Internal Rate of Return (IRR) Calculator

What is the internal rate of return?

The internal rate of return (IRR) is the annual rate of growth an investment produces, taking into account exactly when money goes in and when it comes out. Technically, it is the discount rate that makes the net present value (NPV) of all cash flows equal to zero. If you could put the same money in a savings account paying the IRR, making the same deposits and withdrawals on the same dates, you would end up in exactly the same place.

IRR is called internal because it depends only on the project's own cash flows, not on any outside rate such as the cost of borrowing or market interest rates. That makes it a convenient way to boil a complicated stream of cash into one percentage. Analysts use it to judge real estate deals, private equity funds, capital projects and business acquisitions, and individuals can use it to evaluate a rental property, an annuity offer, or a portfolio with irregular contributions.

The basic decision rule is simple: an investment is attractive when its IRR exceeds the minimum return you require, often called the hurdle rate or cost of capital. Between two otherwise similar projects, the higher IRR is usually preferred.

How is IRR calculated?

Calculating IRR means solving the NPV equation for the rate. Because the rate appears in exponents across many terms, the equation generally cannot be rearranged by hand, so calculators and spreadsheets search for it numerically. The approach this calculator uses works like this:

• List every cash flow in order, with money invested as negative numbers and money received as positive numbers.
• Pick a trial rate and discount each cash flow to time zero, then add them up to get the NPV.
• If NPV is positive, the trial rate is too low; if negative, it is too high.
• Repeat with a rate between the last high and low guesses until NPV is within a fraction of a cent of zero.

0 = CF₀ + CF₁ ÷ (1 + IRR) + CF₂ ÷ (1 + IRR)² + … + CFₙ ÷ (1 + IRR)ⁿ

CF₀

cash flow at the start, negative for the initial investment

CFₜ

net cash flow in period t

IRR

internal rate of return per period

n

number of periods

There is no algebraic solution once there are more than a few periods, so the rate is found by trial: guess a rate, compute NPV, and narrow the guess until NPV is zero.

What is the use of IRR?

In capital budgeting, companies use IRR to decide which projects to fund. A firm that can raise money at 8% will generally accept projects whose IRR exceeds 8% and reject those below it, because only the former add value for shareholders. When there is more capital demand than supply, ranking projects by IRR helps set priorities, alongside NPV, which measures the size of the gain in dollars.

Private equity and venture capital funds report performance largely in IRR terms, because their investors commit money that is called and returned at uneven intervals. Real estate investors use IRR to compare properties with different purchase prices, rents, holding periods and sale prices. Lenders and borrowers use it to uncover the true cost of a loan with fees or irregular payments; the APR on a loan is, in effect, an IRR.

For individuals, IRR answers questions such as:

• What return did my brokerage account really earn, given the deposits and withdrawals I made along the way?
• Is an insurance or annuity product that charges premiums now and pays benefits later competitive with other investments?
• Does buying solar panels, which cost money up front and save on electricity bills for 25 years, beat leaving the money invested?
• Is a rental property with a modest yearly cash flow and an expected sale price worth its down payment?

Limitations of IRR

IRR is useful but has well-known blind spots, and it is best used alongside NPV rather than on its own.

• Scale is ignored. A 50% IRR on $1,000 earns far less money than a 20% IRR on $1 million. NPV, which is in dollars, captures size; IRR does not.
• Reinvestment is assumed at the IRR. The math implicitly treats interim cash flows as if they could be reinvested at the same rate, which is unrealistic for very high IRRs. The modified internal rate of return (MIRR) lets you specify a more realistic reinvestment rate.
• Multiple or no solutions. When cash flows change sign more than once, such as an investment, then income, then a large cleanup cost, the NPV equation can have two or more valid rates, or none at all.
• Timing can mislead. A project that returns cash quickly can show a high IRR while creating less total value than a slower project with a lower IRR.
• Inputs are estimates. IRR is only as reliable as the forecast cash flows behind it; small changes in a distant sale price can move it substantially.

Frequently asked questions

Sources

• Investor.gov – Introduction to Investing
• CFPB – What is an APR?