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%	1.25	0.55	36.25
40%	60%	1.40	0.60	37.75
50%	50%	1.60	0.65	39.50
60%	40%	1.85	0.75	38.75
70%	30%	1.75	0.70	38.25

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

Debt ratio = 50%; equity ratio = 50%

Debt ratio = 70%; equity ratio = 30%

Debt ratio = 30%; equity ratio = 70%

Debt ratio = 60%; equity ratio = 40%

Debt ratio = 40%; equity ratio = 60%

Consider this case:

Globex Corp. has a capital structure that consists of 40% debt and 60% equity. The firm’s current beta is 1.25, but management wants to understand Globex Corp.’s market risk without the effect of leverage.

2) If Globex Corp. has a 25% tax rate, what is its unlevered beta?

0.91

0.95

0.83

0.79

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 3.5%, and the risk premium on the market is 7%. 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%.

3) First, solve for US Robotics Inc.’s unlevered beta. .95/.86/1.14/1.05 ?

Use US Robotics Inc.’s unlevered beta to solve for the firm’s levered beta with the new capital structure. 2.22/1.82/1.92/2.02 ?

Use US Robotics Inc.’s levered beta under the new capital structure, to solve for its cost of equity under the new capital structure. 17.640/ 15.876/ 20.286/ 14.112% ?  

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

9.86%

8.70%

11.60%

11.02%

Answer 1

1) Optimum capital structure is that which creates maximum shareholder value. Therefore in above case option 4th is correct.

Debt ratio = 60% ; equity ratio = 40%

2)Unlevered beta = Current Beta / 1+[(1- Tax Rate )* Debt Equity Ratio]

=1.25 /1+[(1-0.25)*0.40/0.60]

= .83

Unlevered beta is 3rd option (.83)

3) unlevered beta = 1.25/1+(1-.25)*(.30/.70) = .95

Levered Beta = .95(1+(.75)(.60/.40). = 2.02

Cost of Equity = .035+2.02(.07) = 17.64%

4) Weighted average cost of capital (WACC)

.60(.10)(1-.25)+ .40(.1764) = 11.60%