You have recently learned that the company where you work is being sold for $275,000. The company’s income statement indicates current profits of $10,000 which have yet to be paid out as dividends. Assuming the company will remain a “growing concern” into the infinite future and that the interest rate will remain constant at 10%, at what constant rate does the owner believe the profits will grow? Does this seem reasonable?

Question

You have recently learned that the company where you work is being sold for $275,000. The company’s income statement indicates current profits of $10,000 which have yet to be paid out as dividends. Assuming the company will remain a “growing concern” into the infinite future and that the interest rate will remain constant at 10%, at what constant rate does the owner believe the profits will grow? Does this seem reasonable?

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I have a bunch of formulas but don't know how to go about answering this question

P= � D/k
P= � D1/(k � g)

where P � present price of stock
D � dividends received per year (in year 1, year 2, . . . year n)
k � discount rate applied by financial community, often referred to as cost of
equity capital of company
where D1 � dividend to be paid during coming year
g � annual constant growth rate of dividend expressed as a percentage

Answer 1

To answer this question, we need to use the Price to Dividend ratio formula. This formula allows us to determine the growth rate of the company's profits.

The formula is:
P = D / k
P = D1 / (k * g)

Where:
P is the present price of stock
D is the dividends received per year (in year 1, year 2, etc.)
k is the discount rate applied by the financial community, often referred to as the cost of equity capital of the company
D1 is the dividend to be paid during the coming year
g is the annual constant growth rate of the dividend expressed as a percentage

In this case, we know that the company is being sold for $275,000 and the current profits (dividends) are $10,000. These profits have not been paid out as dividends yet. Assuming the company will continue to grow into the infinite future, we need to determine at what constant rate the owner believes the profits will grow.

To find this growth rate, we can rearrange the formula:
g = D1 / (P * k)

Substituting the given values:
g = 10,000 / (275,000 * 0.10)

Simplifying this calculation, we get:
g = 0.0363 or 3.63%

Therefore, the owner believes that the profits will grow at a constant rate of approximately 3.63% per year.

Whether or not this growth rate seems reasonable will depend on various factors, such as the industry and market conditions, historical growth rates, and the company's track record. It would be important to analyze these factors to determine the reasonableness of the growth rate.