Mathematically you can conclude that the value that you get from perpetuity formula or by annuity formula using 40-50, the answers will be very close. The perpetuity is used as an approximation in valuation as there will be more noise in the estimation when the number of years is very high
Formula what you wrote eventually same as GGM if I assume from your question that NOI is the future (next period) of NOI (in case of GGM will represent D1)
The same conclusion may apply on DCF on DDM while valuing company assuming the most of companies worldwide (especially SMEs) even doesn’t survive more than two decades.
That’s why they invented a Going concern priciple. Likely same kind of going concerns apply on RE with DCF or capitalization approach.