Math Problem Statement

A company had the following activity during the year: Net Income = TZS 100,000,000 No preferred dividends Shares outstanding at the beginning of the year = 500,000 shares Issued 100,000 additional shares halfway through the year. Required: Estimate the earnings per share from this company.

Solution

To estimate the earnings per share (EPS) for this company, we need to calculate the weighted average number of shares outstanding during the year and then divide the net income by this number.

Step 1: Calculate the weighted average number of shares

The company had:

  • 500,000 shares at the beginning of the year.
  • 100,000 additional shares issued halfway through the year (6 months after the start).

The weighted average number of shares takes into account how long each group of shares was outstanding during the year.

  • 500,000 shares were outstanding for the full year (12 months).
  • 100,000 shares were outstanding for only 6 months.

Now, we calculate the weighted average number of shares:

Weighted average shares=(500,000×12/12)+(100,000×6/12)\text{Weighted average shares} = (500,000 \times 12/12) + (100,000 \times 6/12)

Weighted average shares=500,000+50,000=550,000 shares\text{Weighted average shares} = 500,000 + 50,000 = 550,000 \text{ shares}

Step 2: Calculate the Earnings Per Share (EPS)

Now, we can calculate the earnings per share using the formula:

EPS=Net IncomeWeighted Average Shares\text{EPS} = \frac{\text{Net Income}}{\text{Weighted Average Shares}}

EPS=100,000,000550,000\text{EPS} = \frac{100,000,000}{550,000}

EPS=181.82 TZS per share\text{EPS} = 181.82 \text{ TZS per share}

Conclusion:

The estimated earnings per share (EPS) for the company is TZS 181.82.

Would you like further details or have any questions on this calculation? Here are some related questions for you to explore:

  1. How would the EPS change if the company issued 100,000 shares at the start of the year instead of halfway?
  2. What is the difference between basic and diluted EPS?
  3. How do stock splits affect the calculation of EPS?
  4. Why is the weighted average number of shares used instead of the total number of shares outstanding at the end of the year?
  5. How would EPS be affected if the company had preferred dividends?

Tip: Always account for the timing of share issuance to accurately calculate the weighted average number of shares.

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Math Problem Analysis

Mathematical Concepts

Financial Mathematics
Earnings Per Share (EPS)
Weighted Average Shares
Basic Arithmetic

Formulas

EPS = Net Income / Weighted Average Shares
Weighted Average Shares = (Shares1 * Time1/Total Time) + (Shares2 * Time2/Total Time)

Theorems

Weighted Average Shares Calculation

Suitable Grade Level

Grades 10-12