How to Calculate IRR: Step-by-Step Guide with Examples

IRR rests on present value, what a future payment is worth today at a given rate. A dollar received in one year is worth 1 ÷ (1 + r) today. ILPA, a trade body for fund investors, defines IRR as the rate at which the present value of what comes out equals what went in (ILPA Principles 3.0). Put simply, it is the rate at which the investment exactly breaks even, measured at today’s value.

Formula

NPV = CF₀ + CF₁ ÷ (1 + r) + CF₂ ÷ (1 + r)² + … + CFₙ ÷ (1 + r)ⁿ. IRR is the r at which NPV = 0.

CF

Each cash flow. Money you pay in is negative, money you receive is positive.

n

The period of each flow: 0 for today, 1 for one year from now, and so on.

NPV

Net present value: the sum of all flows, each converted to today’s money.

1. 1.0
   List the cash flowsWrite down every payment in and out, in order. Use a minus sign for money you pay, a plus sign for money you receive.
2. 2.0
   Add the current valueIf you still hold the investment, add its current value as a final inflow. Without it, the IRR comes out far too low.
3. 3.0
   Put each flow on a timelineUse equal periods, such as years, or the real dates. With real dates, use XIRR or a dated method.
4. 4.0
   Find the rateTest a rate, work out the NPV and adjust until it reaches zero. Or enter the flows into a calculator or spreadsheet.
5. 5.0
   Check and state itPlug the answer back in: the NPV should be zero. Say whether the IRR is per year, before or after fees, and as of which date.

By hand, you find IRR by trial and error. Take an illustrative investment. You pay $1,000 today and receive $300, $400 and $600 over the next three years. Start with a guess of 10% and discount each payment.

At 10% the NPV is positive, so the rate is too low. At 15% it is negative, so the rate is too high. The answer sits between 12% and 13%. To narrow it, draw a straight line between those two results. This is called interpolation:

• Interpolation12% + 13.80 ÷ (13.80 + 5.42) × 1% = 12.72%
• Exact answer from a solver12.71%

Two rounds of testing got within a hundredth of a point. Calculators repeat the same loop many times. Excel stops when it is accurate within 0.00001 percent, or after 20 tries (Microsoft Support).

Real investments rarely pay on neat yearly dates. Here is one investor’s position in an illustrative private fund, with $1,000,000 committed. The fund calls money four times and pays out twice. The last line is the value still held at the end of 2025, treated as if it were paid out that day.

• XIRR on the real dates14.1% a year
• Plain IRR on the seven rows15.1%, as if each row came exactly one year after the last

The dated answer, 14.1%, is the right one. Treating the rows as one year apart shrinks the real gaps and overstates the rate by a point. Why the two differ is explained in IRR vs XIRR. The pace of the payments in is set by capital calls.

The Texas Instruments BA II PLUS is a common financial calculator. It does IRR in its cash flow worksheet, with five keys: [CF], [NPV], [IRR], [↑] and [↓] (Texas Instruments). Here is the $1,000 example from above:

1. 1.0
   Open and clearPress [CF], then [2nd] [CE|C] to clear old entries.
2. 2.0
   Enter the outlayType 1000, press [+|-] to make it negative, then [ENTER] and [↓]. This is CF0.
3. 3.0
   Enter each inflowType 300, [ENTER], [↓]. The calculator asks for its frequency. Leave it at 1 and press [↓]. Repeat for 400 and 600.
4. 4.0
   ComputePress [IRR], then [CPT]. The display shows 12.71, meaning 12.71% per period.

Use the frequency field when the same amount repeats. TI’s own example is a $7,000 machine that returns $3,000, then $5,000 for four years, then $4,000. Enter 5,000 once with a frequency of 4. IRR comes out at 55.63%. The worksheet holds up to 32 cash flows, and TI warns that more gives a wrong answer.

The TI-84 Plus does IRR with one function: irr(CF0, CFList, CFFreq). CF0 is the first cash flow. CFList is a list of the cash flows after it, in braces. CFFreq is optional and says how many times each amount repeats in a row (Texas Instruments).

