thisisbrianly

Here's another way to look at it.

Think of a perpetuity as an "ordinary perpetuity" (like an ordinary annuity). In an OA, there's always a one period offset between the first payment and the PV (i.e. if the first payment occurs in one year's time, the PV is "as of today", and nif it occurs in two year's time, the PV would be "as of year 1).

So, if the first payment occurs in 4 years, the PV of the Perputuity would be as of year 3. Therefore, you discount for 3 periods.