Contents
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

Annuities

An Annuity is a bunch of structured payments or equal payments made regularly, like every month or every week.

You win the lottery. The lottery guy comes to your house and says you have to choose between getting \$ 1,000,000 now in one lump sum, or getting structured payments of \$ 50,000 a year for the next 22 years. Which do you take?? Or, similarly, let's say you were injured on the job or whatever and were awarded an annuity of structured payments of \$50,000 a year for the next 22 years. Perhaps you want to sell your annuity (the payments) to someone and get a lump sum of cash today. Is it worth \$1,000,000?

First you have to choose an interest rate. Money is generally worth less in the future, right? So that \$50,000 payment you get in 22 years is not going to be worth as much as it is today? You know, stuff will be more expensive then, right? So guess an interest rate, in this case, the rate of inflation for the next 22 years. Lets say 4%. Now, you have to figure out what is the present value of the \$50,000 times 22 years discounted by 4% and then compare it with the million bucks. There are basically 2 ways to do this.
• Use a financial calculator.
• Use an annuity table.

Use a financial calculator - The PV of an Annuity.

1. Enter n (the number of compounding periods - in this case the number of years). Press 22 and then push the N button.
2. Enter i (the interest rate per period - in this case the number of years). Press 4 and then push the i button.
3. Enter FV (the future value). It is zero. You want to know the Present Value, not the future value, right? Push 0 and then push the FV button.
4. Enter PMT (the payment). You are not making a payment, you are getting one. So you have to show a negative number. Press 50000, then the CHS (change sign button), then push the PMT button.
5. Push the PV (present value) button.
6. Answer = \$722,555. This means 22 annual structured payments of 50,000 each is worth only \$722,555 of today's dollars. So you should take the million bucks from the lottery guy in one lump sum.

Use an annuity table - The PV of an Annuity.

Somewhere in your book, I bet there is a table that looks something like this:

 1% 2% 3% 4% 1 00.9901 00.9804 00.9703 00.9615 2 01.9704 01.9416 01.9135 01.8861 3 02.9410 02.8839 02.8286 02.7751 4 03.9020 03.8077 03.7171 03.6299 5 04.8534 04.7135 04.5797 04.4518 6 05.7955 05.6014 05.4172 05.2421 7 06.7282 06.4720 06.2302 06.0021 8 07.6517 07.3255 07.0197 06.7327 9 08.5660 08.1622 07.7861 07.4353 10 09.4713 08.9826 08.5302 08.1109 11 10.3676 09.7868 09.2526 08.7605 12 11.2551 10.5753 09.9450 09.3851 13 12.1337 11.3484 10.6350 09.9856 14 13.0037 12.1062 11.2961 10.5631 15 13.8651 12.8493 11.9379 11.1184 16 14.7179 13.5777 12.5611 11.6523 17 15.5623 14.2919 13.1661 12.1657 18 16.3983 14.9920 13.7535 12.6593 19 17.2260 15.6785 14.3238 13.1339 20 18.0456 16.3541 14.8775 13.5903 21 18.8570 17.0112 15.4150 14.0292 22 19.6604 17.6580 15.9369 14.4511
1. Find this table.
2. On the left, find the number of compounding periods (in this case years) - 22
3. On the top, find the interest rate - 4%
4. Find below where they meet. It says 14.4511
5. Multiply 14.4511 times the Payment - \$50,000
6. Answer = \$722,555. This means 22 annual structured payments of 50,000 each is worth only \$722,555 of today's dollars. So you should take the million bucks from the lottery guy in one lump sum.

Detailed Explanation

An annuity is a financial instrument that provides a series of payments at regular intervals for a specific period of time or for the lifetime of the annuitant. An annuity can be purchased by making a lump-sum payment or by making a series of payments over time. The payments made to the annuitant can be fixed or variable depending on the type of annuity chosen. Annuities are used as a retirement income source, to fund education expenses, and to achieve other long-term financial goals.

There are several types of annuities available in the market, and each type has its own unique features and benefits. The most common types of annuities are fixed, variable, indexed, immediate, and deferred annuities.

Fixed annuities are annuities that offer a fixed interest rate on the invested amount. The interest rate is guaranteed for a specific period of time, and the payments made to the annuitant are also fixed. The interest rate offered by fixed annuities is generally lower than the interest rate offered by variable annuities.

Fixed annuities are a good option for individuals who want a stable income stream and are not willing to take on market risk. Fixed annuities are also suitable for individuals who are risk-averse and want to protect their principal investment. The disadvantage of fixed annuities is that they offer lower returns compared to other types of annuities.

