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Math 126 Survey - Preferred Stock - Annual Dividend










































Preferred Stock – Annual Dividend

Keyes Corporation preferred stock pays an annual dividend of $7 per share.

Which of the following statements is true for an investor with a required return of 9%?

(Points : 1)

The value of the preferred stock is $7 because the dividend is fixed at $7 each year.

The value of the preferred stock is $63.00 per share.

The value of the preferred stock is $77.78 per share.

The value of the preferred stock is $6.30 per share because of the 9% required return.


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Aug 02, 2012
Preferred Stock - Annual Dividend
by: Staff


Part I

Answer:

The question asks about a 9% return.

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Before I answer your question, I’m going to take a little space to review the definition and use of a percent.

Think about what a percent means in real terms – about the definition of a percent.

9% expresses a proportion. You are already familiar with proportions such as 1/3, or ¼, or 1/5, etc.

In fact, if someone asked you to give them ¼ of a berry pie, you know exactly what that means: cut the berry pie into four pieces, and give one of the pieces to the person who asked for one-fourth.

Similarly, if someone asked you to give them 2/3 of an apple, you would also know what that means: cut the apple into three pieces, and give two of the pieces to the person who asked for two-thirds.


A percent should be viewed in exactly the same light. However, a proportion which stands for a percent always has a denominator equal to 100.

The following proportions stand for a percentage: 10/100 (stands for 10%), 15/100 (stands for 15%), 37/100 (stands for 37%), etc.

Notice that the denominator is always 100.

If someone asked you to give them 10/100 (that’s 10%) of a dollar, you would divide the dollar into 100 pieces (by converting the dollar to pennies), and give 10 pieces (10 pennies) to the person who asked for 10/100.

If someone asked you to give them 37/100 (that’s 37%) of a dollar, you would divide the dollar into 100 pieces (by converting the dollar to pennies), and give 37 pieces (37 pennies) to the person who asked for 37/100.

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Aug 02, 2012
Preferred Stock - Annual Dividend
by: Staff


Part II


Back to your immediate problem.

A 9% return represents a proportion of 9/100.

What is the value of the preferred stock that pays an annual dividend of $7 per share?

(Mathematically, it’s just like dividing up the berry pie. However, in this case you keep the entire berry pie AND ALSO receive a dividend of 9/100 more berry pie.)

(your 9% proportion) * (value of stock) = $7

(9/100) * (value of stock) = $7


Multiply each side of the equation by 100

(9/100) * (value of stock) * 100 = $7 * 100

9 * (value of stock) * (100 / 100)= $7 * 100

9 * (value of stock) * (1)= $7 * 100

9 * (value of stock) = $700


Divide each side of the equation by 9

9 * (value of stock) / 9 = $700 / 9

(value of stock) * (9 / 9) = $700 / 9

(value of stock) * (1) = $700 / 9

(value of stock) = $700 / 9

(value of stock) = $77.7778

(value of stock) = $77.78

>>> the final answer to your question is: $77.78


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Usually it will be easier to work with decimals rather than fractions. Your teacher will expect you to use decimals.

If you use decimals, the equation would be:

(your 9% proportion) * (value of stock) = $7

(9/100) * (value of stock) = $7

(.09) * (value of stock) = $7

(.09) * (value of stock) / (.09) = $7 / (.09)

(value of stock) * (.09 / .09) = $7 / (.09)


(value of stock) * ( 1) = $7 / (.09)

(value of stock) = $7 / (.09)

(value of stock) = $77.7778

(value of stock) = $77.78




Thanks for writing.

Staff
www.solving-math-problems.com


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