after tax cost of debt

why is after tax cost of debt used in computing WACC? WACC is what the firm shd earn at a minimum. Why does the firm want to earn less by subtracting taxes? Why will it pay taxes out of its own pocket? My take is a firm should use before tax cost of debt so it gives a “true” WACC. Where am I wrong here?

Fixed that for you.

(And please, please, please spell out all the words; it’s not that much harder to write “should” than “shd”, and it makes it so much easier for the people from whom you want help.)

WACC is the weighted average _ cost _ of debt. If you borrow at 5% and your marginal tax rate is 30%, then, assuming that you have enough income to take full advantage of the tax deduction for interest paid, the debt costs you only 3.5%; the government loves you and pays the other 1.5% for you. You may want to earn 5% on a project funded solely by debt – you may want to earn 25% for that matter – but for the project to make business sense you _ need _ to earn only 3.5%.

Here in the United States and many other countries interest expense is tax deductibe so debt is favored. If you used before tax cost of debt you would not be accurately portraying the decrease in taxable income through the use of debt. The decrease in taxable income means less taxes paid and more (though still less nominally than a 100% equity financing). This is why after tax cost of debt is used