MAT 152: Mathematics in the Modern World
Module #18 Student Activity Sheet
Name: _________________________________________________________________
Section: ____________ Schedule: ________________________________________
Lesson Title: Solving Problems Involving Stocks
Lesson Objectives: At the end of this module, you should be
able to:
1. Understand the concept of buying stocks.
2. Read stock market table.
3. Solve problems involving stocks.
Class number: _______
Date: ________________
Materials:
Student Activity Sheets, Calculator
References:
Mathematics of Investment, 2nd edition,
by Rogelio M. Hernandez, et al
https://corporatefinanceinstitute.com/res
ources/knowledge/trading investing/stockmarket/
Productivity Tip: At the beginning of each study session, write down the task you’re going to work on. It’s easy
to get sidetracked during a work session, which is where this study tip comes in handy. On a rough sheet of
paper, write down the specific task you’re going to work on and put it on your study table. This will remind you
to maintain your focus on that task as you’re working on it.
A. LESSON PREVIEW/REVIEW
Introduction
The stock market refers to public markets that exist for issuing, buying and selling stocks that trade on a
stock exchange or over-the-counter. Stocks, also known as equities, represent fractional ownership in a
company, and the stock market is a place where investors can buy and sell ownership of such investible
assets. An efficiently functioning stock market is considered critical to economic development, as it gives
companies the ability to quickly access capital from the public. Stock means ownership. As an owner, you
have a claim on the assets and earnings of a company as well as voting rights with your shares. Stocks have
a low barrier to entry. You don't need to already be wealthy to own them. They are the perfect place for a
beginner to start building wealth. No need to save up, raise money or take out a loan to begin collecting shares
of stock that generate profits. Investing in stocks is an excellent way to grow wealth. For long-term investors,
stocks are a good investment even during periods of market volatility — a stock market downturn like the one
we've seen this year simply means that many stocks are on sale. But we also need a good knowledge, intuition
and luck when buying stocks.
B. MAIN LESSON
Content Notes
This document is the property of PHINMA EDUCATION
MAT 152: Mathematics in the Modern World
Module #18 Student Activity Sheet
Name: _________________________________________________________________
Section: ____________ Schedule: ________________________________________
Class number: _______
Date: ________________
Understanding Stocks
Stock is a share in the ownership of a company. The price of the stock is called the market value.
Dividends or the stockholder’s share of corporate earnings, are based on par not on the market value.
Stock prices change according to supply and demand. There are many factors influencing prices, the most
important of which is earnings.
Two main types of stock:
1) Preferred stock is further divided into categories known as non-participating, which means the
stockholders receive only the fixed dividend and no more; and participating means the stockholders
may receive additional dividends if the company does well.
2) Common stock is one of the common stocks. They are observed over time to yield returns for as long
as company is doing well.
Dividends per share for common stock formula is
𝑇𝑜𝑡𝑎𝑙 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑
DPS(𝐶𝑜𝑚𝑚𝑜𝑛 𝑆𝑡𝑜𝑐𝑘) =
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠ℎ𝑎𝑟𝑒𝑠 (𝑐𝑜𝑚𝑚𝑜𝑛)
To solve the amount of dividend:
Dividend = rate of dividend x DPS x no. of shares
Steps to distribute dividends in preferred and common stock follow:
1. If the preferred stock is cumulative, any dividends that are in arrears are paid first; then the preferred
dividend is paid for the current period. When the dividend per share is stated in pesos (no-par stock), go
to Step 2. When the dividend per share is stated in percent (par stock), multiply the par value by the
dividend rate. (The entity that issues a financial instrument like a bond or stock assigns a par value to it.
Par value refers to the "face value" of a security and the terms are interchangeable.) Dividend per
share (preferred) = Par value x Dividend rate
2. Calculate the total amount of the preferred stock dividend by multiplying the number of preferred shares
by the dividend per share.
