MM Proposition II

Can someone explain how to interpret the red components in the below equations? What information should we look for in a vignette to assign to this?

r0 = all equity charge.

It is the cost of equity in an unlevered firm (firm financed by 100% equity).

So if r0=rd, then the formula reduces to re=r0=rd, which is weird. What is the intuition here?

True, you have a point there… the intuition behind the formula seems not through-n-through.

Maybe other members will be able to profer solution.

In general, _r_d < _r_e; therefore _r_0 ≠ _r_d.

You can put into the formula that _r_0 = _r_d, but so what? You can put into a macroeconomic return model that GDP growth is 100,000%. It’s meaningless.

Such a GDP growth, though unlikely, will still produce a relevant output according to the model. Here the formula kind of collapses. One of the many reasons I am a big critic of this whole MM model.

Anyway, the takeaway here is that r0 is the unlevered cost of capital so I’ll rather get over this very soon :slight_smile:


I have a simple explanation [for the first Modigliani-Miller proposition]. It’s after the ball game, and the pizza man comes up to Yogi Berra and he says, ‘Yogi, how do you want me to cut this pizza, into quarters?’ Yogi says, ‘No, cut it into eight pieces, I’m feeling hungry tonight.’ Now when I tell that story the usual reaction is, ‘And you mean to say that they gave you a [Nobel] prize for that?’"

–Merton H. Miller, from his testimony in Glendale Federal Bank’s lawsuit against the U.S. government, December 1997

If you honestly think that 100,000% GDP growth will produce a relevant output in a macroeconomic return model, then there’s no reason not to believe that _r_0 = _r_d produces a relevant output in the MM model. It doesn’t collapse; it gives a perfectly accurate description of _r_e: it’s constant, and equal to _r_d. What’s wrong with that?

lol, @ Krokodilizm… The guys deserved commendation for their work… Try to improve on it, and i am sure you will get your Nobel as well…

Yes but re=r0=rd means “cost of equity is equal to cost of capital with zero leverage and that is equal to cost of debt” which sounds like some kind of superposition in finance: if a company recognizes its cost of debt, how can it also be zero-leveraged? This is the kind of entanglement currently in my brain.

So the cost of equity equals the cost of debt. So what?

If you don’t like that, don’t set _r_0 = _r_d.

But if, in fact, _r_0 = _r_d, then _r_e = _r_d. Same WACC regardless of capital structure. Big deal.

As D/E changes, re changes as well. I am fine with that. But what happens to r0?

  1. Is it a constant? (assuming it is the intercept, looks like it is constant).

  2. Why is it still part of the formula, since D/E>0 and de facto the company can’t be zero-leveraged?

_r_0 is a constant.

Why can’t the company have zero leverage?

It can, but the moment it “acquires a positive D/E ratio” it moves to a second state, i.e. it can’t be considered unleveraged any more.

Again, so what?

I guess my issue is accepting that r0 is constant, because we know from other models that cost of equity itself is a function of other market factors, but then again, there is no model without an implicit assumption, so rest in peace Miller and Modigliani.

The good thing is I will probably not forget this formula ever again, which is the underlying purpose of these discussions. Thanks for keeping it up.