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Perpetuity Formula
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 equal amount of cash with no end.
In the UK, a bond is issued which has perpetuity inherent within. These Britishissued bonds are called “Consols”.
Let’s look at the formula of perpetuity.
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
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Perpetuity Example
Let’s take a practical perpetuity example to understand formula of perpetuity.
Smith has invested into a bond that pays him coupon payment for the 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.
We will use the formula to solve this 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 of time with a discount rate of 8%, the perpetuity would be $1250.
Explanation 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.
Conceptwise, it may seem 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 of Perpetuity Formula
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.
Here are the uses of perpetuity formula –
 As mentioned above, if there’s any bond like Consols, the formula of perpetuity 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 the formula of perpetuity 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. In dividend discount model also, formula of perpetuity is also used.
Perpetuity Calculator
You can use the following formula of perpetuity Calculator
D  
R  
PV of Perpetuity Formula =  
PV of Perpetuity Formula = 


Perpetuity Formula 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 Article
This has been a guide to Perpetuity formula, its uses along with practical perpetuity example. Here we also provide you with Perpetuity Calculator with downloadable excel template. Learn more from below articles –
 Formula of Time Value of Money
 Examples of Simple Interest Formula
 Time Value of Money Examples
 NPV vs XNPV  Top Differences
 Simple Interest
 Payback Period
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