Variable annuities are annuities that offer a variable interest rate on the invested amount. The interest rate is not guaranteed and varies based on the performance of the underlying investments. Variable annuities offer a higher potential for returns compared to fixed annuities, but also come with higher risks.

Variable annuities are suitable for individuals who are willing to take on market risk and want the potential for higher returns. Variable annuities also offer the option to invest in a variety of funds, allowing investors to diversify their portfolio. The disadvantage of variable annuities is that they offer no guaranteed returns and are subject to market volatility.

Indexed annuities are a type of annuity that offer returns based on the performance of a stock market index such as the S&P 500. Indexed annuities offer a guaranteed minimum interest rate, but also offer the potential for higher returns based on the performance of the underlying index.

Indexed annuities are suitable for individuals who want to take on market risk but also want some protection for their principal investment. Indexed annuities offer the potential for higher returns compared to fixed annuities, but also offer some downside protection in the event of a market downturn.

Immediate annuities are annuities that offer immediate payments to the annuitant. Immediate annuities are purchased with a lump-sum payment, and the payments to the annuitant begin immediately. Immediate annuities are suitable for individuals who want to start receiving payments immediately and do not want to wait for a specific period of time.

Deferred annuities are annuities that offer payments at a later date. Deferred annuities can be fixed, variable, or indexed, and the payments to the annuitant begin at a later date. Deferred annuities are suitable for individuals who want to defer their payments to a later date and accumulate interest on their investment.

Annuity Contract Features - An annuity is a contract between an individual and an insurance company that provides a steady stream of income for a certain period of time or for the rest of the individual's life. An annuity can be a great investment option for those who want a stable source of income in retirement or for those who want to accumulate funds tax-deferred for future use. However, annuity contracts can be complex, and it is important for finance students to learn about the different features of annuity contracts.

One of the key features of an annuity contract is the payout options. There are several payout options available, and the choice of payout option will affect the amount of income that the individual will receive. The most common payout options include:

Life annuity: With a life annuity, the individual will receive a guaranteed income for the rest of their life. This payout option is suitable for those who want a stable source of income in retirement and who do not want to worry about outliving their savings.

Joint and survivor annuity: With a joint and survivor annuity, the individual and their spouse will receive a guaranteed income for the rest of their lives. This payout option is suitable for those who want to provide for their spouse in the event of their death.

Period certain annuity: With a period certain annuity, the individual will receive a guaranteed income for a certain period of time, such as 10 or 20 years. This payout option is suitable for those who want a steady stream of income for a specific period of time.

Another important feature of an annuity contract is the death benefit. The death benefit is the amount that is paid out to the individual's beneficiary in the event of their death. The death benefit can be a fixed amount or a percentage of the value of the annuity contract. The choice of death benefit will affect the cost of the annuity contract.

Surrender charges are another feature of an annuity contract that finance students should learn about. Surrender charges are fees that are charged if the individual withdraws funds from the annuity contract before a certain period of time, such as five or 10 years. The surrender charges can be a percentage of the value of the annuity contract, and they can be significant. It is important for finance students to understand the surrender charges associated with an annuity contract before investing in one.

Fees are another feature of an annuity contract that should be considered. Annuity contracts can have various fees, such as administrative fees, mortality and expense fees, and investment management fees. These fees can reduce the value of the annuity contract and the income that the individual will receive.

Lastly, riders are additional features that can be added to an annuity contract for an additional fee. Riders can provide additional benefits, such as a guaranteed minimum income benefit or a long-term care benefit. Riders can be a valuable addition to an annuity contract, but they can also increase the cost of the annuity contract.

Taxation of Annuities - Annuities are commonly used by individuals to supplement their retirement income or to provide a guaranteed stream of income for a specific period of time. One of the important aspects of annuities that finance students should understand is the taxation of annuities.

Annuities are subject to tax in a variety of ways, including the taxation of contributions, earnings, and withdrawals. The tax treatment of annuities can be complex and confusing, so it is important for people to have a solid understanding of the tax implications of annuities.

Contributions to annuities are typically made on a pre-tax basis, meaning that contributions are made with pre-tax dollars. This means that the individual does not have to pay income tax on the contributions at the time they are made. Instead, the contributions are allowed to grow tax-deferred until they are withdrawn. This tax-deferred growth can be a significant advantage for individuals who are looking to accumulate retirement savings.

