How to calculate internal rate of return, step by step
Internal rate of return is one rate that answers one question: what does this investment earn? The calculation needs three numbers: the initial investment, the annual cash inflow and the number of years. On $10,000 invested with $3,000 a year coming back for 5 years, the internal rate of return is 15.24% — a rate, not a value in dollars, and it beats a 10% hurdle, so the investment creates value.
The definition is the rate at which the net present value is exactly zero. The net present value is the present value of the inflows minus the investment, and the present value of the inflows is each year’s inflow divided by (1 + rate) raised to that year, added up. The discount rate is what a dollar next year is worth today — a dollar a year from now is worth less than a dollar today, because today’s dollar could be invested. So the IRR is the rate that makes the discounted inflows exactly equal to the investment — the rate the project itself earns.
The worked example, line by line. Step 1 — the investment: $10,000. Step 2 — the annual cash inflow: $3,000. Step 3 — the years: 5. Step 4 — the present value of each year’s inflow at 10%: $2,727.27, $2,479.34, $2,253.94, $2,049.04 and $1,862.76. Step 5 — the present value of the inflows: $11,372.36. Step 6 — the net present value at 10%: $11,372.36 − $10,000 = $1,372.36. Step 7 — the trial at 15%: the net present value is $56.47 — still positive, so the internal rate of return is above 15%. Step 8 — the trial at 16%: the net present value is −$177.12 — negative, so the internal rate of return is below 16%. Step 9 — the internal rate of return: the rate where the net present value is zero sits between 15% and 16%, at 15.24%. Work it yourself in the internal rate of return calculator.
A note on the rounding: the five yearly figures are each rounded to two decimals, and the rounded figures add to $11,372.35 — one cent less than the $11,372.36 the unrounded figures add to. The one cent is rounding, not a mistake.
What the answer means
An internal rate of return of 15.24% means the investment earns 15.24% a year on the money, so on $10,000 invested the inflows are worth $11,372.36 today at a 10% discount rate — for every dollar of the investment, the inflows return about $1.14 in present value. A rate above your hurdle means the project creates value: at a 10% hurdle, a 15.24% project has an NPV of $1,372.36. A rate below your hurdle means the project destroys value: at a 16% hurdle the same project would fall short and the net present value would be −$177.12. A rate exactly at your hurdle means the project breaks even. The number alone never says whether 15.24% is a lot or a little — that depends on your hurdle. Compare it against your hurdle and the next best project before you decide.
When there is no internal rate of return
Some investments have no rate at which the net present value is zero, and the honest answer is that there is no internal rate of return. At $0 of investment there is no outlay to earn back, so there is no rate to earn — and the NPV is $11,372.36. At a negative inflow each year loses money, so no rate makes the NPV zero — and the NPV is −$21,372.36. At one year the inflow cannot return the investment, so no rate makes the NPV zero — and the NPV is −$7,272.73. At a negative investment the NPV is positive at every rate, so no rate makes it zero — and the NPV is $21,372.36. In each case the calculator says so plainly — there is no internal rate of return — and shows the net present value instead.
IRR vs NPV
The internal rate of return and the net present value answer different questions, and mixing them up is the most common mistake. The internal rate of return is a rate: what the project earns, in percent. The net present value is a value: what the project creates, in dollars, at your hurdle. On $10,000 invested with $3,000 a year coming back for 5 years, the internal rate of return is 15.24% and the net present value at 10% is $1,372.36. One is a rate, the other is a value. A small project can earn a high rate and still create less value than a bigger project earning a lower rate — a $10,000 project and a $1,000,000 project earning 15.24% have the same rate, and the bigger one creates far more value. Use the internal rate of return when you want the rate to compare against other projects, and use the net present value when you want the value in dollars. Work it out in the net present value calculator.
IRR vs payback
The internal rate of return and the payback period answer different questions too. The internal rate of return counts the rate: what the project earns. The payback period counts time: how many years until the cash coming back covers the investment. On $10,000 invested with $3,000 a year coming back, the internal rate of return is 15.24%, and the payback period is 3.33 years. One is a rate, the other is a clock. A project can pay back quickly and still earn a low rate — if the inflows arrive fast but stop soon, the payback is short and the rate is low. Use the internal rate of return when you want to know what the project earns, and use the payback period when you want to know how long the money takes to come back. Work out the years in the payback period calculator.
Common mistakes
The first mistake is forgetting to discount — adding the inflows as $15,000 and calling the profit $5,000.00 the return, which is the undiscounted profit, not the rate. The second is using revenue instead of cash inflow — revenue comes in before costs, and the IRR needs the cash left after costs, so the answer comes out far too high. The third is mixing up the discount rate and the return — a 10% discount rate is what a dollar is worth today, not what the project earns, and the project earns 15.24% here. The fourth is rounding each year’s present value and adding the rounded figures — the rounded figures add to $11,372.35, a cent short of the $11,372.36 the unrounded figures give. Work it out in the internal rate of return calculator, and check the net present value calculator and the payback period calculator before you decide what the answer means.