Calculation of Future Value of Terminal Value using Multiples Method vs. Gordon Growth

Hi, just had a quick question that I was hoping someone may answer.

At my BB, for DCFs (using mid-year convention), we run both the gordon growth and exit multiple method and then for the TV that's calculated using the multiple method, we try to figure out what the implied perpetuity growth rate is on the multiple method TV. In order to do all this, after just calculating the FV of TV (just Terminal Year EBITDA * Terminal Multiple), we discount this FV of TV by 0.5 in order to bring the periods apples-to-apples with the Gordon Growth implied FV of TV. Why would it make sense to haircut the multiple method FV of TV by this 0.5? After all, assuming a 5-year DCF and year-end valuation date, wouldn't any terminal value associated with the gordon growth method be at 4.5 periods and any terminal value associated with the multiples method at 5.0, so if anything, a further 0.5 discounting here means we're discounting the multiples method FV of TV by 5.5 periods?

Apologies if above is confusing, if it's simpler, I'm effectively conceptually confused regarding the below statement in the below link:

"We need to adjust the terminal values by half a period of discounting - we are taking the EMM terminal value and discounting it to get the implied PGM terminal value, which can then be used to derive the implied growth rate. The revised formula is as follows"

https://multipleexpansion.com/2017/11/07/dcf/#Terminal-Value