Assume that investors hold Google stock in retirement accounts that are free from personal taxes.Also assume that Google's current pre-tax WACC is 14% and the corporate tax rate is 21%.If Google were to issue sufficient debt at a pre-tax cost of 7% to give them a debt-to-value ratio of 0.5,then the Google's after-tax WACC would be closest to:

Question

Quizplus · Accepted Answer

First, calculate the weighted average cost of capital (WACC) before issuing debt:
WACC = (E/V) * Re + (D/V) * Rd * (1 - Tc)
where:
E = equity value
V = total value = E + D
D = debt value
Re = pre-tax cost of equity
Rd = pre-tax cost of debt
Tc = corporate tax rate

Assuming no debt, we have:
E/V = 1
D/V = 0
Re = 14%
Rd = N/A
Tc = 21%

WACC = 1 * 14% + 0 * N/A * (1 - 21%) = 14%

Next, calculate the debt-to-value ratio needed to achieve a 0.5 D/V ratio:
D/V = 0.5
D/V + E/V = 1
0.5 + 1 = 1.5
D/V = 1.5 - E/V
0.5 = 1.5 - E/V
E/V = 1

This means that Google needs to issue debt equal to half of its total value, or $50 for every $100 of equity.

Now, calculate the after-tax cost of debt:
Rd = 7%
Tc = 21%
Rd * (1 - Tc) = 7% * (1 - 21%) = 5.53%

Finally, calculate the after-tax WACC:
WACC = (E/V) * Re + (D/V) * Rd * (1 - Tc)
= 1 * 14% + 0.5 * 5.53% * (1 - 21%)
= 12.8%

Assume That Investors Hold Google Stock in Retirement Accounts That