Total preferred dividend = Number of shares x Dividend per share
3. Calculate the total common stock dividend by subtracting the total preferred stock dividend from the
total dividend declared.
Total common dividend = Total dividend – Total preferred dividend
4. Calculate the dividends per share for common stock by dividing the total common stock dividend by
number of shares of common stock.
Stock is equity, bonds are debt. Bondholders are guaranteed a return on their investment and have a higher
claim than shareholders. This is generally why stocks are considered riskier investments and require a higher
rate of return.
This document is the property of PHINMA EDUCATION
MAT 152: Mathematics in the Modern World
Module #18 Student Activity Sheet
Name: _________________________________________________________________
Section: ____________ Schedule: ________________________________________
Class number: _______
Date: ________________
Let’s have an example,
1. The MAX Corporation has 3,200,000 shares of common stock outstanding. If a dividend of
4,500,000 was declared by the company directors last year, what are the dividends per share of
common stock?
Solution:
Now you try number 2!!!
2. The board of directors of NET Inc. declared a dividend of ₱300,000. The company has 60,000
shares of preferred stock that pay ₱0.50 per share and 100,000 shares of common stock. Calculate
the amount of dividends due the preferred shareholders and the dividend per share of common
stock.
“Check your answers against the Key to Corrections found at the end of this SAS.
Write your score on your paper.”
Skill-building Activities
How to Read A Stock Table
Any financial paper has stock quotes that will look something like the image below:
Column 1: Company Name & Type of Stock (If there are no special symbols or letters following the name, it
is common stock)
Column 2: Ticker Symbol - The unique alphabetic name which identifies the stock.
Column 3: Open - The amount the stock price was at the open of the market.
Column 4 & 5: Day High and Low - The maximum and the minimum prices that people paid for the stock.
Column 6: Close - The close is the last trading price recorded when the market closed on the day.
Column 7 & 8: Net Change and % Change- This is the dollar value change in the stock price from the
previous day's closing price.
Column 9: Trading Volume - The total number of shares traded for the day.
Columns 10 & 11: 52-Week High and Low - The highest and lowest prices at which a stock has traded over
the previous 52 weeks (one year).
This document is the property of PHINMA EDUCATION
MAT 152: Mathematics in the Modern World
Module #18 Student Activity Sheet
Name: _________________________________________________________________
Section: ____________ Schedule: ________________________________________
Class number: _______
Date: ________________
Column 12: Dividend Per Share - The annual dividend payment per share. If this space is blank, the
company does not currently pay out dividends.
Column 13: Dividend Yield - The percentage return on the dividend. Calculated as annual dividends per
share divided by price per share.
Column 14: Price/Earnings Ratio - Calculated by dividing the current stock price by earnings per share from
the last four quarters. For more detail on how to interpret this, see our P/E Ratio tutorial.
Column 15: Year to Date % Change - This describes the return so far for this year. The period beginning 1st
of current year up until today’s date.
The column varies depending on the site format. You may visit the market site and data provider. But all
data are available when you visit the accredited sites. https://www.marketwatch.com/investing/index/nya
https://www.nyse.com
It’s you turn to analyze!
Exercise #1: Analyze the Philippine Stock Exchange (in local currency) and answer the questions
below.
1.
2.
3.
4.
5.
What is the trading volume number of Ayala Land? _______________
What is the last trading price of the day of PLDT Inc? ______________
What is the net change of Megaworld Corporation? ______________
What is the total number of shared traded by SM Prime Holdings INC? ______________
What is the %change of Jollibee Foods Corporation? _____________
This document is the property of PHINMA EDUCATION
MAT 152: Mathematics in the Modern World
Module #18 Student Activity Sheet
Name: _________________________________________________________________
Section: ____________ Schedule: ________________________________________
Class number: _______
Date: ________________
Exercise #2: PHINMA Corporation (PHN), formerly
Bacnotan Consolidated Industries, Inc., was incorporated on March 12, 1957. PHN is a holding company with
investments in the education, steel products, housing, business process outsourcing and energy sectors. On
May 27, 2010, the Securities and Exchange Commission approved the change in corporate name to the
present one.
