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A stock is expected to pay a dividend of $1.00 at the end of the year (i.e., D1 = $1.00), and it should continue to grow at a constant rate of 5% a year. If its required return is 12%, what is the stock's expected price 3 years from today? Round your answer to two decimal places. Do not round your intermediate calculations.

User Delirante
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Final answer:

The expected stock price three years from today, using the Gordon Growth Model with a dividend of $1.00, growth rate of 5%, and required return of 12%, is calculated to be $16.52.

Step-by-step explanation:

To calculate the expected stock price three years from today, we use the Gordon Growth Model (also known as the Dividend Discount Model), which is employed to determine the present value of a stock based on a future series of dividends that grow at a constant rate. Given a dividend (D1) of $1.00, a constant growth rate of 5%, and a required return of 12%, we first find the expected dividend payments for the next three years. Then, the price of the stock at the end of the third year, P3, is the present value of all future dividends from that point onwards.The dividends for the next three years will be as follows:D2 = D1 × (1 + growth rate) = $1.00 × (1 + 0.05) = $1.05D3 = D2 × (1 + growth rate) = $1.05 × (1 + 0.05) = $1.1025D4 = D3 × (1 + growth rate) = $1.1025 × (1 + 0.05) = $1.157625 Now, to find P3, the formula becomes:P3 = D4 / (required return - growth rate) = $1.157625 / (0.12 - 0.05)This results in an expected price of P3 = $16.52, after rounding to two decimal places.Conclusion The expected stock price three years from today is $16.52, demonstrating the application of the Gordon Growth Model to project future stock values based on dividends and growth. This is the main answer, which is valuable for investors looking at long-term growth opportunities and for understanding the implications of constant dividend growth on stock valuation.

User PrivateOmega
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