WACC = (D/A)Rd(1-t) + (E/A)Re

Weighted average cost of capital = %of debt in capital structure times rate of debt reduced by tax benefit + %of equity times rate of equity.

We want to minimize WACC, so that NPV increases. That’s fine.

MM’s proposition with taxes says WACC is minimized by employing 100% debt (because Rd < Re). In the above equation if E=0, your cost of capital is only the first part, (D/A)Rd(1-t), so clearly you will have a lower WACC.

But, even *without* taxes, wouldn’t your WACC be lower too?

ok,ok,ok…I think I just answered myself (don’t you love how asking questions is good for you?). Answer is that it is true that WACC will be lower than if you use any equity, but it is *not* minimized. Only if there are taxes it becomes minimum.

As a follow up, they say that without taxes, capital structure is irrelevant:

WACC = (D/A)*Rd + (E/A)*Re

If WACC =15%, then by adding more debt, D goes up, E goes down, so Re must go up for the equation to hold. That’s clear. However, my thinking (which is probably off) is that if Rd < Re, I would just use 100% debt, which will lower the WACC, because E=0. Of course, later on they say that financial distress will prevent you from doing that, but as of Proposition I, if E=0, doesn’t WACC go down? If so, then capital structure in relevant. Help!

If E is 0 then company has no share holders. Then technically the bank own the firm and the banks require return is the cost of debt. Your changing ownership from some SE/common owners to a bank

ok, let us make E=\$1

The point I am naiively arguing is that the capital structure is relevant. Would you say then that Re in this case will be astronomical? …so that WACC stays at 15%?

Yup that’s the point. If your E is \$1 then if you earn \$1 Net income your Re is 100%. Since Re= Ni/E.