Re: Cost of equity
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Even still, I think there's a case for a regression beta to be an observable cost of equity.
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Regression betas over many, many firms over long periods of time might give you average betas that are unbiased. That assumes a rational expectations environment where, on average, investors' expectations of future returns are true. That's a fairly strong assumption - even for a guy living in Famaland, Chicago, like I do.
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You don't get rewarded for diversifiable risk because you can diversify it away. Therefore your cost of equity does not increase due to diversifiable risk.
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Edited to say that I have potentially screwed up the issue and it's probably lead to confusion. There are two things going on: What I require for holding a stock and what the market will give me. If I were to hold only one individual stock in my portfolio, I would require an expected return greater than I would require for holding the index. The market will not give me that return because, by diversifying, they can reduce the risk. I'm talking about what I would require for an individual stock return whereas you seem to be jumping the gun to point out that the market would not give me that return (a point that I agree with). If we look at it from the perspective of the firm, if the market doesn't reward the investor for holding diversifiable risk, the firm's cost of equity shouldn't reflect that. At this point, I can't remember if we're talking about:
- ways that an investor would calculate his required rate of return, or
- ways that a firm would calculate its cost of equity
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Basically you're assuming that all sotcks are fairly valued at the moment, right? That assumes that markets are efficient. You have two inputs (discount rates, cash flows) and one output (value). You have to start with two known variable to calculate the third. If you start with cash flows and value as givens then you're assuming the stock is fairly valued in order to find the true discount rates. If you assume that all stocks are always fairly valued then you assume markets are efficient.
To asnwer your last question, no, the lower stock price does not necessarily mean the cost of equity is higher.
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No - I am assuming that all stocks are valued, period. If the market irrationally prices a firm's shares so that the price is 10% of the "Buffettesque Intrinsic Value", that firm does face a higher cost of equity. Why? Because when they go to issue shares, they have to issue shares into the environment that is underpricing the equity. By issuing shares when the stock is extremely undervalued, the firm is incurring a very high cost of equity.
It's easier to see in the case of debt because the debt rates are observable. If the firm issues a bond into an environment that prices the bond at par value, the (marginal) cost of debt will be equal to the coupon rate of that bond. If the market values that debt at 20% of par, the cost of debt is much higher - that's true regardless of whether the 80% haircut was rational or not.
By the way, have you ever been to a Berkshire Hathaway annual meeting? If not, you should go - it's a good time. You should also get a group of students (I think you're in school) to go visit Buffett in Omaha.
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