Unlevered Beta to Levered Beta

[Aasim]

Greetings everyone,
I’m on reading 36 - Cost of Capital, example 13 in the Corporate Finance-Portfolio Management CFAI books.
http://tinypic.com/r/essz04/8
Do you have any idea how the beta is .96 for the first answer?
I understand the formula would be .90/(1+(1-.36)(X)…I’m having a hard time finding what X is.
Thank you very much.

 

[A_KB]

X is D/E ratio and the formula should be .90*(1+D/E(1-t)). In first case D/E is 1/9 as D/(D+E) is .10
hope this helps

 

[Aasim]

Thank you very much,
How did you get 1/9? I’m trying to figure out the others and still receiving different answers from the book.
What would I use for X in the beta 1.28?

 

[A_KB]

D+E=1, So, if D/(D+E) is .1 i.e debt is 10% of total capital then equity ought to be 90%, which mean D/E ratio of 1/9. In fourth scenario, D/(D+E) is .4, i.e E must be .6 So, D/E must be 2/3.
Hope this helps

 

[Aasim]

You helped me out a lot!
Thank you very much!