$1,000 + $1,100 ÷ 1.05 = $47.62.
What discount rate is used for NPV?
The rate stands for the return required to accept the cash flows’ timing and risk. Common choices are a business’s cost of capital, the return on an alternative of similar risk, or the interest rate on money borrowed for the project, with riskier cash flows usually discounted at higher rates. Because the choice drives the result, testing several rates shows how sensitive the answer is.
Is net present value the same as present value?
No. Present value discounts future cash flows to today. Net present value subtracts the upfront cost from that present value. In the example, present value is $1,047.62 and NPV is $47.62.
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Sources
These references explain the concepts behind the calculation. They do not endorse this site. Estimates leave out any cost or condition you did not enter.