Perpetuity – Present Value
[Watch video for detailed explanation of concept and formula and also for different types]
Perpetuity is a sequence of cash flows that continues indefinitely. Perpetuity is an annuity in which the periodic payments or receipts begin on a fixed date and continue indefinitely or perpetually. That is simply an annuity with an extended life.
The formula for calculating the present value of multi period perpetuity is:
$latex PVA\infty=\frac{R}{\left(1+i\right)^1}+\frac{R}{\left(1+i\right)^2}+\ldots+\frac{R}{\left(1+i\right)^\infty}=\sum_{n=1}^{\infty}\frac{R}{\left(1+i\right)^n}=\frac{R}{i} $
Where, R – the payment or receipt each period, i – the interest rate per payment or receipt period.
Numerical Problems
[Watch video for solution of the problems below with explanation]
Q 1. Calculate the PV of a perpetuity that pays Rs. 100 pa annually in arrears using an annual effective interest rate 10%.
Q 2. Calculate the present value of an annuity that pays Rs. 100 pa quarterly for ever in arrears using an annual effective rate of interest of 10%.