thisisbrianly

Hi not sure where you get the equation equity beat for firm = asset beta*(1+D/E)
The Equity beta for the firm (pre pension) is essentially the weighted average of the equity beta and debt beta.
as debt is assumed to have a beta of zero, the equation collapses to the weight of the firms equity times the equity beta.
so its equity/total assets (firm value) * equity beta
in the above example its (21/(21+9))*1 = 0.7
this must equal the firms operation assets (as both sides need to balance)
with the pension fund
the firm beta is the weighted average of the beta for debt + equity + pension fund liability. Debt and pension fund are again assumed to have beta’s of zero.
So the firms beta equals again the above equation. 21/(21+9+15)*1 = 0.4667
As both sides must equal each other, we can say the weighted average of firms operation beta plus the weighted average of the Pension Asset beta equals 0.4667.
the pension asset beta contribution to the 0.4667 is 15/45*0.6 or 0.2
that means 0.2667 is contributed by the operating assets. so 30/45 * X = 0.2667
solving for x we get 0.4 as the operating asset beta.