The internal rate of return (IRR) is the discount rate at which the net present value (NPV) of a project is equal to zero. In other words, the sum of a project’s expected cash flows is equal to the amount of its initial cost. The IRR method is based on the discounted cash flow technique and is widely used in capital budgeting and investment decisions as a screening criterion for accepting or rejecting projects or investment.
To calculate the IRR of a project, we should use the NPV formula.It is necessary to set the NPV to zero and solve the equation below.
|NPV = CF0 +||CF1||+||CF2||+ … +||CFN||= 0|
|(1 + IRR)1||(1 + IRR)2||(1 + IRR)N|
|(1 + IRR)t|
|t = 0|
The decision rules used in the IRR method are as follows:
Let’s assume two equally risky projects with the same initial cost and the same total expected cash flows. To illustrate the influence of the time value of money concept, Project Y cash flows come in relatively sooner, and Project Z cash flows relatively later.
|Initial Cost, CF0||Cash flows at the end of relevant year, CFt|
Let’s put all data available into the formula above.
|-$20,000,000 +||$10,000,000||+||$8,000,000||+||$6,000,000||+||$4,000,000||+||$2,000,000||= 0|
|(1 + IRRY)1||(1 + IRRY)2||(1 + IRRY)3||(1 + IRRY)4||(1 + IRRY)5|
|-$20,000,000 +||$2,000,000||+||$4,000,000||+||$6,000,000||+||$8,000,000||+||$10,000,000||= 0|
|(1 + IRRZ)1||(1 + IRRZ)2||(1 + IRRZ)3||(1 + IRRZ)4||(1 + IRRZ)5|
To solve these equations, you can use the financial calculator, or to find IRR using Excel, see the figure below.
Thus, the internal rate of return of Project Y is 20.27% and 12.01% for Project Z. The discounted cash flow of both projects is presented in the figure below.
Let’s assume that the WACC for both projects is 9.5%. If the projects are independent, they should be accepted because IRR exceeds WACC. If they are mutually exclusive, Project Y should be accepted because of higher IRR than Project Z.
The internal rate of return method has three serious disadvantages: