## The Internal Rate Of Return

You are likely more familiar with the term return on investment, or ROI, than internal rate of return. The ROI is defined as the interest rate that would result in a return on the invested capital equivalent to the project's return. For illustration, if we had a water treatment project with a ROI of 30 percent, that's financially equivalent to investing resources in the right stock and having its price go up 30 percent. As before, this method is based in the net present value of benefits and costs; however, it does not use a predetermined discount rate. Instead, the present-value equation is solved for the discount rate i. The discount rate that satisfies the zero benefit is the rate of return on the investment, and project selection is based on the highest rate. From a simple calculation standpoint, the present value equation is solved for i after setting the net present value equal to zero, and plugging in the future value, obtained by subtracting the future costs from the future benefits over the lifetime of the project. This approach is frequently used in business; however, the net benefits and costs must be determined for each time period, and brought back to present value separately. Computationally, this could mean dealing with a large number of simultaneous equations, which can complicate the analysis. 