Hong Life CalculatorsUnderstanding the internal rate of return (IRR) — concept and principle
The internal rate of return is the yearly rate of return that an investment's cash flows earn. Formally, it is the discount rate at which the net present value (NPV) of all cash flows, including the initial outlay, equals zero. Businesses use IRR to compare projects, investors use it to judge funds and property deals, and it appears in almost every capital budgeting decision. This calculator takes an initial investment and five yearly cash flows and finds the IRR, the total cash returned and the money multiple. It works with any currency.
How it is calculated
- NPV(r) = −C0 + C1 ÷ (1 + r) + C2 ÷ (1 + r)² + … + C5 ÷ (1 + r)⁵
- IRR = the r for which NPV(r) = 0
- Multiple on investment = (C1 + … + C5) ÷ C0
There is no closed-form formula for IRR, so the calculator solves it numerically by bisection: it repeatedly halves an interval between −99% and 1,000% until it finds where NPV changes sign. Cash flows are assumed to arrive at the end of each year.
The principle
Money received later is worth less today, because it could have been invested in the meantime. Discounting at rate r converts every future amount into today's value. At a low rate the future inflows are worth more than the outlay (NPV above zero); at a high rate they are worth less. The IRR is the break-even rate between the two. If you could borrow or earn elsewhere at exactly that rate, the project would leave you neither better nor worse off.
Worked example
- Cash flows: −100,000, then 30,000, 35,000, 40,000, 30,000, 20,000.
- At 10%, NPV = $19,160, still positive, so the IRR is higher.
- At 20%, NPV = −$5,041, so the IRR lies between 10% and 20%.
- Bisection narrows this to r = 0.17595, shown as 17.6%.
- Total cash returned = 155,000, shown as $155,000.00; multiple = 155,000 ÷ 100,000 = 1.55×.
How to read the result
Compare the IRR with your hurdle rate, usually your cost of capital or the return on an alternative of similar risk. An IRR above it suggests the project adds value. The multiple tells you how much money comes back, and the IRR how fast. When projects differ in size or timing, rank them by NPV at your required rate, because a small project can have a high IRR but add less value.
Common mistakes
- Entering the initial investment as a negative number; here it is entered as positive and subtracted automatically.
- Trusting IRR when cash flows change sign more than once, which can produce several IRRs or none.
- Assuming interim cash can be reinvested at the IRR itself.
- Comparing IRRs of projects with very different sizes or lengths.
Frequently asked questions
What is the difference between IRR and ROI?
ROI usually compares total gain with cost and ignores timing. IRR accounts for when each cash flow arrives, so it is an annual rate.
What is MIRR?
The modified IRR assumes interim cash flows are reinvested at a rate you choose, such as the cost of capital, and always gives one answer.
Is the result the same as Excel's IRR function?
For the same yearly cash flows it should match closely, since both find the rate where NPV is zero.
Sources: Brealey, Myers and Allen, Principles of Corporate Finance (McGraw-Hill)