NPV and IRR Calculator

What this calculator answers

Whether a series of cash flows is worth more than it costs at the return you require, and what return the cash flows earn by themselves. Enter the cash flows, period 0 first, and a discount rate. You get the net present value (NPV), every internal rate of return (IRR) the cash flows have, or the reason there is none, and the modified IRR (MIRR), profitability index, payback period and discounted payback period. The periods can be years, quarters or months, as long as they are evenly spaced.

How to use it

• Enter cash flows in one of three ways:
  • Type or paste a list: one amount per line, period 0 first. You can paste a column or a row straight from a spreadsheet. A heading row, a column of period numbers, $ signs, thousands commas, (5,000) for −5,000 and a lone dash for 0 are all read, and the line under the box says how many cash flows it found.
  • One box per period: the initial cash flow, then one box for each later period, up to 100. On a phone, the ± button beside each box makes it negative.
  • Level or growing amounts: the initial cash flow, the period 1 amount, the number of periods, an optional growth rate per period and an optional extra amount in the last period, such as a resale value.
• Signs: money you pay out is negative, money you receive is positive. An investment usually starts with a negative period 0.
• Period length: the time between cash flows. Every rate is per period, and the rate’s label says which: “Discount rate per quarter”. Changing the period length converts the rates you typed, so 10% per year becomes 2.411369% per quarter, not 10% per quarter.
• Discount rate: the return you require, per period (see the questions below for how to choose one).
• MIRR rates (optional): check the box to give MIRR its own finance rate (what your funding costs) and reinvestment rate (what the cash coming in can earn). Otherwise both equal the discount rate.

Results update as you type. Switching to a list or to boxes carries over the cash flows you already entered (a growing series is written out to the cent). Each Try button loads one of the cases discussed below. To weigh two projects, press Save for comparison after each one: the saved table shows how NPV, IRR, MIRR and payback differ from the first.

How to calculate NPV

Discount each cash flow to period 0 at the rate per period, then add them up. The period 0 cash flow is not discounted.

• $CF_k$ is the cash flow at the end of period $k$; $CF_0$ happens now.
• $r$ is the discount rate per period as a decimal (10% is 0.1).
• $n$ is the last period.

Equivalently, NPV is the present value of the money coming in minus the present value of the money going out. A positive NPV means the cash flows return more than the discount rate, by that many of today’s dollars.

What a negative NPV means

The cash flows earn less than your discount rate. It doesn’t have to mean they lose money. The Growing 3%, then resale example ($60,000 now; $9,000 in year 1 growing 3% a year to $11,068.86 in year 8, plus $15,000 from a resale that year) adds up to $35,031.02 more than it costs, yet at 10% its NPV is −$411.22: its IRR is 9.84%, just below the rate you asked for. It never pays back once discounted, even though the undiscounted payback is 6.17 years.

Worked example: a $38,500 printer at 10% a year

A print shop is weighing a $38,500 wide-format printer. It expects the printer to add $8,500, $12,000, $13,000, $12,500 and $11,000 of cash over the next five years, the last figure including what it can sell the printer for. The shop wants a 10% return.

1. NPV: the present values add up to $4,279.52. The $42,779.52 the inflows are worth today exceeds the $38,500 cost by that much.
2. IRR: the NPV is $78.44 at 14% and −$871.40 at 15%, so the IRR lies between them. Narrowing in gives 14.08%. The cash flows change sign once, so it is the only IRR, and it is above the 10% required return, as the positive NPV says.
3. MIRR: carried forward to year 5 at 10%, the inflows are worth $68,896.85. MIRR = ($68,896.85 ÷ $38,500)^1/5 − 1 = 12.34%.
4. Profitability index: $42,779.52 ÷ $38,500.00 = 1.11, so each dollar spent brings back $1.11 in today’s money.
5. Payback: after year 3 the running total is −$5,000; year 4 brings $12,500, so payback is 3 + $5,000 ÷ $12,500 = 3.4 years.
6. Discounted payback: after year 4 the cumulative present value is −$2,550.61, and year 5 adds $6,830.13, so it is 4 + $2,550.61 ÷ $6,830.13 = 4.37 years.

Undiscounted, the printer returns $18,500 more than it costs, which is its NPV at 0%. The forecasts have some room for error: under What if, with every inflow 10% lower the NPV is still $1.57, so the printer still earns its 10% if the money coming in falls up to about 10% short of the shop’s estimates.

How IRR is calculated (and why it needs a solver)

The IRR is the discount rate at which the NPV is exactly $0. Setting the NPV formula to zero gives an equation in $r$ with a term for every period, which has no direct formula for the rate, so calculators and spreadsheets find it by trying rates and narrowing in, as in step 2 above.

This calculator checks the NPV at more than 11,000 rates from −99.9% to 10,000% per period, closer together at low rates than at high ones, and narrows every change of sign it finds until the rate is within 0.00000001 percentage points. It reports every IRR in that range. A spreadsheet’s IRR function instead starts from one guess (10% unless you give another) and returns the rate its search settles on.

