Internal Rate of Return Calculator
Solve the two-cash-flow IRR = (FV/PV)^(1/n) − 1 for any of its four quantities — the internal rate of return, the future value, the present value, or the number of periods. Includes a live cash-flow timeline, IRR-vs-time and IRR-vs-multiple charts, and a full step-by-step solution with companion return metrics.
For two cash flows, IRR = CAGR
When an investment has exactly one outflow at t = 0 and one inflow at t = n, the IRR formula reduces exactly to the compound annual growth rate: IRR = (FV/PV)^(1/n) − 1. There is no "approximation" for this case — the formula is exact. The label "two-cash-flow approximation" is used because real-world investments almost always have intermediate cash flows (dividends, rent, coupons, reinvestments), and collapsing those to a single FV is an approximation of the true multi-period IRR.
IRR is a rate, not a dollar amount
Two investments can have identical IRRs and completely different profits. A 15 % IRR on a $1,000 investment is $150 of profit over a year; a 15 % IRR on a $1,000,000 investment is $150,000. IRR measures efficiency per dollar invested; profit measures absolute wealth created. Use IRR to compare opportunities of different sizes on equal footing, and always pair it with the absolute profit and NPV to make a final decision. A high IRR on a tiny position may be worth less than a modest IRR on a large one.
Time and multiple both shape the IRR
For a fixed growth multiple, IRR falls steeply as the horizon lengthens. A 2× multiple is 100 % per year over 1 year, 26 % over 3 years, 7.18 % over 10 years, and 2.34 % over 30 years. Conversely, for a fixed holding period, IRR rises with the multiple but with diminishing returns: doubling the multiple does not double the IRR (because of the 1/n root). This is why the two charts on the result side — IRR vs time and IRR vs multiple — are both useful: they show the trade-off between how much you make and how long you wait to make it.
Compare IRR to a hurdle rate, not to zero
An IRR of 8 % sounds great compared to nothing, but if your cost of capital is 10 %, the investment destroys value. The right comparison is always IRR vs the hurdle rate (usually the company's WACC for corporate projects, or the investor's required return for personal investments). Only investments with IRR > hurdle rate create value. Zero is not the benchmark. Common hurdle rates: 4–6 % for low-risk bonds, 7–10 % for equity index funds, 10–15 % for corporate capital budgeting, 20–40 % for venture capital where the failure rate is high.
How to Use This Calculator
The two-cash-flow IRR formula links four quantities: the initial investment PV, the final return FV, the holding period n, and the resulting IRR. Give the tool three and it will find the fourth.
1. Load a scenario preset
Click any preset — index fund, S&P 500, bond, real estate, business startup, venture capital, home purchase, crypto loss — to load representative PV, FV and n values in one click, and see the corresponding IRR immediately.
2. Pick a period unit
Choose year, quarter or month. The IRR and n are then interpreted in that unit. Changing the unit preserves the effective annual rate, so the same underlying investment always produces the same annualized IRR.
3. Choose what to solve for
Pick IRR to compute the rate of return; FV to project the final value at a target IRR; PV to find the required initial investment; or n to find how long it takes to reach a target FV at a stated IRR.
4. Enter the values
PV and FV are entered as positive magnitudes (the calculator interprets PV as the initial outflow and FV as the terminal inflow). If FV is smaller than PV, the resulting IRR will be negative — the investment lost money.
5. Read the result and the timeline
The result card shows the solved value plus a colour-coded verdict comparing the IRR to standard benchmarks. The timeline diagram below draws PV at t = 0, the compound growth curve to FV at t = n, and the shaded profit region.
6. Switch to Advanced for depth
Advanced mode adds an IRR-vs-multiple chart, a +1 % sensitivity check on each input, and a companion metrics panel including the growth multiple, total return %, effective annual rate, doubling time, present-value-of-profit, and IRR at various alternative horizons.
What This Tool Offers
Built around the two-cash-flow IRR relation IRR ≈ (FV/PV)^(1/n) − 1, the essential measure of investment efficiency per dollar and per unit time.
Four-way solving
Solve for IRR, FV, PV, or n. The calculator rearranges the compound-growth relation automatically and enforces the constraints (PV > 0, FV > 0, n > 0, 1 + IRR > 0).
