yes but future time value decreases if this...

yes but future time value decreases if this occurs.

https://wiki.treasurers.org/wiki/Perpetuity



Example 2: Growing perpetuity valuation
Time 1 cash flow = $10m, growing by a constant percentage amount each period thereafter in perpetuity.
Periodic cost of capital = 5%.
Periodic growth rate = 2%
The present value of the growing perpetuity is:= A1 x 1 / (r - g)= $10m x (1 / (0.05 - 0.02) )= $10m x (1 / 0.03)= $10m x 33.3= $333mThe modest rate of growth in the cash flow has added substantially to the total present value.



4. Declining perpetuity.Growth can be negative, in other words, decline.
For a declining perpetuity, the present value formula is the same as the growing perpetuity, but the growth rate (g) is entered as a negative number as follows:
Example 3: Declining perpetuity valuationTime 1 cash flow = $10m, declining by a constant percentage amount each period thereafter in perpetuity.
Periodic cost of capital = 5%.
Periodic growth rate = -(2)% negative = -0.02
The present value of the declining perpetuity is:= A1 x 1 / (r - g)= $10m x (1 / (0.05 - -0.02) )= $10m x (1 / 0.07)= $10m x 14.3= $143m
The small negative rate of growth in the cash flow has reduced the total present value very substantially.
The growing / declining perpetuity concept is applied in many contexts.For example, the Dividend growth model for share valuation.


ie continued loss of FUM is a death bell for the share price. The share price has to be valued as a declining perpetuity.