You are given the following information for a company: EBIT = $4,500,000 30- year maturity, 3,000 semiannual coupon bonds with a coupon rate of 10% and a current market value of $1000 per bond

a) Computation of the value of levered equity:-

Value of Unlevered firm = EBIT *(1-tax rate)/ Cost of unlevered equity

= $4,500,000 * (1-0.21) / 20%

= $17,775,000

Total Debt = (3,000*$1,000) + (2,000 * $1,000)

= $3,000,000 + $2,000,000

= $5,000,000

Value of levered firm = Value of unlevered firm + (Debt *tax rate)

= $17,775,000 + ($5,000,000 * 0.21)

= $17,775,000 + $1,050,000

= $18,825,000

Value of levered equity = Value of levered firm - Value of Debt

= $18,825,000 - $5,000,000

= $13,825,000

b) Computation of the cost of levered equity:-

Weighted average before tax cost of debt = (3000000*10%)+(2000000*8%))/5000000

= (300000+160000)/5000000

= 460000/5000000

= 9.20%

Cost of levered equity = Cost of unlevered equity + ((Cost of unlevered equity-Cost of debt)*(D/E ratio)*(1-Tax rate))

= 20%+((20%-9.20%)*(5000000/13825000)*(1-21%))

= 20%+(10.80%*0.36*79%)

= 20% + 3.09%

= 23.09%

c) Computation of the WACC:-

Weight of debt = Debt / Value of firm

= 5000000/18825000

= 26.56%

Weight of equity = Equity / Value of firm

= 13825000/18825000

= 73.44%

WACC = (Weight of debt*After tax cost of debt)+(Weight of equity*Cost of equity)

= (26.56%*9.20%*(1-21%))+(73.44%*23.09%)

= 1.93%+16.95%

= 18.88%

d)  If the firm wants to decrease the cost of levered equity to 20% then the debt should be zero because the cost of levered equity is become equal to the cost of unlevered equity. and the new WACC is equal to the cost of equity = 20%