Beauty Inc.plans to maintain its optimal capital structure of 40 percent debt,10 percent preferred stock,and 50 percent common equity indefinitely.The required return on each component source of capital is as follows: debt-8 percent; preferred stock-12 percent; common equity-16 percent.Assuming a 40 percent marginal tax rate,what after-tax rate of return must the firm earn on its investments if the value of the firm is to remain unchanged?

Question

Quizplus · Accepted Answer

To calculate the required rate of return, we need to find the weighted average cost of capital (WACC). The WACC is given by:

WACC = (wd x Rd x (1-T) + wp x Rp + wc x Rc)

where:
wd = weight of debt = 40%
Rd = cost of debt = 8%
T = tax rate = 40%
wp = weight of preferred stock = 10%
Rp = cost of preferred stock = 12%
wc = weight of common equity = 50%
Rc = cost of common equity = 16%

Plugging in the values, we get:

WACC = (0.4 x 0.08 x (1-0.4) + 0.1 x 0.12 + 0.5 x 0.16) = 0.1112 or 11.12%

Therefore, the firm must earn an after-tax rate of return of 11.12% on its investments to maintain its value unchanged.