Re: Cost of equity
Charlie Munger made a comment in a recent annual meeting (2003?) that was something like, "At it's core, economics all boils down to opportunity cost." That's what I think about when I think about cost of equity.
The cost of equity is going to be the rate of return that investors require from holding a particular equity instrument. That's unobservable, obviously. What you can do is look at economically similar instruments to get an idea for what that number should be.
Beta is a historically popular number (obviously not popular with Berkshire Hathaway). The most common beta calculation comes from a regression of firm excess returns on market excess returns. The assumption is that there is a common market risk factor and you should earn the risk premium to the extent that the individual stock shares that risk factor.
But academics define lots of different betas, rather than the market beta. A beta is basically just the exposure of a firm to any particular risk factor. In the CAPM case, the singular beta is the exposure to the market factor. You can open that up to multifactor models, where each beta represents exposure to a particular risk factor. (The Fama-French three factor model, perhaps).
So maybe you're not satisfied with betas. You could say, "Screw the math, I just want to figure out my cost of equity." Here are some starting thoughts:
1. It must be higher than the risk-free rate
2. It must be higher than any available instrument with less risk (however you define that)
3. It should be equal to your required equity rate for instruments with similar risk
So you might start by saying, "I need the historical market's rate of return." But that's not exactly true because what you really need is the historical market premium plus the current risk-free rate. But that's not necessarily true because you can invest in an index fund (that many people would describe as less risky) and get that rate. So you need the current real risk free rate, plus expected inflation, plus the risk premium, plus some premium for holding an individual stock rather than an index.
How do you do it? I don't know - it's obviously messy. Using the math-oriented beta is just one way. Maybe you just know that you need at least a 10% return when you invest in something - that's your hurdle rate and therefore your cost of equity. The best estimate you can get for a firm's cost of equity (in my view) is to look at the implied cost of equity in the current share price. Make your best estimate of future free cash flows (or dividends, if available) and figure out the IRR that sets the present value of those cash flows equal to the current stock price. Do that for a number of different firms and maybe that's the current equity cost of capital.
It's an unsatisfactory answer, right? There's no good way to calculate the cost of equity in a rigorous fashion, other than saying it's the opportunity cost across all possible investment opportunities with the same degree of risk.
Which, by the way, comes back to provide some support for the historical beta. Usually when I'm talking to someone about beta, they hate it - just like you do. They usually hate it a little less when I say the following:
When you're buying a stock, imagine that you're only choosing to buy the entire market index or that stock. You can't compare the cost of equity for the entire index to the cost of equity for the individual stock - the index is less risky. But you can adjust for this! If you want to buy the index in such a way to equal the risk inherent in an individual stock, you can lever up or lever down the amount purchased. You can roughly match the risk of a levered index position to the risk of an individual stock by levering up or down until the volatility of the levered position is equal to the volatility of the stock position. Therefore, you should require a return on the individual stock equal to at least the levered return of the index. What's that? Beta is the amount of the leverage, so your required return is beta times the market's excess return. If you can't get at least that from investing in the individual stock, you're better off investing in the levered market position.
I don't know if that's satisfying to you, but it makes me think there's at least some value in beta even though I don't buy into it completely.
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