Williamson, Inc., has a debt–equity ratio of 2.54. The company\'s weighted avera

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.

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.)

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.)

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.

Explanation / Answer

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%

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