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A corporation is having a shareholders meeting. Not all shareholders are able to attend. In fact, most usually do not. The ownership of the corporation is represented by \(2,351,000\) shares of stock owned by \(111,273\) shareholders. a. Must all of the shareholders own more than one share of stock? b. If \(3,411\) shareholders attend the meeting, what percent of the shareholders are represented? Round to the nearest percent. c. If the shareholders who do attend own a combined 1.8 million shares of the corporation, what percent of the shares are represented at the meeting? Round to the nearest percent.

Short Answer

Expert verified
a) No, not all shareholders must own more than one share of stock. b) 3% of the shareholders are represented at the meeting. c) 77% of the shares are represented at the meeting.

Step by step solution

01

Analysis of shareholders stock ownership

Each shareholder can indeed own more than one share because the total number of shares \(2,351,000\) is greater than the total number of shareholders \(111,273\). This means the average number of shares owned by each shareholder (total shares divided by total shareholders) is greater than one.
02

Calculating the percentage of shareholder attendance

The percentage of shareholders in attendance can be calculated by taking the total number of shareholders who attended \(3,411\) and dividing it by the total number of shareholders \(111,273\). After that, multiply the resulting fraction by 100 to convert it into percentage. The formula is: \[ \frac{3411}{111273} \times 100\% \] Solving this, we get \(3.06\%\). But the problem requires the answer to be rounded to the nearest whole number, so the percentage of shareholders represented at the meeting is \(3\%\).
03

Calculating the percentage of shares represented at meeting

The procedure for calculating the percentage of shares represented at the meeting is similar to the previous step, but replacing the number of shareholders in attendance with the number of shares they own collectively and the total number of shareholders with the total number of shares. Hence, the formula is: \[ \frac{1,800,000}{2,351,000} \times 100\% \] Solving this yields \(76.56\%\). Rounding to the nearest percentage, we have \(77\%\).

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Key Concepts

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

Shareholder Meeting
A shareholder meeting is a formal gathering where the owners of a corporation's shares, also known as shareholders, come together to discuss and make decisions about the company's affairs. Such meetings are crucial because they offer a platform for shareholders to voice their opinions, vote on significant issues, and elect the board of directors. They play a pivotal role in corporate governance.
At these meetings, not all shareholders have to attend, but their shares can be represented by others or even through mailed proxies, allowing decisions to be made efficiently. Attendees can be individual investors or representatives of larger groups that own stock in the company. Thus, a shareholder meeting is an intersection of ownership and management, bridging the gap between those who own the company and those who run it.
Stock Ownership
Stock ownership indicates having a piece of a corporation's assets and earnings. When someone owns stock in a company, they effectively own a portion of that company. Stocks are divided into shares, and shareholders can own one, multiple, or even millions of these shares, depending on their investment.
  • Each share represents a fraction of ownership.
  • Shareholders may receive dividends, which are a portion of the company's profits distributed among shareholders.
  • With stock ownership comes both the potential for profit, as the stock’s value might increase, and the risk of loss, should the stock’s value fall.
The number of shares a person owns relative to the total number of shares outstanding affects their level of influence in a company, especially in voting matters during shareholder meetings. For instance, with 2,351,000 total shares in a company and only 111,273 shareholders, the average shareholder owns multiple shares, indicating that not every shareholder holds an equal stake.
Percentage Calculation
Percentage calculation is a mathematical technique used to determine the proportional relationship between two numbers. This method is incredibly useful in evaluating changes, comparing data, and understanding the relationships in financial situations. For instance, to calculate the percentage of shareholder attendance, you compare the number of shareholders who attended against the total number of shareholders.
  • Formula: \[ \left( \frac{\text{number of attendees}}{\text{total shareholders}} \right) \times 100\% \]
  • Example: If 3,411 out of 111,273 shareholders attend, the percentage is calculated as \[ \left( \frac{3411}{111273} \right) \times 100\% = 3.06\% \]
The result is rounded for simplicity, giving a final answer of 3%. Percentage calculations like these are fundamental in financial algebra, helping express complex data in a condensed and more understandable format.
Rounding Numbers
Rounding numbers is a mathematical process to simplify figures to make them easier to understand and work with. This is often done by approximating numbers to the nearest whole number, tenth, hundredth, etc., depending on the context and need for precision.
For example, if you calculate that 76.56% of shares are represented in a meeting, you would round 76.56 to the nearest whole number for simplification, yielding 77%.
  • If a number is 5 or greater, round up to the nearest unit.
  • If it is less than 5, round down.
In financial contexts, rounding helps present data more clearly, making it easier for stakeholders to grasp and utilize. However, one should always balance clarity with the need for precision, especially in complex calculations.

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Most popular questions from this chapter

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