Perpetuity Formula | How to Calculate PV of Perpetuity?

Formula to Calculate PV of Perpetuity

Perpetuity Formula refers to the formula that is used in order to calculate the present value of all the cash flows of equal amount which the person is going to generate in the future with no end i.e., for indefinite period and according to formula present value of perpetuity is calculated by dividing the amount of the continuous cash payment by the yield or interest rate.

In accounting, the perpetuity means which goes on for an indefinite period of time. In finance, perpetuity means that the business or the individual would receive a constant flow of an equal amount of cash with no end.

In the UK, a bond is issued which has perpetuity inherent within. These British-issued bonds are called “Consols”.

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

Example

Let’s take a practical perpetuity example to understand the formula of perpetuity.

You can download this Perpetuity Excel Template here – Perpetuity Excel Template

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?

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This perpetuity example is a classic case of perpetuity.

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 Formula

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 the 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 value of future cash flows to be accurate.

Use and Relevance

Since we find out the present value of a perpetuity, the payment remains equal; but the value of perpetuity changes along the way.

The same concept is used in the following.

As mentioned above, if there are any bond-like Consols, it is used to find out the present value.
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 perpetuity Calculator.

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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.