This document is the property of PHINMA EDUCATION
MAT 152: Mathematics in the Modern World
Module #18 Student Activity Sheet
Name: _________________________________________________________________
Section: ____________ Schedule: ________________________________________
Class number: _______
Date: ________________
*portion of the s
Screenshot from https://www.pse.com.ph/stockMarket/companyInfo.html?id=107&security=184&tab=0
This document is the property of PHINMA EDUCATION
MAT 152: Mathematics in the Modern World
Module #18 Student Activity Sheet
Name: _________________________________________________________________
Section: ____________ Schedule: ________________________________________
Class number: _______
Date: ________________
Directions: Answers the following questions based on the data for May 31,2019:
1. What is the name of company? __________________
2. What is the type of stock? ______________________
3. What name of stock exchange? _________________
4. What is the previous closing price of the stock? ______________
5. What is the opening price? ______________
6. What is the day’s range? ______________
7. What is the 52 Week Range? ___________________
8. What is the number of shares traded? _____________
9. What is the value? ____________________
10. What is the net change? __________
“Check your answers against the Key to Corrections found at the end of this SAS.
Write your score on your paper.”
Check for Understanding
Quiz:
PART A. Solve the following problems.
1. Deep Well Inc. declared a 4.5% dividend on stock with a face value of ₱210. Mr. Santos owned 60
shares. What was the amount of his dividend?
2. Dunkin Coconut declared a ₱1 million dividend on its common stocks. If there were 100,000 such
shares, how much was the dividend per share for common stock?
3. Jackson buys a $40 shares in a company, which pays 10% dividend. Jackson buys the share at such a
price that his profit is 16% on his investment. At what price did Jackson buy the share?
PART B. On the first column, write the word Simple for Simple Interest Rate and write the word
Compound for Compound Interest Rate.
1. Savings Deposit Account of a bank.
2. Time Deposit Account of a bank.
3. Money that doubles after 5 years of maturity.
4. Cash Loan of ₱8,000 that becomes ₱8800 after 2 years at an interest
rate of 5% per years\.
5. An amount of ₱40,000 invested at 2.5% annually that becomes
₱45,256.33 after 5 years.
6. A jewelry priced ₱6420 by January, ₱654.40 by February, and
₱6,676.80 by March.
This document is the property of PHINMA EDUCATION
MAT 152: Mathematics in the Modern World
Module #18 Student Activity Sheet
Name: _________________________________________________________________
Section: ____________ Schedule: ________________________________________
Class number: _______
Date: ________________
7. A credit card unpaid balance of ₱5254.5 becomes ₱5808.89 after 3
months of no payment.
8. Cash Loan of ₱8,000 that becomes P8800 after 2 years at an interest
rate of 5% per year.
9. A dollar deposit account of $450 at PNB with 1.9% annual interest
rate.
10. ₱75,500 invested at 3.7% annually that becomes ₱ 87,309.60 after
4 years
C. LESSON WRAP-UP
Frequently Asked Questions
A) The Top 5 Benefits of Stock Investing
1. Takes advantage of a growing economy: As the economy grows, so do corporate earnings. That's
because economic growth creates jobs, which creates income, which creates sales. The fatter the
paycheck, the greater the boost to consumer demand, which drives more revenues into companies'
cash registers. It helps to understand the phases of the business cycle—expansion, peak, contraction,
and trough.
2. Best way to stay ahead of inflation: Historically, stocks have averaged an annualized return of
10%. That's better than the average annualized inflation rate of 2.9%. It does mean you must have a
longer time horizon. That way, you can buy and hold even if the value temporarily drops.
3. Easy to buy: The stock market makes it easy to buy shares of companies. You can purchase them
through a broker, a financial planner, or online. once you've set up an account, you can buy stocks in
minutes. Some online brokers such as Robin hood let you buy and sell stocks commission-free.
