Perpetuity

What is Perpetuity?

Perpetuity, most commonly used in accounting and finance, means that a business or an individual who receives constant cash flows for an indefinite period of time (like an annuity that pays forever) and according to the formula, its present value is calculated by dividing the amount of the continuous cash payment by the yield or interest rate.

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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For eg:
Source: Perpetuity (wallstreetmojo.com)

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

Smith has invested in a bond that pays him coupon payment for an infinite period of time. This bond pays Smith $100 every year. If we assume that the discount rate is 8%, how much Smith should pay for this bond?

• 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 of time with a discount rate of 8%, the perpetuity would be $1250.

Interpretation of Perpetuity

The very potent query would be why we should find out the present value of a perpetuity. Actually, every firm has a projected cash flow that may get realized after 2, 5, 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 a bit 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 formula of perpetuity. 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 shareholders, they receive preferred dividends before equity shareholders are paid. And preferred dividends 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 find out the valuation of a business. One of these valuation methodologies is the dividend discount model. This formula is also used in the dividend discount model.

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.

Recommended Articles

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 Money
• Calculate Simple Interest
• Time Value of Money
• NPV vs XNPV