beta(asset) & beta(equity)

[thesame2]

A question from CFA textbook Book 4, Corporate Finance -
(P69) [question removed by admin]
Solution per textbook: B. The textbook also says, “Asset risk does not change with a higher debt-to-equity ratio. Equity risk rises with higher debt”.
My question: as we learned from the CFA textbook, Beta (asset) = Beta (equity) / [1+ [(1-t)*D/E]]. I guess I am sort of confused by this equation’s concept. Let’s say, for example, given the same D/E ratio, how do we know whether it’s the change in Beta (asset) lead to the change in Beta (equity), or vice versa? In addition, when the D/E ratio changes, how do we know whether the changes in D/E ratios impact Beta (asset) or Beta (equity) or both?
Anyone please help to explain… Thank you!!

 

[thesame2]

edupristine wrote:
Asset beta also known as unlevered beta does not depend on the debt amount. So, an increae or decreae in debt, has no impact on asset beta.
On the other hand, levered beta or equity beta is dependent on the debt amount. So, as debt-to-equity increases (decreases), equity beta increases (decreases).
Rearrange the formula as, Beta (equity) = Beta (asset)*[1+ [(1-t)*D/E]]
In this formula, treat asset beta as constant. So, an increase in D/E just increases Beta (equity) and not Beta (asset).
Equity beta is equal to asset beta when D/E is equal to zero.
Hope this helps !!!

it helps!! thanks a lot!!