Question

U.S. 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%. Use the Hamada equation to unlever and relever the beta for the new level of debt. What will the firm’s weighted average cost of capital (WACC) be if it makes this change in its capital structure? (Hint: Do not round intermediate calculations.) The optimal capital structure is the one that the WACC and the firm’s stock price. Higher debt levels the firm’s risk. Consequently, higher levels of debt cause the firm’s cost of equity to .

Answer 1

Missing question at inception is also below "US Robotics has a current capital structure of 30% debt and 70% equity. Its current before-tax cost of debt is 6%, and it's tax rate is 35%. It currently has a levered beta of 1.15. The risk free rate is 3% and the risk premium on the market is 7%"

Unlevered beta = Levered Beta / [1+(1-Tax) (D/E)

= 1.15/[1+(1-0.35)(0.3/0.7)

= 1.15/1.27857

= 0.90

Levered Beta = Unlevered beta *[1+(1-Tax)(D/E)

= 0.90 * {1+(1-0.35)(1.6/0.4)

= 0.90*1.975

= 1.78

Cost of equity = Risk free return + Levered Beta*Market risk premium

= 0.03 + 1.78 * 0.07

= 0.1546

= 15.46%

WACC = (Weight of equity * Cost of equity) + (Weight of debt*Cost of debt *(1-Tax)

= (40% * 15.46%) + 60% * 10% * (1-0.35)

= 0.06184 + 0.039

= 6.18% + 3.9

= 10.08%

The new WACC of the company is 10.08%

The optimal capital structure is the one that the WACC and the firm’s stock price. Higher debt levels the firm’s risk. Consequently, higher levels of debt cause the firm’s cost of equity to increase.