Multiple IRRs and NPV Profiles for Combined Cash Flows

Summary

The document considers how to evaluate a pooled investment made up of projects with different start dates and a common sale date. It contrasts summing the project cash flows and calculating a combined internal rate of return with weighting separate project IRRs or using net present value. The response cautions that aggregating cash flows can produce multiple sign changes, making the combined IRR ambiguous or non-unique.

It recommends plotting net present value against a range of discount rates. Each crossing of the zero-NPV line indicates an IRR, making multiple candidate rates visible. The proposed decision rule is to assess whether NPV is positive at the required rate of return. The document gives no project cash-flow figures or numerical profile, so it illustrates a diagnostic approach rather than calculating a specific result. Its conclusion depends on the chosen required return and the cash-flow assumptions.

Key ideas

• Combining project cash flows with multiple sign changes can produce more than one IRR.
• Weighting individual project IRRs does not resolve ambiguity in the pooled cash flows.
• An NPV profile plots net present value across discount rates and reveals each IRR as a zero crossing.
• Evaluate the combined project by checking NPV at the required rate of return.

Tags

# IRR for multiple series of cash flows


# IRR for multiple series of cash flows












I have a question on how to calculate a single IRR for a group of projects that have different start dates, but have been sold on the same date. This causes the aggregate cash flows to go from negative to positive to negative. I have laid out a basic example below:

I have been asked to come up with a single IRR for Project 1 and Project 2. Would I simply add the cash flows to get a pooled IRR or would I weight the individual IRR's based on the original investment and sum those %'s? Alternatively, would an NPV be more appropriate instead of a single IRR?

Thanks!

## Answer by Alex C (score 0, accepted)

https://quant.stackexchange.com/a/49468

With two changes in the sign of the cash flows, the IRR of the combined cash flows may no longer be unique (there may be two IRRs). You have to be very careful.

What I would recommend is drawing the "NPV profile graph" with the NPV on the y axis and different discount rates (0%, 5%, 10%, ..., 35%) on the x axis. The IRRs are the places where the curve crosses the horizontal axis. This will make the situation clearer.

As long as your Required Rate of Return is in a range where NPV is positive it is OK to accept the combined project.

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.