Perpetuity

An indefinite cash flow payment

What is a perpetuity?

A perpetuity in the financial system is a situation where a stream of cash flow payments continues indefinitely or is an annuity which has no end. In valuation analysis, perpetuities is used to find the present value of a company’s future projected cash flow stream and company’s terminal value.

perpetuity formula

 

Finite present value of perpetuity

Although the total value of a perpetuity is infinite, it has a limited present value. The present value of an infinite stream of cash flow is calculated by adding up the discounted values of each annuity and the decrease of the discounted annuity value in each period until it reaches close to zero.

The finite present value of a perpetuity is used by an analyst to determine the exact value of the company if it continues to perform at the same rate.

 

Real-life example

There aren’t many real life examples of a perpetuity. One of the examples of a perpetuity is the UK’s government bond, known as a Consol.  Bondholders will receive annual fixed coupons (interest payment) as long as they hold the amount and the government does not discontinue the Consol.

The second example is in the real-estate sector when an owner purchases a property and then rents it out. The owner is entitled to an infinite stream of cash flow from the renter as long as the property continues to exist (assuming the renter will rent)

Another real-life example is preferred stock; the perpetuity calculation assumes the company will continue to exist indefinitely in the market and keep paying dividends.

 

Present Value of perpetuity formula

Here is the formula:

PV = C / R

 

Where:

PV = Present value

C = Amount of continuous cash payment

r = Interest rate or yield

 

Example calculation

Company “Rich” pays $2 dividends annually and estimates they will pay it indefinitely. How much are investors willing to pay for the dividend with a yield of 5%?

PV = 2/5% = $40

An investor will consider investing in the company if it’s worth $40 or less.

 

Perpetuity with growth formula

Formula:

PV = C / (r – g)

 

Where:

PV = Present value

C = Amount of continuous cash payment

r = Interest rate or yield

r = Growth Rate

 

Example calculation

Taking the above example, imagine if the $2 dividend is expected to grow annually by 2%.

PV = $2 / (5 – 2%) = $66.67

 

Importance of a growth rate

The growth model is important for some terminal value calculations in the discounted cash flow model. The last, or terminal year, in the DCF model will be assumed to grow at a constant rate forever. This, in essence, means that the terminal year cash flow is a continues stream of cash flow.

 

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