Question

Modigliani and​ Miller's world of no taxes. Roxy​ Broadcasting, Inc. is currently a​ low-levered firm with a​ debt-to-equity ratio of ​/. The company wants to increase its leverage to ​/ for debt to equity. If the current return on assets is ​% and the cost of debt is ​%, what are the current and the new costs of equity if Roxy operates in a world of no​ taxes? What is the current cost of equity if Roxy operates in a world of no​ taxes?

Answer 1

Answer and Explanation:

The computation is shown below:

For Current  

Total assets = Debt + Equity

= 2 + 7 9

Now

Debt ratio = Debt ÷ Total assets = 2 ÷ 9  

Equity ratio = Equity ÷ Total assets = 7 ÷ 9  

Return on assets = Cost of debt × Debt ratio + Cost of equity × Equity ratio

11% = 9% × 2 ÷ 9 + Cost of equity × 7 ÷ 9  

Cost of equity × 7 ÷ 9 = 11% - (9% × 2 ÷ 9)  

Cost of equity = ( 11% - (9% × 2 ÷ 9) ) × 9 ÷ 7

= 12%

For New  

Total assets = Debt + Equity = 7 + 2 = 9

Debt ratio = Debt ÷ Total assets = 7 ÷ 9  

Equity ratio = Equity ÷ Total assets = 2 ÷9  

Return on assets = Cost of debt × Debt ratio + Cost of equity × Equity ratio

11% = 9% × 7 ÷ 9 + Cost of equity × 2 ÷ 9  

Cost of equity × 2 ÷ 9 = 11% - (9% × 7 ÷ 9)  

Cost of equity = ( 11% - (9% × 7 ÷ 9) ) × 9 ÷ 2

= 18%