Internal Rate of Return

Internal Rate of Return (IRR)

Based on the concept of Time Value of Money. Closely related to Present Value and Net Present Value.

The Internal Rate of Return (IRR) is the discount rate that makes the Net Present Value of all future cash flows equal to zero.

It represents the effective annual rate of return on an investment.

Mathematically, it satisfies:

$$0=\sum _{t=0}^n\frac{C{F}_t}{(1+r{)}^t}$$

Where:

• $C{F}_t$: cash flow at time $t$
• $r$: internal rate of return (the unknown being solved for)
• $n$: number of periods

In other words, the IRR is the rate $r$ that sets $NPV=0$.

There is no closed form solution for this equation.

Can also be calculated using the excel function Excel Function - IRR.