Question 4) Dickson, Inc., has a debt-equity ratio of 2.35. The firm's weighted average cost of capital is 12 percent and its pretax cost of debt is 9 percent. The tax rate is 24 percent.

a) What is the company's cost of equity capital?

b) What is the company's unlevered cost of equity capital?

c) What would the company's weighted average cost of capital be if the company's debt-equity ratio was 1.35?

 

a) 24.126%, or 24.13%

b) 14.4292893%, or 14.43%

c) 12.43988942%, or 12.44%

Step-by-step explanation

a)

Debt-equity ratio = Debt / Equity

2.35 = Debt / 1.0

Debt = 2.35 x 1.0

Debt = 2.35

Total value = Debt + Equity = 2.35 + 1.0 = 3.35

After tax cost of debt = 9% x (1-0.24) = 6.84%

WACC = (Cost of equity x (Equity / Total value)) + (After tax cost of debt x (Debt / total value))

12% = (cost of equity x (1 / 3.35)) + (6.84% x (2.35 / 3.35))

12% = 0.2985074627 cost of equity + 4.798208955%

0.2985074627 cost of equity = 12% - 4.798208955%

0.2985074627 cost of equity = 7.201791045%

Cost of equity = 7.201791045% / 0.2985074627

Cost of equity = 24.126%, or 24.13%

b)

Cost of equity = Unlevered cost of equity + (Unlevered cost of equity - Cost of debt) x (debt/Equity) x (1-tax rate)

24.126% = Unlevered cost of equity + (Unlevered cost of equity - 9%) x (2.35 / 1) x (1-0.24)

24.126% = Unlevered cost of equity + 1.786 Unlevered cost of equity - 16.074%

Unlevered cost of equity + 1.786 Unlevered cost of equity = 24.126% + 16.074%

Unlevered cost of equity + 1.786 Unlevered cost of equity = 40.2%

2.786 Unlevered cost of equity = 40.2%

Unlevered cost of equity = 40.2% / 2.786

Unlevered cost of equity = 14.4292893%, or 14.43%

c)

Debt-equity ratio = Debt / Equity

1.35 = Debt / 1.0

Debt = 1.35 x 1.0

Debt = 1.35

Total value = Debt + Equity = 1.35 + 1.0 = 2.35

Cost of levered equity = Unlevered cost of equity + (Unlevered cost of equity - Cost of debt) x (debt/Equity) x (1-tax rate)

Cost of levered equity = 14.4292893% + (14.4292893% - 9%) x (1.35) x (1-0.24)

Cost of levered equity = 19.99974013%

WACC = (Cost of equity x (Equity / Total value)) + (After tax cost of debt x (Debt / total value))

WACC = (19.99974013 x (1 / 2.35)) + (6.84% x (1.35 / 2.35))

WACC = 12.43988942%, or 12.44%