Hatch Corporation's target capital structure is $40\%$ debt, $50\%$ common stock, and $10\%$ preferred stock. Information regarding the company's cost of capital can be summarized as follows:

Long term debt is the only permanent debt financing. Hatch has $30$ year bonds which closed at $$940$ paying an annual coupon rate of $6\%$ semi annual payments

$($par value of $$1000)$

Preferred stock is priced at $$40$ per share and pays $$2$ per share annually. Flotation cost $$2$ per share

Common stock sells for $$32$ per shareand will pay a dividend during the coming year of $$2.$ Growth is estimated at $5\%$

The marginal tax rate is $25\%$

Optimal capital structure is $30\%$ debt and $60\%$ common equity and $10\%$ preferred stock.

a$.$ Find the cost of debt $(r_d)$ and preferred stock.

b$.$ Find the cost of retained earnings $($Use the DCF model for the cost of retained earnings$).$

c$.$ Calculate the weighted average cost of capital.