# Internal Rate of Return (IRR)

## What is Internal Rate of Return (IRR)?

**Internal rate of return (IRR)** is the interest rate at which the net present value of all the cash flows (both positive and negative) from a project or investment equal zero.

Internal rate of return is used to evaluate the attractiveness of a project or investment. If the IRR of a new project exceeds a company’s required rate of return, that project is desirable. If IRR falls below the required rate of return, the project should be rejected.

## IRR Formula & Example

You can use the following formula to calculate IRR:

0 = P_{0} + P_{1}/(1+IRR) + P_{2}/(1+IRR)^{2} + P_{3}/(1+IRR)^{3} + . . . +P_{n}/(1+IRR)^{n}

where P_{0}, P_{1}, . . . P_{n} equals the cash flows in periods 1, 2, . . . n, respectively; and

IRR equals the project's internal rate of return.

Let's look at an example to illustrate how to use IRR.

Assume Company XYZ must decide whether to purchase a piece of factory equipment for $300,000. The equipment would only last three years, but it is expected to generate $150,000 of additional annual profit during those years. Company XYZ also thinks it can sell the equipment for scrap afterward for about $10,000. Using IRR, Company XYZ can determine whether the equipment purchase is a better use of its cash than its other investment options, which should return about 10%.

Here is how the IRR equation looks in this scenario:

0 = -$300,000 + ($150,000)/(1+.2431) + ($150,000)/(1+.2431)^{2} + ($150,000)/(1+.2431)^{3} + $10,000/(1+.2431)^{4}

The investment's IRR is 24.31%, which is the rate that makes the present value of the investment's cash flows equal to zero. From a purely financial standpoint, Company XYZ should purchase the equipment since this generates a 24.31% return for the Company --much higher than the 10% return available from other investments.

A general rule of thumb is that the IRR value cannot be derived analytically. Instead, IRR must be found by using mathematical trial-and-error to derive the appropriate rate. However, most business calculators and spreadsheet programs will automatically perform this function.

[See How to Calculate IRR Using a Financial Calculator or Microsoft Excel]

IRR can also be used to calculate expected returns on stocks or investments, including the yield to maturity on bonds. IRR calculates the yield on an investment and is thus different than net present value (NPV) value of an investment.

## Why is IRR Important?

IRR allows managers to rank projects by their overall rates of return rather than their net present values, and the investment with the highest IRR is usually preferred. This easy comparison makes IRR attractive, but there are limits to its usefulness.

One downside for example: IRR works only for investments that have an initial cash outflow (the purchase of the investment) followed by one or more cash inflows. In addition, IRR does not measure the absolute size of the investment or the return. This means that IRR can favor investments with high rates of return even if the dollar amount of the return is very small. For example, a $1 investment returning $3 will have a higher IRR than a $1 million investment returning $2 million, but the latter brings in $1 million dollars instead of just $2.

Another short coming is that IRR can't be used if the investment generates interim cash flows. Finally, IRR does not consider cost of capital and can't compare projects with different durations.

Overall, IRR is best-suited for analyzing venture capital and private equity investments, which typically entail multiple cash investments over the life of the business, and a single cash outflow at the end via IPO or sale.

Typically, the higher the IRR, the higher the rate of cash inflow a company can expect from a project or investment.

That said, organizations may prefer a lower IRR on a large project rather than a high IRR on a small one. For example, expecting a 15% IRR from a proposed project may seem better than earning a 10% return on another investment at first glance. But put in dollar terms, earning $1,500 from a $10,000 project would not add as much overall value or cash flow to your organization as earning $100,000 from a $1 million project, even though the IRR would be higher on the first project (15% versus 10%).

A positive IRR means a project or investment is expected to return some value to the organization. A negative IRR would mean that the proposed project or investment is expected to cost more than it returns, or lose value for the company. Generally a company would forgo making an investment in something with a negative IRR.

Before you make a decision, double check your math to make sure the IRR figure you found is correct!

WACC, or the Weighted Average Cost of Capital, is how much it costs for a company to borrow money from bondholders, shareholders, and other lenders and is expressed in percentages. In relation to the IRR formula, WACC is the "required rate of return" that a project or investment's IRR must exceed to add value to the company. This return rate may also be referred to as a "hurdle rate" or "cost of capital."

For example, if a company's WACC is 10%, a proposed project must have an IRR of 10% or higher to add value to the company. If a proposed project yields an IRR lower than 10%, the company's borrowed money (cost of capital) is costing more than what the proposed project or investment is expected to yield and probably wouldn't yield a positive return to the company.

Here's another way to look at it. If you were to use your credit card with a 10% annual interest rate (think of it like the WACC) to buy a lemonade stand, you'd need the lemonade stand to return 10% or more every year (similar to the IRR) if you wanted to make any money. Otherwise, you'd be losing money every year and not adding value to your net worth!

Because IRR is expressed as a percentage, IRR makes it easy for companies to compare and decide which project or investment will generate the highest percentage return on investment (ROI).

By contrast, net present value (NPV) measures how much value a project or investment could add in absolute dollar amounts. Using both IRR and NPV can give analysts a clearer picture of which project or investment can add the most value to an organization.

Looking back at the definition example from earlier, we would find that the $300,000 machine would return $460,000 in additional profits ($150,000 + $150,000 + $150,000 + $10,000 = $460,000), meaning it would have a net present value of $160,000 (NPV = $460,000 -$300,000 = $160,000). That NPV figure gives us a raw dollar amount of value the project would add to the company, giving us more information when making business decisions.