What is Perpetuity?
A Perpetuity refers to a constant stream of cash flows payments anticipated to continue indefinitely.
How to Calculate PV of Perpetuity (Step-by-Step)
In a perpetuity, the series of cash flows received by the investor is expected to be received forever (i.e. a never-ending stream of cash flows).
For instance, if an investment comes with terms stating that a $1,000 payment will be paid out at the end of each year with an indefinite end, this represents an example of a zero-growth perpetuity (i.e. the annual payout remains the same through the life of the investment).
Despite the cash flows theoretically lasting “forever,” the present value (PV) – i.e. the approximate valuation of the total potential stream of cash flows as of the current date – can still be calculated.
The “time value of money,” a fundamental concept in corporate finance, states that the further away from the date of when a cash flow payment is received, the greater the reduction in its value today.
As a result, the present value (PV) of the future cash flows of a perpetuity eventually reaches a point where the cash flow payments in the far future have a present value of zero.
Perpetuity vs. Annuity: What is the Difference?
- Perpetuity: To reiterate, perpetuities are cash flows are expected to continue forever with no ending date.
- Annuity: In contrast, annuities comes with a pre-determined maturity date, which is when the final cash flow payment is received.
Growing Perpetuity vs. Zero-Growth Perpetuity
In the prior example, the size of the cash flow (i.e. the $1,000 annual payment) is kept constant throughout the entire duration of the perpetuity.
However, for growing perpetuities, there is a perpetual (or “continuous”) growth rate attached to the series of cash flows.
If we assume equal initial payment amounts, a growing perpetuity will thus be valued higher than one with zero-growth, all else being equal.
For example, if the investment stated that $1,000 would be issued in the following year but at a 2% growth rate, then the annual cash flows would increase 2% year-over-year (YoY).
Since the cash flows increase each year, the growth rate helps offset the discount rate used to calculate the present value (PV).
Perpetuity Formula
In order to calculate the present value (PV) of a perpetuity with zero growth, the cash flow amount is divided by the discount rate.
The discount rate is a function of the opportunity cost of capital – i.e. the rate of return that could be obtained from other investments with a similar risk profile.
For a growing perpetuity, on the other hand, the formula consists of dividing the cash flow amount expected to be received in the next year by the discount rate minus the constant growth rate.
