Calculating Present Values of Perpetuities
This calculator is designed to provide the user with the present value of either a perpetuity or growing perpetuity. The calculation only requires four inputs:
- A user selection from a drop-down menu with the choice of perpetuity or growing perpetuity
- The dollar value of the cash flow
- The discount rate, which is the rate used to discount the cash flows
- The expected growth rate, which is the rate at which the cash flows grow each year. Note that this value is only used when calculating a growing perpetuity
Using this information, the calculator then provides the user with the following:
- The present value, or PV, of the cash flows for the selected perpetuity type
What is a Perpetuity?
In finance, a perpetuity is a series of cash payments that will continue indefinitely into the future. There is no end date with a perpetuity. In fact, the word perpetuity comes from the Latin word perpetuus, which means continuous. There are many examples of investments that act like a perpetuity such as preferred stock, and perpetual bonds. Annuities are another example of a perpetuity since they make payments to the annuitant often for as long as the person is alive.
It’s easy to calculate the value of a perpetuity if the interest rate is known:
Value of Perpetuity = Cash Payments / Interest Rate
Perpetuities are an important financial planning tool since they provide investors with the ability to receive an indefinite stream of income. This is especially important to retirees that may be looking for a reliable source of income for the rest of their life.
Growing Perpetuities
One interesting type of perpetuity is a growing perpetuity since the payments increase at a fixed rate over time. For example, a growing perpetuity providing the investor with 20,000 per year, growing by the rate of inflation (3%) and earning a 5% return on investment would have a present value of 1,030,000. This means an investor would be willing to pay around 1,000,000 for this type of asset. If the investment were not a growing perpetuity, then the annuitant would receive 20,000 per year – the same amount every year. The value of growing this amount by 3% is substantial since this second type of perpetuity would have a present value of only 400,000.