Question

Williamson, Inc., has a debt–equity ratio of 2.54. The company's weighted average cost of capital is 9 percent, and its pretax cost of debt is 7 percent. The corporate tax rate is 40 percent.

  

a.	What is the company’s cost of equity capital? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

  

Cost of equity capital

%

  

b.	What is the company’s unlevered cost of equity capital? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

  

Unlevered cost of equity

%

  

c.	What would the company’s weighted average cost of capital be if the company's debt–equity ratio were .80 and 1.70? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

  

	Weighted average cost of capital
Debt–equity ratio = .80	%
Debt–equity ratio = 1.70	%

Answer 1

a. Given that Williamson Inc has a debt-equity ratio of 2.54

that is to say if equity is 1 then debt is 2.54 times

Therefore total debt + equity = 2.54 + 1 = 3.54

Weight of Equity in total = 1 / 3.54 = 0.282486

Weight of Debt in total = 2.54 / 3.54 = 0.717514

Now given that pre tax cost of debt is 7%

Therefore post tax cost of debt = 7 * (1 - Tax Rate)

= 7 * ( 1 -0.4)

= 7 * 0.6

= 4.2%

Now Weighted Average cost of capital(WACC) is 9%

From this we can find out cost of equity

WACC = (Weight of Debt in total * Post tax cost of debt ) + (weight of equity in total * Cost of equity)

9 = (0.717514 * 4.2) + (0.282486 * Cost of Equity)

9 = 3.0135588 + (0.282486 * Cost of Equity)

9 - 3.0135588 = 0.282486 * Cost of Equity

5.9864412 = 0.282486 * Cost of Equity

Cost of Equity = 5.9864412 / 0.282486

= 21.19%

b. Unlevered Cost of Capital means when there is no debt in the firm and it is entirely equity financed.

It is found out through unlevered beta, risk free return & market risk premium.

But in the absence of information here it shall be same as the cost of equity capital as 100% weight would be assigned to equity.

Therefore unlevered cost of Equity Capital = 21.19%

c.

WACC when debt equity ratio is 0.8

that is to say if equity is 1 then debt is 0.8 times

Therefore total debt + equity = 0.8 + 1 = 1.8

Weight of Equity in total = 1 / 1.8 = 0.555555

Weight of Debt in total = 0.8 / 1.8 = 0.444444

WACC = (Weight of Debt in total * Post tax cost of debt ) + (weight of equity in total * Cost of equity)

= (0.444444 * 4.2) + (0.555555 * 21.19)

= 1.8666648 + 11.77221045

WACC = 13.64%

WACC when debt equity ratio is 1.7

that is to say if equity is 1 then debt is 1.7 times

Therefore total debt + equity = 1.7 + 1 = 2.7

Weight of Equity in total = 1 / 2.7 = 0.370370

Weight of Debt in total = 1.7 / 2.7 = 0.629630

WACC = (Weight of Debt in total * Post tax cost of debt ) + (weight of equity in total * Cost of equity)

= (0.629630 * 4.2) + (0.370370 * 21.19)

= 2.644446 + 7.8481403

WACC = 10.49%