Present Value of a Perpetuity

A perpetuity is a type of annuity that pays equal cash flows that occur periodically such as monthly, quarterly or annually for an infinite period of time.

The present value of an annuity is calculated using the following formula:

$PV = \frac{A}{r}$

Where:

• A is the annuity payment
• r is the interest rate

Let's look at a practical example:

Assume that an perpetuity pays $500 per year. The rate of return is 8%. The present value of this perpetuity is calculated as follows:

$PV = \frac{500}{0.08} = 6,250$

This means if an investor places $6,250 in an investment paying an 8% rate of return, they will receive a payment of $500 annually for an infinite period. This concept is particularly relevant when analyzing certain types of preferred stocks and some British government bonds known as consols.

Key Points to Remember:

• The higher the interest rate, the lower the present value of the perpetuity
• The formula assumes constant interest rates and payment amounts
• While no actual financial instrument lasts forever, the concept of perpetuity is useful for analyzing long-term investments