 # Question 5, Schweser Book 2, Page 66

The equity beta for a firm=(Asset Beta)*(1+ D/E). Is this correct? If so, then why for this problem do they calculate the operating assets beta as (Equity/Total Assets)*Beta, which is 0.7 before the inclusion of pension assets and liabilities, and 0.47 after the inclusion of pension assets and liabilities? Here’s the example taken straight from the book: Firm’s Equity Beta: 1.00 Risk-Free Rate: 5% Market Risk Premium: 8% Debt: \$9 million Equity: \$21 million Pension assets beta: 0.60 Pension assets=\$15 million The firm’s operation assets beta before including the pension liabilities into the balance sheet and the operating assets beta after including the the pension assets into the balance sheet would be what? Answer: Since Operating assets before pension A/L=(21/30)*1=0.7, Total assets beta= (21/45)*1=0.47. Solving for operating assets beta after inclusion of pension assets and liabilities=0.4.

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.

sorry just realised one or two of the names i’ve used isn’t quite right. (The logic and the maths is right though) so you should get the jist.

Ah just found the formula beat for firm = asset beta*(1+D/E) using this you get 1 = X (1+9/21) solving for x gives 0.7 using this with the pension assets you get 1 = X (1+ (9+15)/21) = 0.4667 as the total asset beta. Using logic listed above this means operating asset beta equals 0.4. so both methods should give same answer.

Assuming from the above example, a firm’s operating asset beta is (21/(21+9))*1 = 0.7 before including pension assets. Then, after including pension assets, the operation asset beta is 21/(21+9+15)*1 = 0.4667. What happens to the firm’s asset beta if more of the pension assets are invested in equity rather than bonds? Say the 60% allocation to equity were raised to 80% for example?

for calculating WACC, do you use Operating Assets Beta * MRP + Risk-Free or is it total Assets Beta? I’ve seen both used. Also, in the 2009 AM section, they substitute “equity risk premium” with “market risk premium”. I always thought the two weren’t the same?

You use the new operating asset beta calculated including the pension assets. WACC = RFR + βAo[E(RM) – E(RFR)] The market risk premium (MRP) is the equity risk premium (ERP) for the CAPM model I believe.

I see. Thanks!