What is the value of a stock that is expected to pay a $10 per share dividend in a year's time, and to be selling for $30 per share at the end of the year? The appropriate discount rate is 10% per year.
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A. B. C. D.B
Value = $40/1.10=$36.36.
To calculate the value of the stock, we can use the dividend discount model (DDM), which calculates the present value of the expected future dividends.
The formula for the DDM is: Stock Value = Dividend / (Discount Rate - Dividend Growth Rate)
In this case, we are given the following information: Dividend (D) = $10 per share Discount Rate (r) = 10% per year Dividend Growth Rate (g) = Not provided
Since the dividend growth rate is not provided, we assume that it remains constant or that it equals zero (no growth). In other words, we assume that the $10 dividend will remain the same in the future.
Using the DDM formula, we can calculate the stock value:
Stock Value = $10 / (0.10 - 0) Stock Value = $10 / 0.10 Stock Value = $100
However, we also need to consider the future selling price of the stock at the end of the year. According to the question, the stock is expected to sell for $30 per share at the end of the year. We need to discount this future selling price back to the present value using the same discount rate.
Present Value of Future Selling Price = Future Selling Price / (1 + Discount Rate) Present Value of Future Selling Price = $30 / (1 + 0.10) Present Value of Future Selling Price = $30 / 1.10 Present Value of Future Selling Price = $27.27
Finally, we can calculate the total value of the stock by adding the present value of the expected future dividend and the present value of the future selling price:
Total Stock Value = Present Value of Dividend + Present Value of Future Selling Price Total Stock Value = $10 + $27.27 Total Stock Value = $37.27
Based on the available options, none of them matches the calculated value of $37.27. Therefore, the correct answer is D. Not able to compute with the above data.
It's worth noting that the absence of the dividend growth rate makes it challenging to compute an accurate valuation. The growth rate assumption can significantly impact the stock value, and without it, the calculation may not be reliable.