What IRR tells you, and where it misleads
What the internal rate of return means, how it is found by trial, how it differs from NPV, CAGR and XIRR, and the cases in which a high IRR leads you to the wrong decision.
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In short
- IRR is the discount rate at which the net present value of a set of cash flows is zero.
- Cash flows of −₹5,00,000 followed by ₹1,00,000, ₹1,50,000, ₹2,00,000 and ₹2,50,000 have an IRR of 12.83 percent.
- If IRR is above your required return, the project passes. NPV tells you how much it adds in rupees.
- IRR ignores size. A 50 percent return on ₹1,000 adds less than a 20 percent return on ₹1,00,000.
- For dates that are not exactly a year apart, you need XIRR. This calculator assumes equal yearly gaps.
IRR turns a messy series of payments into one percentage, which is why it appears in business plans, property pitches, insurance illustrations and private equity reports. A single number is easy to compare with a bank rate or a hurdle rate. It also hides a good deal. A proposal can show a fine IRR and still be the wrong choice. This page explains what the number means, how it is found, how it relates to NPV, and the situations where you should not rely on it alone.
What IRR means
Money today is worth more than money later, because it can earn interest in the meantime. To compare cash at different dates, we discount future amounts back to today. The net present value does this for all the cash flows at a chosen rate:
NPV = CF₀ + CF₁ ÷ (1 + r) + CF₂ ÷ (1 + r)² + … + CFₙ ÷ (1 + r)ⁿ
Here, CF is the cash flow in each year, and an outflow is negative. Year 0 is today, so its amount is not discounted.
The internal rate of return is the rate r that makes this sum exactly zero. It is the rate at which what you put in and what you get back balance out. You can think of it as the interest rate earned on the money that remains in the project.
A worked example
Suppose a machine costs ₹5,00,000 today and is expected to bring in ₹1,00,000, ₹1,50,000, ₹2,00,000 and ₹2,50,000 over the next four years.
| Year | Cash flow | Discounted at 12% | Discounted at 12.83% |
|---|---|---|---|
| 0 | −₹5,00,000 | −₹5,00,000 | −₹5,00,000 |
| 1 | ₹1,00,000 | ₹89,286 | ₹88,629 |
| 2 | ₹1,50,000 | ₹1,19,579 | ₹1,17,826 |
| 3 | ₹2,00,000 | ₹1,42,356 | ₹1,39,238 |
| 4 | ₹2,50,000 | ₹1,58,880 | ₹1,54,256 |
| Total | ₹10,100 | About zero |
At 12 percent, the NPV is ₹10,100, a positive figure, so the project earns more than 12 percent. At 12.83 percent, the discounted amounts add up to zero, and so that is the IRR.
There is no algebra formula for IRR in general. It is found by trial, trying rates until the NPV reaches zero. Excel's IRR function and this calculator both do that, moving in on the answer step by step.
IRR and NPV together
The two measures answer different questions.
IRR asks what return this produces. Compare it with your required return, which is often your cost of borrowing or what you could earn elsewhere. If it is higher, the project clears the bar.
NPV asks how much value this adds in today's rupees, at your required return. If it is positive, the project adds value.
For a normal project, with money out first and money in later, they agree on whether it passes. In the example above, the IRR of 12.83 percent beats a 12 percent hurdle, and the NPV at 12 percent is ₹10,100.
They can disagree when choosing between projects, however. In that case, NPV is usually the better guide.
The calculator also shows two simple measures. Payback is the time to recover the outlay, which is 3.20 years in this example, and the money multiple is the total received divided by the total paid in, here 7,00,000 ÷ 5,00,000 = 1.40 times.
Where IRR misleads
It ignores size. Project A turns ₹1,000 into ₹1,500 in a year, an IRR of 50 percent. Project B turns ₹1,00,000 into ₹1,20,000, an IRR of 20 percent. At a 10 percent cost of money, A's NPV is ₹364 and B's is ₹9,091. If you can only do one, B is clearly better, despite the lower IRR.
It assumes you can reinvest at the same rate. A project with an IRR of 25 percent and early cash flows only earns that overall if each receipt can be reinvested at 25 percent too. This usually cannot be done. So a high IRR with fast payouts overstates the real return on the whole amount over the full period. A related measure, modified IRR, sets a realistic reinvestment rate to deal with this.
There may be more than one answer. If the signs of the cash flows change more than once, there can be several IRRs. For flows of −100, +230 and −132, both 10 percent and 20 percent make the NPV zero. Mining and projects with big closure costs behave like this. When you see two sign changes, use NPV.
It may not exist. If all the cash flows have the same sign, no rate can bring the NPV to zero. The calculator will say so.
It depends on forecasts. An IRR is only as reliable as the numbers put in. A small change to the last year's sale price can move the IRR by several points. Try lower cash flows to see how much margin you really have.
It ignores risk. An IRR of 14 percent from a business plan is not the same as 7 percent from a government bond. Risky projects need a higher hurdle rate.
IRR, CAGR and XIRR
These names get mixed up.
CAGR is for a single amount in and a single amount out. ₹1,00,000 growing to ₹2,00,000 in 10 years has a CAGR of 7.18 percent. Use the CAGR calculator for this. With only two cash flows, IRR and CAGR are the same number.
IRR handles many cash flows, but assumes that they come at equal intervals, usually one year.
XIRR is IRR for real dates. Investors in mutual funds or those who make uneven payments should use it. A SIP has monthly flows, so a yearly IRR would be wrong for it, and the fund reports you see use XIRR. The SIP calculator deals with regular monthly investments. Excel has an XIRR function if you need to enter exact dates.
If your cash flows are monthly, IRR on monthly periods gives a monthly rate, and that must be annualised, as (1 + monthly rate)¹² − 1.
Common uses
Insurance policies. Endowment plans are often sold on the total return, which sounds large over 20 years. Put the premiums and the maturity amount through an IRR calculation, and the real return is often in the low single digits. That is a very useful check before you buy.
Property. Enter the purchase price and costs, then each year's rent after expenses, and the sale value in the final year. This gives a much better picture than a claim of the property having "doubled in ten years".
Business investment. Compare a machine or a shop fit-out with your cost of funds. If you borrow at 11 percent, the project should clear that with a margin to cover risk.
Fixed deposits and bonds. A bond's yield to maturity is an IRR, using the price today, the coupons and the final repayment. This makes it fair to compare a bond with a deposit.
Loans. The true rate on a loan with fees is an IRR, where the amount you receive is the inflow, and the instalments are outflows. This is why a loan's annual percentage rate is higher than its headline rate once processing fees are included.
What this calculator assumes
- Cash flows are at equal yearly intervals, starting with year 0, and are entered in order.
- Outflows are negative and inflows are positive.
- There is at least one of each, or no IRR exists.
- NPV uses the discount rate you enter, and year 0 is not discounted.
- If several IRRs exist, one is shown, so check the signs in your flows. Tax and inflation are not included.