# M&M Proposition II with no taxes

Hi all,

I fully understand the M&M propositions but the below graph is driving me crazy.

The proposition makes sense - the cost of equity increases linearly when the firm adds more (lower cost ) debt thus offsetting the benefit from the lower cost of debt; therefore WACC is constant. Makes logical sense. What I am having trouble with is that if say the cost of equity for the unlevered firm is 10% and the cost of debt is 5% - isn’t the WACC lowest with the firm being 100% financed with debt? And again these propositions assume no financial distress costs so debt would be held at a constant 5% no matter what your D/E ratio is. That’s why the graph above is giving me pause – how can the WACC be constant if the firm has 100% debt financing at a lower cost than the initial cost of capital to the firm with 0 debt?

Sorry cant answer your question well enough, but can there even be a firm consisting of all debt & no equity? Seems impossible, that would mean all the economical benefits (& risks of uncertain cash flows) of the firm are being passed along to the bondholders.

The basis of MM w/o taxes is that the value of the firm is based on the discounted future cash flows & should not matter how much of the firm is financed by debt or equity. That value then gets split amongst stakeholders.

Per a CFA powerpoint I found based off of an interwebs search, I am proved basically correct:

“•Why isn’t the optimal capital structure not 100% debt? Because in this extreme, debt would be, essentially, the equity of the firm.”

google: “Chapter 5 Capital Structure - CFA Institute” it is in the notesof slide 8

Wow - that’s an extreme workaround. Ha ha ha. Thanks for looking into that. I guess that makes sense.

Where’s 100% debt on your graph? (Note: your abscissa is not measured as M&M measure it.)

And what’s the cost of equity at that point?

There’s no 100% debt in the graph. If the corporation’s got 100% debt, the wacc= cost of debt (assuming no taxes) which is a constant. 100% debt is optimal if there are no distress costs.

If there are no taxes (and no distress costs), then WACC is constant irrespective of the capital structure: 10% debt is optimal, and so is 20% debt, and 30% debt and so on.

Right - I get the point on all that its just the graph annoys me. I guess you are right they measure 100% debt at that intercept where WACC=Ru.

The point of where the firm is 100% debt financed the debt is essentially all equity makes sense - you are recieving the residual of EBIT. Which ties into Proposition I - no matter how you divide the pie up the pie is still the same size. If you are all equity then you get the residual of EBIT -> if you are all debt then you get the residual of EBIT -> therefore your risk/return profile of the CFs of the firm would be the same and so should the cost of capital at those extremes (or any others as well). It makes logic sense.

I highly doubt they have a graph with points A,B, and C on it and as which one is all debt on the exam…

Where did you get those graphs? As I wrote above, the abscissa value is not the same as M&M used, and I think that that’s what’s confusing (at least, in part).

And there’s still an open question: what’s the cost of equity at 100% debt? (Or, as 100% debt usually isn’t legal, what’s the cost of equity at 99.99999% debt?)

Those graphs are all over the place (with the exception of the cost of equity line is linear). Just goolge M&M Proposition II with no taxes. They are also in my Schweser notes. Its also in the CFAI text.

Thats the other thing the formula is: Re= r0 + D/E(r0-rd). So if debt is 0 then the cost of equity is undefined at least by that formula. Which is partially confusing as well.

However the point made by Yayyywork would mean that the cost of debt at 100% would be the cost of equity at 100% - in either case you are the residual holder to 100% of the EBIT so why should your cost of capital be different?

The cost of equity line is linear when the x-axis is D/E, not when it’s D/A.

That’s the point.

With 100% debt, D/E is infinite, and the cost of equity is infinite. That’s the point.

How are you going to get rid of all of the equity? You can repurchase all of the stock, but how do you get rid of retained earnings?

Don’t base your analysis on a singularity. Understand that it’s a singularity, then ignore it.

The one in the CFA Institute text has D/E on the x-axis; that’s my point.

There’s a lot of stuff you can get by Googling. Most of it is stupid. The M&M graphs with D/A on the x-axis fall into that category.

The graph in your Schweser notes has “% debt in capital structure” as the label on the x-axis. That’s wrong. They have that in all of their M&M graphs. They’re all wrong.