IRR Calculator — Internal Rate of Return
Find the discount rate that makes the net present value of a series of cash flows equal to zero, helping you evaluate project profitability
Formula
0 = Σ [CFt / (1 + IRR)^t]
IRR is the discount rate that makes NPV equal to zero. Higher IRR indicates higher annualized return.
Worked Examples
Example 1: Simple Investment
Problem:Invest $50,000, receive $15,000/year for 5 years.
Solution:Cash flows: -50000, 15000, 15000, 15000, 15000, 15000 Total returns: $75,000 Profit: $25,000 IRR calculation yields ~15.2%
Result:IRR = 15.2%
Example 2: Real Estate
Problem:Buy property for $200,000, rent for 5 years, sell for $250,000.
Solution:Year 0: -$200,000 Years 1-5: $18,000/year rent Year 5: +$250,000 sale Total inflows: $340,000 IRR ≈ 12.5%
Result:IRR = 12.5%
Example 3: Compare Projects
Problem:Project A: -$100k, +$150k in year 3. Project B: -$100k, +$40k/year for 3 years.
Solution:Project A IRR: (150/100)^(1/3) - 1 = 14.5% Project B IRR: ~9.7% (iterative) A has higher IRR but B has better cash flow timing.
Result:A: 14.5%, B: 9.7%
Frequently Asked Questions
What is the internal rate of return?
IRR is the discount rate at which a project's net present value equals zero, meaning the discounted inflows exactly offset the outflows. Interpreted plainly, it is the compound annual rate the invested capital earns while it remains tied up in the project. Because it is expressed as a percentage rather than a dollar figure, it lets you compare investments of different sizes and durations on a single scale.
How does IRR differ from ROI?
Simple ROI is (gain minus cost) divided by cost, and it ignores when the money arrives. IRR discounts every cash flow by the time it occurs, so receiving $100 in year one counts for more than the same $100 in year five. Two projects can show an identical 50% total ROI while their IRRs differ sharply, purely because one returns capital early and the other returns it at the end.
What counts as a good IRR?
There is no universal threshold; the only meaningful test is whether the IRR exceeds your cost of capital or required rate of return for that level of risk. Illiquid, high-risk asset classes such as venture capital demand far higher IRRs than stabilised commercial real estate, which in turn demands more than public equities. For context, long-run US large-cap stock returns have averaged roughly 10% a year in nominal terms.
What are the limitations of IRR?
IRR implicitly assumes interim cash flows are reinvested at the IRR itself, which is unrealistic when the IRR is high. It ignores scale, so a tiny project with a spectacular percentage can create less value than a large one with a modest percentage. Cash flow streams that change sign more than once can produce multiple mathematically valid IRRs, or none at all, making the single number meaningless.
How does IRR relate to NPV?
They are two readings of the same discounted cash flow model. NPV plotted against the discount rate is a downward-sloping curve for a conventional project, and IRR is the point where that curve crosses zero. If your required return sits below the IRR, NPV is positive and the project adds value; if it sits above, NPV is negative. When the two measures disagree on ranking, NPV is the reliable guide.
What is modified IRR (MIRR)?
MIRR removes the unrealistic reinvestment assumption by compounding all positive cash flows forward to the end of the project at an explicit reinvestment rate, usually the cost of capital, and discounting negative flows back to the present at a finance rate. It then solves for the single rate linking those two values. MIRR also produces exactly one answer even when cash flows alternate sign.
How should I use IRR to compare projects?
Use it as a screen rather than a ranking. A project returning 50% on $100,000 generates $50,000 of value, while 15% on $5 million generates $750,000, so the higher percentage is plainly the worse choice when capital is available for both. Rank by NPV when projects are mutually exclusive, and reserve IRR for judging whether a project clears the hurdle rate at all.
Can IRR be negative?
Yes. A negative IRR means total inflows fall short of total outflows, so the investment loses money even before considering the time value of that money. Solvers sometimes fail to converge on deeply negative streams and return an error instead of a value. In either case the conclusion is the same: the project destroys capital and NPV will be negative at any positive discount rate.
What if a cash flow stream has no IRR?
This happens when the NPV curve never crosses zero, typically because every cash flow shares the same sign or the losses are too deep to be offset. Conversely, by Descartes' rule of signs, a stream that changes direction several times can cross zero several times and yield multiple IRRs. In both situations, fall back on NPV at your actual cost of capital, or use MIRR.
How is IRR actually computed?
The IRR equation is a polynomial in the discount rate with no closed-form algebraic solution beyond very short cash flow streams, so it must be solved numerically. Software starts from an initial guess and iterates using Newton-Raphson or bisection until the NPV is acceptably close to zero. That is why spreadsheet functions occasionally return an error on awkward streams and allow you to supply a starting guess.
Background & Theory
IRR is the discount rate that makes the Net Present Value of all cash flows equal to zero.
Formula:
0 = Σ [CFt / (1 + IRR)^t]
Where:
- CFt = Cash flow at time t
- IRR = Internal Rate of Return
- t = Time period
Interpretation:
- IRR > Required Return → Accept
- IRR < Required Return → Reject
- Higher IRR = Higher return
Advantages:
- Accounts for time value
- Single percentage for comparison
- Intuitive interpretation
Disadvantages:
- Reinvestment assumption
- Scale-independent
- Multiple/no solutions possible
Related Metrics:
| Metric | Use |
|---|---|
| NPV | Dollar value created |
| MIRR | More realistic reinvestment |
| Payback | Time to recover investment |
| ROI | Simple return percentage |
Decision Rules:
- Single project: IRR > hurdle rate
- Multiple projects: Use NPV (considers scale)
- Mutually exclusive: Highest NPV