Robotics Inc. has a current capital structure of 30% debt and 70% equity. Its cu

Question

Robotics Inc. has a current capital structure of 30% debt and 70% equity. Its current before tax cost of debt is 10%, and its tax rate is 35%. It currently has a levered beta of 1.10. the risk free are is 2.5% and the risk premium on the market is 8%. U.s. Robotics Inc. is considering changing its capital structue to 60% debt and 40% equity. Inceasing the firms level of debt will cause its before tax cost of debt to increase to 12%. 1.What is Robotics unlevered beta? 2. Reiever U.S. Robotics beta using the firm's new captial structure. 3. Use Robotics levered beta under the new capital structure to solve for its cost of equity under the new capital struature. 4. What will the firms WACC be if it makes the changes in the capital structure?

Explanation / Answer

1.

Unlevered Beta = Levered Beta / (1 + ((1 Tax Rate) x (Debt/Equity)))
Unlevered Beta = 1.1/(1+((1-0.35)*(3/7)) = 1.1/(1+0.65*3/7) = 1.1/1.278 = 0.86

2.
Levered Beta = Unlevered Beta x (1 + ((1 Tax Rate) x (Debt/Equity)))
Levered Beta = 0.86*(1+((1-0.35)*6/4) = 0.86*(1+0.65*6/4) = 1.6985 = 1.70 (rounded to 2 decimal places)

3. Using CAPM, Cost of equity = risk free rate + beta * (market risk premium)
Using levered beta, cost of equity = 2.5% + 1.70*8% = 16.1%

4. WACC = (cost of equity * Equity + (1-tax rate)*cost of debt * debt)/(Equity + Debt)

= (0.161*0.4 + (1-.35)*.12*.6)/1
= 0.0644 + 0.0468 = 0.1112 or 11.12%

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