17 Investments
This chapter introduces foundational concepts in finance related to investing: the time value of money, risk and return, volatility, and diversification.
Time Value of Money
Impact of Time on Saving and Spending
The choice to spend or save and invest is really a choice between consumption today versus consumption in the future. An important aspect of the trade-off between saving and spending involves your short-, intermediate-, and long-term goals. Delaying consumption until later comes with risks. Will your consumption choices still be available? Will the prices be attainable? Will you still be able to consume and enjoy your future purchases?
When saving for short-term objectives, the safety of the principal invested is important, and the value of compounding returns is minimal compared to longer-term investments. Most short-term investors have a low tolerance for risk and hope to beat the rate of inflation with a little extra besides. An example could be to start a holiday savings account at your local bank as a way to save, earn a small rate of return, and assure that you have funds set aside for consumption at the end of the year.
An intermediate investment may be to save for a new car or for the down payment on a house or vacation home. Again, maintaining the principal is important, but you have some time to recover from poor investment returns. Intermediate-term investments tend to earn higher average annual rates of return than short-term investments, but they also have greater uncertainty and risk.
Long-term investments have the advantage of enough time to recover from temporary poor performance and the luxury of compounded returns over a long period. Further, long-term investments tend to have greater risk and higher expected average annual rates of return.
To illustrate, Table 17.1 demonstrates four different investment scenarios. In scenario 1, you invest $5,000 annually from ages 26 through 60 into an account earning an average annual rate of return of 10% per year. Over your lifetime, you invest a total of $175,000, and at age 60, you have an estimated portfolio value of $1,490,634. This is a healthy amount that has almost certainly beaten the average annual rate of inflation. In scenario 1, by investing regularly, you accumulate roughly 8.5 times the value of what you invested.
Compare your results in scenario 1 with your college roommate in scenario 2, who is able to invest $5,000 per year from ages 19 through 25 and leave her investments until age 60 in an account that continues to earn an annual rate of 10%. She makes her investments earlier than yours, but they total only $35,000. However, despite a much smaller investment, her head start advantage and the high average annual compounded rate of return leave her with an expected portfolio value of $1,466,369. Her total is almost as great as the amount you would accumulate, but with a much smaller total investment.
Scenarios 3 and 4 are even more dramatic. In both scenarios, only five $5,000 investments are made, but they are made earlier in the investor’s life. Parents or grandparents could make these investments on behalf of the recipients. In both scenarios, the portfolios grow to amounts greater than those of you or your roommate with smaller total investments. The common factor is that greater time leads to additional compounding of the investments and thus greater future values.
| Average Annual Rate of Return = 10% | ||||
|---|---|---|---|---|
| Assumptions | Scenario 1 | Scenario 2 | Scenario 3 | Scenario 4 |
| Starting investment age | 26 | 19 | 14 | 9 |
| Ending investment age | 60 | 25 | 18 | 13 |
| Total investments | 35 | 7 | 5 | 5 |
| Annual investment | $5,000 | $5,000 | $5,000 | $5,000 |
| Total investment amount | $175,000 | $35,000 | $25,000 | $25,000 |
| Value at age 60 | $1,490,634 | $1,466,369 | $1,838,858 | $2,961,500 |
Time Value of Money Concept
One of the single most important concepts in the study of finance is the time value of money (TVM). This concept puts forward the idea that a dollar received today is worth more than, and therefore preferable to, a dollar received at some point in the future. The three primary reasons for this are that (1) money received now can be saved or invested now and earn interest or a return, resulting in more money in the future; (2) any promise of future payments of cash will always carry the risk of default; and (3) it is simple human nature for people to prefer making their purchases of goods and services in the present rather than waiting to make them at some future time.
The concept of TVM is predicated on the fact that it is possible to earn interest income on cash that you decide to deposit in an investment or interest-bearing account. As times goes by, interest is earned on amounts you have invested (present value), which effectively means that time will add value (future value) to your savings (Figure 17.2). The longer the period of time you have your money invested, the more interest income will accrue. Also, the higher the rate of interest your account or investment is earning, again, the more your money will grow.
Because we can invest our money in interest-bearing accounts and investments, its value can grow over time as interest income accrues or returns are realized on our investments. This concept is referred to as future value (FV). In short, future value refers to how a specific amount of money today can have greater value tomorrow.