4. Make money in two ways: Most investors intend to buy low and then sell high. They invest in fast
growing companies that appreciate in value. That's attractive to both day traders and buy-and-hold
investors. The first group hopes to take advantage of short-term trends, while the latter expect to see
the company's earnings and stock price grow over time. They both believe their stock-picking skills
allow them to outperform the market. Other investors prefer a regular stream of cash. They purchase
stocks of companies that pay dividends. Those companies grow at a moderate rate.
5. Easy to sell: The stock market allows you to sell your stock at any time. Economists use the term
"liquid" to mean you can turn your shares into cash quickly and with low transaction costs. that’s
important if you suddenly need your money in a hurry. Since prices are volatile, you run the risk of
being forced to take a loss.
B) The Top 5 Disadvantages
1. Risk: You could lose your entire investment. If a company does poorly, investors will sell, sending the
stock price plummeting. When you sell, you will lose your initial investment. If you can't afford to lose
your initial investment, then you should buy bonds. You get an income tax break if you lose money
on your stock loss. You also have to pay capital gains taxes if you make money.
This document is the property of PHINMA EDUCATION
MAT 152: Mathematics in the Modern World
Module #18 Student Activity Sheet
Name: _________________________________________________________________
Section: ____________ Schedule: ________________________________________
Class number: _______
Date: ________________
2. Stockholders paid last: Preferred stockholders and bondholders/creditors get paid first if a company
goes broke. But this happens only if a company goes bankrupt. A well-diversified portfolio should keep
you safe if any one company goes under.
3. Time: If buying stocks on your own, you must research each company to determine how profitable
you think it will be before you buy its stock. You must learn how to read financial statements and
annual reports and follow your company's developments in the news. You also have to monitor the
stock market itself, as even the best company's price will fall in a market correction, a market crash,
or bear market.
4. Emotional roller coaster: Stock prices rise and fall second-by-second. Individuals tend to buy high,
out of greed, and sell low, out of fear. The best thing to do is not constantly look at the price fluctuations
of stocks, just be sure to check in on a regular basis.
5. Professional competition: Institutional investors and professional traders have more time and
knowledge to invest. They also have sophisticated trading tools, financial models, and computer
systems at their disposal. Find out how to gain an advantage as an individual investor.
Thinking about learning (5 mins)
Great Job! Let’s talk about your learning experience.
1. What felt confusing about what you learned today? Why?
________________________________________________________________________________
________________________________________________________________________________
2. What could you have done better to improve your learning today?
________________________________________________________________________________
________________________________________________________________________________
KEY TO CORRECTIONS
Problem #2. (5 points)
This document is the property of PHINMA EDUCATION
MAT 152: Mathematics in the Modern World
Module #18 Student Activity Sheet
Name: _________________________________________________________________
Section: ____________ Schedule: ________________________________________
Class number: _______
Date: ________________
Skill-building Activities
How to Read A Stock Table
Exercise #1 (3 points per item)
1. What is the trading volume number of Ayala Land? 27,118,400
2. What is the last trading price of the day of PLDT Inc? 1,350.00
3. What is the net change of Megaworld Corporation? − 0.02
4. What is the total number of shared traded by SM Prime Holdings INC? 7,313100
5. What is the %change of Jollibee Foods Corporation? 2.13%
Exercise #2 (3 points per item)
1. What is the name of company? PHINMA Corporation
2. What is the type of stock? common
3. What name of stock exchange? Philippine Stock Exchange
4. What is the previous closing price of the stock? 9.08
5. What is the opening price? 17.69
6. What is the day’s range? 9.05 – 9.07
7. What is the 52 Week Range 7.50 – 9.98
8. What is the number of shares traded? 2,000
9. What is the value? 18,120.00
10. What is the net change? – 0.01
This document is the property of PHINMA EDUCATION