Levering & Unlevering Beta - Tax???

How come sometimes the equation is:

Levered Beta = Unlevered Beta x [1 + (1 - tax)(Debt/Equity)]

And other times they ignore this tax adjustment and just do:

Levered Beta = Unlevered Beta x [1 + (Debt/Equity)] ???

At Level I they included (1 − t) in the formula, but at Level II they do not (except in a footnote in the curriculum).

Be thankful that it’s simpler now.

I noticed that too-- do you know the reasoning behind it?

So you’re saying that if on the test you need to unlever and lever a beta, if there’s also WACC type questions in that section and so the tax rate is disclosed, you’re going to IGNORE that tax % and do the “simplified” formula?

Seriously, Mr Magician - what’s the logic? I’ve been memrising this with a (1-t)!!

Weird

There’s no (1-t) because for a small company we’d assume the capital structure is dynamic over time as it matures.

Here’s the explanation behind the formula :

Beta = BetaD * (1-t) * D / (D+E) + BetaE * E / (D+E)

See the two components of beta : BetaD (debt) and BetaE (equity).

Now assume debt has no systematic risk, then BetaD=0, we are left with :

Beta = BetaE * E / (D+E)

The levered Beta is BetaE and the unlevered is Beta.

gnrocks, no, that’s not why there’s no (1-t) in Level II. You’re thinking about debt beta, which is usually only for high yield bonds where interest payments are less certain, and defaults may not cover all losses. You could take your methodology a step further even and strip out debt beta, equity beta, and operational beta due to the ratio of fixed costs per variable costs. We are valuing the operations of small companies now, not mature companies as we were in Level I. With these smaller companies, we assume a continuous rebalance of financial leverage (D/E), not a constant absolute debt float. Since this ratio is always a proportionate value to the unleveraged company, the tax shield itself become a perpetuity with an expected return equal to the cost of capital in MM1 w/o taxes. Look at the curriculum footnotes. Check out the Robert Hamada’s equation from 1972 and the critique by Harris and Pringle in 1985. It’s company size/prospects here that dictates why we’ve left out (1-t). It’s similar to how real estate is valued with capitalization, actually.

Can we summarize that on the exam day if we have to unlever beta we should use the formula without (1-t)? Or still to look for small/ large company?

Send a message to the magician - if he doesn’t reply, I’ll use without 1-t because everyhwere in the book they’ve done it that way.

That said it’s really bizarre how formulas can evolve with levels - it’s not santa claus…

Don’t use the (1-t) for L2.