acalculator

What is my project's NPV?

Enter a discount rate, what you invest today and the cash flow at the end of each period to see the net present value, profitability index and IRR.

Your numbers

Per period: per year for yearly cash flows.
Read as: 5,000; 6,000; 7,000; 8,000One number per period. Negative for money out.
Net present value
$1,210.73

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.

Present value of the cash flows
$21,210.73
Cash flows minus investment (not discounted)
$6,000.00
Profitability index
1.061
IRR
10.48%

Net present value: $1,210.73. 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.

The results are estimates for information only. They are not financial, tax, or legal advice. Check the numbers with your lender or a qualified professional before you decide. Terms of use

How to calculate

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.

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.

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.

  • 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.

Machine-readable copies: Markdown, JSON.

Worked examples

Each example is checked against the calculator on every build.

  1. Discount rate 10%, Invested today $50,000.00, Cash flows at the end of each period 12,000, 15,000, 18,000, 20,000 gives Net present value $489.72, Present value of the cash flows $50,489.72, Cash flows minus investment (not discounted) $15,000.00, Profitability index 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. Discount rate 7%, Invested today $0.00, Cash flows at the end of each period -10, -20, -25, -20, 10, 30, 35, 35, 35, 20 gives Net present value $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. Discount rate 8%, Invested today $10,000.00, Cash flows at the end of each period 3,000, 3,000, 3,000, 3,000, 3,000 gives Net present value $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

How NPV is worked out

NPV = −C₀ + CF₁ ÷ (1 + r)¹ + CF₂ ÷ (1 + r)² + … + CFₙ ÷ (1 + r)ⁿ

  • C₀ is the amount invested today (time 0). It is not discounted.
  • CFₜ is the net cash flow at the end of period t (money in minus money out). It can be negative.
  • r is the discount rate per period, as a decimal (8% is 0.08). For yearly cash flows use a yearly rate.

The calculator also shows:

  • present value of the cash flows: PV = Σ CFₜ ÷ (1 + r)ᵗ, so NPV = PV − C₀
  • cash flows minus investment, not discounted: Σ CFₜ − C₀
  • profitability index: PV ÷ C₀, when C₀ is more than 0
  • IRR: the rate r at which the NPV is 0, found by searching rates from −99.9999% to 99,999,900% per period (discount factors 1 ÷ (1 + r) from 10⁻⁶ to 10⁶), and shown only when exactly one rate in that range works. A rate outside the range, for example below −99.9999% when almost nothing comes back, is not shown

Assumptions

  • Cash flows happen at the end of each period, and the rate is the same every period.
  • The rate is above −100%.
  • Tax and inflation are not included unless they are in your cash flows and rate.

Worked examples by hand

$50,000 invested, then $12,000, $15,000, $18,000 and $20,000 at 10%.

  • period 1: 12,000 ÷ 1.1 = 10,909.09
  • period 2: 15,000 ÷ 1.1² = 15,000 ÷ 1.21 = 12,396.69
  • period 3: 18,000 ÷ 1.1³ = 18,000 ÷ 1.331 = 13,523.67
  • period 4: 20,000 ÷ 1.1⁴ = 20,000 ÷ 1.4641 = 13,660.27

PV = $50,489.72. NPV = 50,489.72 − 50,000 = $489.72. Undiscounted: 65,000 − 50,000 = $15,000. Profitability index = 50,489.72 ÷ 50,000 = 1.010.

OMB Circular A-94's example. Net benefits (benefits minus costs) for years 1 to 10 are −10, −20, −25, −20, 10, 30, 35, 35, 35 and 20, with nothing invested at time 0. Discounting each by 1 ÷ 1.07ᵗ and adding gives $36.01, the net present value in the circular.

$10,000 invested for $3,000 a year for 5 years at 8%. PV = 3,000 × (1 − 1.08⁻⁵) ÷ 0.08 = 3,000 × 3.99271 = $11,978.13. NPV = $1,978.13. The IRR, the rate where the NPV is 0, is 15.24%.

Other questions people ask

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.