Cash-flow timeline
A live drawing of the investment: initial outflow PV at t = 0, compound growth curve at the implied IRR, and final inflow FV at t = n, with the shaded profit region between PV and FV.
IRR vs time and multiple
Two charts showing how IRR falls as the horizon lengthens for a fixed multiple, and how IRR rises with the growth multiple for a fixed horizon. Each plots three curves at nearby parameters.
Full return metrics
Growth multiple, total return %, annualized IRR, effective annual rate (for non-annual periods), doubling time, present value of profit at a chosen discount rate, and IRR at alternative horizons.
Scenario preset library
Nine presets spanning the return spectrum from negative-return crypto losses through bond yields and index funds to venture-capital-style 30–40 % IRRs.
Reference tables
A growth-multiple lookup grid across rates and horizons, a comparison table of IRR vs alternative return measures, typical IRR ranges by asset class, and the full variable reference.
Reference Tables & Conversions
A growth-multiple lookup grid, typical IRRs by asset class, and the variable reference.
Growth Multiple Lookup — (1 + IRR)ⁿ
The multiple by which PV grows at a given IRR over n periods. Multiply PV by the tabulated number to get FV.
| IRR \ n | 1 | 3 | 5 | 10 | 20 | 30 |
|---|
Typical IRR Ranges by Asset Class
Long-run historical returns and typical investment horizons. Actual returns vary widely year to year; past performance is not a guarantee.
| Asset class | Typical IRR | Holding period | Risk | Notes |
|---|
Variable Reference
| Symbol | Meaning | Formula | Notes |
|---|---|---|---|
| IRR | Internal rate of return | (FV/PV)^(1/n) − 1 | Per-period compound rate |
| PV | Present value (initial investment) | FV / (1 + IRR)ⁿ | Positive magnitude; outflow at t = 0 |
| FV | Future value (final return) | PV · (1 + IRR)ⁿ | Positive magnitude; inflow at t = n |
| n | Number of periods | ln(FV/PV) / ln(1 + IRR) | Requires 1 + IRR > 0 |
| M | Growth multiple | FV / PV = (1 + IRR)ⁿ | Unitless |
| Total return | Total non-annualized return | M − 1 | e.g., 2.5× → 150 % total return |
| CAGR | Compound annual growth rate | M^(1/n) − 1 | Identical to two-cash-flow IRR |
| t₂ | Doubling time at IRR | ln(2) / ln(1 + IRR) | Rule of 72: ≈ 72 / (IRR %) |
What Does IRR = (FV/PV)^(1/n) − 1 Measure?
The internal rate of return is the compound rate at which an investment grows from its initial value to its final value over a given holding period. For the two-cash-flow case — a single investment at the start and a single return at the end — the IRR formula is exactly the compound annual growth rate (CAGR): the geometric rate that turns PV into FV in n periods. It is the single most widely used performance metric in finance because it captures both the size of the return (the multiple) and the time it took to earn it (the holding period) in one comparable number.
The Two-Cash-Flow IRR Formula
The defining relationship is:
where PV is the initial investment, FV is the final return, and n is the number of periods. Rearranged to solve for the other three quantities:
PV = FV / ( 1 + IRR )n
n = ln( FV / PV ) / ln( 1 + IRR )
The growth multiple and total return are:
Total return = M − 1 (non-annualized)
Because this formula is mathematically identical to CAGR for a two-cash-flow investment, all the same intuitions apply:
IRR Variables
| Symbol | Meaning | Notes |
|---|---|---|
| IRR | Internal rate of return | Per-period compound rate |
| PV | Present value (initial investment) | Cash outflow at t = 0 |
| FV | Future value (final return) | Cash inflow at t = n |
| n | Number of periods | Can be fractional |
| M | Growth multiple | FV/PV; unitless |
How Each Input Affects IRR
The IRR is a ratio, so each input has a distinct effect on it. FV enters the numerator of the root: doubling FV raises the multiple by 2× and increases the IRR but with diminishing returns — the 1/n root dilutes the effect as n grows. PV is the denominator of the root: doubling PV halves the multiple and pushes the IRR down sharply. n is the exponent's reciprocal: doubling n raises the multiple to half its power and approximately halves the log of the IRR.
