Internal Rate of Return (IRR)

Lesson

The internal rate of return (IRR) is a financial metric used to evaluate the profitability of an investment. The discount rate makes the net present value (NPV) of a project's cash flows equal to zero. In other words, it is the rate at which an investment breaks even in terms of NPV. The IRR compares and ranks different investment opportunities and helps investors determine which projects to undertake.

Practice Question #1

What is the primary purpose of calculating the internal rate of return (IRR)?

Terms

Internal Rate of Return (IRR):

The discount rate that makes the net present value of a project's cash flows equal zero.

Net Present Value (NPV):

The difference between the present value of cash inflows and the present value of cash outflows over a period of time.

Discount Rate:

The interest rate used to determine the present value of future cash flows.

Cash Flow:

The total amount transferred into and out of business.

Practice Question #2

Which of the following is NOT a factor in calculating the internal rate of return (IRR)?

Do Not Confuse With

Present Value (PV):

The current value of a future sum of money or stream of cash flows given a specified rate of return.

Future Value (FV):

The value of an asset or cash at a specified date in the future based on an assumed growth rate.

Practice Question #3

If a project has an internal rate of return (IRR) greater than the required rate of return, should the project be accepted?

Real-World Example

A small business owner is considering expanding their operations by opening a second location. They estimate the initial investment will be $100,000 and expect to generate an additional $20,000 in annual profits. By calculating the IRR, they can determine if this investment is worthwhile compared to other potential investments or simply keeping the money in a savings account.

Rhyme

IRR, a rate we must discern, to find the break-even point where profits we will earn.

Formulas to Remember

IRR = Internal Rate of Return NPV = Net Present Value CFt = Cash Flow at time t r = Discount rate t = Time period n = Number of periods Formula: NPV = SUM[CFt / (1 + r)^t] - Initial Investment The IRR is the discount rate (r) that makes the NPV equal to zero.

Formula Examples

Suppose a project has an initial investment of $10,000 and generates cash flows of $4,000, $5,000, and $6,000 in the first, second, and third years, respectively. Calculate the IRR. 1) To find IRR, set up the discounted cash flows and set the NPV to zero: 0 = (-$10,000 / (1 + IRR)^0) + ($4,000 / (1 + IRR)^1) + ($5,000 / (1 + IRR)^2) + ($6,000 / (1 + IRR)^3) 2) Guess a value like 20%, and see how close the NPV is to 0: NPV = $278 = (-$10,000 / (1 + 20%)^0) + ($4,000 / (1 + 20%)^1) + ($5,000 / (1 + 20%)^2) + ($6,000 / (1 + 20%)^3) 3) Since the NPV is greater than 0, we can deduce IRR must be a little higher. Try 21.5%: NPV = $24 = (-$10,000 / (1 + 21.5%)^0) + ($4,000 / (1 + 21.5%)^1) + ($5,000 / (1 + 21.5%)^2) + ($6,000 / (1 + 21.5%)^3) 4) Proceed iteratively to achieve whatever precision you like. In this case, the IRR is 21.65%.

Pitfalls to Remember

Multiple IRRs:

When a project has unconventional cash flows (cash flow pattern changes from positive to negative or vice versa more than once), it may have multiple IRRs, making the IRR useless.

No IRR:

If a project has no cash inflows or all cash flows are negative, it may not have an IRR.

Different project sizes:

IRR does not consider large versus small projects.