Future Value and Compounding
Let’s illustrate the concept with the following example. Your friend is considering putting money in a bank account that will pay 4% interest per year and is particularly interested in knowing how much money they will have one year from now if they deposit $1,000 in this account. By using the TVM principle of future value (FV), you can tell your friend that the answer is $1,040. The additional $40 that will be in the account after one year will be due to interest earned over that time. You can calculate this amount relatively easily by taking the original deposit (also referred to as the principal) of $1,000 and multiplying it by the annual interest rate of 4% for one period (in this case, one year):
Interest Earned = $1,000 × 0.04 = $40
By taking the interest earned amount of $40 and adding it to the original principal of $1,000, you will arrive at a total value of $1,040 in the bank account at the end of the year. So, the $1,040 one year from today is equal to $1,000 today when working with a 4% earning rate. Therefore, based on the concept of TVM, we can say that $1,040 represents the future value of $1,000 one year from today and at a 4% rate of interest.
The Impact of Compounding
What would happen if your friend were willing to wait one more year to receive their lump sum payment? What would the future dollar value in their account be after a two-year period? Returning to our example, assume that during the second year, your friend leaves the principal ($1,000) and the earned interest ($40) in the account, thereby reinvesting the entire account balance for another year. The quoted interest rate of 4% reflects the interest the account would earn each year, not over the entire two-year savings period. So, during the second year of savings, the $1,000 deposit and the $40 interest earned during the first year would both earn 4%:
($1,000 × 0.04) + (40 × 0.04) = $41.60
The additional $1.60 is interest on the first year’s interest and reflects the compounding of interest. Compound interest is the term we use to refer to interest income earned in subsequent periods that is based on interest income earned in prior periods. To put it simply, compound interest refers to interest that is earned on interest. Here, it refers to the $1.60 of interest earned in the second year on the $40 of interest earned in the first year. Therefore, at the end of two years, the account would have a total value of $1,081.60. This consists of the original principal of $1,000 plus the $40 interest income earned in year one and the $41.60 interest income earned in year two.
The amount of money your friend would have in the account at the end of two years, $1,081.60, is referred to as the future value of the original $1,000 amount deposited today in an account that will earn 4% interest every year.
Simple interest applies to year 1 while compound interest or “interest on interest” applies to year 2. This is calculated as follows:
Year 1: $1,000 × 0.04 = $40
Year 2: $1,040 × 0.04 = $41.60
So, the total amount that would be in the account after two years, at 4% annual interest, would be:
$1,000 + $40 + $41.60 = $1,081.60
To determine any future value of money in an interest-bearing account, we multiply the principal amount by 1 plus the interest rate for each year the money remains in the account. From this, we can develop the future value formula:
Future Value = Original Deposit × (1 + r) × (1 + r)
In this formula, the number of times we multiply by (1 + r) depends entirely on the number of years the money will remain in the bank account, earning interest, before it is withdrawn in a final lump sum distribution paid out from the account at the end of the chosen savings period. The 1 in the formula represents the principal amount, or the original $1,000 deposit, which will be included in the final total lump sum payment when the account is closed and all money is withdrawn at the end of the predetermined savings period.
We can write the above equation in a more condensed mathematical form using time value of money notation, as follows:
FV = Future value
PV = Present value
r = Interest rate
n = number of periods
Using these inputs, we have the following formula:
FV = PV × (1 + r)n
With this equation, we can calculate the value of the savings account after any number of years. For example, suppose we are considering 3, 10, and 50 years from the original deposit date at the annual 4% interest rate:
3 years: FV = $1,000 × (1.04)3 = $1,000 × 1.12486 = $1,124.86
10 years: FV = $1,000 × (1.04)10 = $1,000 × 1.48024 = $1,480.24
50 years: FV = $1,000 × (1.04)50 = $1,000 × 7.106683 = $7,106.68
How can this savings account have grown to be so large after 50 years? This question is answered by the impact of compounding interest. Every year, the interest earned in previous years will also earn interest along with the initial deposit. This will have the effect of accelerating the growth of the total dollar value of the account.
This is the important effect of the compounding of interest: money grows in larger and larger increments the longer you leave it in an interest-bearing account. In effect, the compounding of interest over time accelerates the growth of money.
In order to determine the FV of any amount of money, it will always be necessary to know the following pieces of information: (1) the principal, initial deposit, or present value (PV); (2) the rate of interest, usually expressed on an annual basis as r; and (3) the number of time periods that the money will remain in the account (n).
