Acetate, Inc., has equity with a market value of $22.5 million and debt with a m

Question

Acetate, Inc., has equity with a market value of $22.5 million and debt with a market value of $6.75 million. Treasury bills that mature in one year yield 5 percent per year, and the expected return on the market portfolio is 12 percent. The beta of Acetate’s equity is 1.10. The firm pays no taxes.

a. What is Acetate’s debt–equity ratio? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Debt–equity ratio

b. What is the firm’s weighted average cost of capital? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Weighted average cost of capital %

c. What is the cost of capital for an otherwise identical all-equity firm? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Cost of capital %

Explanation / Answer

Acetate’s debt–equity ratio= Market Value of debt/Market Value of equity

= 6.75/22.5

Acetate’s debt–equity ratio=0.3

Weighted avergae cost of capital= weight of equity*cost of equity+ weight of debt*after tax cost of debt

Cost of equity using CAPM eqution= Risk free rate+ beta(return on market portfolio- risk free rate)

=5%+1.1*(12%-5%)

Cost of equity using CAPM eqution=12.7%

Note cost of debt is not given. Let us assume that it will be 8%(higher than risk free rate of 5% i.e. 3% risk premium)

WACC= 22.5/(22.5+6.75)*12.7%+6.75/(22.5+6.75)*(1-0%)*8%

WACC=11.61%

c. What is the cost of capital for an otherwise identical all-equity firm?

First we need to find unlevered beta for this using below formula

Beta unlevered= beta levered/(1+(1-tax rate)*D/E)

=1.1/(1+(1-0%)*(6.75/22.5))

Beta unlevered=0.85

Cost of capital = Risk free rate+ beta unlevered(return on market portfolio- risk free rate)

=5%+0.85*(12%-5%)

Cost of capital =10.95%

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