Perpetuity

Perpetuity, most commonly used in accounting and finance, means that a business or an individual receives constant cash flows for an indefinite period (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.

The payment is received at fixed intervals, which do not have any maturity or expiration. In the investment field, it is used to value bonds, stocks or assets where the issuers promise to give perpetual payments to the security holders. They are not very usual situations because most payments are for limited timeframe.

Perpetuity in finance is a kind of financial arrangement which refers to the flow of a fixed amount of money for indefinite time period in future. It is a cash flow stream which does not have any expiry date or maturity period.

It is also called perpetual payment that is received at a fixed interval of time which may be monthly, quarterly or annually. Cash flows are expected to carry on in cases of bonds, stocks, or any other assets. However, in reality, it is not always the case, because every investment usually has an expiration date or a maturity period. This may be due to terms of contract, or market conditions of the security strategy followed by the issuer.

The perpetuity rule is used in the case of investments where the issuer promises to pay the holder a fixed payment at certain intervals.

The present value of perpetuity can be calculated as follows -

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

Let us try to understand the concept of perpetuity in finance with the help of some examples.

Smith has invested in a bond that pays him coupon payments for an infinite period. This bond pays Smith $100 every year. Assuming that the discount rate is 8%, how much should Smith 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 with a discount rate of 8%, the perpetuity would be $1250.

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, they needs to know the present value of that future cash flow. The perpetuity rule 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 particular sort of bond, she will receive infinite cash flows at the end of each period. But it may have a finite present value. So we can use the perpetuity formula to determine what an investor will receive. And we need to know the present value of future cash flows to be accurate.

Let us now do the same and calculate perpetuity 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.

 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 perpetuity value 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..

Both the above terms are very frequently used in financial situations where the securities involve caontinuous cash flows. However, there are some differences between them, as follows:

• The former is for indefinite time period whereas the latter refers to a cash flow which is for a fixed time period, meaning, it has a maturity date.
• The former will have cash flows that are fixed over the entire time, where the latter may have fixed as well as variable cash flows.
• Perpetuity value is commonly used in finance where the concept is more theoretical and cash flow assumptions are made for simple study purpose, whereas annuity is used in real cases like retirement savings, insurance plans, etc.
• The valuation method of both of them are completely different having two different formula.