However, when withdrawals are made from an annuity, they are subject to income tax. The amount of tax that is due on a withdrawal depends on a variety of factors, including the individual's tax bracket, the type of annuity, and the amount of the withdrawal.

Annuities can be structured in a variety of ways, and the tax implications of different types of annuities can vary significantly. For example, variable annuities are often subject to more complex tax rules than fixed annuities. In addition, some types of annuities, such as immediate annuities, may be subject to different tax rules than deferred annuities.

In addition to the tax implications of contributions and withdrawals, people should also understand the tax treatment of earnings within an annuity. The earnings on an annuity are also subject to tax when they are withdrawn. However, the tax rate on the earnings may be different than the tax rate on the contributions, depending on a variety of factors.

People should also be aware of the tax treatment of annuity death benefits. When an individual who owns an annuity dies, the death benefit is typically paid out to the individual's beneficiaries. Depending on the type of annuity and the circumstances of the individual's death, the death benefit may be subject to income tax. In addition, the timing of the death benefit payout can also impact the tax treatment of the benefit.

Another important aspect of the taxation of annuities is the impact of surrender charges and fees. Many annuity contracts include surrender charges and fees, which can impact the amount of money that an individual receives when they withdraw money from the annuity. People should understand how surrender charges and fees are calculated, and how they impact the overall value of the annuity.

Finally, people should also be aware of the tax implications of annuity riders. Annuity riders are optional features that can be added to an annuity contract to provide additional benefits or protections. These riders can include features such as guaranteed minimum income benefits, long-term care benefits, and death benefit riders. The tax treatment of annuity riders can vary depending on the specific rider and the circumstances of the individual's annuity contract.

Annuity Benefits and Risks - Annuities are primarily used to provide retirement income, and they come in various types, including fixed, variable, and indexed annuities. However, like any financial product, annuities have benefits and risks that should be understood by anyone considering them. In this chapter, we will discuss the benefits and risks of annuities.

One of the primary benefits of annuities is the potential for guaranteed income. An annuity can provide a guaranteed income stream for a specified period or for the lifetime of the individual. This can be particularly attractive for retirees who want a predictable income stream that will last for the remainder of their lives. Fixed annuities offer a set rate of return, while variable and indexed annuities offer the potential for higher returns.

Another benefit of annuities is tax-deferred growth. Annuities are tax-deferred, which means that the earnings on the investment are not subject to taxes until they are withdrawn. This can be particularly beneficial for individuals who are in a higher tax bracket during their working years and expect to be in a lower tax bracket during retirement.

Finally, annuities can provide a measure of protection against market volatility. Fixed annuities provide a set rate of return, while variable and indexed annuities offer the potential for higher returns. However, even variable and indexed annuities come with guarantees that protect against market losses. For example, many variable and indexed annuities come with minimum guarantees that protect against market losses.

While annuities have many benefits, they also come with risks that should be considered. One risk of annuities is the impact of inflation. Over time, the value of the income stream provided by an annuity can be eroded by inflation. For example, if an individual purchases an annuity that pays \$1,000 per month, the purchasing power of that income will decrease over time as the cost of living increases.

Another risk of annuities is the fees and expenses associated with them. Annuities can come with a variety of fees, including surrender charges, mortality and expense fees, and administrative fees. These fees can be substantial and can eat into the returns provided by the annuity.

Finally, there is the risk of not keeping up with inflation. While annuities can provide a measure of protection against market volatility, they do not offer the same potential for growth as other investments. As a result, individuals who rely solely on annuities for their retirement income may find that their income does not keep up with inflation over time.

Bibliography

Bodie, Zvi; Kane, Alex; Marcus, Alan J. (2018). Investments. McGraw-Hill Education. ISBN 978-1-259-68106-0.

Harrington, S. E., Niehaus, G., & Seward, J. K. (2016). Annuities and Individual Welfare. The Journal of Risk and Insurance, 83(3), 551-578.

IRS. (2021). Topic No. 411 Pensions and Annuities. Retrieved from https://www.irs.gov/taxtopics/tc411 Milevsky, Moshe A. The Calculus of Retirement Income: Financial Models for Pension Annuities and Life Insurance. Cambridge University Press, 2006. ISBN 978-0521842580.

Shao, A. W., & Zhang, H. (2014). The Value of Government Annuities for Longevity Risk Management. Insurance Mathematics and Economics, 58, 158-167.

Wang, T. (2015). Taxation and Investment in Annuities. Journal of Pension Economics and Finance, 14(2), 221-237.