What this calculator does
Net present value discounts every future cash flow back to today and nets it against the initial investment. If the result is positive, the project earns more than the discount rate you required; if negative, it does not. It is the standard test in capital budgeting because it answers in dollars rather than percentages.
The internal rate of return is the discount rate at which NPV falls to exactly zero: the project’s own break-even return. Comparing it against your cost of capital gives the same accept-or-reject answer as NPV, expressed as a rate. This calculator finds it numerically by bisection, since there is no closed-form solution.
The formula
Each cash flow is divided by (1+r) raised to the power of its year, then summed and reduced by the initial outlay. To find the IRR, the calculator narrows the interval where NPV changes sign until it converges on the crossing point.
| Term | Meaning |
|---|---|
| NPV | Net present value: total discounted inflows less the initial investment. |
| IRR | The discount rate at which NPV equals zero. |
| C₀ | The initial investment, paid at time zero. |
| CFₜ | The cash flow received at the end of year t. |
| PI | Profitability index: discounted inflows divided by the initial investment. |
The inputs explained
| Field | What to enter |
|---|---|
| Initial investment ($) | The up-front investment, entered as a positive number. |
| Cash flow each year (comma separated) | Cash flows for each subsequent year, separated by commas. The first value is year one, and the list can be any length. |
| Discount rate (%) | Your required return or cost of capital. This is the hurdle the project must clear. |
When to use it
Deciding whether to fund a project
Enter the cost and the expected cash flows. A positive NPV at your cost of capital means the project creates value; a negative one means the capital is better used elsewhere.
Ranking competing projects
When capital is limited, NPV ranks by dollars created and the profitability index ranks by dollars created per dollar invested. The second is usually the right test when the constraint is capital rather than opportunities.
Evaluating equipment or a property purchase
Put the purchase price as the initial investment and the net annual cash generated as the flows. Include any resale value in the final year’s figure.
Testing sensitivity to the discount rate
Raise the discount rate until NPV turns negative. The rate at which it flips is the IRR, and how close it is to your hurdle tells you how much margin for error the project has.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the discount rate changes NPV
A $100,000 project returning $25,000, $30,000, $35,000 and $40,000 over four years, tested against different required returns.
| Discount rate | Net present value | Verdict | Profitability index |
|---|---|---|---|
| 0% | $30,000.00 | Accept: value created at this discount rate | 1.300 |
| 5% | $14,162.82 | Accept: value created at this discount rate | 1.142 |
| 8% | $6,053.64 | Accept: value created at this discount rate | 1.061 |
| 10% | $1,137.22 | Accept: value created at this discount rate | 1.011 |
| 12% | −$3,429.72 | Reject: the project destroys value at this rate | 0.9657 |
| 15% | −$9,693.36 | Reject: the project destroys value at this rate | 0.9031 |
The effect of project size at a fixed 8% hurdle
Identical cash flows with different up-front costs, all discounted at 8%.
| Initial investment | Net present value | IRR | Profitability index |
|---|---|---|---|
| $80,000 | $26,053.64 | 20.7% | 1.326 |
| $100,000 | $6,053.64 | 10.5% | 1.061 |
| $106,000 | $53.64 | 8.02% | 1.001 |
| $110,000 | −$3,946.36 | 6.50% | 0.9641 |
| $130,000 | −$23,946.36 | -5.5511e-15% | 0.8158 |
Questions
What discount rate should I use?
Your cost of capital, or the return available on an equivalent-risk alternative. Higher-risk projects warrant higher rates, which penalises distant cash flows more heavily.
Why can the IRR be undefined?
The calculation requires NPV to change sign somewhere in the tested range. If a project never turns positive, or has an unusual pattern of cash flows with several sign changes, there may be no single IRR, or several. NPV remains reliable in those cases.
Which is better, NPV or IRR?
NPV, generally. It measures value created in dollars and handles unconventional cash flows correctly. IRR is more intuitive to quote and is fine for straightforward projects, but it can mislead when comparing projects of very different sizes.
How do I enter cash flows that vary or go negative?
Enter them in order, separated by commas, and use a minus sign for years with net outflows. The list can be any length, and the first entry is always year one.
What does the profitability index tell me?
Present value of inflows per dollar invested. Above 1.0 the project is worthwhile; it is most useful when capital is rationed and you must choose between several positive-NPV projects.
For a single amount rather than a series, use present and future value. For a realised investment return, see the ROI calculator.