Hello~ Is there anyone can tell me why WACC use (1-T_c) to multiply D/V*r_D? Please use a example to help me to understand it, I really don't get how to explain this formula verbally. Thanks a lot^^

[NEAS: The weighted average cost of capital is an after-tax return.

~ Case #1: The firm is funded entirely by equity and investors require a 10% return. If the firm earns 10% pre-tax on its capital, its after-tax return is 6.5%, which is not sufficient to pay its stockholders.

~ Case #2: The firm is funded entirely by debt and creditors require a 10% return. If the firm earns 10% pre-tax on its capital, its after-tax return is 6.5%. But the creditors are paid with pre-tax funds, which are a 10% return, which is sufficient.]

I understand the WACC as the weighted average of the return on debt and the return on equity. the return on equity is sensible to the tax, and this is what we are doing in the exercises, but the return on debt is not . for example:

if equity = 100 and Debt = 50 with 10% cost of debt. the return of the company are annually (and for ever) 10 before interest and tax. the tax rate is 25%.

return available for shareholders is (10- 10%*50)*(1-25%)=3.75 so return on equity is 3.75/100=3.75% so here we cater for the tax completely.

but regarding the debt, the company will pay the "debt-holders" 50*10%=5 whatever the tax rate is. so when calculating the weighted average , why are we adjusting the debt rate (10%) to cater for tax, knowing that tax will not affect the 5 that the company will pay anyway???

[NEAS: Suppose the tax rate is 35% and both shareholders and bondholders require a 10% return. The firm's after-tax return is the pre-tax return times (1 - 35%).

To pay shareholders, the firm must earn an after tax return of 10%, or a pre-tax return of 10% / (1 - 35%).

To pay bondholders, the firm must earn a pre tax return of 10%, or an after tax return of 10% x (1 - 35%).]

ELIE