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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

Use the following spreadsheet to answer Exercises 13鈥�15. The split-ratio is entered in cells B2 and C2. For example, the ratio of 2-for-1 would be entered as a 2 in B2 and a 1 in C2. The number of pre-split shares is entered in B3 and the pre-split price is entered in B4. Write the spreadsheet formula that will calculate the post-split number of outstanding shares in C3. $$\begin{array}{|c|c|c|c|}\hline & {A} & {B} & {C} & {} \\ \hline 1 & {} & {\text { Pre-split }} & {\text { Post-spit }} \\ \hline 2 & {\text { Split ratio }} & {2} & {1} \\ \hline 3 & {\text { Outstanding shares }} & {} & {} \\\ \hline 4 & {\text { Price per share }} & {} & {} \\ \hline 5 & {\text { Market cap }} & {} & {} \\ \hline\end{array}$$

For Exercises \(12-15\) , round answers to the nearest tenth of a percent. The Revreg Corporation pays an annual dividend of \(\$ 1.60\) per share. On Friday it closed at \(\$ 44\) per share with a net change of \(+0.35 .\) The dividend did not change. a. What was the yield on Friday? b. At what price did Revreg close on Thursday? c. What was the yield at Thursday's close? d. Thursday's net change was + \(1.22 .\) At what price did Reverg close on Wednesday?

Julie and Kristen are the partners in a local sporting goods shop. They needed \(\$ 51,000\) to start the business. They invested in the ratio \(5 : 12,\) a. How much money did each invest? b. What percent of the business was owned by Kristin? Round to the nearest tenth of a percent. If the business grows to \(\$ 3,000,000,\) what percent of it will Julie own? Round to the nearest tenth of a percent.

The Walt Disney Company paid a \(\$ 0.35\) annual dividend on a day it closed at a price of \(\$ 33.86\) per share. a. What was the annual dividend for 500 shares? b. What was the quarterly dividend for 500 shares? c. Express the yield as a fraction. d. What was the yield to the nearest tenth of a percent?

Kristy owns 200 shares of Nortel stock. On November 30 the company instituted a 1 -for-10 reverse split. The pre-split price per share was \(\$ 2.15\) . The number of shares outstanding before the split was 4.34 \(\mathrm{B}\) . a. How many shares did Kristy hold after the split? b. What was the post-split price per share? c. What was the post-split number of outstanding shares? d. What was the post-split market cap?
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