ABC Lid has the following capital structure, which it thinks is optimal:

Debt $30\%$

Preferrcd Stock $20$

Common Equity $50$

Total $100\%$

ABC Ltd tax rate is $40\%,$ and investors expect earnings and dividends to grow at a constant rate of $7\%$ in the future. ABC Ltd paid a dividend of $$2\mathrm{.}50$ per share last year $($Do$).$ and its stock currently sells at a price of S$70$ per share.

The company can obtain new capital in the following ways:

Preferred $-$ New preferred stock with a dividend of $$20$ can be sold to the public at a price of $$90$ per share.

Debt$-$ Debt can be sold at an interest rate of $10\%.$

$($i$)$ What is the after$-$tax cost of debt? $(2$ Marks$)$

$($ii$)$ What is the cost of preferred equity? $(3$ Marks$)$

$($ii$)$ Whatis the cost of common equity?

$($iv$)$ Determine ABC's weighted average cost of capital.

b$.$ Sportex Plc$\text{'}$s earnings and stock price are expected to grow at a rate of $6\%$ per year. Their common stock currently sells for $$50\mathrm{.}00$ per share, and the last dividend was $ $6\mathrm{.}00$ per share. A flotation cost of $10\%$ will be paid for raising new common equity.

$($i$)$ Using the information provided, calculate the cost of external equity $($ke$).$

$(4$ Marks$)$

$($ii$)$ If the firm's beta is $1\mathrm{.}25,$ risk$-$free rate is $7\mathrm{.}5\%,$ and the return on the market is $8\mathrm{.}4\%,$ what will be the firm's cost of common equity using the CAPM approach? $(5$ Marks$)$

c$.$ RST Limited is expected to pay dividend of $$8$ per share one year from now on its common stock, which has a current market price of $$150.$ Dividends are expected to grow at $11\%.$

Calculate the cost of the company's retained earnings.

$(3$ Marks$)$