Math Problem Statement

Calculate the preferred and common dividend per share for a personal electronics manufacturer with 1,000,000 preferred shares (7%, $100 par value), 9,000,000 common stock shares, and a total declared dividend of $5,000,000. The preferred stock is non-cumulative, and no arrears are declared.

Solution

To solve this, we calculate the preferred dividend per share and the common dividend per share based on the given data. Here’s the breakdown:

Step 1: Preferred Dividend per Share

The formula for the preferred dividend per share is: Preferred Dividend/Share=Total Preferred DividendNumber of Preferred Shares\text{Preferred Dividend/Share} = \frac{\text{Total Preferred Dividend}}{\text{Number of Preferred Shares}}

From the table:

  • Total Preferred Dividend = $5,000,000
  • Number of Preferred Shares = 1,000,000

Preferred Dividend/Share=5,000,0001,000,000=5$ per share.\text{Preferred Dividend/Share} = \frac{5,000,000}{1,000,000} = 5 \, \text{\$ per share.}

Step 2: Common Dividend per Share

Since the preferred stock is non-cumulative and no arrears are declared, the common shareholders do not receive a dividend if the total dividend of $5,000,000 is fully allocated to preferred shareholders. This means the Common Dividend/Share is:

Common Dividend/Share=NONE.\text{Common Dividend/Share} = \text{NONE.}

Final Answers:

  • Preferred Dividend per Share: $5
  • Common Dividend per Share: NONE

Would you like a detailed explanation of any of the steps? Here are five related questions to consider:

  1. What is the significance of cumulative vs. non-cumulative preferred stock in dividends?
  2. How would the result change if declared arrears existed for the preferred shares?
  3. What happens if the company declares a larger dividend than $5,000,000?
  4. How does the dividend yield affect investor decisions for preferred stock?
  5. How is the dividend per share affected when the number of shares increases?

Tip: Always check whether preferred stock is cumulative or non-cumulative when calculating dividends; this determines whether past unpaid dividends impact current payments.

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Math Problem Analysis

Mathematical Concepts

Dividend Distribution
Preferred vs. Common Stock

Formulas

Preferred Dividend/Share = Total Preferred Dividend / Number of Preferred Shares
Common Dividend/Share = Total Remaining Dividend / Number of Common Shares

Theorems

Dividend Distribution Rule for Preferred and Common Stock

Suitable Grade Level

Undergraduate (Finance/Accounting)