Math Problem Statement

What is the value​ (today's price) of a preferred stock that pays an annual dividend of ​$2.37 when the required rate of return is 8.6 ​percent? What is the value when the required rate of return changes to 5.7 percent and 13.9 ​percent? Question content area bottom Part 1 The value of a preferred stock that pays an annual dividend of ​$2.37 when the required rate of return is 8.6 percent would be ​$

enter your response here. ​ (Round to the nearest​ cent.) Part 2 When the required rate of return changes to 5.7 ​percent, the value of the preferred stock would be ​$

enter your response here. ​(Round to the nearest​ cent.) Part 3 When the required rate of return changes to 13.9 ​percent, the value of the preferred stock would be ​$

enter your response here. ​ (Round to the nearest​ cent.)

Solution

The value of a preferred stock can be calculated using the formula:

P=DrP = \frac{D}{r}

Where:

  • PP = Price of the preferred stock
  • DD = Annual dividend
  • rr = Required rate of return (as a decimal)

Part 1: Required rate of return = 8.6% (r=0.086r = 0.086)

P=2.370.086=27.56P = \frac{2.37}{0.086} = 27.56

The value of the preferred stock is $27.56.


Part 2: Required rate of return = 5.7% (r=0.057r = 0.057)

P=2.370.057=41.58P = \frac{2.37}{0.057} = 41.58

The value of the preferred stock is $41.58.


Part 3: Required rate of return = 13.9% (r=0.139r = 0.139)

P=2.370.139=17.05P = \frac{2.37}{0.139} = 17.05

The value of the preferred stock is $17.05.


Final Values:

  1. At 8.6% required return: $27.56
  2. At 5.7% required return: $41.58
  3. At 13.9% required return: $17.05

Do you need further explanation on this calculation or related topics?

Related Questions:

  1. How does a higher required rate of return impact the value of a preferred stock?
  2. Why is the value of the preferred stock inversely proportional to the required rate of return?
  3. What is the formula used to calculate the value of a preferred stock, and why does it work?
  4. How do changes in interest rates affect the required rate of return for stocks?
  5. What is the difference between preferred stock and common stock valuation?

Tip:

Always compare the required rate of return to the market's prevailing rates to determine whether a preferred stock is a

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Math Problem Analysis

Mathematical Concepts

Finance
Stock Valuation
Proportional Relationships

Formulas

P = D / r

Theorems

Inversely proportional relationship between price and rate of return

Suitable Grade Level

Undergraduate (Finance or Economics) or Advanced High School (AP Economics/Finance)