Time Value of Money
Annuities
Perpetuities
Kinds of Interest Rates
Future Value of an Uneven Cash flow
Probability Distribution
Standard Deviation
CAPM
Security Market Line
Bond Valuation
Stock Valuation
Cost of Capital
The Balance Sheet
Financial Terms
Scientific Terms
Disclaimer
Perpetuities
| Perpetuities - | are equal payments made regularly, like every month or every year, that go on forever. |
You are rich. (Yes, but are you really happy?) You want to start the YOUR NAME HERE Scholarship at your university. Every year, some student will receive a $1000 scholarship. You're paying for it. Even after you, your kids and your grandkids are dead, you are still paying for it. Forever.
The question is....How much money will it cost you. In today's dollars. What is the present value of this perpetuity. (Hint: starting now and going on forever and ever, you assume the interest rate at your bank is going to be 3%).
| PV (of a perpetuity) = payment / interest rate |
Every year the interest you earn is used to pay for the scholarship. The principal in your bank account doesn't really change year to year.
- PV (of a perpetuity) = payment / interest rate
- PV = $ 1000 / .03
- PV = $ 33,333
So, you put $ 33,333 into the bank. Each year the money earns $1000 interest. That interest becomes the scholarship.
Detailed Explanation
Perpetuities are financial instruments that pay a fixed amount of money each period indefinitely. They are essentially a type of annuity that does not have an end date, and the payments continue for as long as the instrument exists. While perpetuities are not as common as other financial instruments like bonds or stocks, they can be used in a variety of ways to create diversified portfolios and manage risk.
Uses - One way in which perpetuities are used is in preferred stock. Preferred stock is a type of stock that pays a fixed dividend, and perpetuities are often used to calculate the value of preferred stock. The value of preferred stock can be calculated by dividing the dividend by the discount rate, which is the rate of return required by investors. Because preferred stock dividends are fixed, they can be treated as perpetuities, and the value of preferred stock can be calculated using the perpetuity formula.
Perpetuities are also used in bonds. A bond is a debt instrument that pays a fixed amount of interest to the bondholder each period until the bond matures, at which point the bondholder receives the principal amount back. Perpetuities can be used to calculate the value of certain types of bonds, such as perpetuities or consols, which are bonds that do not have a maturity date. Consols were first issued by the British government in the 18th century and were used to finance wars. The British consols paid a fixed amount of interest indefinitely, making them a form of perpetuity.
In addition to preferred stock and bonds, perpetuities can also be used in dividend-paying stocks. Dividend-paying stocks are stocks that pay a fixed dividend each period, and the value of these stocks can be calculated using the perpetuity formula. Perpetuities can be useful in this context because they allow investors to compare the value of different dividend-paying stocks using a standardized formula.
Perpetuities can also be used to create diversified portfolios with different risk and return profiles. Because perpetuities pay a fixed amount of money each period, they can be used to generate a stable stream of income. This can be useful for investors who are looking to generate income in retirement or for those who are looking to create a stable source of income for their families. Perpetuities can also be used to hedge against inflation, as the fixed payments will maintain their value over time.
While perpetuities have many benefits, they also come with risks. One risk is the risk of default, which is the risk that the issuer of the perpetuity will not be able to make the payments. This risk is especially high in the case of preferred stock, as preferred stock is lower in the capital structure than other forms of debt. In addition, perpetuities are sensitive to changes in interest rates. If interest rates rise, the value of a perpetuity will decrease, and vice versa.
Limitations - One major limitation of perpetuities is their lack of flexibility. Once a perpetuity is established, the payment amount and frequency are fixed and cannot be changed. This means that if the recipient's financial situation changes, they cannot adjust the payments to better suit their needs. For example, if the recipient suddenly requires more money each period to cover medical expenses, they cannot increase the payments from the perpetuity to help cover those costs.
Another limitation of perpetuities is their potential for interest rate risk. Because perpetuities pay out a fixed amount of money each period, their value is sensitive to changes in interest rates. If interest rates rise, the value of a perpetuity will decrease, as the fixed payments become less valuable in comparison to other investment opportunities that offer higher returns. This can lead to a significant loss in value for perpetuity holders.
Additionally, perpetuities are not suitable for all investors or financial contexts. For example, they may not be the best option for investors who require a lump sum of money for a specific expense, such as a down payment on a house or a child's college tuition. In these cases, a lump sum payment or a finite period annuity may be more appropriate.
Furthermore, perpetuities may not be the best option for those who wish to leave a financial legacy for their heirs. Because perpetuities are designed to last indefinitely, they do not allow for the transfer of remaining funds to beneficiaries upon the recipient's death. This means that any remaining funds in the perpetuity will be absorbed by the issuer, rather than being passed down to the recipient's heirs.
Finally, perpetuities are not immune to the risks inherent in any investment, such as default risk or inflation risk. If the issuer of a perpetuity defaults on their payments, the recipient may not receive the promised payments. Additionally, the fixed payments of a perpetuity may not keep pace with inflation over time, meaning that the purchasing power of the payments may decrease.
Perpetuities in Practice - While perpetuities are not commonly used in modern finance, they can still be found in certain financial instruments and investments.
One way that perpetuities are used in practice is through the issuance of preferred stock. Preferred stock is a type of stock that provides a fixed dividend payment to the holder, usually on a quarterly basis. In some cases, preferred stock is issued as a perpetuity, meaning that the fixed dividend payment will continue indefinitely. This can provide a stable source of income for investors, particularly those who are seeking income in retirement.
Perpetuities are also used in the bond market. Bonds are debt securities that provide a fixed interest payment to the holder. While most bonds have a finite maturity date, some bonds are issued as perpetuities. These perpetual bonds provide a fixed interest payment to the holder for an indefinite period of time. However, perpetual bonds are relatively rare, and most bonds have a fixed maturity date.
Finally, some dividend-paying stocks can be considered perpetuities. These stocks provide a fixed dividend payment to the holder on a regular basis, and can continue to do so for an indefinite period of time. While these stocks are not technically perpetuities, they can provide a similar source of stable income for investors.
In addition to their use in financial instruments, perpetuities can also be used in portfolios to achieve diversification. By including perpetuities alongside other investments, such as stocks and bonds, investors can create a diversified portfolio with different risk and return profiles. This can help to mitigate risk and ensure a more stable return over time.
However, it is important to note that perpetuities have limitations and risks that must be considered. For example, perpetuities lack flexibility, as the payment stream is fixed and cannot be adjusted over time. Additionally, perpetuities are subject to interest rate risk, meaning that their value can fluctuate based on changes in interest rates. Finally, perpetuities are not as commonly used in modern finance, and can be difficult to find in the market.
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About the author
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Author: Mark McCracken is a corporate trainer and author living in Higashi Osaka, Japan. He is the author of thousands of online articles as well as the Business English textbook, "25 Business Skills in English". |