Stock Valuation

Explanation

Value = $55/1.12=$49.11

To calculate the value of a stock using the dividend discount model (DDM), we need to determine the present value of all expected future dividends.

In this case, we know that the stock is expected to pay a $15 dividend in one year. To calculate the present value of this dividend, we need to discount it back to the present using the appropriate discount rate. The discount rate provided is 12% per year.

The formula to calculate the present value of a dividend using the DDM is:

Present Value = Dividend / (1 + Discount Rate)^n

Where:

• Dividend is the amount of the dividend to be received in the future
• Discount Rate is the appropriate discount rate
• n is the number of periods until the dividend is received

Let's calculate the present value of the dividend in this case:

Present Value = $15 / (1 + 0.12)^1 Present Value = $15 / (1.12) Present Value ≈ $13.39

Next, we need to determine the value of the stock at the end of the year. It is expected to be selling for $40 per share. To find the present value of this future stock price, we can use the same formula:

Present Value = Stock Price / (1 + Discount Rate)^n

Present Value = $40 / (1 + 0.12)^1 Present Value = $40 / (1.12) Present Value ≈ $35.71

Finally, to calculate the total value of the stock, we add the present values of the dividend and the future stock price:

Total Value = Present Value of Dividend + Present Value of Stock Price Total Value = $13.39 + $35.71 Total Value ≈ $49.10

Therefore, the value of the stock is approximately $49.10.

The closest answer choice to $49.10 is C. $49.11.