Final answer:
The false statement about growing perpetuities is that we assume r < g, when in fact the growth rate must be less than the discount rate for a growing perpetuity to be possible.
Step-by-step explanation:
The statement that is FALSE about growing perpetuities is option b) We assume that r < g for a growing perpetuity. In reality, for a growing perpetuity to exist, the rate of growth (g) must be less than the discount rate (r), not the other way around. If g were greater than r, it would lead to a scenario where the perpetuity grows faster than the rate at which the future payments are discounted, which would yield an infinite present value, making it unrealistic and theoretically impossible.
To solve completely for the present value (PV) of a growing perpetuity, the correct formula is indeed PV = C / (r - g), where C is the initial cash flow, r is the discount rate, and g is the growth rate. This formula assumes that the cash flows occur at regular intervals and grow at a constant rate forever, as stated in option c).
Calculating future values using compound growth is a common method, but it is not applicable directly to growing perpetuities because the number of periods 'n' would be infinite.