when to use these formulas to lever/unlever

CFA Level I Corporate Finance
#1

Hello guys,

I am confused about when to use the following equations to lever/unlever betas.

In the CFAI problems, they use the following:

Bequity: [1/1+[(1-t)D/E]]

and in other exercises they use

Bequity: [1+[(1-t)D/E]]

In what cases shopuld I use each equation?

thanks a lot!

E.

#2

If you are taking a beta from a comparable company, you UNLEVER it first.

You then LEVER it when you apply it to the capital structure of the company of interset.

#3

You’re getting your formulae confused. The first should be:

βasset = βequity[1/[1+[(1-t)D/E]]]

This is the formula for the asset beta for a pure-play company, where:

  • βequity is the pure-play company’s (equity) beta
  • t is their (marginal) tax rate
  • D/E is their debt-to-equity ratio

The second should be:

βequity = βasset[1+[(1-t)D/E]]

This is the formula for the (equity) beta for your company, where:

  • βasset is your asset beta, which you assume is the same as the pure-play company’s asset beta
  • t is your (marginal) tax rate
  • D/E is your debt-to-equity ratio
#4

you´re totally right. thanks a lot for your help!!

E.

#5

Sometimes that happens; it’s nearly always an accident.

My pleasure.