Perpetuity

A perpetuity is a stream of equal cash flows that occur at regular intervals and last forever.

The first cash flow does not occur immediately; it arrives at the end of the first period.

A perpetuity is created by depositing cash into an account with interest, and using the interest earnings as the perpetuity:

• We deposited $100intoanaccountwith5$5 of interest, which we withdraw. This way, we have a $5 perpetuity.

This means that the present value of a perpetuity is:

$$PV(C\text{ in perpetuity})=\frac{C}{r}$$

By depositing the amount $\frac{C}{r}$, we can withdraw interest of $\frac{C}{r}\times r=C$ each period.