# WACC and changing leverage

I get confused about these questions, and I know they should be easy. Let’s say you have the following: Equity beta = 2 Equity = 10 Debt = 10 Operating assets = 20 Therefore your OA beta is 1 (or 10/20 * 2 + 10/20 * 0 = 1). If you leverage up and reduce equity, say to 5 equity and 15 debt, which one changes, your equity beta or your OA beta? is it THIS: equity beta becomes such that 1 = 5/20*Be => Be = 4 or THIS: operating asset beta becomes 5/20*2 = 0.5?

you have to consider the two sides of the balance sheet. See the tables in CFAI text… Operating assets are on the asset side, and that’s where operating asset beta sits. On liability side you have equity and debt. Debt has beta 0 equity beta, 2 in your case, and Liability beta = 10/20*2. The total Asset beta has to equal the liability beta, hence operating asset beta (the only asset within total assets) =liability beta. Changing the debt/equity mix will affect the liability beta, and then the operating asset beta has to equal it. However, the logic is, if you increase leverage, investors of equity will require a higher rate of return (to compensate for more risk) so equity beta goes up and it all stays the same. I don’t think we’ll be questioned on just this, more likely to add in a pension asset & liability, and ask about changing the level of equity in the pension scheme.

I think this is important for the pension on balance sheet questions. I get the balance sheet and how both sides have to equal, but it’s sort of an algebra exercise whereby I was unsure which one is fixed and which one varies (between OA beta and Eq beta). You seem to be saying the equity beta would increase such that it falls back to an unchanged OA beta. i.e. lower equity weight, higher equity beta, unchanged overall beta. Is this always the case when you lever up? Would it ever be that the overall beta declines with less equity? What about when you add pension liabilities and assets, thereby decreasing the weight of equity on the liability side of the balance sheet. Does this decrease overall beta, or does the equity beta increase to offset the decreased weight (sort of like the levering)?

on the first point, curriculum doesn’t really talk about changing leverage without doing it via the pension scheme. It does say equity beta comes from the market, it’s how investors perceive the risk of your stock. So you would start here then get op asset beta. Then it moves on to adding pension risk. Decreasing the weight of equity on the liability side does decrease the overall beta. On the asset side you solve backwards to your operating beta (by taking out of total beta the beta of shares your pension scheme invests in) which is used to find wacc. Further on from that, when they fiddle with the proportion of shares of pension scheme, they say that more shares = more risk for firm => higher equity beta. But it’s highlighted as a “framework for thinking about the effects of different asset allocation on the risk of the enterprise”. So to me that says it’s what you could expect to observe in the mkt.

Thanks so much. I re-did all the end of chapter questions yesterday, eventually getting them all correct. Then I re-read some notes today and I started second guessing myself. The key I believe is to understand your third point that you just mentioned. Decrease beta overall, fixed pension beta, solve for operating asset. You must be from the UK? Pension “scheme”? Thanks!!

What page are the tables on? TIA