# Internal Rate of Return - IRR

## Internal Rate of Return - IRR - the break-even interest rate

A primary measure of an investments worth (or value) is based on yield and known as the *internal rate of return - IRR*.

The* internal rate of return* can be defined as the *break-even interest rate* which equals the Net Present Worth - NPW - (Net Present Value) of a project in and out cash flows.

P(i_{rr}) = F_{cash_in}- F_{cash_out}

= 0 (1)

where

i_{rr}= internal rate of return

F= future cash flow in (_{cash_in}discounted)

F= future cash flow out (_{cash_out}discounted)

*(1)* can be expressed as

P(i_{rr}) = F_{0 }/ (1 + i_{rr})^{0 }+ F_{1 }/ (1 + i_{rr})^{1 }+ F_{2}/(1 + i_{rr})^{2 }+ .... + F_{n}/(1 + i_{rr})^{n}

= 0 (2)

where

F_{0..n}= cash flow in period 0 to n (positive value for cash flow in - negative value for cash flow out)

For a given cash flow equation *(2)* can be solved by iteration.

### Cash Flow Internal Rate of Return Calculator

- money out - negative values
- money in - positive values

### Minimum Attractive Rate of Return - MARR

*Minimum Attractive Rate of Return - MARR* - represents the required or minimum acceptable Internal Rate of Return for a project investment.

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