What Is a Perpetuity? Definition, Formula, and Examples

In the world of corporate finance, a perpetuity refers to a never-ending series of cash flows. These cash flows are characterized by regular payments that may (in case of a growing perpetuity) or may not (in case of a non-growing perpetuity) increase with each payment period.

Comprehending the concept of perpetuity can help you better understand your business’s present market value. Reasonable expectations of future cash flows are used to calculate your business’s current financial value.

We’ll discuss what a perpetuity is, explain how to calculate the value of a perpetuity, and provide a few practical examples. Feel free to skip to any section by clicking on the links below:

• What is a perpetuity?
• Present value of a perpetuity
• Formula for present value of a perpetuity
• What is a growing perpetuity?
• Present value of a growing perpetuity formula
• Perpetuity vs. annuity
• Perpetuity vs. royalty
• 2 practical examples of a perpetuity

What is a perpetuity?

An annuity is a financial product that gives periodic cash flows. As the name suggests, a perpetuity is a type of annuity with no end. As you may have guessed, perpetuity is a financial term that indicates an infinite stream of cash flows.

If your business purchases a perpetuity-based investment, you can expect payments to go on for an indefinite period. The most common forms of investments that classify as perpetuities are:

• Common stocks
• Bonds
• Real estate investments

Present value of a perpetuity

The present value of a perpetuity is the amount of money you can expect to earn by selling the perpetuity right at this time. For example, if you own a bond that entitles you to constant payments for perpetuity, the current selling price of the bond on the market is its present value. While a perpetuity is infinite, its present value is finite. But how is that possible?

This is because of a slightly paradoxical concept called the time value of money (TVM). TVM states that a sum of money is worth more now than it would be in the future because the money, if invested now, will compound over time.

Because of the TVM, each perpetuity payment is worth a fraction of the previous one, despite both of them being identical sums of money.  This is what causes the value of an infinite stream of payments to collapse onto itself and become a finite number.

Formula for present value of a perpetuity

We can calculate the present value of a perpetuity using this equation:

Where:

• PV = present value of a perpetuity
• C = cash flow, which refers to the steady income your company receives from a perpetuity periodically
• r = interest rate or yield, which is the required rate of return for the perpetuity

Let’s assume you receive $100,000 from a perpetuity as an annual payment. This is your cash flow. The interest rate for this period is 10%.

In this case, the present value of your perpetuity would be:

Simply put, the present value of a perpetuity helps you calculate what your asset is worth currently. It’s important to know this to calculate and analyze the net value of income streams that your business currently projects.

What is a growing perpetuity?

While a perpetuity gives you fixed cash flows for an infinite period, a growing perpetuity involves cash flows that aren’t fixed. For example, if you invest in a perpetuity with payments that grow at a constant rate every year, this is called a growing perpetuity.

Present value of a growing perpetuity formula

The present value of a growing perpetuity can be calculated as follows:

The three elements of the formula are:

• Year 1 cash flow, which refers to the first cash flow of the endless cash flows you’re entitled to receive
• Interest rate or yield, which is the required rate of return on the perpetuity
• Growth rate, which is the rate at which the cash flow payments are expected to grow

Let’s assume your company invests in a perpetuity with a first-year cash flow of $60,000 and is set to grow at a rate of 3% with an interest rate of 6%.

The present value of the growing perpetuity your business owns would be:

If you want to better understand perpetuities and other financial considerations, you may want to hire an independent financial analyst. Upwork is a platform built to connect independent professionals with businesses seeking specialized talent. If you need a financial analyst to help with all of this, we have you covered.

Perpetuity vs. annuity

While annuities and perpetuities are both periodic payments you’re entitled to receive from the issuer when you make a particular investment, annuities have a distinct end date. On the other hand, perpetuities are never-ending.

Both instruments use discounted cash flow methods to determine present value.

Perpetuity vs. royalty

Royalties are your claim to a share of a particular entity’s sales, such as a book or music album. If you get 15% royalty for a book, it means you’re entitled to 15% of its total sales volume. Royalties usually have an expiration date. However, a perpetuity is a dividend payment that’s due infinitely. A perpetuity is similar to a bond with no maturity date.

2 practical examples of a perpetuity

Perpetuity can mean many things and can be applied in many ways. Here are some examples to help you better understand the concept of perpetuity and the present value of a growing perpetuity.

Perpetuity from an investment home

Imagine that you purchase an investment home. Once you pay off the property’s purchase price, you’re entitled to receive an endless stream of annual rental cash payments of $14,000 from your tenants. On paper, you’ll receive payments until the end of time (or until you decide to sell the house or the renter stops renting the property), making the real estate income a perpetuity.

If the annual interest rate is 7%, the present value of this perpetuity, not considering any outflows for managing the property, would be:

Growing perpetuity from stock dividends

Let’s say you’ve purchased some company’s stock that pays a growing dividend of $500 per share annually. The current value of the dividend payment is $500. Theoretically, you can hold a stock forever, and you’re entitled to an endless stream of future dividends from that company.

Assuming the dividends are expected to grow at a rate of 10% per year and there’s a 15% discount rate (or interest rate or yield), the present value of your growing perpetuity would be:

When corporations, governments, or federal reserves need an influx of cash, they sometimes issue bonds. If your company purchases these bonds, you’re essentially extending a loan to the issuer. In exchange for these loans, issuers agree to make interest payments to you indefinitely, making it a growing perpetuity.

Track your business’s perpetuity the right way

Perpetuity investments can be made to ensure steady streams of cash flow. You can track your perpetuity the right way and ensure maximum returns on your investments and finances by engaging the best independent financial analysts through Upwork.

Our independent financial analysts can help you better understand valuation without needing to hire a full-time professional.