Section PF.4 – Investments


Four Basic Types of Investment Assets
Stock: A unit of ownership in a publicly traded company

Bond: A unit of debt that a company or government offers to investors, paying back interest over time

Cash:  Money available in checking and demand deposit accounts, or other savings account like certificates of deposit (CD), and U.S. treasury bills

Property:  Ownership of a physical item (car, house, art, baseball card, etc.) that might become more valuable over time

Investment Considerations: Liquidity, Risk, and Return

Liquidity refers to the ease with which an asset is turned to cash.  Cash is the most liquid, followed in order by checking accounts, savings accounts, CD’s, stocks and bonds, real estate, and art, which is the least liquid.

Risk is the potential for an investment to lose or make money.  Low risk would be checking and savings, which are insured, followed by bonds, with individual stocks being the riskiest investment.

In general, younger investors have a higher tolerance for risk, since they have more time to recoup any losses.  An older investor, closer to retirement, might want to reduce risk.  They are reducing their chance of losing money but at the cost of reducing their chance to gain money.

Return is the change in value of an investment.  A return can be positive (gain money) or negative (lose money).  Higher risk investments typically have high returns (positive or negative).  Low risk investments

Capital Gains is the profit earned from an investment.  If the investment stays at the same value or loses money then there are no capital gains.  Only positive returns are called capital gains.  This term is often seen when discussing taxes.  Capital gains is considered investment income and typically taxed by governments at a different rate than earned income.

Financial Portfolio is the total list of all investment assets (stocks, bonds, cash, and property).  A Diversified Portfolio has a variety of different types of assets in it.  A diversified portfolio reduces the overall risk of the portfolio, since one asset losing value will not sink the entire portfolio.  This is especially true if you diversify within each asset type (multiple different stocks, different bonds, different properties, etc.).

Stocks

It is important to conduct research on all potential stock purchases, with analysis of the company, their industry, and their potential for growth and profit.  After a stock purchase, there are two main ways to profit from stocks.

  • Sale of Stock: If the price of a share of stock rises then you sell your stock for a profit. The profit is a positive return which is capital gains.  If stocks are sold for less than the original cost, this creates a capital loss.
  • Dividends: A company that earns a profit may decide to share the profit with its shareholders.  Each shareholder is paid an amount of money per share called a dividend.  The more shares a shareholder owns, the greater the dividend, since the dividend is per share.

Individual stocks are the riskiest, but also have the highest potential reward.  It is possible for a company to outperform the general market and rise very high very quickly, earning high rates of returns for investors.  However, the opposite is also true. A company could lose value or even go out of business.  It is possible that investments in individual stocks may result in the total loss of investment dollars.

Stocks are bought and sold on a stock exchange.  The buying and selling of stock is called trading.   Financial firms have brokers who buy and sell stocks based on customer orders.  Sometimes these trades are in individual stocks (which have higher risk and potential reward), and sometimes the trades are for mutual funds.  These specialized funds employ a fund manager who is responsible for doing the research and diversifying the portfolio with multiple stocks.

There are many different mutual funds available, and these investments have a lower risk than individual stocks because of the diversification of the fund among multiple stocks.  Many mutual funds are tied to various sectors, such as Large Capitalization Stocks or Small Capitalization stocks.  Additionally, funds can operate within a particular sector, like energy, utilities, or healthcare.

There are a few different places to research stock offerings and prices.  For general information, sites like Yahoo and Google can provide data.  Many investors rely on the site or app provided by their own brokerage, which is the place they house and trade their stocks.  There are many brokerage firms that handle investments for clients, including Fidelity, Schwab, Robinhood and E-Trade.  And of course, one can find investment news and information on traditional media such as television (CNN, MSNBC) or newspaper (Wall Street Journal).

