# Intuition behind Internal Rate of Return (IRR)

What is the intuition behind Internal Rate of Return.

From Wikipedia:

The internal rate of return on an investment or project is the "annualized effective compounded return rate" or rate of return that sets the net present value of all cash flows (both positive and negative) from the investment equal to zero.

What I'm looking for is a more intuitive example of:

sets the net present value of all cash flows (both positive and negative) from the investment equal to zero.

Why would I want my net present value of a project to be \$0.00, or break-even?

Why would I want my net present value of a project to be \$0.00, or break-even?

You wouldn't. IRR is only useful to compare to your required rate of return, or the rate or return of other investments of equivalent risk.

So if one investment has an IRR of 10%, but you can invest in other projects of similar risk that earn 20%, you would choose them over your prospective investment.

Put another way, if your required rate of return is higher than the IRR of the project, then the project's NPV (using the required return as the discount rate) will be negative, so you wouldn't invest. If it's lower than the IRR, the NPV is positive, so you could invest (provided there are not other projects with an even higher IRR). If it's equal, then your NPV would be zero and you'd be indifferent.

The payout options of the lottery is a common example. Suppose you win the lottery and can take either \$1 Million today or \$100,000 per year for the next 20 years (or until you die). Which is better? Most people don't have a "required" rate of return to calculate an NPV, but you can calculate the IRR of the 20-year payout at about 8%. Compare that to, say, investing in the S&P 500 index, which averages about 10% annually with relatively low risk over 20-year periods. So from a pure return point of view, you'd be better off taking the lump sum and investing it. (not buying yachts and mansions; that would be stupid...)

** I know that lottery annuities and the equity market are not equivalent risk, but I'm assuming they are when you add in the "or until you die" clause of the lottery payout, which does not exist in reality.

• There is no "or until you die" clause of most lottery payouts. – stannius Dec 4 '18 at 21:12
• @stannius fair enough; it was a hypothetical situation anyways... – D Stanley Dec 4 '18 at 21:21