8. Faris currently has a capital structure of 40 percent debt and 60 percent equ

Question

8. Faris currently has a capital structure of 40 percent debt and 60 percent equity, but is considering a new product that will be produced and marketed by a separate division. The new division will have a capital structure of 70 percent debt and 30 percent equity. Faris has a current beta of 1.1, but is not sure what the beta for the new division will be. AMX is a firm that produces a product similar to the product under consideration by Faris. AMX has a beta of 1.6, a capital structure of 40 percent debt and 60 percent equity and a marginal tax rate of 40 percent. Faris' tax rate is 40 percent. What will be Faris' weighted cost of capital for this new division if the after-tax cost of debt is 7 percent, the risk-free rate is 8 percent, and the market risk premium is 5 percent?

A. 12.15%

B. 11.41%

C. 18.15%

D. 14.27%

Explanation / Answer

Answer

So, First we have to find asset (unlevered) beta of similar firm.

AMX is a firm that produces a product similar to the product under consideration by Faris. AMX has a beta of 1.6, a capital structure of 40 percent debt and 60 percent equity and a marginal tax rate of 40 percent.

Asset (unlevered) beta = Equity(levered beta) / 1 + (debt/equity)(1- tax rate)

                                       = 1.6 / 1 + (0.4 / 0.6)(1- 0.40)

                                       = 1.6 / 1 + 0.4

                                       = 1.6 / 1.4

Asset (unlevered) beta = 1.14

Now, We have to re-leverage above asset(unlevered) beta with new capital structure of our division to find out new Equity(levered beta) of our division.

Faris is considering a new product that will be produced and marketed by a separate division. The new division will have a capital structure of 70 percent debt and 30 percent equity. Faris' tax rate is 40 percent.

Asset (unlevered) beta = Equity(levered beta) / 1 + (debt/equity)(1- tax rate)

1.14 = Equity(levered beta) / 1 + (0.7/0.3)(1-0.4)

1.14 = Equity(levered beta) / 1+1.4

1.14 = Equity(levered beta) / 2.4

Equity(levered beta) = 2.4*1.14

Equity(levered beta) = 2.736

Cost of Equity = Risk Free rate + Equity Beta * Market risk premium

The risk-free rate is 8 percent, and the market risk premium is 5 percent. Equity(levered beta) is 2.736 (as calculated above).

                      = 8% + 2.736 ( 5% )

                      = 8% + 13.68%

Cost of equity = 21.68%

The after-tax cost of debt is 7 percent (given).

Weighted cost of capital = Cost of equity * ( equity / Debt + equity) + Cost of debt after tax * ( Debt / Debt + equity)

                                         = 21.68% ( 0.3 ) + 7.00% ( 0.7)

                                         = 6.504 % + 4.90 %

Weighted cost of capital = 11.404 %

Answer : Faris' weighted cost of capital for this new division will be : B. 11.41%

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