A perpetuity makes payments starting five years from today T

A perpetuity makes payments starting five years from today. The first payment is $1,000 and each payment thereafter increases by k% per year. The present value of this perpetuity is equal to $4,096 when computed at i=25%. Find k.

Solution

Present value of perpetuity = Annual cash flow / require rate - growth

Present value of perpetutiy is 4,096

We deal with this annuity as a 4-year deferred perpetuity immediate

Future value = present value ( 1 + 0.25)⁴

Future value = 4096 * 2.441406

Future value = 10,000

10,000 = 1000 / 0.25 - K

0.25 - K = 0.10

K = 0.15 or 15%