The interest rate is often referred to as the growth rate, or the annual percentage increase on savings or on an investment. When the rate is raised to the power of the number of periods, the formula (1+r)n will yield a number that is commonly referred to as the future value interest factor (FVIF). As a result of this process, as n (time, or the number of periods) increases, the future value interest factor will increase. Also, as r (interest rate) increases, the FVIF will increases. For these reasons, the future value calculation is directly determined by both the interest rate being used and the total amount of time—specifically, the number of periods—being considered.
Present Value and Discounting
There will often be situations when you need to determine the present value (PV) of a cash flow that is scheduled to occur several years in the future. We can again use the formula for present value to calculate a value today of future cash flows over multiple time periods.
An example of this would be if you wanted to buy a savings bond. The face value of the savings bond you have in mind is $1,000, which is the amount you would receive in 30 years (the future value). If the government is currently paying 5% per year on savings bonds, how much will it cost you today to buy this savings bond?
The $1,000 face value of the bond is the future value, and the number of years n that you must wait to get this face value is 30 years. The interest rate r is 5.0% and is the discount rate for the savings bond. Applying the present value equation, we calculate the current price of this savings bond as follows:
PV = $1,000 × (1/(1+0.05)30) = $1,000 × 0.231377 = $231.38
Thus, it would cost you $231.38 to purchase this 30-year, 5%, $1,000 face-valued bond.
What we have done in the above example is reduce, or discount, the future value of the bond to arrive at a value expressed in today’s dollars. Effectively, this discounting process is the exact opposite of compounding interest that we covered earlier in our discussion of future value.
An important concept to remember is that compounding is the process that takes a present valuation of money to some point in the future, while discounting takes a future value of money and equates it to present dollar value terms.
Common applications in which you might use the present value formula include determining how much money you would need to invest in an interest-bearing account today in order to meet your retirement plans 40-50 years from now.
Risk and Return
Risk and return are often referred to as the two Rs of finance. Investors are interested in both risk and return because understanding one without the other is really meaningless. In terms of investment, the concept of return is fairly straightforward; return is the benefit, or profit, the investor expects from an expenditure. It is the reward for investing—the reason an investment is made in the first place. However, no investment is a sure thing. The return may not be what the investor was expecting. This uncertainty about what the return will be is referred to as risk.
Return could be the interest earned on an investment in a bond or the dividend from the purchase of stock. Return could be the higher income received and the greater job satisfaction realized from investing in a college education. Individuals tend to be risk averse. This means that for investors to take greater risks, they must have the expectation of greater returns. Investors would not be satisfied if the average return on stocks and bonds were the same as that for a risk-free savings account. Stocks and bonds have greater risk than a savings account, and that means investors expect a greater average return.
The overall uncertainty of returns has several components:
- Default risk on a financial security is the chance that the issuer will fail to make the required payment. For example, a homeowner may fail to make a monthly mortgage payment, or a corporation may default on required semiannual interest payments on a bond.
- Inflation risk occurs when investors have less purchasing power from the realized cash flows from an investment due to rising prices or inflation.
- Diversifiable risk, also known as unsystematic risk, occurs when investors hold individual securities or smallish portfolios and bear the risk that a larger, more well-rounded portfolio could eliminate. In these situations, investors carry additional risk or uncertainty without additional compensation.
- Non-diversifiable risk, or systematic risk, is what remains after portfolio diversification has eliminated unnecessary diversifiable risk.
- Political risk is associated with macroeconomic issues beyond the control of a company or its managers. This is the risk of local, state, or national governments “changing the rules” and disrupting firm cash flows. Political risk could come about due to zoning changes, product liability decisions, taxation, or even nationalization of a firm or industry.
Volatility
Investors purchase a share of stock hoping that the stock will increase in value and they will receive a positive return. However, even with well-established companies, returns are highly volatile. Investors can never perfectly predict what the return on a stock will be, or even if it will be positive.
Volatility refers to the fluctuations in a security or index over time. Why are stock returns so volatile? The value of the stock of a company changes as the expectations of the future revenues and expenses of the company change. These expectations may change due to a number of events and new information. Good news about a company will tend to result in an increase in the stock price. For example, Delta (ticker symbol DAL) announcing that it will be opening new routes and flying to cities it has not previously serviced suggests that DAL will have more customers and more revenue in future years. Or if CVS announces that it has negotiated lower rent for many of its locations, investors will expect the expenses of the company to fall, leading to more profits. Those types of announcements are often associated with a higher stock price. Conversely, if the pilots and flight attendants for DAL negotiate higher salaries, the expenses for DAL will increase, putting downward pressure on profits and the stock price.
