As I argue in Market Prices & Imbedded Discounts the price of a stock as set in an active market should usually be higher than the price set by a willing seller and a willing buyer in a one-on-one negotiation. Most stock is held by diversified investors who avoid company-specific risk. Thus, stock prices reflect the value of stocks as part of a portfolio and as if there is no company-specific risk involved. Less risk means higher price. The bottom line is that in most cases market prices are higher than they would be if they were set by well informed buyers and sellers of whole companies. In other words, the notion that market prices are inherently low is a total myth.
This analysis implies that when a bidder makes an offer for a target company at a premium over the market price, the real premium from the point of view of the bidder is bigger than it would appear to be in comparison to market price. In other words, the market acts as a natural barrier to takeovers motivated by marginal gains. The fact that bidders must clear this hurdle in order to make a bid, suggests that target managers should bear a significant burden in justifying takeover defenses (which generally they do).
It is also possible that bidders find targets by looking for companies that trade at a discount to the price that CAPM indicates should be the price. Indeed, I am sure that they do. But if the premium offered is nothing more than the difference between a market price that is depressed for some reason and the price calculated under CAPM, then really the premium is no premium at all. I am not aware of any studies that have sought to determine the extent to which takeovers are prompted by discounts rather than offering true premiums. It is also possible that many takeovers involve mixed motives, that is, exploitation of a discount combined with some amount of premium.
If it turns out that most takeovers (or even a significant number of them) are motivated by discounts, then the idea that a court in an appraisal proceeding should tack on a premium is nonsense.
To put it bluntly, if bidders use CAPM to find undervalued targets, and then bid up to the CAPM price, it makes no sense for a court to add on another premium.