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In finance, rate of return (ROR), also known as return on investment (ROI), rate of profit or sometimes just return, is the ratio of money gained or lost (realized or unrealized) on an investment relative to the amount of money invested. The amount of money gained or lost may be referred to as interest, profit/loss, gain/loss, or net income/loss. The money invested may be referred to as the asset, capital, principal, or the cost basis of the investment. ROI is usually expressed as a percentage rather than a fraction.

ROI does not indicate how long an investment is held. However, ROI is most often stated as an annual or annualized rate of return, and it is most often stated for a calendar or fiscal year. In this article, “ROI” indicates an annual or annualized rate of return, unless otherwise noted.

ROI is used to compare returns on investments where the money gained or lost — or the money invested — are not easily compared using monetary values. For instance, a $1,000 investment that earns $50 in interest generates more cash than a $100 investment that earns $20 in interest, but the $100 investment earns a higher return on investment.

$50/$1,000 = 5% ROI
$20/$100 = 20% ROI

Whereas,

The internal rate of return (IRR) is a capital budgeting metric used by firms to decide whether they should make investments. It is an indicator of the efficiency or quality of an investment, as opposed to net present value (NPV), which indicates value or magnitude.

The IRR is the annualized effective compounded return rate which can be earned on the invested capital, i.e., the yield on the investment. Put another way, the internal rate of return for an investment is the discount rate that makes the net present value of the investment’s income stream total to zero.

A project is a good investment proposition if its IRR is greater than the rate of return that could be earned by alternate investments of equal risk (investing in other projects, buying bonds, even putting the money in a bank account). Thus, the IRR should be compared to any alternate costs of capital including an appropriate risk premium.

In general, if the IRR is greater than the project’s cost of capital, or hurdle rate, the project will add value for the company.

In the context of savings and loans the IRR is also called effective interest rate