# What is my project's NPV?

Computes the net present value (NPV) of an investment from a discount rate, the amount invested today and the cash flows at the end of each period, with the IRR.

- Page: https://www.acalculator.org/finance/npv-calculator
- JSON spec: https://www.acalculator.org/finance/npv-calculator.json
- Version: eb3f5363e299

## Default answer

Example with the default inputs (Discount rate 8%, Invested today $20,000.00, Cash flows at the end of each period [5,000, 6,000, 7,000, 8,000]): At 8%, investing $20,000.00 for cash flows of 5,000, 6,000, 7,000, 8,000 has a net present value of $1,210.73.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| rate | Discount rate | The rate per period used to discount future cash flows, for example the return you could get elsewhere. |
| initial | Invested today | The amount paid out at the start (time 0). It is not discounted. |
| flows | Cash flows at the end of each period | The net cash flow at the end of period 1, 2, 3 and so on, separated by spaces, commas or new lines. Negative for money paid out. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| npv | Net present value | The present value of the cash flows minus the amount invested today. |
| pv | Present value of the cash flows | Each cash flow divided by (1 + rate)^period, added up. |
| net | Cash flows minus investment (not discounted) | All the cash flows added up, minus the amount invested today, with no discounting. |
| pi | Profitability index | The present value of the cash flows divided by the amount invested today. |
| irr | IRR | The internal rate of return: the discount rate that makes the NPV zero, when there is exactly one. |

## Method

NPV = −C₀ + Σ CFₜ ÷ (1 + r)ᵗ for t = 1 to n, where C₀ is the amount invested today, CFₜ the cash flow at the end of period t and r the discount rate per period.

## Assumptions

- Each cash flow happens at the end of its period; the amount invested today is not discounted (OMB Circular A-94’s year-end convention).
- The discount rate is per period and stays the same for every period.
- The IRR is shown only when exactly one rate makes the NPV zero within the search range of −99.9999% to 99,999,900% per period; a rate outside that range is not shown.

## Worked examples

1. rate = 10%, initial = $50,000.00, flows = 12,000 or 15,000 gives npv = $489.72, pv = $50,489.72, net = $15,000.00, pi = 1.009794. Source: hand calculation in content.mdx: 12,000 ÷ 1.1 + 15,000 ÷ 1.1² + 18,000 ÷ 1.1³ + 20,000 ÷ 1.1⁴ − 50,000.
2. rate = 7%, initial = $0.00, flows = -10 or -20 gives npv = $36.01. Source: OMB Circular A-94 (1992), appendix B: benefits minus costs for years 1 to 10 at 7% give a net present value of $36.01 (discount factors rounded to 4 decimals, hence the tolerance).
3. rate = 8%, initial = $10,000.00, flows = 3,000 or 3,000 gives npv = $1,978.13, irr = 15.238237%. Source: hand calculation in content.mdx: 3,000 × (1 − 1.08⁻⁵) ÷ 0.08 − 10,000 = 1,978.13; IRR by Python bisection.

## FAQ

### How do I calculate NPV?

Divide each future cash flow by (1 + r)^t, where r is the discount rate and t the period it arrives in, add them up, and subtract the amount invested today. $50,000 invested for $12,000, $15,000, $18,000 and $20,000 over four years at 10% has an NPV of $489.72.

### What does a positive or negative NPV mean?

A positive NPV means the cash flows are worth more today than they cost, at your discount rate: the investment beats the return you could get elsewhere. A negative NPV means it falls short. An NPV of 0 means it earns exactly the discount rate.

### What discount rate should I use?

The return you could get on another investment with similar risk, or your cost of borrowing. For federal benefit-cost studies, OMB Circular A-94 (1992) used a real rate of 7% as its base case. Try a few rates to see how much the answer depends on it.

### What is the difference between NPV and IRR?

NPV is a dollar amount at a chosen rate. IRR is the rate at which the NPV is exactly 0. When the cash flows change sign more than once there can be several IRRs or none, so this calculator shows the IRR only when there is exactly one.

### When do the cash flows happen?

The amount invested today is at time 0 and is not discounted. Each cash flow you list is at the end of its period: the first after one period, the second after two. This matches the year-end convention in OMB Circular A-94. Spreadsheet NPV functions instead discount the first value too, so enter today's amount separately.

### What is the profitability index?

The present value of the cash flows divided by the amount invested today. Above 1 means a positive NPV. It helps compare projects of different sizes.

## Sources

- Office of Management and Budget, Circular A-94 (1992), Guidelines and Discount Rates for Benefit-Cost Analysis of Federal Programs: net present value is discounted benefits minus discounted costs; discount factor 1/(1 + i)^t; year-end flows; appendix B example NPV $36.01 at 7%. https://georgewbush-whitehouse.archives.gov/omb/circulars/a094/text/a094.html
- Brealey, R. A., Myers, S. C., and Allen, F. Principles of Corporate Finance (McGraw Hill): present value, net present value, internal rate of return and profitability index.
- Microsoft Support, NPV function: the investment begins one period before value1; a cash flow at the start of the first period is added to the result, not included in the values. https://support.microsoft.com/en-us/office/npv-function-8672cb67-2576-4d07-b67b-ac28acf2a568