# Internal Rate of Return (IRR)

## What is IRR?

An investment's **internal rate of return (IRR)** is the discount rate that makes the net present value of the investment's cash flows equal to zero (the "break even" point).

IRR 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

The formula for IRR is:

0 = IO + CF1/(1 + IRR) + CF2/(1 + IRR)^2 + .... CFT/(1 + IRR)^T

or

NPV = IO + CF1/(1 + IRR) + CF2/(1 + IRR)^2 + .... CFT/(1 + IRR)^T

Where:

IO = Initial Outlay or Investment (usually a negative number because you're paying for the investment)

CF1, CF2, ... CFT= Cash flows/additional profits expected during time period 1, 2, ... T, respectively

IRR = The project or investment's internal rate of return.

How do we find these variables? The "IO" part is probably the easiest to find, as that's the expected cost to start the investment or project. For "CF1" through "CFN," a team or organization may estimate the cash flows/ additional profits that a project or investment may produce over each of the next few months or years.

To find the "IRR" part of the formula, you need to either calculate IRR using a Financial Calculator or Microsoft Excel or use a "trial and error" process where you keep trying different discount rates (percentage rates for IRR) until the IRR formula equals zero, or NPV = 0.

Let's walk through an example. Let's say Company XYZ is deciding 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 profit per year 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 purchase is a better use of cash than some of Company XYZ's other investment options, which return about 10%. The return for this project must be higher than 10% to be approved, as this is what the company expects from alternative investments (organizations sometimes call this a "hurdle rate").

After calculating IRR in Excel or a financial calculator, we find 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.

Just to check, here is how this example looks in the IRR formula:

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

Conclusion? 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.

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.

## Comparing IRR vs NPV

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. The downside is, IRR does not measure the investment return in dollar amounts.

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.

NPV, by contrast, 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.

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!