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The risk-free rate is 1.05% and the market risk premium is 6.86%. A stock with a β of 1.29 just paid a dividend of $1.34. The dividend is expected to grow at 23.19% for five years and then grow at 3.75% forever. What is the value of the stock?

User Lise
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Final answer:

The value of the stock is $39.04.

Step-by-step explanation:

To calculate the value of the stock, we need to use the dividend discount model (DDM). The DDM formula is: Stock Value = Dividend / (Required Rate of Return - Dividend Growth Rate). Using the given information, the required rate of return is the risk-free rate plus the market risk premium, which is 1.05% + 6.86% = 7.91%. The first step is to calculate the present value of the expected dividends for the five-year growth period using the formula: Present Value = Dividend / (1 + Required Rate of Return)^t, where t is the number of years. The present value of the expected dividends after five years is: Present Value = $1.34 / (1 + 0.0791)^5 = $0.884. Next, we need to calculate the present value of the terminal value, which is the perpetuity formula: Present Value = Terminal Dividend / (Required Rate of Return - Dividend Growth Rate), where the terminal dividend is the dividend in year six. The present value of the terminal value is: Present Value = $1.34 * (1 + 0.0375) / (0.0791 - 0.0375) = $38.16. Finally, we can calculate the value of the stock by summing the present value of the expected dividends for the five-year growth period and the present value of the terminal value: Stock Value = $0.884 + $38.16 = $39.04.

User KisnardOnline
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