$23)$ Weighted average cost of capital $(15$ points$)$

A firm$$s CEO has set the company$$s target capital structure as $40\%$ long$-$term debt, $10\%$ preferred stock, and $50\%$ common stock equity. The firm's corporate tax rate is $20$ percent. To finance its planned capital expenditures, the firm is looking at the following sources of capital:

$$ Debt: The firm can sell $30-$year, $$1,000$ par value bonds that pay an $9\%$ coupon, with interest paid semi$-$annually, for $$950.$ To issue the bond, the firm will have to pay $$20$ in flotation costs per bond.

$$ Preferred Stock: The firm can sell a $8\%$ preferred stock at a par value of $$100$ per share. The cost of issuing and selling the preferred stock is $$10$ per share.

$$ Common Stock: The firm's common stock is currently selling for $$50$ per share. This year, the firm paid $$4$ in dividends per share. The firm$$s dividends have been growing at a constant rate of $2\%$ per year for the last ten years and are expected to sustain this growth rate thereafter.

$$ New common stock issue: If the firm decides to issue new common stock, its underwriter indicated that the new stocks would sell for $$47$ per share. Further, the firm will have to pay $$3$ per share in flotation costs. Dividend and dividend growth rate are expected to remain the same.

a$)$ Find the firm$$s after$-$tax cost of debt financing $(2$ points$)$

b$)$ Find the firm$$s cost of preferred stock financing $(2$ points$)$

c$)$ Find the firm$$s cost of financing using the retained earnings $(2$ points$)$

d$)$ Find the firm$$s cost of financing using a new common stock issue $(2$ points$)$

e$)$ Find the firm$$s weighted average cost of capital, if the firm uses debt, preferred stock and retaining earnings to finance its investments $(2$ points$)$

f$)$ Find the firm$$s weighted average cost of capital, if the firm uses debt, preferred stock, retaining earnings, and the new stock issue to finance its investments $(2$ points$)$

g$)$ Given your findings in part $($e$)$ and $($f$),$ explain what minimum rates of return the firm must require from its long$-$term investments $(3$ points$).$