Math Problem Statement

In each case in the following​ table, A Cumulative 80 4.00 3 B Noncumulative 110 2.0 2 C Noncumulative 100 3.00 1 D Cumulative 60 1.5 4 E Cumulative 70 3.0 0​, how many dollars of preferred dividends per share must be paid to preferred stockholders before common stock dividends are​ paid?

Question content area bottom

Part 1 The amount of preferred dividends that must be paid in Case A before common dividends are paid is $16.00 ​(Round to the nearest​ cent.)

Part 2

The amount of preferred dividends that must be paid in Case B before common dividends are paid is

​$2.00 (Round to the nearest​ cent.)

Solution

In order to determine how much preferred dividends must be paid to preferred stockholders before common stock dividends are paid, we need to understand the key terms in the table:

  1. Cumulative vs Noncumulative:

    • If the preferred stock is cumulative, any missed dividend payments in previous years must be paid before any dividends are paid to common stockholders.
    • If the preferred stock is noncumulative, only the current year’s dividend must be paid before paying common stockholders.
  2. Par Value: The dollar value of the preferred stock (face value of the stock).

  3. Dividend Rate: This percentage or dollar figure is the annual dividend that the preferred stockholders are entitled to.

Now, let’s calculate the preferred dividends in each case:

Case A: Cumulative, $80 par value, 4.00% dividend, 3 years unpaid

  • The dividend is cumulative, and 3 years' worth of dividends have been unpaid.
  • Dividend per year = 4.00% of $80 = 4100×80=3.2\frac{4}{100} \times 80 = 3.2 dollars per share per year.
  • Since dividends are cumulative and unpaid for 3 years:
    • Total dividends = 3.2×3=9.63.2 \times 3 = 9.6 dollars.
    • Plus the current year's dividend = 3.2 dollars.
    • Total dividends = 9.6+3.2=12.89.6 + 3.2 = 12.8 dollars per share.

However, the prompt states the dividend for this case is $16.00, so there might be rounding factors or additional clarification not captured in this basic model.

Case B: Noncumulative, $110 par value, 2.00% dividend, 2 years unpaid

  • The dividend is noncumulative, so only the current year’s dividend is paid.
  • Dividend per year = 2.00% of $110 = 2100×110=2.2\frac{2}{100} \times 110 = 2.2 dollars per share per year.
  • Since the dividend is noncumulative, we only pay the current year’s dividend.
    • Total dividends = 2.2 dollars per share (this differs from the $2.00 amount stated).

Case C: Noncumulative, $100 par value, 3.00% dividend, 1 year unpaid

  • Noncumulative means only the current year’s dividend is paid.
  • Dividend per year = 3.00% of $100 = 3100×100=3\frac{3}{100} \times 100 = 3 dollars per share per year.
  • Since it is noncumulative:
    • Total dividends = 3 dollars per share.

Case D: Cumulative, $60 par value, 1.5% dividend, 4 years unpaid

  • Dividend per year = 1.5% of $60 = 1.5100×60=0.9\frac{1.5}{100} \times 60 = 0.9 dollars per share per year.
  • Since dividends are cumulative and unpaid for 4 years:
    • Unpaid dividends for 4 years = 0.9×4=3.60.9 \times 4 = 3.6 dollars.
    • Plus the current year’s dividend = 0.9 dollars.
    • Total dividends = 3.6+0.9=4.53.6 + 0.9 = 4.5 dollars per share.

Case E: Cumulative, $70 par value, 3.00% dividend, 0 years unpaid

  • Dividend per year = 3.00% of $70 = 3100×70=2.1\frac{3}{100} \times 70 = 2.1 dollars per share per year.
  • No years unpaid.
    • Total dividends = 2.1 dollars per share.

Final Overview of Dividend Amounts:

  1. Case A: $16.00 (according to the prompt, though calculated $12.80)
  2. Case B: $2.00 (according to the prompt)
  3. Case C: $3.00
  4. Case D: $4.50
  5. Case E: $2.10

Do you need further clarifications or have any additional questions?

Relative Questions:

  1. How does the par value of stock influence dividend payments?
  2. What is the key difference between cumulative and noncumulative preferred stock?
  3. How are missed dividends treated in cumulative preferred stock?
  4. How do you calculate the percentage dividend for preferred stock?
  5. What happens if a company fails to pay cumulative preferred dividends for several years?

Tip:

Always ensure to distinguish between cumulative and noncumulative dividends when calculating payments, as missed payments in cumulative cases compound over time.

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Math Problem Analysis

Mathematical Concepts

Percentage Calculation
Cumulative vs Noncumulative Dividends
Par Value

Formulas

Dividend per year = (Dividend Rate / 100) × Par Value
Total Dividends for Cumulative = (Dividend per year × Unpaid years) + Current year’s dividend
Total Dividends for Noncumulative = Dividend per year

Theorems

Dividend Payment Rules for Preferred Stock

Suitable Grade Level

Grades 10-12