Determining the optimal capital structure 3. Determining the optimal capital str

ID: 2763014 • Letter: D

Question

Determining the optimal capital structure

3. Determining the optimal capital structure Aa Aa Understanding the optimal capital structure Review this situation: Universal Exports Inc. is trying to identify its optimal capital structure. Universal Exports Inc. has gathered the following financial information to help with the analysis Debt Ratio Equity Ratio rd 30% 40% 50% 60% 70% 70% 60% 50% 40% 30% 6.02% 6.75% 7.15% 7.55% 8.24% 9.40% 9.750% 10.60% 11.30% 12.80% WACC 9.71% 9.55% 10.02% 10.78% 11.45% Which capital structure shown in the preceding table is Universal Exports Inc.'s optimal capital structure? Debt ratio = 50%; equity ratio = 50% Debt ratio = 60%; equity ratio = 40% Debt ratio = 30%; equity ratio = 70% Debt ratio = 70%; equity ratio = 30% Debt ratio = 40%; equity ratio = 60%

Explanation / Answer

Universal Exports

Debt Ratio

Equity Ratio

WACC

30%

70%

6.02%

9.40%

0.3*6.02 + 0.7*9.40 = 8.39%

40%

60%

6.75%

9.75%

0.4*6.75 + 0.6*9.75 = 8.55%

50%

7.15%

10.60%

0.5*7.15 + 0.5*10.6 = 8.87%

60%

40%

7.55%

11.30%

0.6*7.55 + 0.4*11.3 = 9.05%

70%

30%

8.24%

12.80%

0.7*8.24 + 0.3*12.8 = 9.61%

Based on the above calculation of WACC, Debt Equity ratio of 30:70 is optimal capital structure since WACC is minimum

However, as per WACC given in the question, Debt Equity ratio of 40:60 is optimal capital structure since WACC is minimum

Globo-Chem Co

Since Globo-Chem is an all equity firm, beta of 1 is unlevered beta.

New capital structure Debt / Equity = 30/70

Levered Beta = Unlevered Beta*[1 + (1-t)*D/E]

= 1*[1 + (1 - 0.45)*30/70]

= 1.236

Beta under new capital structure will 1.236

U.S. Robotics

Current Capital structure (Debt / Equity) = 30/70

Tax rate = 45%

Pre-tax cost of debt = 10%

Current levered beta = 1.15

Unlevered Beta = Levered Beta / [1 + (1 – t)*D/E]

= 1.15 / [1 + (1 – 0.45)*30/70]

= 0.93

Unlevered Beta for U.S. Robotics = 0.93

Proposed Capital Structure (Debt / Equity) = 60/40

Relevered Beta = Unlevered Beta*[1 + (1 - t)*D/E]

= 0.93*[1 + (1 – 0.45)*60/40]

= 1.70

Re-levered Beta for U.S. Robotics under new capital structure = 1.70

Cost of Equity under new capital structure

Ke = Rf + (Rm – Rf)*Beta Rf = Risk free rate; Rm – Rf = Market Risk Premium

= 3.5 + 8*1.7

= 17.10%

WACC under new capital structure

Debt / Equity = 60/40

Cost of Equity = 17.10%

Post-tax Cost of Debt = 12*(1 – 0.45) = 6.60%

WACC = Weight of Debt*Cost of Debt = Weight of Equity*Cost of Equity

= 60%*6.6 + 40%*17.10

= 10.8%

WACC under new capital structure = 10.8%