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If I will be received a cash flow of $50,000 each year for infinite end date, but the cash flow will be received starting at year 5. Why do we discount the perpetuity at year 4 discount factor rate?
The perpetuity factor give the PV ‘now’ when the first receipt is in 1 years time.
If the first receipt is in 5 years time, then this is 4 years later than in 1 years time. Therefore the value from the perpetuity factor is the PV in 4 years time and needs discounting for 4 years to get the PV ‘now’.
I do explain this in my free lectures for both Paper MA and Paper FM 🙂