a. If the tax rate is 21%, what is the value of the firm?

EBIT = 100000

Less: Interesrt = 0 ( as no debt )

EBT = 100000

Less: Tax = 21000 ( 21% of EBT )

Profit after Tax = 79000

Value of Firm = PAT / Ke = 79000 / 13% = 607692.3

b. What will the value Antarctica if the firm uses the borrows 200000 at 6% to repurchase shares? Notice that by doing so, the firm increases its debt and accordingly decreases its equity.

EBIT = 100000

Less: Interesrt = 12000 ( 200000 * 6% )

EBT = 88000

Less: Tax = 18480 ( 21% of EBT )

Profit after Tax = 69520

Value of Firm = PAT / Ke = 69520 / 13% = 534769.2

c. What is the cost Of equity after recapitalization?

Cost of equity won't change after recapitalization. So it will be same as 13%.

d. What is the WACC after recapitalization?

Total Debt + Equity = 200000 + 534769.2 = 734769.2

Weight of Debt = 200000 / 734769.2 = 0.2722

Weight of Equity = 1 - Debt = 1 - 0.2722 = 0.7278

WACC = { Weight of debt * [ Interest rate* ( 1 - Tax ) ] } + {Weight of Equity * Cost of equity Ke}

WACC = { 0.2722 * ( 6% ( 1 - 21% ) } + { 0.7278 * 13% }

WACC = 10.75%

e. What are the implications for the firm's capital structure?

Cheaper cost of capital. Higher returns to equity. As we can see from above WACC reduced from 13% to 10.75% with use of debt.