The IRR of a project with many potential outcomes

This article shows that the internal rate of return (IRR) of a project's expected cash flow stream is a weighted average of the IRRs offered by the project's (many) possible future outcomes, where the weights are calculated using the outcome probabilities and invested capital balances. Because the invested capital associated with a particular realization is a function of the Macaulay duration of the cash flows in that outcome, the weights depend on the outcome probabilities and the effective length of each cash flow stream.