The most important practical consequence is the horizon effect. For a fixed total return, IRR falls steeply as the horizon lengthens. A 2× multiple earned over 1 year is a spectacular 100 % per year; the same 2× multiple over 30 years is only 2.34 % per year, well below inflation and well below the return of a simple savings account. This is why IRR is the correct metric for comparing investments of different durations and why a raw "I made 150 %" claim is meaningless without knowing the holding period.
The horizon effect also explains why patient capital can earn much higher dollar profits than impatient capital. Given the same IRR, extending the horizon multiplies wealth exponentially. A 10 % IRR over 10 years turns $10,000 into $25,937; over 30 years into $174,494. The extra 20 years multiply the ending balance by 6.7× — but the IRR itself does not change. Only the length of time the rate is allowed to compound changes.
IRR Calculation Examples
Multiple = 25,000 / 10,000 = 2.5×
IRR = 2.5^(1/10) − 1 = 9.60 % / yr
Total return = 150 %
Multiple = 2.2333×
IRR = 2.2333^(1/10) − 1 = 8.36 % / yr
Multiple = 10×
IRR = 10^(1/7) − 1 = 38.95 % / yr
Multiple = 0.6×
IRR = 0.6^(1/1) − 1 = −40.00 % / yr
PV = 200,000 / 1.15⁸ = 200,000 / 3.0590 = $65,381
Frequently Asked Questions
For a two-cash-flow investment, yes — they are mathematically identical. CAGR (compound annual growth rate) is the rate at which an investment grows from an initial value to a final value over a number of years. IRR (internal rate of return) is the discount rate that makes the NPV of all cash flows equal to zero. When there are exactly two cash flows, the equation NPV = 0 reduces to PV = FV/(1+r)ⁿ, whose solution is r = (FV/PV)^(1/n) − 1 — the CAGR. The two terms become different when there are three or more cash flows (e.g., intermediate dividends or reinvestments), at which point IRR must be found numerically and can differ from any simple CAGR computed on the endpoints. This calculator uses the two-cash-flow form, so its output is best thought of as both the IRR and the CAGR.
The formula IRR = (FV/PV)^(1/n) − 1 is exact when the investment really does have exactly one outflow and one inflow — that is, no intermediate cash flows. The word "approximation" is used because real-world investments almost always have intermediate cash flows: a stock pays dividends, a rental property produces rent, a business generates annual profits that get reinvested or distributed. Collapsing all those intermediate flows into a single FV is an approximation — it implicitly assumes everything gets reinvested at the IRR, which is rarely true. For a precise IRR of a multi-cash-flow investment, you would solve Σ CFₜ/(1+IRR)ᵗ = 0 numerically. But the two-cash-flow form is a very good sanity check and is the correct calculation for genuine end-point investments like zero-coupon bonds, single-period flips, or VC exits with no interim distributions.
There is no universal answer — "good" depends on the risk, the asset class, and the benchmark you are comparing against. As rough guides: 2–4 % is what you might earn on a savings account or short-term government bond; 4–6 % is typical for investment-grade bonds and long-term government debt; 7–10 % is the long-run historical average return on broad equity indices; 10–15 % is a common corporate capital-budgeting hurdle rate; 15–25 % is what private equity and real estate developers typically target; 25–40 % is the venture-capital range (but with very high failure rates that pull the portfolio average down). The right comparison is always IRR vs your own cost of capital or required return. An investment with an IRR of 8 % is excellent if your required return is 5 %, but poor if your required return is 12 %. Zero is not the benchmark — your hurdle rate is.
They are two sides of the same coin. NPV asks: at a chosen discount rate, what is the dollar value of the investment? IRR asks: at what discount rate does the NPV equal zero? If you discount the two cash flows at the IRR, you get exactly zero NPV. If you discount at any rate lower than the IRR, you get positive NPV. If you discount at any rate higher than the IRR, you get negative NPV. The practical consequence is that IRR and NPV always give the same accept/reject decision when comparing a single investment against a hurdle rate: accept if IRR > hurdle (equivalently, NPV > 0). They can disagree when ranking multiple mutually-exclusive projects of different sizes, because IRR ignores scale. For that reason many practitioners prefer NPV for ranking, and use IRR as a supplementary communication metric.