Diversification
Most investors own shares of stock in multiple companies. This collection of stocks is known as a portfolio. Let’s explore why it is wise for investors to hold a portfolio of stocks rather than to pick just one favorite stock to own.
Suppose, for example, you have saved $50,000 that you want to invest. If you purchased $50,000 of DAL stock, you would not be diversified. Your return would depend solely on the return on DAL stock. If, instead, you used $5,000 to purchase DAL stock and used the remaining $45,000 to purchase nine other stocks, you would be diversifying. Your return would depend not only on DAL’s return but also on the returns of the other nine stocks in your portfolio. Investors practice diversification, or owning a variety of stocks in their portfolios, to manage risk.
It is akin to the saying “Don’t put all of your eggs in one basket” (Video 17.1). If you place all of your eggs in one basket and that basket breaks, all of your eggs will fall and crack. If you spread your eggs out across a number of baskets, it is unlikely that all of the baskets will break and all of your eggs will crack. One basket may break, and you will lose the eggs in that basket, but you will still have your other eggs. The same idea holds true for investing. If you own stock in a company that does poorly, perhaps even goes out of business, you will lose the money you placed in that particular investment. However, with a diversified portfolio, you do not lose all your money because your money is spread out across a number of different companies.
Watch Video 17.1: BizBasics: “What is Diversification” with Rich Evans to learn about diversification.
Chapter Review
Optional Resources to Learn More
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Articles |
| “Asset Allocation and Diversification” https://www.finra.org/investors/investing/investing-basics/asset-allocation-diversification | |
| “Going All-in: Investing vs. Gambling” https://www.investopedia.com/articles/basics/09/compare-investing-gambling.asp | |
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Books |
| The Intelligent Investor by Benjamin Graham | |
| The Little Book of Common Sense Investing by John C. Bogle | |
| The Psychology of Money by Morgan Housel | |
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Podcasts |
| Planet Money https://www.npr.org/sections/money/ | |
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Videos |
| William Ackman: Everything You Need to Know About Finance and Investing in Under an Hour https://youtu.be/WEDIj9JBTC8 | |
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Websites |
| Introduction to Investing https://www.investor.gov/introduction-investing | |
| TeenVestor https://www.teenvestor.com/ |
Chapter Attribution
Chapters 1, 7, and 15 of Dahlquist, J. & Rainford, K. (2022). Principles of finance. OpenStax. https://openstax.org/details/books/principles-finance. Licensed with CC BY 4.0.
Media Attributions
Figure 17.2: Rice University. (2022, March 24). Determining future cash flow. OpenStax. https://openstax.org/books/principles-finance/pages/7-4-applications-of-tvm-in-finance#fig-00001. Licensed with CC BY 4.0.
Video 17.1: Darden MBA. (2015, April 13). BizBasics: “What is diversification” with Rich Evans. [Video]. YouTube. https://youtu.be/Z8qGf3_d3PQ
The concept that an amount of money is worth more today than the exact same amount of money at some point in the future.
The amount of money that is paid by a borrower to a lender for the use of their money, typically calculated from an annualized rate.
The value that a current amount will grow to at a given interest rate over a given period of time.
The continual addition of interest to the original principal sum of a loan or deposit, often referred to as interest on interest.
The percentage increase of a specific variable within a specific time period; synonymous with interest rate in the context of the time value of money.
The current value of a future amount, calculated by discounting the future value back at a known discount or interest rate for a specified period of time.
The interest rate used to determine the present value of future cash inflows; may derive from several sources, such as stated contract rates, costs to borrow, or expected rates of return on investments.
The process that takes a present valuation of money to some point in the future.
The process that takes a future value of money and equates it to present dollar value terms.
In finance, the opportunity for profit.
The potential to lose time and money or otherwise not be able to accomplish an organization’s goals.
The risk that the issuer of a financial security will be unable to make payments as specified in the terms of a financial contract.
The risk of reduced purchasing power of goods and services due to rising prices.
Also called unsystematic risk, a risk that can be eliminated without the loss of expected return by holding a portfolio of securities.
Risk that cannot be eliminated by simply holding a portfolio of securities; also known as systematic risk.
The risk of local, state, or national governments “changing the rules” and disrupting firm cash flows.
Fluctuations in a security or index over time.
A collection of financial investments, such as stocks, bonds, mutual funds, certificates of deposit, etc.
Holding a variety of assets in a portfolio, in order to manage risk.
