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Chapter 1: Problem 4

If you own \(r\) shares of a stock with an annual dividend of \(p\) dollars, express the amount of your quarterly dividends algebraically.

Short Answer

Expert verified
The algebraic expression for your quarterly dividends is \(\frac{rp}{4}\).

Step by step solution

01

Calculate Annual Dividends

The total annual dividends from owning \(r\) shares with an annual dividend of \(p\) dollars per share can be calculated by multiplying the number of shares (\(r\)) by the annual dividend per share (\(p\)). This gives \(rp\).
02

Calculate Quarterly Dividends

The dividends are distributed quarterly, which means the total annual dividends should be divided by 4 to obtain the quarterly dividends. This gives \(\frac{rp}{4}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Quarterly Dividends
Understanding quarterly dividends is essential for investors receiving periodic payments from their investments. When companies distribute dividends, they often do so on a quarterly basis, meaning four times a year. The quarterly dividend is a portion of the annual dividend paid every three months.

To determine your quarterly dividends, you must start with your annual dividends and then divide by 4. This is because there are four quarters in a year, and dividends are paid out in these periods.
  • Annual dividend total: Represented by the formula where you multiply the number of shares you own (\(r\)) by the annual dividend per share (\(p\)), resulting in \(rp\).
  • Quarterly dividend: The annual dividend (\(rp\)) divided by 4, giving \(\frac{rp}{4}\).
This distribution allows investors to receive a steady income and helps them plan their finances effectively.
Annual Dividends
Annual dividends represent a company's yearly payout to its shareholders as a share of the profits. It is calculated on a per-share basis and often indicates the company's profitability and its earnings distribution strategy.

The total annual dividend you receive can be calculated using the simple multiplication of two factors:
  • Number of Shares (\(r\)): Represents the total number of shares you own in a company.
  • Annual Dividend per Share (\(p\)): The amount paid per share each year.
Together, they give the formula \(rp\), which is your total annual dividend. These dividends provide insight into the company's financial health and can be a reliable source of income for shareholders.
Shares Calculation
Calculating shares is a fundamental aspect of understanding your investment's value and future returns. Shares represent the ownership units in a company, entitling you to dividends and possible voting rights.
  • Number of Shares (\(r\)): The amount of shares you own determines your slice of the company's pie. More shares mean more dividends.
  • Calculation Impact: The total dividends you earn are dependent on the shares you own. By calculating your shares accurately, you can assess your overall investment returns.
When planning investments, understanding how shares and resulting dividends fit into financial growth strategies is vital. This calculation not only affects dividend income but also reflects your influence as an investor in the company's decision-making process.

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Most popular questions from this chapter

Alex purchases \(x\) dollars worth of stock on his broker's advice and pays his broker a 1\(\%\) broker fee. The value of the shares falls to \(y\) dollars years later, and Alex uses a broker who charges 1.25\(\%\) commission to make the sale. Express his net proceeds algebraically.

Mitchell bought 600 shares of Centerco two years ago for \(\$ 34.50\) per share. He sold them yesterday for \(\$ 38.64\) per share. a. What was the percent increase in the price per share? b. What was the total purchase price for the 600 shares? c. What was the total selling price for the 600 shares? d. What was the percent capital gain for the 600 shares? e. How does the percent increase in the price of one share compare to the percent capital gain for all 600 shares?

Mike owns \(2,400\) shares of JDS Uniphase Corp. The company instituted a 1 -for-8 reverse stock split on October \(17 .\) The pre-split market price per share was \(\$ 2.13 .\) a. How many shares did Mike hold after the split? b. What was the post-split price per share? c. Show that the split was a monetary non-event for Mike.

Jon noticed that most traditional splits are in the form \(x\) -for-1. He says that in those cases, all you need do is multiply the number of shares held by \(x\) and divide the price ber share by \(x\) to get the post-split numbers. Answer Exercises \(8-9\) based on Jon's method. Verify that Jon's method works to determine the post-split price and shares outstanding for Hansen Natural Corporation which executed a \(4-\) for-1 split on July 10 with \(22,676,800\) outstanding shares and a market price of \(\$ 203.80\) per share before the split.

Elliott purchased shares of Microsoft in 2008 for \(\$ 28\) per share. He plans to sell them as soon as the price rises 20\(\% .\) At what price will he sell his shares?
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