What is Perpetuity?

Perpetuity Formula

The present value of perpetuityPresent Value Of PerpetuityPerpetuity can be defined as the income stream that the individual gets for an infinite time. Its present value is derived by discounting the identical cash flows with the discounting rate. Here the cash flows are endless, but its current value amounts to a limited value.read more can be calculated as follows –

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Here. PV = Present Value, D = Dividend or Coupon payment or Cash inflow per period, and r = Discount rate

Alternatively, we can also use the following formula –

Here n = time period

Perpetuity Example

  • First of all, we know that the coupon payment every year is $100 for an infinite amount of time.And the discount rate is 8%.Using the formula, we get PV of Perpetuity = D / r = $100 / 0.08 = $1250.

For a bond that pays $100 every year for an infinite period with a discount rate of 8%, the perpetuity would be $1250.

Interpretation of Perpetuity

The very powerful query would be why we should find out the present value of a perpetuity. Every firm has a projected cash flow that may get realized after 2, 5, or 10 years.

For an investor to be interested in the firm, she needs to know the present value of that future cash flow. Perpetuity is one sort of annuity that pays forever.

Concept-wise, it may seem illogical; but it happens in the case of bonds issued by the British government. If an investor invests in this special sort of bond, she will receive an infinite amount of cash flows at the end of each period. But it may have a finite present value. To find out where an investor will receive, we can use the perpetuity formula. And we need to know the present valuePresent ValuePresent Value (PV) is the today’s value of money you expect to get from future income. It is computed as the sum of future investment returns discounted at a certain rate of return expectation.read more of future cash flows to be accurate.

Use and Relevance

 In the case of preferred shareholdersPreferred ShareholdersA preferred share is a share that enjoys priority in receiving dividends compared to common stock. The dividend rate can be fixed or floating depending upon the terms of the issue. Also, preferred stockholders generally do not enjoy voting rights. However, their claims are discharged before the shares of common stockholders at the time of liquidation.read more, they receive preferred dividends before equity shareholders are paid. And preferred dividendsPreferred DividendsPreferred dividends refer to the amount of dividends payable on preferred stock from profits earned by the company, and preferred stockholders have priority in receiving such dividends over common stockholders.read more are fixed. That’s why we can use this formula to find out the present value of these preferred dividends.·       In finance, valuation methodologies are used to determine a business’s valuation. One of these valuation methodologies is the dividend discount model. This formula is also used in the dividend discount model.Dividend Discount Model.The Dividend Discount Model (DDM) is a method of calculating the stock price based on the likely dividends that will be paid and discounting them at the expected yearly rate. In other words, it is used to value stocks based on the future dividends’ net present value.read more.

Perpetuity Calculator

You can use the following calculator.

Perpetuity Calculation in Excel (with excel template)

Let us now do the same perpetuity example in Excel. This is very simple. You need to provide the two inputs of Dividend and Discount Rate. You can easily calculate the ratio in the template provided.

This has been a guide to Perpetuity and its meaning. Here we learn how to calculate PV of perpetuity using its formula along with examples and a downloadable excel template. Learn more from the below articles –

  • Formula of Time Value of MoneyCalculate Simple InterestCalculate Simple InterestSimple Interest (SI) is a way of calculating the amount of interest that is to be paid on the principal and is calculated by multiplying the principal amount with the rate of interest and the number of periods for which the interest has to be paid.read moreTime Value of MoneyNPV vs XNPV