Wednesday, October 13, 2010

Unlevered Beta

A quick recap:
Beta of a company is determined by a statistical regression of returns of a given security against returns of the market.

As a result, "beta" usually refers to a company's equity beta or observable beta. Using CAPM, we can calculate the expected cost of equity (ke) using:

ke = RFR + beta * ERP

Where ERP is Equity Risk Premium

So what is unlevered beta and why is it important?

Well, recall from CAPM that you can change a company's capital structure in order to add leverage to increase beta and thereby increase expected return of equity (with a company's cost of equity being the investors return on equity).

Unlevered beta tells you how much a company's industry is expected to return, regardless of the leverage employed by looking at the systematic risk of an industry regardless of the financing decisions. Theoretically, the unlevered beta should be constant across companies in an industry.

Why is this important? Here is one example. You are trying to determine the cost of equity (so you can determine WACC for DCF) of a new company in an industry. However, because it is a new company, there is no previous history in terms of what they can be expected to return relative to the market. So it is impossible to calculate its equity beta. So what can you do?

You can look at a variety of other companies in the space, unlever all their betas to get asset betas and average them (as they should be theoretically the same, but will most likely differ slightly) and then relever it to the new company’s capital structure to approximate its expected equity beta. Armed with its equity beta, you can calculate its cost of equity using CAPM.

While this is how it would work in theory, there are some major problems with this model, the most obvious being:

  • How do you do “comps”? How do you define “a variety of companies in the space”, especially if few or none of the companies are exactly the same?
  • CAPM has its own issues which make it a less than perfect model
  • As a new company, they will probably not behave in the same manner as more mature companies in the space.

Here is an example:

There are four companies with different betas and leverage levels. By unlevering all the equity betas, you can have various approximations for what the asset beta should be. An average of all four gives you a decent approximation for the beta of the industry.

Now assume we have a new company in this space that will have a D/E of 50% at the same tax rate. We can use the leverage formula to calculate what the beta equity should be:

Equity Beta = Asset Beta * (1+(1-Tax)*D/E)

In this case, the equity beta would be approximately 1.3, which makes sense as it has a leverage between B and C and therefore should have an equity beta in between.

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