Reading Stock Tables

Consider the following stock listing for Home Depot on a particular day:

Stock The Home Depot, Inc. SYM HD
52-Week High $347.25 52-Week Low $264.51
Hi $289.47 Lo $285.92
Dividend $8.36 Yield 2.89%
PE Ratio 17.29 Volume 830,227
Close $287.93 Net Change $+0.39

Stock – the name of the company
SYM – stock exchange symbol
52-Week High – the highest the stock price has been in the last year
52-Week Low – the lowest the stock price has been in the last year
Hi – the highest price of the stock in the previous day’s trading.
Lo – the lowest price of the stock in the previous day’s trading.
Dividend – the amount of dividends paid per share in the previous year.
Yield – the percentage of income provided by the dividends alone in the past year.
PE Ratio – the price of a share of stock divided by the earnings per share.
Volume – the total number of shares traded the previous day.
Close – price of the stock at the end of the market day.
Net Change – the change in price of a share of the stock from two previous days before to the previous day.

Example 1
Use the Target Corporation stock table, from a particular day, to answer the questions.

Stock Target Corporation SYM TGT
52-Week High $228.75 52-Week Low $137.16
Hi $157.86 Lo $155.42
Dividend $4.32 Yield 2.76%
PE Ratio 26.05 Volume 819,217
Close $156.50 Net Change $-0.49

a. What were the high and low prices for the past 52 weeks?

b. If you owned 2000 shares of Target Corporation stock last year, what total dividend did you receive?

c. What is the annual return for dividends alone? How does this compare to a bank account offering a 3.85% annual percentage yield rate?

d. How many shares of Target Corporation were traded yesterday?

e. What were the high and low prices for Target Corporation shares yesterday?

f. What was the price at which Target Corporation shares traded when the stock exchange closed yesterday?

g. What was the closing price two days ago?

h. Compute Target Corporation’s annual earnings per share using:

Annual Earnings Per Share = [latex]\frac{Yesterday's~closing~price~per~share}{PE~ratio}[/latex]

a. What were the high and low prices for the past 52 weeks?

High $228.75, Low $137.16

b. If you owned 2000 shares of Target Corporation stock last year, what total dividend did you receive?

2000 shares x $4.32/share = $8640.00

c. What is the annual return for dividends alone? How does this compare to a bank account offering a 3.85% annual percentage yield? 2.76%.

This is lower than the 3.85% you would get from a bank.

d. How many shares of Target Corporation were traded yesterday?

819,217 shares

e. What were the high and low prices for Target Corporation shares yesterday?

High $157.86, Low $155.42

f. What was the price at which Target Corporation shares traded when the stock exchange closed yesterday?

$156.50

g. What was the closing price two days ago?

$156.50 + $0.49 = $156.99

h. Compute Target Corporation’s annual earnings per share using:

Annual Earnings Per Share = [latex]\frac{Yesterday's~closing~price~per~share}{PE~ratio}[/latex] =

$156.50 / $26.05 = $6.01

You Try PF.4.A
Use the Walmart Inc. stock table, from a particular day, to answer the questions.

Stock Walmart Inc. SYM WMT
52-Week High $154.64 52-Week Low $117.27
Hi $153.14 Lo $152.34
Dividend $2.28 Yield 1.50%
PE Ratio 35.81 Volume 1,741,808
Close $152.72 Net Change $+0.19

 

a. What were the high and low prices for the past 52 weeks?

b. If you owned 1500 shares of Walmart stock last year, what total dividend did you receive?

c. What is the annual return for dividends alone? How does this compare to a bank account offering a 2.85% annual percentage yield?

d. How many shares of Walmart were traded yesterday?

e. What were the high and low prices for Walmart shares yesterday?

f. What was the price at which Walmart shares traded when the stock exchange closed yesterday?

g. What was the closing price two days ago?

h. Compute Walmart’s annual earnings per share using:

Annual Earnings Per Share = [latex]\frac{Yesterday's~closing~price~per~share}{PE~ratio}[/latex]

