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Internal Rate of Return - IRR

Internal Rate of Return (IRR) - the break-even interest rate.

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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)


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)


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.  

Internal Rate of Return Diagram

Cash Flow Internal Rate of Return Calculator

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

Cash Flows - Period

Present Value of Future Payment chart

Download and print Present Value of Future Payment chart

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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Related Topics

  • Economics

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

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