Question

Droz's Hiking Gear, Inc. has found that its common equity capital shares have a beta equal to 1.5 while the risk-free return is 8 percent and the expected return on the market is 14 percent. It has 7-year semiannual maturity bonds outstanding with a price of $767.03 that have a coupon rate of 7 percent. The firm is financed with $120,000,000 of common shares (market value) and $80,000,000 of debt. What is the after-tax weighted average cost of capital for Droz's, if it is subject to a 35 percent marginal tax rate? Round your final percentage answer to two decimal places.

A) 10.20%
B) 11.76%
C) 11.88%
D) 13.32%

Answer 1

To calculate the after-tax weighted average cost of capital (WACC) for Droz's Hiking Gear, Inc., we need to consider the cost of equity and the cost of debt. The WACC is 17.9525%, which rounds to 18% when rounded to two decimal places.

Step-by-step explanation:

To calculate the after-tax weighted average cost of capital (WACC) for Droz's Hiking Gear, Inc., we need to consider the cost of equity and the cost of debt. The formula for WACC is:

WACC = (E/V) * Re + (D/V) * Rd * (1 - tax rate)

Where:

E = market value of equity

V = total market value of the firm's capital

Re = cost of equity

Rd = cost of debt

Let's calculate the components:

Cost of Equity (Re):

The beta of common equity shares is 1.5. The risk-free rate is 8% and the expected return on the market is 14%. We can calculate the cost of equity using the capital asset pricing model (CAPM):

Re = risk-free rate + beta * (market return - risk-free rate

Re = 8% + 1.5 * (14% - 8%)

Re = 8% + 1.5 * 6%

Re = 8% + 9%

Re = 17%

Cost of Debt (Rd):

The bonds have a price of $767.03 and a coupon rate of 7%. We can calculate the yield to maturity (YTM) to determine the cost of debt. The YTM is the effective interest rate of the bond:

YTM = (Annual Interest + (Face Value - Price) / Years to Maturity) / ((Face Value + Price) / 2)

Annual Interest = Coupon Rate * Face Value / 2

Annual Interest = 7% * $1,000 / 2

Annual Interest = $35

YTM = ($35 + ($1,000 - $767.03) / 14) / (($1,000 + $767.03) / 2)

YTM = ($35 + $232.97) / $883.52

YTM = $267.97 / $883.52

YTM = 30.35%

Weighting of Equity and Debt:

The market value of equity is $120,000,000 and the market value of debt is $80,000,000. The total market value of the firm's capital (V) is $120,000,000 + $80,000,000 = $200,000,000.

Calculating WACC:

WACC = (E/V) * Re + (D/V) * Rd * (1 - tax rate)

WACC = ($120,000,000 / $200,000,000) * 17% + ($80,000,000 / $200,000,000) * 30.35% * (1 - 35%)

WACC = 0.6 * 17% + 0.4 * 30.35% * 0.65

WACC = 10.2% + 7.7525%

WACC = 17.9525%

Therefore, the after-tax weighted average cost of capital (WACC) for Droz's Hiking Gear, Inc. is 17.9525%, which rounds to 18% when rounded to two decimal places.