Final answer:
The value of a share of stock one year from now that paid a $6 dividend last year and grows at 5% per year with a required rate of return of 12% is calculated using the Dividend Growth Model to be $90. This is not matching any of the options provided in the question, indicating a potential error in the options.
Step-by-step explanation:
The value of a share of common stock one year from now, which paid a $6 dividend at the end of last year and is expected to pay a growing cash dividend indefinitely, can be determined using the Gordon Growth Model (also known as the Dividend Growth Model). This model considers the next expected dividend payment, the required rate of return, and the growth rate of dividends. Given that the dividend is expected to grow at a rate of 5% per year, and the required rate of return is 12%, the formula to calculate the price of the stock is:
P = D / (k - g)
Where P is the price of the stock, D is the expected dividend next year, k is the required rate of return, and g is the growth rate of the dividend. The expected dividend next year (D1) will be $6 * (1 + 5%) = $6.30. Thus, the calculation would be:
P = $6.30 / (12% - 5%)
P = $6.30 / 0.07
P = $90
Therefore, the value of the stock one year from now is $90, which is not one of the provided options (A) $94.50 (B) $87.50 (C) $82.40 (D) $80.70. It seems there might be an error in the options provided.