Interpreting IRR with Compounding and Irregular Cash Flows

Summary

The document addresses whether an internal rate of return should be described as a nominal or effective interest rate. It distinguishes a quoted rate with a specified compounding frequency from an effective rate converted to a different period. For instance, a stated annual rate compounded monthly produces a different annualized effective rate than the quoted figure.

The answer argues that the nominal-versus-effective distinction is less useful when discussing IRR, because IRR is calculated from the timing and amounts of the cash flows themselves. Cash flows need not occur at regular intervals, so an IRR can be computed for irregular dates without first fitting them to a conventional compounding period. The explanation is brief and conceptual: it does not cover multiple IRRs, annualization conventions for dated cash flows, or the assumptions required to interpret an IRR as a realized investment return.

Key ideas

• A nominal rate specifies a compounding convention, while an effective rate expresses growth over a chosen period.
• Converting between nominal and effective rates matters when the compounding and reporting periods differ.
• IRR is determined by cash-flow timing and amounts rather than a preset compounding frequency.
• IRR can be calculated for cash flows that occur at irregular intervals.
• The explanation does not address cases where cash flows produce multiple possible IRRs.

Tags

# Is IRR a Nominal or Effective Interest Rate?


# Is IRR a Nominal or Effective Interest Rate?












The definition of the internal rate of return is the interest rate that causes the net present value to equal zero. However, interest rates can be given in two forms: nominal and effective. So, is the internal rate of return a nominal or effective interest rate? Or both?

## Answer by Pythonista anonymous (score 1)

https://quant.stackexchange.com/a/66725

It's a bit of a moot question, to be honest.

If your saving account pays you 5% annual, with monthly compounding, then the effective interest rate is = (1 + 0.05/12)^12 -1 = 5.116%

In other words, if you have an investment which compounds every month or quarter, and you want to know the effective rate over another period (typically over a year), you use the calculation above. This is because there is a difference between the frequency of the compounding (in the example, monthly) and the frequency of the effective rate you want to calculate (typically annually).

When you are calculating an IRR, all of these become moot points. There is no more any distinction between the frequency of the compounding and that of the effective rate you are after; in fact, you can calculate IRRs for sets of cashflows which pay at irregular intervals.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.