Why a project can have more than one IRR, or none

More than one: each time the cash flows change sign, from money out to money in or back, the NPV can cross $0 once more. By Descartes’ rule of signs, the number of IRRs is at most the number of sign changes. The Two IRRs example is the textbook pattern of a cost, a payoff and then a cleanup bill: −$100, then $230, then −$132. Its NPV is $0 at both 10% and 20%, positive between them ($0.19 at 15%) and negative outside. Neither rate is “the” return, so the calculator lists both, marks both on the NPV profile and points you to the NPV at your rate and the MIRR (15.05% at 15%) instead. Extra sign changes don’t always add IRRs: the Pasted quarterly data example has a $15,000 refit in quarter 6, three sign changes, and still only one IRR.

None: if every cash flow has the same sign, the NPV never reaches $0. The usual cause is a cost typed without its minus sign; when period 0 is positive and nothing is negative, the calculator offers a Make period 0 negative button. If the cash flows do change sign but the NPV stays away from $0 between −99.9% and 10,000% per period, the calculator says so rather than inventing a rate.

NPV vs. IRR: which to use when comparing projects

Use NPV. When you can take only one of two projects, the one with the higher NPV at your discount rate adds more value, even if its IRR is lower. Suppose the print shop could instead buy a smaller printer for $18,000 that brings in $5,500, $6,500, $6,500, $5,500 and $4,000:

The small printer earns the higher rate on less money; the large one adds more value in dollars at 10%. The ranking flips at the crossover rate, the discount rate at which the two NPVs are equal. To find it, enter the difference between the two projects’ cash flows (−$20,500, $3,000, $5,500, $6,500, $7,000, $7,000): its IRR, 11.32%, is the crossover. Below 11.32% the large printer has the higher NPV; above it, the small one does.

IRR vs. MIRR

The IRR treats the money a project returns as if it earned the IRR itself until the end, which is optimistic for a high IRR. The MIRR instead carries the money coming in forward at a reinvestment rate you choose and discounts the money going out at a finance rate, then finds the one rate that links the two. It always has a single value. For the printer, MIRR at 10% is 12.34% against an IRR of 14.08%.

Converting a monthly or quarterly IRR to an annual rate

Compound it: an annual rate is (1 + rate per period)^m − 1, with m periods in a year. For a positive rate, multiplying by 12 or 4 understates it. In the Monthly rental, then sale example ($55,000 in, $450 a month for 60 months, then $68,000 from a sale, at 0.75% a month, which is 9.38% a year), the IRR is 1.1% a month (1.0985% before rounding). As a yearly rate that is (1.010985)¹² − 1 = 14.01%, not 1.0985% × 12 = 13.18%. The calculator shows every rate per period and, for quarters and months, as a yearly rate too. The same works in reverse for the discount rate: 10% a year is 0.797414% a month.

Reading the result

• Net present value is the headline, with a sentence saying what it means in today’s dollars at your rate.
• IRR shows the rate, or all of them, or why there is none. The note below the tiles counts the sign changes, compares the IRR with your discount rate when that comparison holds, and says how the search was done.
• MIRR, profitability index, payback and discounted payback follow. “Not reached” means the running total is still below $0 after the last cash flow.
• How this was calculated repeats the formulas with your numbers. Check it in a spreadsheet gives the matching =NPV(), =IRR() and =MIRR() formulas with your cell ranges and rates.
• Present value of each cash flow lists the discount factor, present value and both running totals for every period. Download it as a CSV file.
• Charts: the NPV profile plots NPV against the discount rate and marks each IRR where the curve crosses $0; Present values sets each cash flow beside what it is worth today.
• What if reruns the calculation at discount rates 1 and 2 points either side of yours (a quarter and half a point for quarters, a tenth and a fifth for months) and with all money coming in 10% and 20% higher or lower.

Assumptions and limitations

• Cash flows are evenly spaced, and each one arrives at the end of its period. Cash flows on irregular dates need a dated method, such as XNPV and XIRR in a spreadsheet.
• One discount rate applies to every period. If you expect rates to change over the life of the project, the NPV here is an approximation.
• The results are only as good as the cash-flow forecasts. Taxes, inflation and risk count only as far as your cash flows and discount rate include them.
• Payback periods assume each period’s cash arrives evenly through the period.
• IRRs are searched for between −99.9% and 10,000% per period.
• The results are educational estimates, not investment, tax or accounting advice.

Common mistakes

• Entering the cost as a positive number. With every cash flow positive there is no IRR, and the NPV counts the cost as income.
• Using a yearly rate for monthly cash flows. At 10% a month, five years of monthly cash flows are discounted far too heavily. Switch the period length first; the calculator converts the rate for you.
• Dividing a yearly rate by 12. 10% ÷ 12 = 0.833% a month compounds to 10.47% a year. The equivalent monthly rate is 0.797414%.
• Leaving a period blank. Spreadsheet NPV and IRR skip empty cells, which moves every later cash flow a period earlier. Enter 0 for a period with no cash flow. The calculator skips blanks the same way, but says how many it skipped.
• Picking the project with the higher IRR. Compare NPVs at your discount rate, as in the printer comparison above.

Why your answer may differ from Excel’s NPV or IRR

Spreadsheet NPV discounts its first value by a full period. Putting period 0 inside it, =NPV(10%, B1:B6), gives the printer an NPV of $3,890.48 instead of $4,279.52, as if every cash flow came a year later. Keep period 0 outside: =NPV(10%, B2:B6)+B1. For IRR, a spreadsheet returns only the rate its search reaches from the guess, or #NUM! if it doesn’t settle within 20 tries, so with several IRRs it shows one of them and says nothing about the others.