 # Perpetuity Calculator: Present Value of Infinite Annuity + Growth Rate

A perpetuity is an infinite annuity, i.e. a never-ending series of payments. These cash flows can be even or subject to an even growth rate (source). You can use the present value of a perpetuity to determine the value of an endless series of cash flows, e.g. if you are evaluating assets such as real estate or companies. Read more about these uses in the dedicated section below.

## The Perpetuity Calculator – Calculate the Present Value of a Perpetuity (incl. Growth Rate)

Provide the requested values, i.e. the projected annuity, the discount rate as well as a growth rate (if applicable, fill in 0 otherwise). The calculator processes your input automatically and shows you the present value of a perpetuity.

## Input Data

In order to calculate the present value of a perpetuity, you will have to provide the following input parameters.

### Perpetuity or Infinite Annuity

The perpetuity or annuity can be negative or positive. However, if you are investing your money, you are most likely expecting a positive cash flow.

If you wish to calculate the present value of an infinite liability payment (e.g. from the perspective of a government that issues a perpetual bond).

### Discount Rate

Provide a discount rate for the calculation. This can be a market interest rate, your expected rate of return or – in case of company projects – the accounting interest rate or the weighted average cost of capital (WACC)

### Growth Rate

If you expect the annuity being subject to an even growth rate, enter the growth rate in this field. The growth rate is deducted from the discount rate which in turn leads to a higher present value.

## Calculating the Present Value of an Annual Perpetuity

The Formula for calculating the present value of an annual perpetuity is:

Present Value = Perpetuity / (Discount Rate – Growth Rate).

This is the formula implemented for the above calculator. Use the annual perpetuity as well as an annualized discount and growth rate to achieve valid results.

## Calculating the Present Value of Monthly or Quarterly Perpetuities

If you need to calculate the perpetuity based on monthly or quarterly infinite annuities, you can use the standard formula but insert monthly or quarterly values. The formulas read as follows:

Present Value of monthly perpetuity = Perpetuity_month / (DiscountRate_month – GrowthRate_month), and

Present Value of quarterly perpetuity = Perpetuity_quarterly / (DiscountRate_quarterly – GrowthRate_quarterly).

You can convert your annual discount and growth rate into monthly or quarterly compound rates using this formula:

Monthly rate = (1 + annual rate) ^ (1/12) – 1 and

Quarterly rate = (1 + quarterly rate) ^ (1/4) – 1.

## Uses of Perpetuity

Perpetuities can sometimes be found in financial markets, e.g. in the form of sovereign bonds with indefinite tenor. However, these instruments are not too common after all.

The present value of a perpetuity is most commonly used for the valuation of assets or investments. For real estate or land, for instance, it is not uncommon to calculate the market value by applying a multiplicator to the annual net returns. This multiplier is just another form of presentation of a perpetuity. In real estate markets, the multipliers used are typically in a range from 14 to 50 (depending on the region, type and condition of the object, interest rates, seller vs. buyer market etc.) which is equals the present value of a perpetuity using a discount rate between 2% and 7%.

Similar approaches are also popular in markets for websites, software, licenses and other rights of use.

Another typical use is the evaluation of companies or projects based on their cash flows. If a constant revenue or net profit is assumed, the company or the project can be evaluated using the present value of its infinite cash flows. More common though is using perpetuities in conjunction with the net present value. When calculating the net present value (NPV), the couple of cash flows are often subject to a detailed projection while long-term cash flows are hard to predict and prone to unforeseen developments. Therefore, the present value of a perpetuity can be used as residual value, representing the long-term cash flow and growth rate expectations.

## Final Thoughts

We hope that this calculator and article have helped you solve your perpetuity calculation. Take also a look at our other finance calculators that you might find useful as well.