NPV Calculator
Net present value of a series of cash flows, discounted at your cost of capital.
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Your details
The first figure is period 0 — enter the initial outlay as a negative number.
Result
- Net present value
- $267.95
- Sum of cash flows
- $600.00
- Cost of discounting
- $332.05
- Break-even discount rate (IRR)
- 21.86%
Clears the discount rate — the project adds value
Before any discounting
The rate at which this NPV would be zero
5 flows at 10.00%…
NPV = Σ CFₜ ÷ (1 + r)ᵗ
t=0: $-1,000.00 ÷ (1+0.1000)^0 = $-1,000.00
t=1: $400.00 ÷ (1+0.1000)^1 = $363.64
t=2: $400.00 ÷ (1+0.1000)^2 = $330.58
t=3: $400.00 ÷ (1+0.1000)^3 = $300.53
NPV = $267.95
Formula — written step by step
1,000 out, then 400 back four times, at 10%…
NPV = Σ CFₜ ÷ (1 + r)ᵗ
t=0: −1,000 ÷ 1.10⁰ = −1,000.00
t=1: 400 ÷ 1.10¹ = 363.64
t=2: 400 ÷ 1.10² = 330.58
t=3: 400 ÷ 1.10³ = 300.53
t=4: 400 ÷ 1.10⁴ = 273.21
NPV = 267.95
CFₜ is the cash flow in period t and r the discount rate. A positive NPV means the project returns more than the 10% you demanded, so it adds value; a negative one means it falls short.
A worked example
A machine that pays back unevenly
- Purchase
- −50,000 at t=0
- Year 1
- 10,000
- Year 2
- 20,000
- Year 3
- 25,000
- Cost of capital
- 9%
- 10,000 ÷ 1.09 = 9,174.31
- 20,000 ÷ 1.09² = 16,833.60
- 25,000 ÷ 1.09³ = 19,304.59
- Sum of inflows = 45,312.50
- NPV = 45,312.50 − 50,000
NPV = −4,687.50 — reject
The undiscounted flows total 55,000 against a 50,000 outlay, which looks like a 5,000 profit. Discounting reverses the verdict entirely: the money arrives too late to justify the cost of capital. This gap between the raw sum and the discounted one is the whole point of the method.
How to use this calculator
- Enter your discount rate — the cost of capital, or the minimum return the project must clear to be worth doing.
- Enter the cash flows in order, starting with period 0. The initial outlay goes first and must be negative.
- Read the NPV: positive means the project beats your discount rate, negative means it does not.
- Check the table to see which periods actually carry the value, and the break-even rate to see how much room the project has before the verdict flips.
What NPV is for
Net present value answers one question: is this project worth more than the money it consumes? It discounts every future cash flow back to today at a rate representing what that capital costs, then subtracts the outlay. What remains is the value the project creates in today’s money.
Its advantage over simpler measures is that it accounts for both the size and the timing of every flow. Payback period ignores everything after the break-even point; accounting profit ignores timing altogether. NPV ignores neither.
The discount rate decides the answer
NPV is only as sound as the rate fed into it, and the sensitivity is severe. The same set of cash flows can be comfortably positive at 8% and clearly negative at 12%. Anyone presenting an NPV without stating the rate has not really told you anything.
The rate should reflect the risk of these particular flows, not the company’s average. A speculative project funded by a business with cheap debt still deserves a high rate, because the risk lives in the project rather than in the financing. The break-even rate shown alongside the result — the IRR — tells you how much cushion the assumption has.
What the formula leaves out
The model assumes flows arrive at the end of neatly spaced periods. Real cash arrives unevenly, and for projects with strong seasonality that assumption alone can move the answer materially. Working with shorter periods helps, at the cost of having to forecast in more detail than the estimates really support.
It also has nothing to say about strategic value, optionality or risk to reputation. A project that opens the door to a larger one later is worth more than its own cash flows suggest, and no discount rate captures that. NPV is a strong input to a decision, not a substitute for making one.
Formula & methodology
What this calculator assumes
- Cash flows are assumed to arrive at the end of evenly spaced periods, and the discount rate is constant across all of them.
- The discount rate should be the cost of capital for a project of this risk. A rate chosen for convenience makes the verdict meaningless.
- Excludes tax, working-capital movements and any terminal value beyond the flows entered.
Sources
- Brealey, Myers & Allen, Principles of Corporate Finance, 13th edition, McGraw-Hill, 2019 — net present value and capital budgeting.
How to read the result
| NPV | Meaning | Decision |
|---|---|---|
| Above zero | Returns more than the discount rate demanded | Accept — it adds value |
| Exactly zero | Returns precisely the discount rate | Indifferent — the IRR equals your cost of capital |
| Below zero | Returns less than the discount rate | Reject, or revisit the assumptions |
A negative NPV does not mean the project loses money in cash terms — it may still show an accounting profit. It means the money would do better elsewhere at the rate you specified.
Frequently asked questions
Why must the first cash flow be negative?
By convention period 0 is the initial outlay — money leaving you. Entering it as a positive number tells the calculator you received it, and the NPV becomes meaningless. If your project has no upfront cost, enter 0 for period 0.
What discount rate should I use?
Typically the weighted average cost of capital for a project of this risk, or the return available on the next-best alternative use of the money. When in doubt, calculate the NPV at two or three rates and see whether the decision actually changes.
Positive NPV but negative IRR verdict — which do I trust?
NPV. It is the more reliable rule when the two disagree, because IRR implicitly assumes interim cash flows are reinvested at the IRR itself, which is often unrealistic.
Can I use months instead of years?
Yes, provided the discount rate is per month too. A 12% annual cost of capital is roughly 0.949% a month compounded, not 1%.
Each flow, discounted
| Period | Cash flow | Factor | Present value |
|---|---|---|---|
| 0 | $-1,000.00 | 1.000000 | $-1,000.00 |
| 1 | $400.00 | 0.909091 | $363.64 |
| 2 | $400.00 | 0.826446 | $330.58 |
| 3 | $400.00 | 0.751315 | $300.53 |
| 4 | $400.00 | 0.683013 | $273.21 |