IRR's re-investment assumption question

CFA Level I Quant
#1

Hey guys,

If there is an investment in the market which asks you to pay $100 and in return you receive $40 in Y1, $30 in Y2, and $80 in Y3, I want to ask where does the re-investment assumption kick in?

  • The IRR to this question is 20%. However, IRR assumes we re-invest interim cash flows at IRR to achieve the CF’s, but in this case we are getting paid in Y1, Y2, and Y3, so does the IRR assumption of re-investment still hold? I just want to tie this concept to the curriculum’s saying that reinvestment at IRR is unrealistic - but I want to understand if the project promises to pay these CF’s, do I need to depend on the reinvestment assumption? I know how to construct the below, but the below still does not answer my question, because investments assume to pay me the interim cash flows instead of extracting them from my investment of $100 (so essentially I do not own the $100 after I pay it to the project manager for example).

Year CF In Account (CF @ 20%) Withdrawal (Net) 0 -100 -100 N/A N/A 1 100 120 40 80 2 80 96 30 66 3 66 80 80 0

#2

It kicks in from Year 1 onwards and the cashflows are reinvested until the end of the project, i.e. Year 3. So for your example the IRR = 20.261%

Year 1: Receive $ 40, invest it at 20.261% until Year 3, future value(3) = $57.851

Year 2: Receive $30, invest it at 20.261% until Year 3, FV(3) = 36.078

Year 3: Receive $80, not reinvested (end of project).

Total FV at end of year 3 = 57.851 + 36.078 + 80 = 173.929

173.929 = 100(1 + r)^3

r = (173.929/100)^3 - 1 = 20.261% (IRR)

Hence why IRR is called the assumed reinvestment rate of the project’s cash flows.

#3

Thank you!