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You are over complicating this. IRR is simply your compounded rate of return that is then money-weighted based on when cashflows occur.

Assuming your investment has no interim distributions and a single bullet payment at maturity, your IRR is simply the compounded growth rate (outflow to the power of number of periods to exit). Very easy to approximate in your end...if cashflows are front weighted then your IRR goes up.

 

Bump, haven’t heard of this methodology / approach but would be curious to learn other explanations 

 
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