Question

Understanding the optimal capital structure

Review this situation: Transworld Consortium Corp. is trying to identify its optimal capital structure. Transworld Consortium Corp. has gathered the following financial information to help with the analysis.

Debt Ratio	Equity Ratio	EPS	DPS	Stock Price
30%	70%	1.55	0.34	22.35
40%	60%	1.67	0.45	24.56
50%	50%	1.72	0.51	25.78
60%	40%	1.78	0.57	27.75
70%	30%	1.84	0.62	26.42

Which capital structure shown in the preceding table is Transworld Consortium Corp.’s optimal capital structure?

Debt ratio = 30%; equity ratio = 70%

Debt ratio = 70%; equity ratio = 30%

Debt ratio = 60%; equity ratio = 40%

Debt ratio = 50%; equity ratio = 50%

Debt ratio = 40%; equity ratio = 60%

Consider this case:

Globo-Chem Co. is an all-equity firm, and it has a beta of 1. It is considering changing its capital structure to 70% equity and 30% debt. The firm’s cost of debt will be 8%, and it will face a tax rate of 25%.

What will Globo-Chem Co.’s beta be if it decides to make this change in its capital structure?     

Now consider the case of another company:

US Robotics Inc. has a current capital structure of 30% debt and 70% equity. Its current before-tax cost of debt is 8%, and its tax rate is 25%. It currently has a levered beta of 1.25. The risk-free rate is 2.5%, and the risk premium on the market is 8%. US Robotics Inc. is considering changing its capital structure to 60% debt and 40% equity. Increasing the firm’s level of debt will cause its before-tax cost of debt to increase to 10%.

First, solve for US Robotics Inc.’s unlevered beta.     

Use US Robotics Inc.’s unlevered beta to solve for the firm’s levered beta with the new capital structure.     

Use US Robotics Inc.’s levered beta under the new capital structure, to solve for its cost of equity under the new capital structure.     

What will the firm’s weighted average cost of capital (WACC) be if it makes this change in its capital structure?

12.00%

9.00%

7.80%

11.40%

Answer 1

Answer 1:

Correct answer is:

Debt ratio = 60%; equity ratio = 40%

Explanation:

We know optimal capital structure is one which maximizes shareholder value or minimizes WACC.

Shareholder value will be maximum when stock price is maximum. From the table given we observe stock price is maximum at  $27.75 with capital structure where debt ratio = 60%; equity ratio = 40%.

Hence option C is correct and other options A, B, D and E are incorrect.

Answer 2:

Given:

Globo-Chem Co. is an all-equity firm, and it has a beta of 1

Leevered beta = Unlevered beta * (1 + (1 - Tax rate) * (Debt / Equity))

= 1 * (1 + (1 - 25%) * (30%/70%))

= 1.32

Globo-Chem Co.’s beta be if it decides to make this change in its capital structure = 1.32

Answer 3 (a)

Given:

US Robotics Inc. has a current capital structure of 30% debt and 70% equity. It currently has a levered beta of 1.25.

(a) US Robotics unlevered beta = Levered beta / (1 + (1 - Tax rate) * (Debt / Equity))

= 1.25 / (1 + (1 - 25%) * (30%)/70%))

= 0.95

US Robotics unlevered beta = 0.95

Answer 3 (b)

US Robotics Inc.’s levered beta under the new capital structure = 0.95 * (1 + (1 - 25%) * (60%/40%)) = 2.02

US Robotics Inc.’s levered beta under the new capital structure = 2.02

Answer 3 (c)

Correct answer is:

12.00%

Explanation:

Cost of equity = Risk free rate + beta * Risk premium = 2.5% + 2.02 * 8% = 18.7%

WACC = Cost of equity * Weight of equity + Before tax cost of debt * (1 - tax rate) * weight of debt

= 18.7% * 40% + 10% * (1 - 25%) * 60%

= 12.0%

Hence option A is correct and other options B, C and D are incorrect.