9.1. Let PV be the present value of a growing perpetuity

(the “time 1 perpetuity”) with an initial payment of C beginning one period from now and a growth rate of g. If we move all the cash flows back in time one period, the present value becomes PV  (1  r).

Note that this is the present value of a growing perpetuity with an initial payment of C beginning today (the “time 0 perpetuity”).

a. How do the cash flows of the time 1 perpetuity compare to those of the time 0 perpetuity from time 1 on?

b. How do the present values of the cash flows discussed in part a compare with each other?

c. How do the cash flows (and present values) for the two perpetuities described in part a compare?

d. Write out a different value for the present value of the time 0 perpetuity in relation to the value of the time 1 perpetuity based on your analysis in parts b and c.

e. Solve for PV from the equation PV  (1  r)  value from part d.