# Rate of return on investment

In economics the rate of return on investment refers to the benefits to an investor (the profit) relative to the cost of the initial investment. It is similar to the rate of profit as a measure of profitability.

The simplest way to measure the rate of return on investment is measure the internal rate of return, i.e., the discount rate that implies that the discounted flow of costs and benefits of the project add up to zero. That is, it is the interest rate used to discount future net incomes that gives a net present value (NPV) equal to zero.

Suppose that simple two-period investment costs I in period 0 and pays net income of Y in period 1. Looking at this project from period 0, the future income must be discounted using an interest rate d, so that the NPV equals (discounted future net benefits) minus (current net costs) or

Y/(1 + d) - I

Setting this equal to zero, the internal rate of return equals:

d = (Y - I)/I

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