Question

Give the present value of a perpetuity that pays $1,000 at the end of every year. The first payment occurs at the end of the fifth year and the annual effective interest rate is 3%.

Answer 1

First we will find the value of perpetuity at the end of fifth year by the following formula:

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

Given: Cash inflows per period = $1000, Discount rate = 3%

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

Present value of perpetuity = $1000 / 3% = $33333.33

Now, we will further discount the above value of $33333.33 to its present value because it is the value at the end of fifth year. Now, we will use the following formula:

PV = FV / (1 + r%)n

where, FV = Future value = $33333.33, PV = Present value, r = rate of interest = 3%, n= time period = 5

Now,putting the values in the above equation, we get,

PV = $33333.33 / (1 + 3%)5

PV = $33333.33 / (1 + 0.03)5

PV = $33333.33 / (1.03)5

PV = $33333.33 / 1.1592740743

PV = $28753.63

So, required present value of perpetuity is $28753.63