The internal rate of return is used in capital budgeting to measure the profitability of investments or projects. Learn more about IRR, see example calculations, and learn how to use this tool to make decisions about whether your business should pursue a project.
What Is the Internal Rate of Return?
The internal rate of return is the annualized effective compound rate of return for a project or investment that makes the net present value equal zero. In other words, the IRR is the annualized return that makes the project or investment break even. The term “internal” refers to the fact that the calculation doesn’t include any external factors, such as inflation or interest rates.
The Internal Rate of Return Formula
The formula for the IRR takes four variables into account:
P(0) = The initial cash flow of the project or investmentP(t) = The cash flow at period tt = the time period in questionIRR = the internal rate of return
Remembering that the IRR is found to equate the project’s cash flows to zero, the formula is:
0 = P(0) + P(1)/(1 + IRR) + P(2)/(1 + IRR)^2 + P(3)/(1 + IRR)^3 + … + P(t)/(1 + IRR)^t
You can’t really find the IRR numerically. You have to find the solution by using an iteration process to converge on a net present value of $0. You can do this easily within a spreadsheet by using “what if” and “goal seek” functions. Also, in cases where there are odd patterns of cash flow, such as positive ones followed by negative ones, followed by positive again, multiple IRR solutions can arise.
Example Internal Rate of Return Calculations
Assume a project has an initial capital outlay of $450,000. It will last for five years and the cash flows generated from the project are estimated to be:
- Year 1: $125,000
- Year 2: $150,000
- Year 3: $150,000
- Year 4: $100,000
- Year 5: $60,000
The IRR equation is set up as:
$0 = $125,000/(1+IRR)^1 + $150,000/(1+IRR)^2 + $150,000/(1+IRR)^3 + $100,000/(1+IRR)^4 + $60,000/(1+IRR)^5
Through iteration, the solution for IRR in this equation is 10.56%.
Making Business Decisions with the Internal Rate of Return
A higher IRR means the project is more attractive. When you have to decide between two projects, you should select the one with the higher IRR. However, it’s very important that the IRR exceeds your company’s cost of capital. If not, the project will lose money for the company, even if the IRR is positive.
The cost of capital is the cost of funds that the business uses. Debt and equity tend to have different costs associated with them, so the weighted average cost of capital should be calculated.
For example, assume a manager runs the numbers on three projects and finds the following IRR values:
- Project 1 IRR = 9%
- Project 2 IRR = 12%
- Project 3 IRR = 5%
The company’s cost of capital is 6.5%.
The company should avoid Project 3 and should pursue Project 2. If the company has enough capital, it should pursue Project 1 also.