Yes — whenever FV is less than PV. If you invest $10,000 and get back $6,000 one year later, the multiple is 0.6 and the IRR is 0.6^(1/1) − 1 = −40 % per year. A negative IRR means the investment lost money in real terms. It can go as low as −100 % (a total loss, where FV = 0) but not below that, because you can never lose more than the full amount invested. Note that many real-world returns distribution tables use "IRR" as a signed number: positive for gains, negative for losses. If your result is −60 %, the investment lost 60 % of its value over the period. Negative IRR does not mean the arithmetic is wrong; it means the investment was a losing one.
IRR has several well-known limitations. (1) It ignores scale — a 50 % IRR on a $100 investment is worth $50 of profit, while a 10 % IRR on $1,000,000 is worth $100,000. Always pair IRR with absolute profit or NPV. (2) It assumes reinvestment at the IRR itself, which is usually unrealistic for high-IRR investments — the reinvestment assumption of NPV (at the cost of capital) is more conservative and more accurate. (3) It can give multiple solutions when cash flows change sign more than once, a phenomenon called "multiple IRRs." (4) It cannot compare projects of different lives without an explicit reinvestment or replacement-chain assumption. (5) It is a rate, not a dollar amount, so it does not tell you how much wealth was created. For these reasons, most corporate finance textbooks recommend NPV as the primary decision criterion and IRR as a secondary metric for communication.
Compound it: annual IRR = (1 + monthly IRR)¹² − 1. If the monthly IRR is 1 %, the annual IRR is 1.01¹² − 1 = 12.68 %. Similarly, quarterly IRR annualizes as (1 + quarterly IRR)⁴ − 1. The reverse conversion is to take the nth root: monthly IRR = (1 + annual IRR)^(1/12) − 1. For example, an annual IRR of 10 % corresponds to a monthly IRR of (1.10)^(1/12) − 1 = 0.797 %. The period unit selector in this calculator performs these conversions automatically — switch units and the existing IRR and n values are converted to preserve the same underlying investment. Never simply divide the annual IRR by 12 to get the monthly rate; that understates the compounding effect and gives a materially different number (10 % / 12 = 0.833 % monthly, which annualizes to 10.47 %, not 10 %).
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| IRR | Approximate internal rate of return | % |
| FV | Final cash inflow | currency |
| PV | Initial cash outflow | currency |
| n | Number of periods |
What it means
The internal rate of return (IRR) is the discount rate that makes the net present value of all cash flows from a project equal to zero. For a simple investment with one initial outflow and one future inflow, the IRR can be approximated as (FV/PV)^(1/n) − 1, assuming compounding. This is useful for quick comparisons and for rough estimates. A project is generally acceptable if its IRR exceeds the required rate of return. Understanding IRR is essential for capital budgeting and for evaluating investment opportunities.
Worked example
IRR (Approx.) – Two Detailed Examples
Real‑World| Parameter | Value |
|---|---|
| Initial Investment | 10000 |
| Final Value | 20000 |
| n | 5 |
| Parameter | Value |
|---|---|
| Investment | 5000 |
| Final | 9000 |
| n | 4 |
Common mistakes
- IRR approximation: For a two‑cash‑flow scenario (initial investment and one future value).
- FV: Future value (including interest).
- PV: Present value (initial investment).
- n: Number of periods.
- IRR: The rate that makes NPV = 0 – this formula works only for simple cash flows.
- For multiple cash flows: Use Excel’s IRR function or iterative methods.
Applications
The Internal Rate of Return (IRR) is the discount rate that makes the net present value of all cash flows equal to zero. For a simple investment with two cash flows (e.g., initial outflow and a single future inflow), IRR can be approximated as (FV/PV)^(1/n) − 1. IRR is used to evaluate the profitability of projects and investments. A higher IRR is preferred, and it is often compared to the cost of capital. Investors use IRR to rank projects and to decide which investments to pursue. While more complex cash flows require iterative calculation, this approximation is useful for quick assessments. Understanding IRR is crucial for capital allocation and portfolio management.
- Project ranking and selection
- Investment performance evaluation
- Hurdle rate comparison and decision‑making
- Private equity and venture capital analysis
- Capital rationing and resource allocation
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