# The analysis of perpetuity

### The analysis of perpetuity

This perpetuity example is a classic case of perpetuity. Due to its stringent time period, Perpetuity is not utilized for many financial assets, as compared to Annuity. Sometimes, we exchange a lump sum value for a finite stream of future payments. One can calculate the present value of Annuity by discounting annuity cash flows and future value of Annuity by compounding annuity cash flows at the specified interest rate. Similarly consider the example of real estate. Although the property may be sold in future or even the very near future , the assumption is that other investors will apply the same valuation approach to the property. Underlying this valuation is the assumption that rents will rise at the same rate as inflation. For this reason, the terminal year is a perpetuity, and analysts use the perpetuity formula to find its value. Perpetuity Formula The basic method used to calculate a perpetuity is to divide cash flows by some discount rate. A perpetuity is a type of annuity that lasts forever, into perpetuity. Because of the time value of money , each payment is only a fraction of the last. The most counter-intuitive part of perpetuity is the fact that it has a finite value. Therefore in the later years as and when inflation keeps on increasing, the real value of the payments are continuously decreasing.

Sometimes, we exchange a lump sum value for a finite stream of future payments. Therefore the shareholder is entitled to an infinite stream of future dividends for paying the stock price now.

To find out where an investor will receive, we can use the formula of perpetuity.

## Future value of perpetuity

Perpetuity is one sort of annuity that pays forever. Many universities have endowment funds that pay scholarships to students. Concept-wise, it may seem bit illogical; but it happens in the case of bonds issued by the British government. They have been doing so for centuries and plan to continue to do so forever. Although the property may be sold in future or even the very near future , the assumption is that other investors will apply the same valuation approach to the property. A perpetuity is basically a stream of cash flows that never terminates. Effectively, the use of a cap rate to value a piece of real estate assumes that the current income from the property continues in perpetuity. However, in case of perpetuity, the payments will never cease. Sometimes, it is even referred to as perpetual annuity. As an Annuity has a specified time period, it uses the compound interest rate to calculate the future value of a stream of cash flow. And we need to know the present value of future cash flows to be accurate. The answer is because the real value of future cash flows keeps on falling. Calculation formula of perpetuity The value of perpetuity or a perpetual annuity is calculated by a simple formula: where, PV represents the present value of the perpetuity, A represents the amount of periodic payments, and r represents the discount rate, yield, or interest rate.

The same concept is used in the following. Bonds issued by UK Government which will make the coupon payments till the infinity or stocks paying a constant dividend are the best examples of Perpetuity.

And we need to know the present value of future cash flows to be accurate. Hence using the formula for sum of an infinite series, the value of a perpetuity can be calculated. Plain Vanilla Bonds make their coupon payments at the end of each period till the life of the Bond.

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