1. 1.0
   Open the functionOpen the Finance menu and choose irr(, item 8 in the list.
2. 2.0
   Type the flowsEnter irr(−1000, {300, 400, 600}). Use the (−) key for the minus sign.
3. 3.0
   Read the answerPress [ENTER]. The result is about 12.71, in percent.

For TI’s machine example, type irr(−7000, {3000, 5000, 4000}, {1, 4, 1}). The frequency list tells the calculator that 5,000 comes four times. The npv( function next to it takes the same lists plus a rate.

Put the cash flows in one column, first payment first. For equal periods, type =IRR(A1:A4). Excel says IRR needs flows at regular intervals, such as monthly or yearly (Microsoft Support). For real dates, put the dates in a second column and type =XIRR(A1:A7, B1:B7). XIRR always returns a yearly rate.

• Check the signsBoth functions need at least one negative and one positive value, or they return #NUM!.
• Use a guess if neededBoth start from 10%. If no answer comes back, add a guess as the last argument.
• Mind the first rowXIRR measures every date from the first one. An earlier date further down returns #NUM!. ILPA notes it also fails if the first value is zero.
• Annualize periodic resultsIRR on monthly rows returns a monthly rate. Convert it: (1 + monthly)¹² − 1.

Microsoft’s own example: −$70,000, then $12,000, $15,000, $18,000, $21,000 and $26,000. IRR over five years is 8.7%. Over the first four years it is −2.1%, because the last payment is missing. ILPA’s fund reporting guidance adds workarounds for XIRR’s leading-zero error (ILPA, 2025).

If you know the multiple and the holding period, you can get IRR in one line. MOIC, multiple on invested capital, is what an investment returned divided by what went in. With one payment in and one payment out, IRR = MOIC^(1 ÷ years) − 1.

• 2.0x in 3 years2.0^(1 ÷ 3) − 1 = 26.0% a year
• 2.0x in 5 years14.9% a year
• 2.5x in 5 years20.1% a year
• 3.0x in 5 years24.6% a year

The shortcut works only for a single payment in and a single payment out. A fund pays in and out many times, so its IRR needs the full cash flow list. The same multiple earned faster always means a higher IRR. Going the other way, from IRR to a multiple, is covered in how to calculate MOIC.

• Wrong signsEvery outlay must be negative and every receipt positive. All-positive flows have no IRR.
• Missing the final valueIf you still own the investment, its current value is the last inflow.
• Using IRR on uneven datesPlain IRR assumes equal periods. Use XIRR for real dates.
• Reading a periodic rate as yearlyMonthly or quarterly rows give a rate per month or quarter. Annualize it.
• Several sign changesIf money goes out, comes in, then goes out again, more than one rate can solve the formula. Check the answer with NPV.
• Too many flows on a calculatorA BA II PLUS holds 32. Group repeats with the frequency field.

IRR is arithmetic, so you rarely need help to calculate it. You may need help with what goes into it, and with what it triggers.

Valuations

The final value of an unsold holding is an estimate. If a decision depends on it, ask how it was set.

Fund terms

A fund’s IRR decides whether the manager earns carry. How that test works is in hurdle rate vs IRR. A lawyer can read the agreement for you.

Tax

An IRR before tax can look very different after it. A tax adviser can model your own cash flows, including the tax on each payout.

IRR (internal rate of return)

The rate at which the present value of all cash flows in and out equals zero.

Present value

What a future payment is worth today at a given rate.

NPV (net present value)

The sum of all cash flows, each converted to today’s money. It is zero at the IRR.

XIRR

The spreadsheet function that returns a yearly IRR for cash flows on any dates.

Interpolation

Estimating a value between two tested points by drawing a straight line between them.

MOIC

Multiple on invested capital: what an investment returned and is worth, over what went in.

NAV (net asset value)

What a fund’s holdings are worth at their estimated value, minus what it owes.

Capital call

A fund’s request for part of the money an investor committed.

Function descriptions and standards were last checked on November 9, 2026. Calculator steps are as documented by Texas Instruments. Spreadsheet behavior is as documented by Microsoft. All worked examples are illustrative and contain no market data.