Re: Cost of equity
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It's not obvious that the required cost of equity is unobservable? What kind of situation are you talking about? What kind of observable measures of costs of equity are you thinking about? I still think it's pretty obvious that costs of equity are completely unobservable, short of taking a poll of investors (and even then you're in the world of distinguishing between stated preferences and revealed preferences).
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I guess I took "observable" to mean something more along the lines of "attainable". Even still, I think there's a case for a regression beta to be an observable cost of equity.
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I don't think I mentioned the S&P 500.
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You didn't. The point was that if you don't feel that "the market" reflects a good benchmark for a stock you don't have to use the standard. I wasn't really correcting you, just expanding on your point.
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I believe you need a premium for holding an individual security rather than an index (talking about your only holding here, not talking about a basket of individual securities) because you need to be compensated for the total risk, both systematic and unsystematic, whereas you can diversify away part of that risk by buying an index. I'm not sure what you're arguing here. Is it possible that a firm's total risk will be less than an index's total risk? Obviously, if the firm has a beta of less than 1, it's theoretically possible, but it doesn't seem very likely for a normal, publically-traded operating firm (as opposed to a firm that just owns some treasury notes).
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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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Yeah, I have no idea what you're talking about here. I'm not making any assumptions about efficient markets. Empirically, the IRR that equates future cash flows to the current stock price is the firm's current cost of equity. Are you saying that if the stock prices drops by 50% without a corresponding drop in the expected future cash flows, the firm doesn't face a higher cost of equity than they did prior to the stock price?
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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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