Question

Dickson, Inc., has a debt-equity ratio of 2.55. The firm’s weighted average cost of capital is 12 percent and its pretax cost of debt is 10 percent. The tax rate is 23 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.)
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.)
c.	What would the company’s weighted average cost of capital be if the company's debt-equity ratio were .55 and 1.55? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

    

Answer 1

Answer a.

Debt-Equity Ratio = 2.55

Weight of Debt = 2.55 / 3.55
Weight of Debt = 0.7183

Weight of Equity = 1.00 / 3.55
Weight of Equity = 0.2817

WACC = Weight of Debt * Pretax Cost of Debt * (1 - tax) + Weight of Equity * Levered Cost of Equity
0.1200 = 0.7183 * 0.1000 * (1 - 0.23) + 0.2817 * Levered Cost of Equity
0.1200 = 0.0553 + 0.2817 * Levered Cost of Equity
0.0647 = 0.2817 * Levered Cost of Equity
Levered Cost of Equity = 0.2297 or 22.97%

Answer b.

Levered Cost of Equity = Unlevered Cost of Equity + (Unlevered Cost of Equity - Cost of Debt) * (1 - tax) * Debt-Equity Ratio
0.2297 = Unlevered Cost of Equity + (Unlevered Cost of Equity - 0.10) * (1 - 0.23) * 2.55
0.2297 = Unlevered Cost of Equity + (Unlevered Cost of Equity - 0.10) * 1.9635
0.2297 = Unlevered Cost of Equity + 1.9635 * Unlevered Cost of Equity - 0.19635
0.42605 = 2.9635 * Unlevered Cost of Equity
Unlevered Cost of Equity = 0.1438 or 14.38%

Answer c.

If Debt-Equity Ratio is 0.55:

Levered Cost of Equity = Unlevered Cost of Equity + (Unlevered Cost of Equity - Cost of Debt) * (1 - tax) * Debt-Equity Ratio
Levered Cost of Equity = 0.1438 + (0.1438 - 0.10) * (1 - 0.23) * 0.55
Levered Cost of Equity = 0.1438 + 0.0185
Levered Cost of Equity = 0.1623 or 16.23%

Weight of Debt = 0.55 / 1.55
Weight of Debt = 0.3548

Weight of Equity = 1.00 / 1.55
Weight of Equity = 0.6452

WACC = Weight of Debt * Pretax Cost of Debt * (1 - tax) + Weight of Equity * Levered Cost of Equity
WACC = 0.3548 * 0.10 * (1 - 0.23) + 0.6452 * 0.1623
WACC = 0.1320 or 13.20%

If Debt-Equity Ratio is 1.55:

Levered Cost of Equity = Unlevered Cost of Equity + (Unlevered Cost of Equity - Cost of Debt) * (1 - tax) * Debt-Equity Ratio
Levered Cost of Equity = 0.1438 + (0.1438 - 0.10) * (1 - 0.23) * 1.55
Levered Cost of Equity = 0.1438 + 0.0523
Levered Cost of Equity = 0.1961 or 19.61%

Weight of Debt = 1.55 / 2.55
Weight of Debt = 0.6078

Weight of Equity = 1.00 / 2.55
Weight of Equity = 0.3922

WACC = Weight of Debt * Pretax Cost of Debt * (1 - tax) + Weight of Equity * Levered Cost of Equity
WACC = 0.6078 * 0.10 * (1 - 0.23) + 0.3922 * 0.1623
WACC = 0.1105 or 11.05%