Math Problem Statement

Question content area top Part 1 Use the stock table below to answer parts a through g. Assume that the data for Company XYZ stock came from an online quote you looked at during lunch. Company XYZ (XYZ)

Market Cap​ ($ millions) 87 comma 157 Last Change ​%Change Volume ​P/E ratio 17.59 15.89 plus0.38 2.45 68 comma 000 comma 000 Open High Low Dividend​ (latest quarter) 0.74 14.17 16.28 13.26 ​52-Week High ​52-Week Low Dividend Yield 18.63​% 21.08 11.13 Shares Outstanding​ (millions) 5485 Question content area bottom Part 1 a. What is the symbol for Company XYZ​ stock? The symbol is XYZ. Part 2 b. What was the price per share at the end of the day​ yesterday? ​$    15.51 ​(Round to the nearest cent as​ needed.) Part 3 c. Based on the current​ price, what is the total value of the shares that have been traded so far​ today? ​$    1,081 million ​(Round to the nearest whole number as​ needed.) Part 4 d. What percentage of all Company XYZ shares have been traded so far​ today?    1.24​% ​(Round to the nearest hundredth as​ needed.) Part 5 e. Suppose you own 50 shares of Company XYZ. Based on the current price and dividend​ yield, what total dividend should you expect to receive this​ year? ​$______?    enter your response here ​(Round to the nearest cent as​ needed.)

Solution

Let's go step-by-step through each part of the problem using the given data from the stock table.

Part 1a:

The symbol for Company XYZ stock is XYZ (already provided).

Part 1b:

To find the price per share at the end of the day yesterday, use the following:

  • Last price: $15.89
  • Change: +$0.38

The price at the end of yesterday would be the current price minus today's change: Yesterday’s price=15.890.38=15.51\text{Yesterday's price} = 15.89 - 0.38 = 15.51 Thus, the price per share at the end of yesterday is $15.51 (rounded to the nearest cent).

Part 1c:

To find the total value of the shares traded today, use:

  • Volume traded: 68,000,000 shares
  • Current price: $15.89

The total value of shares traded today is calculated as: Total value=Volume×Current price\text{Total value} = \text{Volume} \times \text{Current price} Total value=68,000,000×15.89=1,080,520,000\text{Total value} = 68,000,000 \times 15.89 = 1,080,520,000 Rounded to the nearest million: Total value=1,081million\text{Total value} = 1,081 \, \text{million} Thus, the total value of shares traded today is $1,081 million.

Part 1d:

To find the percentage of all Company XYZ shares that have been traded today, use:

  • Volume traded: 68,000,000 shares
  • Shares outstanding: 5,485,000,000 shares

The percentage of shares traded is calculated as: Percentage traded=(VolumeShares outstanding)×100\text{Percentage traded} = \left(\frac{\text{Volume}}{\text{Shares outstanding}}\right) \times 100 Percentage traded=(68,000,0005,485,000,000)×100=1.24%\text{Percentage traded} = \left(\frac{68,000,000}{5,485,000,000}\right) \times 100 = 1.24\% Thus, 1.24% of all Company XYZ shares have been traded so far today.

Part 1e:

To find the total dividend you would expect to receive for the year, use:

  • Number of shares owned: 50 shares
  • Dividend yield: 18.63%
  • Current price: $15.89

First, calculate the annual dividend per share: Dividend per share=Dividend yield×Current price\text{Dividend per share} = \text{Dividend yield} \times \text{Current price} Dividend per share=0.1863×15.89=2.96\text{Dividend per share} = 0.1863 \times 15.89 = 2.96 Now, calculate the total dividend for 50 shares: Total dividend=2.96×50=148.00\text{Total dividend} = 2.96 \times 50 = 148.00 Thus, the total dividend you should expect to receive this year is $148.00.


Would you like more details on any of the parts or have any questions? Here are some follow-up questions that might be helpful:

  1. How do we calculate the change in stock price based on the day's performance?
  2. What does the P/E ratio indicate in the stock table, and how is it used?
  3. How would a different dividend yield affect your expected total dividend?
  4. How can stock volume affect the stock price during the day?
  5. How does the market capitalization relate to the company's overall stock value?

Tip: When calculating percentage changes or yields, always ensure you have the correct base value (in this case, the current price) for accurate results.

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Math Problem Analysis

Mathematical Concepts

Stock Market Mathematics
Percentages
Multiplication
Dividend Yield Calculations

Formulas

Yesterday's price = Current price - Today's change
Total value = Volume traded × Current price
Percentage traded = (Volume traded / Shares outstanding) × 100
Dividend per share = Dividend yield × Current price
Total dividend = Dividend per share × Number of shares owned

Theorems

Basic Stock Market Math Theorems
Percentage Calculation

Suitable Grade Level

Grades 9-12