What is the calculated value of Rosen Fashions' stock based on dividends and growth rate?

To determine the calculated value of Rosen Fashions' stock using dividends and the growth rate, the Gordon Growth Model (also known as the Dividend Discount Model for constant growth) can be applied. This model values a stock based on the present value of its expected future dividends, assuming those dividends grow at a constant rate.

The formula for the Gordon Growth Model is:

[ P_0 = \frac{D_1}{r - g} ]

Where:

• ( P_0 ) is the price of the stock today.
• ( D_1 ) is the expected dividend next year.
• ( r ) is the required rate of return.
• ( g ) is the growth rate of the dividends.

Given that the calculated value of the stock is $69, this indicates that when the relevant data—such as the expected dividends and the growth rate—are plugged into the formula, the result equals $69. This can happen when the combined effect of the expected dividend and growth rate justifies that valuation in terms of the projected returns relative to the risk.

In practice, if the other choices ($50, $75, and $65) do not accurately reflect the inputs used in the model, they would not