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Using Modified and Generalized IRR for Irregular Cash Flows

Article Quant Q&A · Author: Marky Mark
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Summary

The document addresses how to measure returns when cash flows repeatedly switch between investments and distributions, a pattern that can make ordinary IRR ambiguous or unsuitable. It outlines two alternatives that incorporate an explicit financing assumption.

Modified IRR compounds positive cash flows at a chosen reinvestment rate and discounts negative cash flows at a chosen financing rate. Generalized IRR also uses a financing rate, while treating reinvestment as occurring at the unknown IRR; it estimates that rate iteratively until the calculated present value is zero. The explanation is conceptual and gives no worked calculation or guidance on selecting the assumed rates. Its real estate lending example motivates the issue, but the methods apply more broadly to irregular cash-flow analysis.

Key ideas

  • Modified IRR uses separate assumed rates for reinvesting inflows and financing outflows.
  • It reduces cash flows to an initial present value of outflows and a final value of inflows.
  • Generalized IRR discounts backward using the candidate IRR for positive amounts and a financing rate for negative amounts.
  • Generalized IRR requires iterative root finding because the reinvestment rate is unknown.

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# IRR for irregular cashflow in and out


# IRR for irregular cashflow in and out












So I work for a real estate development umbrella company and the developers that work within it borrow money as needed from the company and receive a percentage of the inflows after repayment of debt. I have been asked to calculate the IRR of this cashflow. It's my understanding that IRR is not appropriate because there are multiple switches from positive casflow to negative, and vice-versa. Is there a better metric that I should suggest be used instead?

Thanks,

## Answer by Magic is in the chain (score 1, accepted)

https://quant.stackexchange.com/a/42155

There are two well known alternatives:

Modified IRR: You assume a reinvestment rate (for positive cash flows) and a financing rate (for negative cash flows). The calculation then is simple. Calculate the Future value (FV) of all positive cash flows using reinvestment rate, and calculate the Present value (PV) of all negative cash flows using the financing rate. Your problem is then reduced to finding the rate of return of a simple investment with alll outflows at the beginning and all inflows at the end. Excel has a built in function for this as well-MIRR.

Generalised IRR: Here again one assumes a financing rate, but reinvestment is assumed to be at the IRR ( which is yet to be estimated). Working backward from the final cash flow, one step at a time, discount the accumulated PV by one period at the IRR if it is positive, and at the fiinancing rate if it is negative. Continue until you reach time 0. Financing rate is assumed to be known, while IRR is to be estimated. You start the algorithm with an initial guess of IRR and apply a root funding algorithm, essentially iteratively updating IRR until PV of the cash flows become zero.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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