Periods and Terminal Values

If you look at financial models that people have put together, Terminal Value usually accounts for a monstrous portion of Price (above 50%).

I wanted to ask myself:

[Question] How far into the future do I have to model into the future to make sure that TV is less than x% of the price?

TV is calculated as
CF (1+g)^n / (r-g)
And the PV of TV is TV / (1+r)^n

x% of the price is calculated as
x% * CF (1+g) / (r-g)

So if I want the TV to represent x% of the total price:
TV = x% * PV

Simplifying we get:
x% = (1+g)^n / [(1+r)^n*(1+g)]
x% (1+g) = [(1+g)/(1+r)]^n

Solving for n:
n = ln [x%/(1+g)] / ln [(1+g)/(1+r)]

While hardly a clean solution, this formula can be used to find out how far you need to model in order to have TV represent a given percentage of your price.

For instance, let's say growth of 2% and discount at 8% (standard "long term" numbers), and you want TV to represent 50%, then n should be about 12.5 periods.

Or:
Percent PV @ 2%
40% 16.4 periods
50% 12.5 periods
60% 9.3 periods
70% 6.6 periods
80% 4.3 periods