Final answer:
The correct option is c. The cost of capital for the new common stock issue by the firm is calculated using the Gordon Growth Model with the known dividend, growth rate, and stock price. The calculated cost of capital is 13.42%.
Step-by-step explanation:
To calculate the cost of capital for the new common stock issue by the firm that paid a $1.80 dividend last year and expects to grow its dividends by 7% annually, we use the Gordon Growth Model (also known as the Dividend Discount Model). The formula for the cost of capital (k) when dividends are expected to grow at a constant rate (g) is:
k = (D1 / P0) + g
Where D1 is the dividend expected next year, P0 is the current stock price, and g is the growth rate.
Assuming that the dividends grow at a constant rate of 7%, the expected dividend next year (D1) will be:
D1 = D0 * (1 + g) = $1.80 * (1 + 0.07) = $1.926
The current stock price (P0) is given as $30.00.
Now we can calculate the cost of capital:
k = ($1.926 / $30) + 0.07 = 0.0642 + 0.07 = 0.1342 or 13.42%
Therefore, the cost of capital for the firm is 13.42%, which corresponds to option c.