in case you want to unlever a beta
I’ve been cleaning out my apartment and came across some notes. I wrote them in August 2007, while sitting at a Starbucks in Calabasas during my lunch break. I was pondering the private equity industry. In case any of you are interested in LBOs (especially from a practical perspective), these excerpts will be of more value to you than they are to me right now:
The Modigliani-Miller theorem is the academic cornerstone of the private equity industry. It proves that in a perfect economy, with no taxes, no transaction costs, and no costs of bankruptcy, capital structure and dividend policy are irrelevant to a firm’s value. So no matter how you slice the pie, it is still worth the same amount…
The real beauty of M-M is that none of its assumptions hold true in the real world. Some would see this as rendering the theorem inapplicable. I see it as a list of the factors to consider in capital structure decisions. If the assumptions are exhaustive, then we know exactly what to analyze and balance.
The most unrealistic assumption of M-M is that it calls for no taxes. When you factor in taxes, the value of the theorem is immediately revealed. The great insight? Because most governments allow interest to be expensed, taxes are reduced. More cash —> more value. All else equal, this means that the ideal structure of a firm should be nearly 100% debt!
So why don’t we see this kind of leverage? Let’s explore the other factors. In the real world, there are costs associated with defaulting on debt and going into bankruptcy. Duh. So from the starting point of D = 100%, how do you back into an optimal capital structure? On this there are several opinions. There are two that I like, and they can work hand-in-hand:
Trade-Off Theory. There is a complex body of research that goes into the decision model that this supports (economics, game theory, sociology [probably]), but basically it says that a firm should strive to strike a balance between the benefits and risks associated with debt. This is where transaction costs, default costs, and risk come together in statistical harmony. Well, sometimes.
Peking Order Theory. There is a theory that suggests that firms develop a preference for capital sources based on their relative costs. Naturally, it ranks them from lowest to highest cost: internal (funds from operations), debt, equity.
So, that’s an overview of Capital Structure analysis. I am surprised at how many people working in Private Equity have never heard of Franco and Merton. I mean, this is the foundation for their craft. And Franco Modigliani won the 1985 Nobel Prize in Economics, in part for this research.
Oh, and in case you wanted to unlever a beta this weekend:
Variables (excuse the poor notation):
Kr = Risk-Free rate
Km = Market return
Ke = Cost of equity
Bu = Beta, unlevered
Bl = Beta, levered
t = Tax Rate
Capital Asset Pricing Model (CAPM):
Ke = Kr + Bu (Km - Kr)
The leverage premium on Ke can be considered a constant or a multiplier. If taken as a multiplier (“M”), we can define Bl as Bu x M. The value of M is accomplished by Hamada:
Bl = Bu [1 + (1 - t) (D/E)]
You can flip that around to unlever a beta, which is a good thing to do before using Modigliani-Miller to determine your new capital structure. Bu is the best metric to use for “real” business risk measurement, therefore it is the one you should use when applying CAPM. It also goes well with EBITDA when you are trying to evaluate a company independently of its structure. You know, in the real world.
