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# 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(irr) = Fcash_in - Fcash_out

= 0                    (1)

where

P = Present Worth (Value)

irr = internal rate of return

Fcash_in = future cash flow in (discounted)

Fcash_out = future cash flow out (discounted)

(1) can be expressed as

P(irr) = F0 / (1 + irr)0 + F1 / (1 + irr)1 + F2 /(1 + irr)2 + .... + Fn /(1 + irr)n

= 0                    (2)

where

F0..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

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### 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.

## Related Topics

• Economics - Engineering economics - cash flow diagrams, present value, discount rates, internal rates of return - IRR, income taxes, inflation

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