Reading Stock Tables

A bond is a unit of debt that a company or government offers to investors, paying back interest over time.  Domestic bonds are bought from withing the United States.  Foreign bonds are from foreign companies or countries.  Bonds are the next level of risk, considered less risky than stocks because bond holders are first to receive liquidated assets if a company does declare bankruptcy.  Government bonds are considered to be safer than corporate bonds because the chances of the government defaulting on its debts is usually lower than any particular company.  The most common type of U.S government bond is a standard Savings Bond, which is available to purchase at many different face values, from $20 to $1000 and more.  Purchasers pay half the face value up front, and the bond accrues interest for the time to maturity, usually 30 years.  After this maturity period, the bond will be worth the face value, and it will continue to accrue interest for as long as it is held.  The potential return on bonds is lower than stocks because of the lower risk factor, and the fact that bond returns are set from purchase.

Cash

In the United States, cash in bank accounts is the lowest risk of all these investments, and for this reason has the lowest potential reward.  The federal government insures deposits in most banks through the Federal Deposit Insurance Corporation (FDIC), up to $250,000 per account.  The rate of return on savings accounts has been at historic lows through 2021, and though it has risen since then, the rate still represents a lower potential return than other investments.

Banking accounts types range from checking to savings to CDs and Money Markets.  Checking accounts are accessible with debit cards and checks but usually pay no interest.  Traditional savings accounts are accessed by ATM or transfer.  These savings accounts earn interest, and the interest rate is based on the main rates set by the Federal Reserve.  So rates can rise or fall in these accounts which is called floating.  Many financial experts believe that investors should maintain an emergency fund of three to six months of living expenses, and usually these emergency funds are kept in very liquid accounts like savings since potentially they need to be available immediately.  Certificates of Deposit (CDs) are timed deposits that require the investor to commit money for a period of time, usually somewhere between six months and five years, in different increments.  The rate of interest is fixed for the entire time period, and the rate rises as the period is increased.  CDs are unique in that they have less risk if the floating interest rate falls during that time because the rate is fixed and cannot go down.  At the same time, if the rates are rising, there is more risk because the rate cannot float up.  Since the money is tied up for some time period, that is also a greater risk if one needs access to the funds before the end of the period.  If investors have other opportunities and need capital, they may have to borrow or pay a penalty to get their CD money early.  Money Markets are special funds that usually have a higher rate of interest but may require larger minimum balances to get that rate.

Retirement Accounts

Saving for retirement is a common activity, and the U.S. government offers tax incentives to people who save for their future retirement.  Individual Retirement Accounts, or IRAs, are accounts that let people save money tax deferred; the money they put in these accounts is untaxed until it is used later in life.  Savers are allowed to put aside up to $6000 per year in this tax-deferred method which is also called a traditional IRA.  Roth IRAs are a similar instrument, but the money taxed before it is invested and is thus tax-free upon when it is used later in life.  There are various scenarios where a traditional IRA or Roth IRA might be better from a financial standpoint.

Another form of retirement savings is a 401K or 403B, named after the section of the tax code that created them.  These accounts are linked to employers, and savers can invest up to about $15,000 per year through these programs.  Some companies will match contributions of employees, further increasing the amount of money invested.

All these retirement accounts are designed to be long-term, with penalties for early withdrawals.  The money is available after age 59 and a half, and money needs to start being disbursed at age 70 and a half.

Example 2
An investor purchased 600 shares of stock for $84.64 per share and sold them later for $88.72 per share.  The broker’s commission was 1.6% of the purchase price and 1.6% of the selling price.  Find the amount the investor gained or lost on the stock.
Bought 600 shares x $84.64per share. 600(84.64) = -50,784.00
1.6 % commission on the purchase of the shares. 0.016(50,784) = -812.54
Sold 600 shares x $88.72 per share. 600(88.72) = 53,232.00
1.6 % commission on the sale of the shares. 0.016(53,232) = -851.71
Total +783.75

The investor will gain $783.75.

