For a firm whose debt is risk free, the overall firm beta is Firm = 0.5 .
Question:
For a firm whose debt is risk free, the overall firm beta is βFirm
= 0.5 . βEquity
+ 0.5 . βDebt. Thus, 0.5 . βEquity
+ 0.5 . 0 = 2. Solve for βEquity
= βFirm/0.5 = 4. For the (90%, 10%) case, the equity beta jumps to βEquity
= 2/0.1 = 20.
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