# 1.29 What Does “IRR” Mean? (A Brief Review)

In our earlier definition of IRR, we said that the IRR is the discount rate, which causes the NPV to be equal to zero. For present purposes, think of IRR in its mathematically equivalent expression, that is once again, as the discount rate, which causes the present value of the future cash flows to equal the project’s initial cost, or investment. Thus, you will find that IRR is a return on investment (where investment = cost) calculation. Think of this in the following manner.

If you invested \$1 in cash, and in five years it grew to \$2, that would imply a certain rate of return, or return on investment (where the investment is \$1), based on a calculation involving the time value of money. Mathematically, this statement may be written as \$1 (1+R)5 = \$2. You can then solve for R and will find that it is 0.1487 (approximately 15%.) This math is based on TVM, as below:

PV (1 + R) n = FV

Let’s say that R = IRR

And therefore:

FV / PV = (1 + IRR)

(FV / PV) 1/n = 1 + IRR

(FV / PV) 1/n – 1 = IRR

“R” is the annual compounded rate of return. Nothing we didn’t already know here. In our example, it means that your return on investment is about 15%, that the \$1 grows to \$2 in five years at a rate of 15%, and, finally, that the present value of \$2 discounted at 15% is equal to \$1. Thus at 15%, the investment cost (\$1) and the present value of the future, in this case, singular, cash flow (\$2) are the same; this is the same as saying that the NPV equals zero, a condition which holds when cost/investment less PV of future cash flows equals zero. This does not say that you earned nothing. You earned 15%!

This is as true for a series of cash flows, whether even or uneven, as it is for one initial outflow (say \$1, as in the former “\$1 to \$2” example) and one “terminal inflow” (say \$2). Actually, by calculating the future, or terminal- value of the cash inflows, we are “translating” the multiple cash flows into its equivalent single dollar value, such as \$1.

Thus, IRR is the discount rate, which equates the present value of an investment’s (multiple) future cash flows with its initial cost (or investment). So, “IRR” is a kind of rate of return, or “return on investment” measure, utilizing the time value of money. Later we will discuss why it is viewed as an “internal” rate of return measure, what the phrase “internal” means, and what problems may be associated with the IRR measure.

Soon, we will see if we can calculate the IRR for multiple cash inflows, while importing an “external” reinvestment rate, which may – or may not – be different than the originally calculated IRR. First, we shall have some more ground to cover relative to certain IRR nuances.