TVM of a perpetual annuity starting in the future
Hi All, I am challenged by this practice question:
“A perpetual preferred stock makes its first quarterly dividend payment of $2.00 in five quarters. If the required annual rate of return is 6% compounded quarterly, the stock’s present value is closest to …”
- We know the quarterly rate is annual rate / number of periods so 6% / 4 = 1.5%
- We know the present value of the perpetual annuity is Cash flow / rate so 2 / 1.5% = 133.33
However because the cash flows start 5 quarters from now we need to discount this value of 133.33. I would have discounted 5 periods (from year 5 to 4, year 4 to 3, year 3 to 2, year 2 to 1, 1 to today) and visibly this is wrong and we should discount only 4 periods.
Can anyone explain why we discount 4 quarters and not 5?
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