What is Perpetuity?
A perpetuity is a security, like a bond, that makes payments to its holder without an end date, creating a perpetual source of income.
🤔 Understanding perpetuity
When you buy something like a bond, you put in a sum of money and receive payments based on the amount that you put in and the discount rate. The bond comes with a term, for example, 10 years. Once the 10-year term ends, you get the face value (usually the amount you paid to buy it) of the bond back and stop receiving interest payments. A perpetuity is like a bond with an infinite term length. You’ll keep getting cash from the perpetuity forever unless the group paying the perpetuity dissolves or redeems it. In some cases, you can pass the perpetuity to your heirs in your will, letting them continue collecting payments. In finance, perpetuities are a consistent stream of equal flows of cash, with no set end. You can calculate the current value of a perpetuity to determine its worth.
One real-world example of a perpetuity is a type of bond issued by the United Kingdom, called Consols. Consols were bonds that had no maturity date and which only Parliament could redeem by passing a law to redeem them. The first British consols were issued in 1751 and sold more as time passed, with the last issue coming after World War I. Holders of Consols received a payment based on the original price they paid to purchase the bond. For consols issued in 1751, these payments continued for centuries until Parliament redeemed them in 2015.
Takeaway
A perpetuity is like a water fountain in a park…
When you’re at the park and feel thirsty, you can go to the water fountain and use it to get a drink. The water fountain keeps spouting water, without limit. As long as you’re near the fountain and the plumbing keeps working, you can keep getting water forever. In the same way, as long as you keep holding a perpetuity and the issuer has funds to pay, you keep receiving a payment forever.
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What is perpetuity?
A perpetuity is a never-ending stream of cash payments. There is no set end date to the payments.
Typically, if you buy a bond, you get interest payments until the bond matures. Once the bond matures, you get the face value of the bond back and stop receiving payments.
A perpetuity, however, is like a bond that has no maturity date. If you hold a perpetuity, you can rely on receiving the payments for the rest of your life. When you pass away, you may be able to leave the perpetuity to your heirs, and they start receiving the payments.
Perpetuities are rare. There are very few situations where someone is willing to offer a never-ending stream of cash payments.
Despite their rarity, the concept of a perpetuity is a useful one in the world of finance. You can use perpetuities to calculate the value of an endless stream of cash payments. This can be useful for people valuing a stock that pays dividends or determining how much to charge for a retirement annuity.
What are examples of a perpetuity
Bonds without a maturity date are one example of a perpetuity. With a typical bond, the issuer sells bonds at their face value (typically the amount you pay and will receive from the issuer) and makes regular interest payments based on the value of the bond and the interest rate. Once the bond matures, the issuer returns the face value and stops making payments.
If a bond has no maturity date, the bond issuer continues making interest payments forever. There is no fixed date where the issuer must return the face value and cease interest payments.
Depending on the terms of the bond, the issuer may have the option to redeem the bonds at certain times, which lets them stop making payments. However, if the bond issuer never redeems the bonds, the interest payments continue forever.
Some trusts can function as perpetuities. People often place assets in trust and leave those trusts to benefit their heirs. The trust prevents the inheritors from squandering their fortune and provides them with a regular income. If the terms of the trust don’t allow for withdrawals, only making payments to the heirs, it functions as a perpetuity. When the original heirs pass away, they can leave their regular trust payments, in turn, to their heirs.
Most annuities are not examples of a perpetuity. Generally, annuities make payments for several years or until the person who owns the annuity passes away. Because there is an end date to the annuity, even if the precise end isn’t known, it is not a perpetuity. Annuities that continue payments forever, allowing the purchaser to leave the payments in his will, are perpetuities, but are also exceedingly rare.
What is perpetuity growth?
Perpetuity growth is when the payment that you receive from a perpetuity grows over time.
For example, if you buy a perpetuity that pays $100 in the first year, then increases its payment by 2% each year, the perpetuity exhibits perpetuity growth. Your payments would increase like this:
- Year 1: $100
- Year 2: $102
- Year 3: $104.04
- Year 4: $106.13
- Year 5: $108.24
The payments continue to grow forever.
Perpetuity growth, and knowing how to calculate the value of a growing perpetuity, has many applications. For example, companies that pay dividends tend to increase the size of their payments each year. Finding the worth of a growing perpetuity based on a stock’s dividend and its dividend growth rate can help investors value companies.
Some perpetuities offer shrinking payments instead of growing payments. If you received $100 in the first year, a decreasing perpetuity might only pay $98 in the second year. Decreasing perpetuities have a lower value than growing or normal perpetuities.
How do you calculate the present value of perpetuity?
The formula for the present value of a perpetuity is:
Payment per period / Discount rate = Present value of the perpetuity
The discount rate here is essential for valuing investments such as bonds and stocks because it offers a comparison between the present values of different cash flows. If you can expect to earn 8% returns annually by investing in a relatively stable company, what return would you need to earn to justify investing in a riskier venture? You’d want to earn more than 8%. The riskier the investment, the more you’d have to earn to justify the risk.
When it comes to perpetuities, the discount rate you should use is the expected rate of return on a similar bond or another source of cash flow.
So, if you can expect to earn a return of 5% from a similar bond and need to find the value of a perpetuity that pays $500 per year, you can use the formula.
$500 / .05 = $10,000
The perpetuity is worth $10,000 based on your analysis.
How do you calculate the present value of a growing or decreasing perpetuity?
The formula to find the present value of a growing perpetuity is:
Amount of the first payment / (Discount rate – Growth rate) = Present value of an increasing perpetuity
The faster the payment grows, the higher the perpetuity’s value.
The formula to find the present value of a decreasing perpetuity is:
Amount of the first payment / (Discount rate + Growth rate) = Present value of a decreasing perpetuity
What is the difference between a perpetuity and an annuity?
Perpetuities and annuities may seem similar at first glance, but they have a few key differences.
One is the end date. Perpetuities have no set end date. They continue to make payments to the holder forever. The holder of a perpetuity generally has the power to bequeath the perpetuity to their heirs. The heirs then continue receiving payments.
Annuities do have an end date, even if that date is not known for sure. Some annuities have set terms, ending after several years. Others continue until the person purchasing the annuity passes away. Even though no one knows when the purchaser will die, it is safe to assume that they will eventually die. At that point, the annuity payments stop, which means annuities are not perpetuities.
Another difference between annuities and perpetuities is how often people encounter them. Annuities are incredibly popular, and there are many insurance companies that sell them. By contrast, perpetuities are very rare. It’s almost impossible to find and purchase a true perpetuity. Even many perpetuities that existed in the past are gone now or redeemed by their issuers.
With an annuity, you can calculate the future value of the cash payments that you receive — or a range of potential values, if the annuity expires at death. Because you know, or can estimate, how many payments you’ll get and the end date of those payments, you can know the value of those payments once the annuity ends. Because perpetuities never stop making payments, you cannot calculate the future value of a perpetuity.
New customers need to sign up, get approved, and link their bank account. The cash value of the stock rewards may not be withdrawn for 30 days after the reward is claimed. Stock rewards not claimed within 60 days may expire. See full terms and conditions at rbnhd.co/freestock. Securities trading is offered through Robinhood Financial LLC.
