MM Proposition I

[MrSmart]

Does the first proposition imply that Kd=Ke?

How else would

[onlysimon]

V(u) = V(l) - debt*tax

proposition I assumes no taxes, so doesnt imply Ke=Kd

[MrSmart]

There is a no tax and a taxable version.

I did some searching, proposition I implies that there is no seniority with debt, and both Kd and Ke are equal.

[S666]

I don’t remember proposition 1 explicitly stating that Ke = Kd…in fact Proposition 2 handles that relationship and states that cost of equity rises with the amount of debt used so that WACC stays constant.

I guess you could argue it’s implied…

[tickersu]

@MrSmart

There is a no tax and a taxable version.

I did some searching, proposition I implies that there is no seniority with debt, and both Kd and Ke are equal.

Where did you find that? I was under the impression that Ke still rises linearly with increased debt in a world without taxes. Vu = Vl because taking on debt only “cuts the value pie differently”; debt doesn’t add any value to the firm in a world without corporate taxes. People can reverse or add leverage as they like, which is another reason debt doesn’t add value to the firm in the no taxes situation.

[tickersu]

@S666

I don’t remember proposition 1 explicitly stating that Ke = Kd…in fact Proposition 2 handles that relationship and states that cost of equity rises with the amount of debt used so that WACC stays constant.

I guess you could argue it’s implied…

+1…Mathematically, this is how Vu = Vl-- since WACC is unaffected the firm value doesn’t change.

[MrSmart]

@tickersu

@MrSmart

There is a no tax and a taxable version.

I did some searching, proposition I implies that there is no seniority with debt, and both Kd and Ke are equal.

Where did you find that? I was under the impression that Ke still rises linearly with increased debt in a world without taxes. Vu = Vl because taking on debt only “cuts the value pie differently”; debt doesn’t add any value to the firm in a world without corporate taxes. People can reverse or add leverage as they like, which is another reason debt doesn’t add value to the firm in the no taxes situation.

Under the first proposition, the costs of debt and equity are the same.

If the cost of debt was cheaper (which would make no sense with no seniority), then the value of a fully levered firm would be larger than the unlevered firm, naturally. So it assumes they are equal.

This is tackled in the second proposition, the cost of levered equity is higher than unlevered equity in a linear manner, leaving both the WACCs and the firm value unchanged.

No taxes for both in this post.

[tickersu]

@MrSmart

@tickersu

@MrSmart

There is a no tax and a taxable version.

I did some searching, proposition I implies that there is no seniority with debt, and both Kd and Ke are equal.

Where did you find that? I was under the impression that Ke still rises linearly with increased debt in a world without taxes. Vu = Vl because taking on debt only “cuts the value pie differently”; debt doesn’t add any value to the firm in a world without corporate taxes. People can reverse or add leverage as they like, which is another reason debt doesn’t add value to the firm in the no taxes situation.

Under the first proposition, the costs of debt and equity are the same. I don’t believe they are…

If the cost of debt was cheaper (which would make no sense with no seniority), It should make sense, though-- you’re promising coupon payments on the debt, but nothing on the equity.

then the value of a fully levered firm would be larger than the unlevered firm, naturally. No, because there is zero value created in taking on debt when there are no taxes-- MM described it as cutting a pie into 12 pieces instead of 8 slices-- in the end, you have no more “pie” than when you started (again, assuming MM no taxes).

So it assumes they are equal. Respectfully, I don’t believe this is correct. Anything I’ve read (and any problems I’ve worked) states that the value of the firm is independent of leverage (for MMI no taxes) because the investor can lend and borrow at the same rate as the company, which effectively allows the investor to create the leverage structure they prefer. This ties into what would happen if Vu didn’t equal Vl…there would be an arbitrage opportunity because you would be able to sell shares of a “more expensive firm” and buy shares of the identical (except for leverage), yet “cheaper firm” (and make your preferred adjustments to leverage). Overall, this is a big part of why they concluded capital structure is irrelevant without taxes.

This is tackled in the second proposition, the cost of levered equity is higher than unlevered equity in a linear manner, leaving both the WACCs and the firm value unchanged. The second proposition addresses what happens to Ke as leverage changes-- it doesn’t explain why unlevered Ke is higher than Kd. If the cost of unlevered equity was equal to the cost of debt, you still wouldn’t see any change in the cost of equity as leverage varied. You can’t assume unlevered Ke = Kd, yet calculate levered Ke with a “premium” of zero (if unlevered Ke = Kd).

No taxes for both in this post.

http://en.wikipedia.org/wiki/Modigliani%E2%80%93Miller_theorem I would start here, but more credible sources will show you the same thing.

[MrSmart]

In MMI, you’re not promising anything. Cash flows are divided proportionately. Therefore the cost of debt would always equal the cost of equity in this scenario.

Actually, you’re reiterating what I’ve said when you say

Anything I’ve read (and any problems I’ve worked) states that the value of the firm is independent of leverage (for MMI no taxes) because the investor can lend and borrow at the same rate as the company, which effectively allows the investor to create the leverage structure they prefer. This ties into what would happen if Vu didn’t equal Vl…there would be an arbitrage opportunity because you would be able to sell shares of a “more expensive firm” and buy shares of the identical (except for leverage), yet “cheaper firm” (and make your preferred adjustments to leverage). **Overall, this is a big part of why they concluded capital structure is irrelevant without taxes.

**

I never said that Ke=Kd in the second proposition, because debtholders have a senior claim on cash flows. It tells you in a linear manner how Ke changes with more leverage, leaving the firm value unchanged from a constant WACC.

I don’t understand where we disagree. Maybe I’m misunderstanding your argument.