NPV Formula With a Worked Example
NPV = Σ CFt ÷ (1 + r)t, for t = 0 to n
The first value is today and is not discounted. Discounted payback comes from the running total of present values: after year 2 it stands at −$3,792.87, and the year-3 present value of $3,969.16 covers it 0.96 of the way through the year, so payback is 2.96 years.
How NPV Moves With the Discount Rate
NPV falls as the rate rises and crosses zero at the IRR, 15.32%. Between 12% and 20% the project goes from adding value to destroying it, which is why the choice of rate matters as much as the cash-flow forecast.
Choosing a Discount Rate: Benchmarks for 2026
- A company: its weighted average cost of capital, adjusted up for riskier projects.
- A personal investment: what you could earn at similar risk. For near-riskless flows of a year or less, a Treasury bill is the floor: the 52-week bill yielded 4.49% (coupon-equivalent) on October 21, 2026.
- Federal programs: OMB Circular A-94 Appendix C (revised March 6, 2026) sets nominal rates of 3.4% for 3 years up to 4.1% for 30 years, and real rates of 1.1% to 2.0% for constant-dollar flows.
Match the rate to the cash flows: nominal rates for flows that include inflation, real rates for flows in today’s dollars, and a per-month rate if each value is a month.
Common NPV Mistakes
- Checking against Excel’s NPV function. Excel’s NPV discounts the first value too. Use =NPV(rate, flows from period 1) + the period-0 flow to match this calculator.
- Two definitions of profitability index. This calculator divides the PV of inflows by the PV of outflows (1.165); some textbooks divide NPV by the initial cost (0.165). Both say the same thing about whether the project pays.
- Annual rate on monthly flows. Enter the rate per period. 8% a year is about 0.643% a month compounded, not 8%.
- Mixing real and nominal. Discounting inflation-adjusted flows at a nominal rate understates NPV, and the reverse overstates it.
- Leaving out a terminal value. If the asset still has value at the end, add the expected sale price to the last flow.
What the Result Does Not Include
NPV is only as good as the cash-flow forecast and the rate. The calculator does not adjust for taxes, inflation, risk scenarios or financing; it discounts exactly the numbers you enter at one constant rate. For a large business or investment decision, run several scenarios and have a financial adviser or accountant review the inputs.
Frequently Asked Questions
What does a positive NPV mean?
The investment earns more than the discount rate after accounting for when the money arrives, so it adds value at that rate.
What discount rate should I use for NPV?
Your cost of capital or the return you require for the risk. For low-risk flows a Treasury yield is a floor; companies usually use their WACC plus a risk adjustment.
How is NPV different from IRR?
NPV gives the dollar value added at a chosen rate; IRR is the rate at which NPV is zero. NPV is the better tool when comparing projects of different sizes.
Why does Excel give a different NPV?
Excel’s NPV function treats the first value as one period away and discounts it. This calculator treats the first value as today.
Can NPV be negative even if I get more money back than I put in?
Yes. $14,000 back on $10,000 has a negative NPV at any rate above that deal’s IRR, because later dollars are worth less today.
What is a profitability index?
PV of inflows divided by PV of outflows. Above 1.0 the project has a positive NPV; it helps rank projects when capital is limited.
What is discounted payback?
The time it takes for discounted inflows to repay the initial investment. It is always longer than simple payback because later dollars are discounted.
How to Use This Calculator
- Enter the discount rate — per period: an annual rate for yearly flows, a monthly rate for monthly flows.
- Enter cash flows — the first value is today (usually the negative investment); then one value per period, separated by commas.
- Calculate — the NPV, PV of inflows and outflows, profitability index and discounted payback.
- Compare — with the IRR shown alongside and the present value of each period’s flow.
📚 Sources & References- [1] Microsoft. IRR function (method and the worked example used to test this calculator; accessed Oct 2026). support.microsoft.com
- [2] OpenStax. Principles of Finance, Chapter 16: How Companies Decide Which Projects to Invest In (NPV, IRR, MIRR, payback, profitability index; 2022). openstax.org
- [3] Office of Management and Budget. Circular A-94, Appendix C: discount rates for 2026 (revised Mar 6, 2026). www.whitehouse.gov
- [4] U.S. Treasury. Daily Treasury Bill Rates, Oct 21, 2026. home.treasury.gov
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