Question

what is the value of a perpetuity starting in 12 years paying 300 year if the discount rate is 9% per year ?

Answer 1

First we will calculate the value of perpetuity after 12 years from now as per below:

The formula for present value of perpetuity is:

Present value of Perpetuity = Cash inflows per period / Discount rate

Given: Cash inflows per period = 300, Discount rate = 9%

Putting the given values in the above formula. we get,

Present value of perpetuity = 300 / 9% = 3333.33

Now, we will calculate the value of perpetuity as of today as per below:

Here we will use the following formula:

PV = FV / (1 + r%)n

where, FV = Future value = 3333.33, PV = Present value, r = rate of interest = 9%, n= time period = 12

now, putting theses values in the above equation, we get,

PV = 3333.33 / (1 + 9%)12

FV = 3333.33 / (1 + 0.09)12

FV = 3333.3 / (1.09)12

FV = 3333.33 / 2.81266478178

FV = 1185.11

So, the value of perpetuity is 1185.11.