Example 3
An investor purchased 480 shares of stock at $62.50 per share. She later sold it at $59.80.  The broker’s commission on the purchase was 1.4% and 1.9% on the sale.  Find the amount of money the investor made or lost on the stock.
Bought 480 shares x $62.50 per share. 480(62.50) = -30,000.00
1.4 % commission on the purchase of the shares. 0.014(30,000) = -420.00
Sold 480 shares x $59.80 per share. 480(59.80) = 28,704.00
1.9 % commission on the sale of the shares. 0.019(28,704) = -545.38
Total -2261.38

The investor will lose $2261.38.

You Try PF.4.B
An investor purchased 350 shares of stock at $71.04 per share. She later sold it at $92.66.  The broker’s commission on the purchase was 1.5% and 2.5% on the sale.  Find the amount of money the investor made or lost on the stock.

Remember that a mutual fund is a collection of stocks that is managed by a fund manager. Fund managers are paid a percentage of the fund’s value, called a management or expense fee.  It is important to know the management fee when choosing what mutual funds to invest in.

Example 4
Mutual Fund A has 7.2% rate of return and a management fee of 1%.  Mutual Fund B has an 8.1% rate of return and a management fee of 2%.  Which is a better investment?
Mutual Fund A Mutual Fund B
Rate of Return 7.2% 8.1%
Management Fee 1% 2%
Real Rate of Return 7.2% – 1% = 6.2% 8.1% – 2% = 6.1%

Mutual Fund A is the better investment even though it has a lower rate of return.

Example 5
Suppose that you buy 300 shares of stock at $28.00 in a company that pays an annual dividend of $1.92 per share, then sell all of your shares at $41.00 five years later.  Not including commission fees, what would your profit be five years later?
Profit from Dividend $576.00
$2880.00
Bought 300 shares -$8400.00
Sold 300 shares $12,300.00
Profit on 300 shares 12300 – 8400 = $3,900.00
Total Profit $2880 + $3900 = $6,780.00

Not including commission fees, the investor will make a profit of $6,780.00.

Example 6
Shares of stock reached a low of $3.79 on December 18, 2020.  One year later, the stock closed at $9.53.  Suppose you had invested $30,000.00 in the stock on 12/18/2020, buying as many whole shares as possible.  You paid an online brokerage fee of $39.99 for the purchase, and then sold the stock a year later with the same fee.  How much profit would you have made?
Bought Shares [latex]\frac{$30,000}{1}[/latex] • [latex]\frac{1~share}{$3.79}[/latex] = 7,915 shares
7915 shares x $3.79 = $29.997.85
Sold Shares [latex]\frac{7915~shares}{1}[/latex] • [latex]\frac{$9.53}{1~share}[/latex] = $74,429.95
Bought Shares -$29,997.85
Brokerage Fee -$39.99
Sold Shares +$75,429.95
Brokerage Fee -$39.99
Total Profit $45,352.12

You would have made $45,352.12 profit.

You Try PF.4.C
Shares of stock reached a low of $223.97 on August 12, 2021.  One year later, the stock closed at $315.88.  Suppose you had invested $10,000.00 in the stock on 8/12/2021, buying as many whole shares as possible.  You paid an online brokerage fee of $29.99 for the purchase, and then sold the stock a year later with the same fee.  How much profit would you have made?

Section PF.4 – Answers to You Try Problems

PF.4.A
a. High $154.64, Low $117.27
b. $3,420.00
c. 1.5%, The bank is offering a better rate
d. 1,741,808 shares
e. High $153.14, Low $152.34
f. $152.72
g. $152.53
h. $4.26

PF.4.B
Made $6,383.26

PF.4.C
Profit $3984.06

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College Mathematics - MAT14X - 3rd Edition Copyright © by Adam Avilez; Shelley Ceinaturaga; and Terri D. Levine is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License, except where otherwise noted.

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