The Abco Co. maintains a debt-equity ratio of .70 and has a tax rate of 39 percent. The ﬁrm does not issue preferred stock. The cost of equity is 12 percent and the after-tax cost of debt is 5 percent.
What is Abco's weighted average cost of capital?

Question

Quizplus · Accepted Answer

First, we need to calculate the weights for debt and equity:
Debt weight = Debt / (Debt + Equity) = 0.70 / (0.70 + 1) = 0.41
Equity weight = Equity / (Debt + Equity) = 1 / (0.70 + 1) = 0.59

Next, we can calculate the weighted cost of capital (WACC):
WACC = (Equity weight x Cost of Equity) + (Debt weight x After-tax Cost of Debt x (1 - Tax Rate))
WACC = (0.59 x 0.12) + (0.41 x 0.05 x (1 - 0.39))
WACC = 0.071 + 0.012
WACC = 0.083 or 8.3%

However, we need to convert this to a before-tax WACC so that we can compare it to other companies or investment opportunities. We can do this using the formula:
Before-tax WACC = [After-tax WACC x (1 - Tax Rate)] + [Debt weight x (Cost of Debt) x (1 - Tax Rate)]
Before-tax WACC = [0.083 x (1 - 0.39)] + [0.41 x 0.05 x (1 - 0.39)]
Before-tax WACC = 0.0505 + 0.012

Therefore, the before-tax WACC is 0.0625 or 6.25%.

Finally, we need to convert this back to an after-tax WACC by multiplying by (1 - Tax Rate):
After-tax WACC = 0.0625 x (1 - 0.39)

After-tax WACC = 0.0381 or 3.81%.

Therefore, the weighted average cost of capital for Abco Co. is 9.1% (rounded to one decimal place).